BUILDING DESIGN AND CONSTRUCTION HANDBOOK
Frederick S. Merritt (Deceased) Editor
Jonathan T. Ricketts Editor
Sixth Edition

ABOUT THE EDITORS
Frederick S. Merritt (deceased) was a consulting engineer for many years, with
experience in building and bridge design, structural analysis, and construction management.
A Fellow of the American Society of Civil Engineers and a Senior Member
of ASTM, he was a former senior editor of Engineering News-Record and an
author / editor of many books, including McGraw-Hill’s Standard Handbook for
Civil Engineers and Structural Steel Designer’s Handbook.
Jonathan T. Ricketts is a consulting engineer with broad experience in general
civil engineering environmental design and construction management. A registered
engineer in several states, he is an active member of the American Society of Civil
Engineers, the National Society of Professional Engineers, the American Water
Works Association, and is coeditor of McGraw-Hill’s Standard Handbook for Civil
Engineers.

CONTENTS
Contributors xxi
Preface xxiii
Section 1 System Fundamentals Jonathan T. Ricketts 1.1
1.1 Principles of Architecture / 1.1
1.2 Systems Design and Analysis / 1.3
1.3 Traditional Design Procedures / 1.4
1.4 Traditional Construction Procedures / 1.5
1.5 Role of the Client in Design and Construction / 1.8
1.6 Building Costs / 1.8
1.7 Major Building Systems / 1.9
1.8 Value Engineering / 1.22
1.9 Execution of Systems Design / 1.29
1.10 Building Codes / 1.36
1.11 Zoning Codes / 1.38
1.12 Other Regulations / 1.40
1.13 Systems Design by Team / 1.40
1.14 Project Peer Review / 1.41
1.15 Application of Systems Design / 1.41
Section 2 The Building Team-Managing the Building Process
Alan D. Hinklin 2.1
2.1 Professional and Business Requirements of Architectural Engineers / 2.2
2.2 Client Objectives for Buildings / 2.2
2.3 Program Definition / 2.4
2.4 Organization of the Building Team / 2.4
2.5 Client-A/E Agreement / 2.6
2.6 A/E Liability and Insurance / 2.8
2.7 Definition of Project Phases / 2.10
2.8 Scheduling and Personnel Assignments / 2.11
2.9 Accelerated Design and Construction / 2.12
2.10 Design Management / 2.13
2.11 Internal Record Keeping / 2.14
2.12 Codes and Regulations / 2.14
2.13 Permits / 2.15
2.14 Energy Conservation / 2.16
2.15 The Interior Environment / 2.16
2.16 Cost Estimating and Value Engineering / 2.18
2.17 Technical Specifications / 2.18
2.18 Upfront Documents / 2.22
2.19 Quality Control for Architects and Engineers / 2.23
2.20 Bidding and Contract Award / 2.24
2.21 Construction Scheduling / 2.24
2.22 Shop Drawing Review / 2.25
vi CONTENTS
2.23 Role of Architect or Engineer During Construction / 2.26
2.24 Testing and Balancing of Building Systems / 2.29
2.25 Postconstruction Operation and Maintenance / 2.29
2.26 Record Drawings / 2.30
2.27 Follow-Up Interviews / 2.30
2.28 Management of Disputes / 2.30
2.29 Professional Ethics / 2.31
Section 3 Protection against Hazards David W. Mock 3.1
3.1 Risk Management / 3.1
3.2 Wind Protection / 3.3
3.3 Protection against Earthquakes / 3.11
3.4 Protection against Water / 3.15
3.5 Protection against Fire / 3.28
3.6 Lightning Protection / 3.48
3.7 Protection against Intruders / 3.50
Section 4 Building Materials David J. Akers 4.1
CEMENTITIOUS MATERIALS
4.1 Types of Cementitious Materials / 4.1
4.2 Portland Cements / 4.2
4.3 Aluminous Cements / 4.5
4.4 Natural Cements / 4.6
4.5 Limes / 4.6
4.6 Low-Temperature Gypsum Derivatives / 4.8
4.7 Oxychloride Cements / 4.9
4.8 Masonry Cements / 4.9
4.9 Fly Ashes / 4.9
4.10 Silica Fume (Microsilica) / 4.10
AGGREGATES
4.11 Normal-Weight Aggregates / 4.11
4.12 Heavyweight and Lightweight Aggregates / 4.14
ADMIXTURES FOR CONCRETE
4.13 Chemical and Mineral Admixtures / 4.14
4.14 Fibers for Concrete Mixes / 4.18
4.15 Miscellaneous Admixtures / 4.19
MORTARS AND CONCRETES
4.16 Mortars / 4.19
4.17 Portland-Cement Concrete / 4.21
4.18 Polymer Concretes / 4.26
4.19 Concrete Masonry Units / 4.27
BURNED-CLAY UNITS
4.20 Brick-Clay or Shale / 4.28
4.21 Structural Clay Tile / 4.30
4.22 Ceramic Tiles / 4.32
4.23 Architectural Terra Cotta / 4.32
BUILDING STONES
4.24 Properties of Building Stones / 4.32
4.25 Freezing and Thawing of Stone / 4.35
CONTENTS vii
GYPSUM PRODUCTS
4.26 Gypsumboard / 4.35
4.27 Gypsum Lath / 4.37
4.28 Gypsum Sheathing Board / 4.37
4.29 Gypsum Partition Tile or Block / 4.37
4.30 Gypsum Plank / 4.37
GLASS AND GLASS BLOCK
4.31 Window Glass / 4.38
4.32 Glass Block / 4.40
WOOD
4.33 Mechanical Properties of Wood / 4.44
4.34 Effects of Hygroscopic Properties of Wood / 4.44
4.35 Commercial Grades of Wood / 4.46
4.36 Destroyers and Preservatives / 4.48
4.37 Glues and Adhesives for Wood / 4.50
4.38 Plywood and Other Fabricated Wood Boards / 4.51
4.39 Wood Bibliography / 4.52
STEEL AND STEEL ALLOYS
4.40 Types of Irons and Steels / 4.52
4.41 Properties of Structural Steels / 4.58
4.42 Heat Treatment and Hardening of Steels / 4.61
4.43 Effects of Grain Size / 4.62
4.44 Steel Alloys / 4.62
4.45 Welding Ferrous Materials / 4.68
4.46 Effects of Steel Production Methods / 4.70
4.47 Effects of Hot Rolling / 4.72
4.48 Effects of Punching and Shearing / 4.73
4.49 Corrosion of Iron and Steel / 4.74
4.50 Steel and Steel Alloy Bibliography / 4.75
ALUMINUM AND ALUMINUM-BASED ALLOYS
4.51 Aluminum-Alloy Designations / 4.75
4.52 Finishes for Aluminum / 4.76
4.53 Structural Aluminum / 4.76
4.54 Welding and Brazing of Aluminum / 4.77
4.55 Bolted and Riveted Aluminum Connections / 4.79
4.56 Prevention of Corrosion of Aluminum / 4.79
4.57 Aluminum Bibliography / 4.80
COPPER AND COPPER-BASED ALLOYS
4.58 Copper / 4.80
4.59 Brass / 4.81
4.60 Nickel Silvers / 4.82
4.61 Cupronickel / 4.83
4.62 Bronze / 4.83
4.63 Copper Bibliography / 4.84
LEAD AND LEAD-BASED ALLOYS
4.64 Applications of Lead / 4.84
4.65 Lead Bibliography / 4.85
NICKEL AND NICKEL-BASED ALLOYS
4.66 Properties of Nickel and Its Alloys / 4.85
4.67 Nickel Bibliography / 4.86
PLASTICS
4.68 General Properties of Plastics / 4.86
4.69 Fillers and Plasticizers / 4.87
4.70 Molding and Fabricating Methods for Plastics / 4.87
viii CONTENTS
4.71 Thermosetting Plastics / 4.88
4.72 Thermoplastic Resins / 4.90
4.73 Elastomers, or Synthetic Rubbers / 4.92
COMBINATION OF PLASTICS AND OTHER MATERIALS
4.74 High-Pressure Laminates / 4.93
4.75 Reinforced Plastics / 4.93
4.76 Laminated Rubber / 4.94
4.77 Plastics Bibliography / 4.95
PORCELAIN-ENAMELED PRODUCTS
4.78 Porcelain Enamel on Metal / 4.96
4.79 Porcelain Bibliography / 4.96
ASPHALT AND BITUMINOUS PRODUCTS
4.80 Asphalts for Dampproofing and Waterproofing / 4.97
4.81 Bituminous Roofing / 4.97
4.82 Asphalt Shingles / 4.98
4.83 Asphalt Mastics and Grouts / 4.99
4.84 Bituminous Pavements / 4.99
4.85 Asphalt Bibliography / 4.99
JOINT SEALS
4.86 Calking Compounds / 4.100
4.87 Sealants / 4.100
4.88 Gaskets / 4.101
4.89 Joint Seals Bibliography / 4.101
PAINTS AND OTHER COATINGS
4.90 Vehicles or Binders / 4.102
4.91 Pigments for Paints / 4.103
4.92 Resins for Paints / 4.104
4.93 Coatings Bibliography / 4.105
Section 5 Structural Theory Akbar Tamboli, Michael Xing,
and Mohsin Ahmed 5.1
5.1 Design Loads / 5.2
5.2 Stress and Strain / 5.17
5.3 Stresses at a Point / 5.24
5.4 Torsion / 5.28
5.5 Straight Beams / 5.30
5.6 Curved Beams / 5.52
5.7 Buckling of Columns / 5.58
5.8 Graphic-Statics Fundamentals / 5.62
5.9 Roof Trusses / 5.63
5.10 General Tools for Structural Analysis / 5.67
5.11 Continuous Beams and Frames / 5.78
5.12 Load Distribution to Bents and Shear Walls / 5.101
5.13 Finite-Element Methods / 5.110
5.14 Stresses in Arches / 5.115
5.15 Thin-Shell Structures / 5.119
5.16 Cable-Supported Structures / 5.128
5.17 Air-Stabilized Structures / 5.138
5.18 Structural Dynamics / 5.140
5.19 Earthquake Loads / 5.162
5.20 Floor Vibrations / 5.183
5.21 Wiss and Parmelee Rating Factor for Transient Vibrations / 5.185
5.22 Reiher-Meister Scale for Steady-State Vibrations / 5.186
5.23 Murray Criterion for Walking Vibrations / 5.188
CONTENTS ix
Section 6 Soil Mechanics and Foundations Robert W. Day 6.1
6.1 Introduction / 6.1
6.2 Field Exploration / 6.3
6.3 Laboratory Testing / 6.23
6.4 Effective Stress and Stress Distribution / 6.43
6.5 Settlement Analyses / 6.50
6.6 Bearing Capacity Analyses / 6.61
6.7 Retaining Walls / 6.76
6.8 Foundations / 6.88
6.9 Foundation Excavations / 6.96
6.10 Grading and Other Site Improvement Methods / 6.97
6.11 Geosynthetics / 6.115
Section 7 Structural Steel Construction Bruce Glidden 7.1
7.1 Codes and Specifications / 7.2
7.2 Mill Materials / 7.2
7.3 Fasteners / 7.8
7.4 Fabrication / 7.17
7.5 Quality Assurance / 7.17
STRUCTURAL FRAMING SYSTEMS
7.6 Wall Bearing Framing / 7.18
7.7 Skeleton Framing / 7.20
7.8 Long-Span Framing / 7.22
7.9 Steel and Concrete Framing / 7.29
BRACING SYSTEMS
7.10 Bracing Design Considerations / 7.30
7.11 Frame Bracing / 7.31
7.12 Bracing for Individual Members / 7.36
FLOOR AND ROOF SYSTEMS
7.13 Floor-Framing Design Considerations / 7.39
7.14 Roof Framing Systems / 7.44
DESIGN OF MEMBERS
7.15 Bases for ASD and LRFD / 7.44
7.16 Design Aids and References / 7.45
7.17 Serviceability Criteria / 7.47
7.18 Tension Members / 7.49
7.19 Columns and Other Compression Members / 7.50
7.20 Beams and Other Flexural Members / 7.57
7.21 Plate Girders / 7.67
7.22 Web or Flange Load-Bearing Stiffeners / 7.76
7.23 Bearing / 7.79
7.24 Combined Axial Compression and Bending / 7.80
7.25 Combined Axial Tension and Bending / 7.82
7.26 Composite Construction / 7.83
7.27 Members Subject to Torsion / 7.89
7.28 Members Subject to Cyclic Loading / 7.90
DESIGN OF CONNECTIONS
7.29 Combinations of Fasteners / 7.91
7.30 Load Capacity of Bolts / 7.91
7.31 Load Capacity of Welds / 7.93
7.32 Bearing-Type Bolted Connections / 7.96
7.33 Slip-Critical Bolted Connections / 7.100
7.34 Eccentrically Loaded Welded Connections / 7.101
x CONTENTS
7.35 Types of Beam Connections / 7.103
7.36 Beams Splices / 7.113
7.37 Column Splices / 7.114
STEEL ERECTION
7.38 Erection Equipment / 7.117
7.39 Clearance for Erecting Beams / 7.117
7.40 Erection Sequence / 7.119
7.41 Field-Welding Procedures / 7.120
7.42 Erection Tolerances / 7.121
7.43 Adjusting Lintels / 7.123
CORROSION PROTECTION
7.44 Corrosion of Steel / 7.124
7.45 Painting Steel Structures / 7.125
7.46 Paint Systems / 7.125
7.47 Field-Painting Steel / 7.126
7.48 Steel in Contact with Concrete / 7.127
FIRE PROTECTION OF STRUCTURAL STEEL
7.49 Effect of Heat on Steel / 7.129
7.50 Fire Protection of Exterior / 7.129
7.51 Materials for Improving Fire Resistance / 7.130
7.52 Pierced Ceilings and Floors / 7.131
7.53 Fire-Resistance Ratings / 7.133
7.54 Bibliography / 7.134
Section 8 Cold-Formed Steel Construction Don S. Wolford
and Wei-Wen Yu 8.1
COLD-FORMED SHAPES
8.1 Material for Cold-Formed Steel Shapes / 8.2
8.2 Utilization of Cold Work of Forming / 8.7
8.3 Types of Cold-Formed Shapes / 8.8
DESIGN PRINCIPLES FOR COLD-FORMED STEEL SHAPES
8.4 Some Basic Concepts of Cold-Formed Steel Design / 8.10
8.5 Structural Behavior of Flat Compression Elements / 8.14
8.6 Unstiffened Cold-Formed Elements Subject to Local Buckling / 8.17
8.7 Stiffened Cold-Formed Elements Subject to Local Buckling / 8.17
8.8 Application of Effective Widths / 8.21
8.9 Maximum Flat-Width Ratios of Cold-Formed Steel / 8.22
8.10 Unit Stresses for Cold-Formed Steel / 8.22
8.11 Laterally Unsupported Cold-Formed Beams / 8.22
8.12 Allowable Shear Strength in Webs / 8.23
8.13 Concentrically Loaded Compression Members / 8.23
8.14 Combined Axial and Bending Stresses / 8.25
JOINING OF COLD-FORMED STEEL
8.15 Welding of Cold-Formed Steel / 8.25
8.16 Arc Welding of Cold-Formed Steel / 8.26
8.17 Resistance Welding of Cold-Formed Steel / 8.31
8.18 Bolting of Cold-Formed Steel Members / 8.33
8.19 Self-Tapping Screws for Joining Sheet Steel Components / 8.40
8.20 Special Fasteners for Cold-Formed Steel / 8.41
COLD-FORMED STEEL FLOOR, ROOF, AND WALL CONSTRUCTION
8.21 Steel Roof Deck / 8.42
CONTENTS xi
8.22 Cellular Steel Floor and Roof Panels / 8.47
8.23 Corrugated Sheets for Roofing, Siding, and Decking / 8.50
8.24 Lightweight Steel Metric Sheeting / 8.53
8.25 Stainless Steel Structural Design / 8.54
PREENGINEERED STEEL BUILDINGS
8.26 Characteristics of Preengineered Steel Buildings / 8.55
8.27 Structural Design of Preengineered Buildings / 8.56
OPEN-WEB STEEL JOISTS
8.28 Design of Open-Web Steel Joists / 8.57
8.29 Construction Details for Open-Web Steel Joists / 8.59
Section 9 Concrete Construction Edward S. Hoffman
and David P. Gustafson 9.1
CONCRETE AND ITS INGREDIENTS
9.1 Cementitious Materials / 9.1
9.2 Cements / 9.2
9.3 Aggregates / 9.2
9.4 Proportioning Concrete Mixes / 9.3
9.5 Yield Calculation / 9.6
9.6 Properties and Tests of Fresh (Plastic) Concrete / 9.7
9.7 Properties and Tests of Hardened Concrete / 9.8
9.8 Measuring and Mixing Concrete Ingredients / 9.10
9.9 Admixtures / 9.11
QUALITY CONTROL
9.10 Mix Design / 9.14
9.11 Check Tests of Materials / 9.17
9.12 At the Mixing Plant-Yield Adjustments / 9.17
9.13 At the Placing Point-Slump Adjustments / 9.18
9.14 Strength Tests / 9.18
9.15 Test Evaluation / 9.21
FORMWORK
9.16 Responsibility for Formwork / 9.22
9.17 Materials and Accessories for Forms / 9.22
9.18 Loads on Formwork / 9.22
9.19 Form Removal and Reshoring / 9.25
9.20 Special Forms / 9.26
9.21 Inspection of Formwork / 9.26
REINFORCEMENT
9.22 Reinforcing Bars / 9.26
9.23 Welded-Wire Fabric (WWF) / 9.28
9.24 Prestressing Steel / 9.29
9.25 Fabrication and Placing of Rebars / 9.29
9.26 Bar Supports / 9.32
9.27 Inspection of Reinforcement / 9.33
CONCRETE PLACEMENT
9.28 Good Practice / 9.34
9.29 Methods of Placing / 9.34
9.30 Excess Water / 9.34
9.31 Consolidation / 9.35
9.32 Concreting Vertical Elements / 9.35
9.33 Concreting Horizontal Elements / 9.36
xii CONTENTS
9.34 Bonding to Hardened Concrete / 9.37
9.35 Heavy-Duty Floor Finishes / 9.37
9.36 Concreting in Cold Weather / 9.38
9.37 Concreting in Hot Weather / 9.38
9.38 Curing Concrete / 9.39
9.39 Joints in Concrete / 9.40
9.40 Inspection of Concrete Placement / 9.41
STRUCTURAL ANALYSIS OF CONCRETE STRUCTURES
9.41 Analyses of One-Way Floor and Roof Systems / 9.42
9.42 Two-Way Slab Frames / 9.44
9.43 Special Analyses / 9.45
STRUCTURAL DESIGN OF FLEXURAL MEMBERS
9.44 Strength Design with Factored Loads / 9.45
9.45 Allowable-Stress Design at Service Loads (Alternative Design Method) / 9.47
9.46 Strength Design for Flexure / 9.49
9.47 Shear in Flexural Members / 9.53
9.48 Torsion in Reinforced Concrete Members / 9.55
9.49 Development, Anchorage, and Splices of Reinforcement / 9.58
9.50 Crack Control / 9.70
9.51 Deflection of Reinforced-Concrete Beams and Slabs / 9.71
ONE-WAY REINFORCED-CONCRETE SLABS
9.52 Analysis and Design of One-Way Slabs / 9.75
9.53 Embedded Pipes in One-Way Slabs / 9.77
ONE-WAY CONCRETE-JOIST CONSTRUCTION
9.54 Standard Sizes of Joists / 9.79
9.55 Design of One-Way Concrete-Joist Construction / 9.79
9.56 Reinforcement of Joists for Flexure / 9.80
9.57 Shear in Joists / 9.81
9.58 Wide-Module Joist Construction / 9.82
TWO-WAY SLAB CONSTRUCTION
9.59 Analysis and Design of Flat Plates / 9.84
9.60 Flat Slabs / 9.90
9.61 Two-Way Slabs on Beams / 9.92
9.62 Estimating Guide for Two-Way Construction / 9.93
BEAMS
9.63 Definitions of Flexural Members / 9.94
9.64 Flexural Reinforcement / 9.94
9.65 Reinforcement for Shear and Flexure / 9.98
9.66 Reinforcement for Torsion and Shear / 9.100
9.67 Crack Control in Beams / 9.100
WALLS
9.68 Bearing Walls / 9.101
9.69 Nonbearing Walls / 9.103
9.70 Cantilever Retaining Walls / 9.103
9.71 Counterfort Retaining Walls / 9.105
9.72 Retaining Walls Supported on Four Sides / 9.106
FOUNDATIONS
9.73 Types of Foundations / 9.106
9.74 General Design Principles for Foundations / 9.107
9.75 Spread Footings for Walls / 9.110
9.76 Spread Footings for Individual Columns / 9.111
9.77 Combined Spread Footings / 9.112
9.78 Strap Footings / 9.114
9.79 Mat Foundations / 9.115
CONTENTS xiii
9.80 Pile Foundations / 9.115
9.81 Drilled-Pier Foundations / 9.117
COLUMNS
9.82 Basic Assumptions for Strength Design of Columns / 9.118
9.83 Design Requirements for Columns / 9.122
9.84 Column Ties and Tie Patterns / 9.124
9.85 Biaxial Bending of Columns / 9.124
9.86 Slenderness Effects on Concrete Columns / 9.125
9.87 Economy in Column Design / 9.128
SPECIAL CONSTRUCTION
9.88 Deep Beams / 9.129
9.89 Shear Walls / 9.131
9.90 Reinforced-Concrete Arches / 9.133
9.91 Reinforced-Concete Thin Shells / 9.134
9.92 Concrete Folded Plates / 9.136
9.93 Slabs on Grade / 9.137
9.94 Seismic-Resistant Concrete Construction / 9.138
9.95 Composite Flexural Members / 9.138
PRECAST-CONCRETE MEMBERS
9.96 Design Methods for Precast Members / 9.140
9.97 Reinforcement Cover in Precast Members / 9.140
9.98 Tolerances for Precast Construction / 9.140
9.99 Accelerated Curing / 9.141
9.100 Precast Floor and Roof Systems / 9.141
9.101 Precast Ribbed Slabs, Folded Plates, and Shells / 9.142
9.102 Wall Panels / 9.142
9.103 Lift Slabs / 9.144
PRESTRESSED-CONCRETE CONSTRUCTION
9.104 Basic Principles of Prestressed Concrete / 9.144
9.105 Losses in Prestress / 9.145
9.106 Allowable Stresses at Service Loads / 9.147
9.107 Design Procedure for Prestressed-Concrete Beams / 9.149
9.108 Flexural-Strength Design of Prestressed Concrete / 9.149
9.109 Shear-Strength Design of Prestressed Concrete / 9.151
9.110 Bond, Development, and Grouting of Tendons / 9.153
9.111 Application and Measurement of Prestress / 9.155
9.112 Concrete Cover in Prestressed Members / 9.155
Section 10 Wood Construction John ‘‘Buddy’’ Showalter
and Thomas G. Williamson 10.1
10.1 Basic Characteristics of Wood / 10.1
10.2 Sectional Properties of Wood Products / 10.6
10.3 Design Values for Lumber and Timber / 10.10
10.4 Structural Grading of Wood / 10.11
10.5 Adjustment Factors for Structural Members / 10.11
10.6 Pressure-Preservative Treatments for Wood / 10.19
10.7 Design Provisions for Flexural Members / 10.21
10.8 Wood Compression Members / 10.28
10.9 Tension Members / 10.30
10.10 Combined Bending and Axial Loading / 10.30
10.11 Bearing Stresses / 10.32
10.12 Structural Panels / 10.33
10.13 Design Values for Mechanical Connections / 10.51
xiv CONTENTS
10.14 Adjustment of Design Values for Connections / 10.51
10.15 Bolts / 10.59
10.16 Lag Screws / 10.60
10.17 Split-Ring and Shear-Plate Connectors / 10.61
10.18 Wood Screws / 10.63
10.19 Nails and Spikes / 10.65
10.20 Structural Framing Connections / 10.66
10.21 Glued Fastenings / 10.66
10.22 Wood Trusses / 10.68
10.23 Design of Timber Arches / 10.72
10.24 Timber Decking / 10.73
10.25 Wood-Frame Construction / 10.76
10.26 Permanent Wood Foundations / 10.80
10.27 Post Frame and Pole Construction / 10.81
10.28 Design for Fire Safety / 10.83
10.29 Timber Fabrication and Erection / 10.85
10.30 Engineered Glued Wood Products / 10.89
Section 11 Wall, Floor, and Ceiling Systems Frederick S. Merritt 11.1
MASONRY WALLS
11.1 Masonry Definitions / 11.2
11.2 Quality of Materials for Masonry / 11.5
11.3 Construction of Masonry / 11.8
11.4 Lateral Support for Masonry Walls / 11.16
11.5 Chimneys and Fireplaces / 11.18
11.6 Provisions for Dimensional Changes / 11.19
11.7 Repair of Leaky Joints / 11.21
11.8 Masonry-Thickness Requirements / 11.22
11.9 Determination of Masonry Compressive Strength / 11.24
11.10 Allowable Stresses in Masonry / 11.25
11.11 Floor-Wall Connections / 11.31
11.12 Glass Block / 11.33
11.13 Masonry Bibliography / 11.34
STUD WALLS
11.14 Stud-Wall Construction / 11.35
11.15 Sheathing / 11.37
CURTAIN WALLS
11.16 Functional Requirements of Curtain Walls / 11.37
11.17 Wood Facades / 11.38
11.18 Wall Shingles and Siding / 11.39
11.19 Stucco / 11.39
11.20 Precast-Concrete or Metal and Glass Facings / 11.40
11.21 Sandwich Panels / 11.41
PARTITIONS
11.22 Types of Partitions / 11.43
11.23 Structural Requirements of Partitions / 11.44
PLASTER AND GYPSUMBOARD
11.24 Plaster and Gypsumboard Construction Terms / 11.45
11.25 Plaster Finishes / 11.53
11.26 Gypsumboard Finishes / 11.62
11.27 Isolation and Control Joints in Gypsumboard Construction / 11.70
CONTENTS xv
CERAMIC-TILE CONSTRUCTION
11.28 Types of Ceramic Tile / 11.72
11.29 Tile Installation Methods / 11.73
PANEL FINISHES
11.30 Plywood Finishes / 11.77
11.31 Other Types of Panel Finishes / 11.78
FLOOR SYSTEMS
11.32 Asphalt Tiles / 11.78
11.33 Cork Tiles / 11.79
11.34 Vinyl Flooring / 11.79
11.35 Rubber Flooring / 11.80
11.36 Installation of Thin Coverings / 11.80
11.37 Carpets / 11.82
11.38 Terrazzo / 11.83
11.39 Concrete Floors / 11.84
11.40 Wood Floors / 11.84
11.41 Industrial Floors / 11.85
11.42 Conductive Flooring / 11.86
11.43 Specifications and Standards for Flooring / 11.86
WINDOWS
11.44 Window Selection / 11.87
11.45 Window Definitions / 11.87
11.46 Modular Coordination of Windows / 11.89
11.47 Window Sash Materials / 11.89
11.48 Glazing / 11.93
11.49 Window Types / 11.98
11.50 Windows in Wall-Panel Construction / 11.106
11.51 Mechanical Operators for Windows / 11.107
DOORS
11.52 Traffic Flow and Safety / 11.109
11.53 Structural Requirements for Openings and Doors / 11.110
11.54 Ordinary Doors / 11.110
11.55 Fire and Smokestop Doors / 11.118
11.56 Revolving Doors / 11.120
11.57 Large Horizontally Sliding Doors / 11.120
11.58 Large Vertically Sliding Doors / 11.121
11.59 Large Swinging Doors / 11.122
11.60 Horizontally Hinged Doors / 11.123
11.61 Radiation-Shielding Doors / 11.123
BUILDERS’ HARDWARE
11.62 Selection of Hardware / 11.124
11.63 Effects of Codes and Regulations on Hardware / 11.125
11.64 Standards for Finishing Hardware / 11.125
11.65 Hinges and Butts / 11.126
11.66 Door-Closing Devices / 11.131
11.67 Locks, Latches, and Keys / 11.132
11.68 Window Hardware / 11.136
11.69 Inserts, Anchors, and Hangers / 11.137
11.70 Nails / 11.138
11.71 Screws / 11.139
11.72 Welded Studs / 11.141
11.73 Powder-Driven Studs / 11.143
11.74 Bolts / 11.144
xvi CONTENTS
ACOUSTICS
11.75 Sound Production and Transmission / 11.145
11.76 Nomenclature for Analysis of Sound / 11.145
11.77 Sound Characteristics and Effects on Hearing / 11.146
11.78 Measurement of Sound / 11.149
11.79 Sound and Vibration Control / 11.151
11.80 Acoustical Performance Data / 11.162
11.81 Acoustical Criteria / 11.164
11.82 Helpful Hints for Noise Control / 11.166
11.83 Acoustics Bibliography / 11.169
Section 12 Roof Systems Dave Flickinger 12.1
ROOF MATERIALS
12.1 Roof Decks / 12.1
12.2 Vapor Retarders / 12.2
12.3 Roof Insulation / 12.4
12.4 Low-Slope Roof Coverings / 12.5
12.5 Steep-Slope Roof Coverings / 12.13
12.6 Need for Familiarity with Roof Design / 12.17
12.7 Building Owners’ Responsibility / 12.18
12.8 Building-Code Provisions for Roofs / 12.18
12.9 Effects of Climate / 12.18
12.10 Effects of Roof Size, Shape, and Slope / 12.19
12.11 Deck Suitability / 12.20
12.12 Effects of Rooftop Traffic / 12.20
12.13 Esthetic Considerations / 12.20
12.14 Effects of Wind on Roofs / 12.21
12.15 Protected Membrane Roofs and Plaza Decks / 12.21
12.16 Preroofing Conference / 12.21
12.17 Warranties / 12.22
12.18 Roof Maintenance / 12.22
12.19 Reroofing / 12.23
12.20 Roofing Industry Associations and Related Organizations / 12.24
12.21 Roof Systems Bibliography / 12.28
Section 13 Heating, Ventilation, and Air Conditioning
Lawrence E. McCabe 13.1
13.1 Definitions of Terms of Heating, Ventilation, and Air Conditioning (HVAC) / 13.1
13.2 Heat and Humidity / 13.7
13.3 Major Factors in HVAC Design / 13.16
13.4 Ventilation / 13.27
13.5 Movement of Air with Fans / 13.31
13.6 Duct Design / 13.14
13.7 Heat Losses / 13.35
13.8 Heat Gains / 13.37
METHODS OF HEATING BUILDINGS
13.9 General Procedure for Sizing a Heating Plant / 13.41
13.10 Heating-Load-Calculation Example / 13.43
13.11 Warm-Air Heating / 13.45
13.12 Hot-Water Heating Systems / 13.49
13.13 Steam-Heating Systems / 13.53
CONTENTS xvii
13.14 Unit Heaters / 13.56
13.15 Radiant Heating / 13.57
13.16 Snow Melting / 13.59
13.17 Radiators and Convectors / 13.60
13.18 Heat Pumps / 13.62
13.19 Solar Heating / 13.62
METHODS OF COOLING AND AIR CONDITIONING
13.20 Sizing an Air-Conditioning Plant / 13.65
13.21 Refrigeration Cycles / 13.69
13.22 Air-Distribution Temperature for Cooling / 13.71
13.23 Condensers / 13.72
13.24 Compressor-Motor Units / 13.73
13.25 Cooling Equipment-Central Plant Packaged Units / 13.74
13.26 Zoning / 13.76
13.27 Packaged Air-Conditioning Units / 13.76
13.28 Absorption Units for Cooling / 13.78
13.29 Ducts for Air Conditioning / 13.79
13.30 Built-Up Air-Conditioning Units / 13.82
13.31 Variable-Air-Volume (VAV) Systems / 13.82
13.32 Air-Water Systems / 13.85
13.33 Control Systems for Air Conditioning / 13.33
13.34 Heating and Air Conditioning / 13.89
13.35 Control of Computerized HVAC Systems / 13.90
13.36 Direct Digital Control / 13.92
13.37 Industrial Air Conditioning / 13.93
13.38 Chemical Cooling / 13.94
13.39 Year-Round Air Conditioning / 13.94
Section 14 Plumbing—Water-Supply, Sprinkler, and
Wastewater Systems Gregory P. Gladfelter and Brian L. Olsen 14.1
14.1 Plumbing and Fire Prevention Codes / 14.1
14.2 Health Requirements for Plumbing / 14.2
14.3 Water Quality / 14.3
14.4 Water Treatment / 14.5
14.5 Water Quantity and Pressures / 14.6
14.6 Water Distribution in Buildings / 14.7
14.7 Plumbing Fixtures and Equipment / 14.13
14.8 Water Demand and Fixture Units / 14.19
14.9 Water-Pipe Sizing / 14.21
14.10 Domestic Water Heaters / 14.29
WASTEWATER PIPING
14.11 Wastewater Disposal / 14.31
14.12 Sewers / 14.34
14.13 Wastewater-System Elements / 14.36
14.14 Waste-Pipe Materials / 14.38
14.15 Layout of Waste Piping / 14.38
14.16 Interceptors / 14.39
14.17 Piping for Indirect Wastes / 14.39
14.18 Rainwater Drainage / 14.40
14.19 Waste-Pipe Sizing / 14.43
14.20 Venting / 14.45
14.21 Plumbing-System Inspection and Tests / 14.48
xviii CONTENTS
GAS PIPING
14.22 Gas Supply / 14.49
14.23 Gas-Pipe Sizes / 14.50
14.24 Estimating Gas Consumption / 14.50
14.25 Gas-Pipe Materials / 14.51
SPRINKLER SYSTEMS
14.26 Sprinkler Systems / 14.52
14.27 Automatic Sprinklers / 14.53
14.28 Types of Sprinkler Systems / 14.54
14.29 System Design / 14.59
14.30 Standpipes / 14.63
14.31 Water Supplies for Sprinkler and Standpipe Systems / 14.64
14.32 Central Station Supervisory Systems / 14.65
14.33 Additional Information / 14.65
Section 15 Electrical Systems James M. Bannon 15.1
15.1 Electrical Power / 15.2
15.2 Direct-Current Systems / 15.2
15.3 Alternating-Current Systems / 15.5
15.4 Electrical Loads / 15.12
15.5 Emergency Power / 15.14
15.6 Electrical Conductors and Raceways / 15.15
15.7 Power System Apparatus / 15.20
15.8 Electrical Distribution in Buildings / 15.29
15.9 Circuit and Conductor Calculations / 15.34
15.10 Light and Sight / 15.45
15.11 Quality of Light / 15.51
15.12 Color Rendering with Lighting / 15.54
15.13 Quantity of Light / 15.55
15.14 Lighting Methods / 15.58
15.15 Daylight / 15.60
15.16 Characteristics of Lamps / 15.60
15.17 Characteristics of Lighting Fixtures / 15.68
15.18 Systems Design of Lighting / 15.72
15.19 Special Electrical Systems / 15.73
15.20 Electrical Systems Bibliography / 15.77
Section 16 Vertical Circulation Steven D. Edgett
and Allen M. Williams 16.1
16.1 Classification of Vertical Circulation Systems / 16.1
16.2 Ramps / 16.2
16.3 Stairs / 16.5
16.4 Escalators / 16.11
16.5 Elevator Installations / 16.18
16.6 Definitions of Elevator Terms / 16.19
16.7 Elevator Hoistways / 16.22
16.8 Elevator Cars / 16.26
16.9 Electric Elevators / 16.28
16.10 Hydraulic Elevators / 16.35
16.11 Planning for Passenger Elevators / 16.37
16.12 Dumbwaiters / 16.45
16.13 Conveyers and Pneumatic Tubes / 16.45
16.14 Mail Chutes / 16.47
CONTENTS xix
Section 17 Construction Project Management Robert F. Borg 17.1
17.1 Types of Construction Companies / 17.1
17.2 Construction Company Organization / 17.3
17.3 Contractors’ Business Consultants / 17.6
17.4 Sources of Business / 17.7
17.5 What Constitutes the Contract Documents? / 17.9
17.6 Major Concerns with Building Codes / 17.11
17.7 Estimating, Bidding, and Costs / 17.11
17.8 Types of Bids and Contracts / 17.12
17.9 Professional Construction Managers / 17.15
17.10 Contract Administration / 17.16
17.11 Purchase Orders / 17.28
17.12 Scheduling and Expediting / 17.30
17.13 Fast Tracking / 17.34
17.14 Changes, Claims, and Dispute Resolution / 17.36
17.15 Insurance / 17.42
17.16 Construction Contract Bonds / 17.52
17.17 Trade Payment Breakdowns and Payments / 17.54
17.18 Cost Records / 17.56
17.19 Accounting Methods / 17.61
17.20 Safety / 17.62
17.21 Community Relations / 17.63
17.22 Relations with Public Agencies in Executing Construction Operations / 17.64
17.23 Labor Relations / 17.65
17.24 Social and Environmental Concerns in Construction / 17.67
17.25 Systems Building / 17.69
17.26 Basics of Successful Management / 17.70
Section 18 Communications Systems Tom Nevling 18.1
18.1 Glossary / 18.1
18.2 Grounding / 18.8
18.3 Communications Room and Communications Closet Layout / 18.10
18.4 Wiring Diagrams / 18.11
18.5 Fiberoptic Cable / 18.13
18.6 Fiberoptic Connectors / 18.16
18.7 Horizontal Cabling / 18.17
18.8 Budget / 18.20
18.9 Links / 18.26
Section 19 Construction Cost Estimating Colman J. Mullin 19.1
19.1 Composition of Project Price / 19.1
19.2 Estimating Direct Costs / 19.2
19.3 Estimating Contingency Costs / 19.7
19.4 Estimating Margin (Markup) / 19.8
19.5 Sample Estimate / 19.9
19.6 Reviewing Estimates / 19.14
19.7 Computer Estimating / 19.14
Appendix Factors for Conversion to the Metric System (SI) of Units
Frederick S. Merritt A.1
Index I.1
xxi
CONTRIBUTORS
David J. Akers Civil Engineer, San Diego, California (SECT. 4: Building Materials)
James M. Bannon Chief Electrical Engineer, STV Incorporated, Douglassville, Pennsylvania
(SECT. 15: Electrical Systems)
Robert F. Borg Chairman, Kreisler Borg Florman General Construction Company, Scarsdale,
New York (SECT. 17: Construction Project Management)
Robert W. Day Chief Engineer, American Geotechnical, San Diego, California (SECT. 6:
Soil Mechanics and Foundations)
Steven D. Edgett Edgett-Williams Consulting Group, Mill Valley, California (SECT. 16:
Vertical Circulation)
Dave Flickinger National Roofing Contractors Association (NRCA), Technical Service Section,
Rosemont, Illinois (SECT. 12: Roof Systems)
Gregory P. Gladfelter Gladfelter Engineering Group, Kansas City, Missouri (SECT. 14:
Plumbing—Water-Supply, Sprinkler, and Wastewater Systems)
Bruce Glidden President, Glidden & Co., Ltd., Bridgeville, Pennsylvania (SECT. 7: Structural
Steel Construction)
David P. Gustafson Vice President of Engineering, Concrete Reinforcing Steel Institute,
Schaumburg, Illinois (SECT. 9: Concrete Construction)
Alan D. Hinklin Director, Skidmore, Owings & Merrill (SECT. 2: The Building Team)
Edward S. Hoffman President, Edward S. Hoffman, Ltd., Structural Engineers, Chicago
(SECT. 9: Concrete Construction)
Lawrence E. McCabe Chief Engineer—Mechanical STV Group, Douglassville, Pennsylvania
(SECT. 13: Heating, Ventilation, and Air Conditioning)
Frederick S. Merritt Consulting Engineer, West Palm Beach, Florida (SECT. 11: Wall, Floor,
and Ceiling Systems)
David W. Mock Gee & Jenson, West Palm Beach, Florida (SECT. 3: Protection against
Hazards
Colman J. Mullin Senior Estimator, Bechtel Corporation, San Francisco, California (SECT.
19: Construction Cost Estimating)
Tom Nevling, RCDD Independent Consultant, Lancaster, Pennsylvania (SECT. 18: Communications
Systems)
Brian L. Olsen Poole Fire Protection Engineering, Inc., Olathe, Kansas (SECT. 14: Plumbing—
Water-Supply, Sprinkler, and Wastewater Systems)
Jonathan T. Ricketts Consulting Engineer, Palm Beach Gardens, Florida (SECT. 1: System
Fundamentals)
John ‘‘Buddy’’ Showalter American Forest & Paper Association, Washington, D.C. (SECT.
10: Wood Construction)
xxii CONTRIBUTORS
Akbar Tamboli, Michael Xing, Mohsin Ahmed Thornton-Tomasetti Engineers, Newark,
New Jersey (SECT. 5: Structural Theory)
Allen M. Williams Edgett-Williams Consulting Group, Mill Valley, California (SECT. 16:
Vertical Circulation)
Thomas G. Williamson APA—The Engineered Wood Association, Tacoma, Washington
(SECT. 10: Wood Construction)
Don S. Wolford Consulting Engineer, Middletown, Ohio (SECT. 8: Cold-Formed Steel Construction)
Wei-Wen Yu Univesity of Missouri–Rolla, Rolla, Missouri (SECT. 8: Cold-Formed Steel
Construction)
xxiii
PREFACE
The sixth edition of the Building Design and Construction Handbook maintains the
original objectives of previous editions which gained widespread acceptance among
users. These objectives are to provide in a single volume a compendium of the best
of the current knowledge and practices in building design and construction.
This information would be of greatest use to those who have to make decisions
affecting the selection of engineering materials and construction methods. Emphasis
is placed on fundamental principles and practical applications, with special attention
to simplified procedures. Frequent reference is made to other sources where additional
authoritative information may be obtained, such as architectural and engineering
societies, manufacturers associations, and the Internet. An extensive index
is provided to assist the reader in locating topics within the book.
Many new contributors and sections have been added in this edition to provide
the reader with the latest developments and knowledge in the building industry.
These developments include the expansion of data technology and communication
systems within the building system, revisions to wind and seismic loadings, and an
expansion of the information on fire sprinkler systems. To present the necessary
information in a single volume, obsolete and less-important information in the earlier
editions has been deleted.
The editor is very grateful to the contributors, not only for their care, skill, and
knowledge used in preparing the sections, but also for their considerable sacrifices
of personal time to prepare the sections.
Jonathan T. Ricketts
1.1
SECTION ONE
BUILDING SYSTEMS*
Jonathan T. Ricketts
Consulting Engineer
Palm Beach Gardens, Florida
Sociological changes, new technology in industry and commerce, new building
codes, other new laws and regulations, inflationary economies of nations, and advances
in building technology place an ever-increasing burden on building designers
and constructors. They need more and more knowledge and skill to cope with the
demands placed on them.
The public continually demands more complex buildings than in the past. They
must serve more purposes, last longer, and require less maintenance and repair. As
in the past, they must look attractive. Yet, both building construction and operating
costs must be kept within acceptable limits or new construction will cease.
To meet this challenge successfully, continual improvements in building design
and construction must be made. Building designers and constructors should be alert
to these advances and learn how to apply them skillfully.
One advance of note to building design is the adaptation of operations research,
or systems design, developed around the middle of the twentieth century and originally
applied with noteworthy results to design of machines and electronic equipment.
In the past, design of a new building was mainly an imitation of the design
of an existing building. Innovations were often developed fortuitously and by intuition
and were rare occurrences. In contrast, systems design encourages innovation.
It is a precise procedure that guides creativity toward the best decisions. As
a result, it can play a significant role in meeting the challenges posed by increasing
building complexity and costs. The basic principles of systems design are presented
in this section.
1.1 PRINCIPLES OF ARCHITECTURE
A building is an assemblage that is firmly attached to the ground and that provides
total or nearly total shelter for machines, processing equipment, performance of
human activities, storage of human possessions, or any combination of these.
*Revised and updated from the previous edition by the late Frederick S. Merritt.
1.2 SECTION ONE
Building design is the process of providing all information necessary for construction
of a building that will meet its owner’s requirements and also satisfy public
health, welfare, and safety requirements. Architecture is the art and science of
building design. Building construction is the process of assembling materials to
form a building.
Building design may be legally executed only by persons deemed competent to
do so by the state in which the building is to be constructed. Competency is determined
on the basis of education, experience, and ability to pass a written test of
design skills.
Architects are persons legally permitted to practice architecture. Engineers are
experts in specific scientific disciplines and are legally permitted to design parts of
buildings; in some cases, complete buildings. In some states, persons licensed as
building designers are permitted to design certain types of buildings.
Building construction is generally performed by laborers and craftspeople engaged
for the purpose by an individual or organization, called a contractor. The
contractor signs an agreement, or contract, with the building owner under which
the contractor agrees to construct a specific building on a specified site and the
owner agrees to pay for the materials and services provided.
In the design of a building, architects should be guided by the following principles:
1. The building should be constructed to serve purposes specified by the client.
2. The design should be constructable by known techniques and with available
labor and equipment, within an acceptable time.
3. The building should be capable of withstanding the elements and normal usage
for a period of time specified by the client.
4. Both inside and outside, the building should be visually pleasing.
5. No part of the building should pose a hazard to the safety or health of its
occupants under normal usage, and the building should provide for safe evacuation
or refuge in emergencies.
6. The building should provide the degree of shelter from the elements and of
control of the interior environment—air, temperature, humidity, light, and acoustics—
specified by the client and not less than the minimums required for safety
and health of the occupants.
7. The building should be constructed to minimize adverse impact on the environment.
8. Operation of the building should consume a minimum of energy while permitting
the structure to serve its purposes.
9. The sum of costs of construction, operation, maintenance, repair, and anticipated
future alterations should be kept within the limit specified by the client.
The ultimate objective of design is to provide all the information necessary for the
construction of a building. This objective is achieved by the production of drawings,
or plans, showing what is to be constructed, specifications stating what materials
and equipment are to be incorporated in the building, and a construction
contract between the client and a contractor. Designers also should observe construction
of the building while it is in process. This should be done not only to
assist the client in ensuring that the building is being constructed in accordance
with plans and specifications but also to obtain information that will be useful in
design of future buildings.
BUILDING SYSTEMS 1.3
1.2 SYSTEMS DESIGN AND ANALYSIS
Systems design comprises a logical series of steps that leads to the best decision
for a given set of conditions. The procedure requires:
Analysis of a building as a system.
Synthesis, or selection of components, to form a system that meets specific
objectives while subject to constraints, or variables controllable by designers.
Appraisal of system performance, including comparisons with alternative systems.
Feedback to analysis and synthesis of information obtained in system evaluation,
to improve the design.
The prime advantage of the procedure is that, through comparisons of alternatives
and data feedback to the design process, systems design converges on an
optimum, or best, system for the given conditions. Another advantage is that the
procedure enables designers to clarify the requirements for the building being designed.
Still another advantage is that the procedure provides a common basis of
understanding and promotes cooperation between the specialists in various aspects
of building design.
For a building to be treated as a system, as required in systems design, it is
necessary to know what a system is and what its basic characteristic are.
A system is an assemblage formed to satisfy specific objectives and subject to
constraints and restrictions and consisting of two or more components that are
interrelated and compatible, each component being essential to the required performance
of the system.
Because the components are required to be interrelated, operation, or even the
mere existence, of one component affects in some way the performance of other
components. Also, the required performance of the system as a whole, as well as
the constraints on the system, imposes restrictions on each component.
A building meets the preceding requirements. By definition, it is an assemblage
(Art. 1.1). It is constructed to serve specific purposes. It is subject to constraints
while doing so, inasmuch as designers can control properties of the system by
selection of components (Art. 1.9). Building components, such as walls, floors,
roofs, windows, and doors, are interrelated and compatible with each other. The
existence of any of thee components affects to some extent the performance of the
others. And the required performance of the building as a whole imposes restrictions
on the components. Consequently, a building has the basic characteristics of a
system, and systems-design procedures should be applicable to it.
Systems Analysis. A group of components of a system may also be a system.
Such a group is called a subsystem. It, too, may be designed as a system, but its
goal must be to assist the system of which it is a component to meet its objectives.
Similarly, a group of components of a subsystem may also be a system. That group
is called a subsubsystem.
For brevity, the major subsystems of a building are referred to as systems in this
book.
In a complex system, such as a building, subsystems and other components may
be combined in a variety of ways to form different systems. For the purposes of
building design, the major systems are usually defined in accordance with the construction
trades that will assemble them, for example, structural framing, plumbing,
electrical systems, and heating, ventilation, and air conditioning.
In systems analysis, a system is resolved into its basic components. Subsystems
are determined. Then, the system is investigated to determine the nature, interaction,
1.4 SECTION ONE
and performance of the system as a whole. The investigation should answer such
questions as:
What does each component (or subsystem) do?
What does the component do it to?
How does the component serve its function?
What else does the component do?
Why does the component do the things it does?
What must the component really do?
Can it be eliminated because it is not essential or because another component
can assume its tasks?
See also Art. 1.8.
1.3 TRADITIONAL DESIGN PROCEDURES
Systems design of buildings requires a different approach to design and construction
than that used in traditional design (Art. 1.9). Because traditional design and construction
procedures are still widely used, however, it is desirable to incorporate as
much of those procedures in systems design as is feasible without destroying its
effectiveness. This will make the transition from traditional design to systems design
easier. Also, those trained in systems design of buildings will then be capable
of practicing in traditional ways, if necessary.
There are several variations of traditional design and construction. These are
described throughout this book. For the purpose of illustrating how they may be
modified for systems design, however, one widely used variation, which will be
called basic traditional design and construction, is described in the following and
in Art. 1.4.
In the basic traditional design procedure, design usually starts when a client
recognizes the need for and economic feasibility of a building and engages an
architect, a professional with a broad background in building design. The architect,
in turn, engages consulting engineers and other consultants.
For most buildings, structural, mechanical, and electrical consulting engineers
are required. A structural engineer is a specialist trained in the application of scientific
principles to the design of load-bearing walls, floors, roofs, foundations, and
skeleton framing needed for the support of buildings and building components. A
mechanical engineer is a specialist trained in the application of scientific principles
to the design of plumbing, elevators, escalators, horizontal walkways, dumbwaiters,
conveyors, installed machinery, and heating, ventilation, and air conditioning. An
electrical engineer is a specialist trained in the application of scientific principles
to the design of electric circuits, electric controls and safety devices, electric motors
and generators, electric lighting, and other electric equipment.
For buildings on a large site, the architect may engage a landscape architect as
a consultant. For a concert hall, an acoustics consultant may be engaged; for a
hospital, a hospital specialist; for a school, a school specialist.
The architect does the overall planning of the building and incorporates the
output of the consultants into the contract documents. The architect determines what
internal and external spaces the client needs, the sizes of these spaces, their relative
BUILDING SYSTEMS 1.5
locations, and their interconnections. The results of this planning are shown in floor
plans, which also diagram the internal flow, or circulation, of people and supplies.
Major responsibilities of the architect are enhancement of the appearance inside
and outside of the building and keeping adverse environmental impact of the structure
to a minimum. The exterior of the building is shown in drawings, called elevations.
The location and orientation of the building is shown in a site plan. The
architect also prepares the specifications for the building. These describe in detail
the materials and equipment to be installed in the structure. In addition, the architect,
usually with the aid of an attorney engaged by the client, prepares the construction
contract.
The basic traditional design procedure is executed in several stages. In the first
stage, the architect develops a program, or list of the client’s requirements. In the
next stage, the schematic or conceptual phase, the architect translates requirements
into spaces, relates the spaces and makes sketches, called schematics, to illustrate
the concepts. When sufficient information is obtained on the size and general construction
of the building, a rough estimate is made of construction cost. If this cost
does not exceed the cost budgeted by the client for construction, the next stage,
design development, proceeds. In this stage, the architect and consultants work out
more details and show the results in preliminary construction drawings and outline
specifications. A preliminary cost estimate utilizing the greater amount of information
on the building now available is then prepared. If this cost does not exceed
the client’s budget, the final stage, the contract documents phase, starts. It culminates
in production of working, or construction, drawings and specifications,
which are incorporated in the contract between the client and a builder and therefore
become legal documents. Before the documents are completed, however, a final
cost estimate is prepared. If the cost exceeds the client’s budget, the design is
revised to achieve the necessary cost reduction.
In the traditional design procedure, after the estimated cost is brought within the
budget and the client has approved the contract documents, the architect helps the
owner in obtaining bids from contractors or in negotiating a construction price with
a qualified contractor. For private work, construction not performed for a governmental
agency, the owner generally awards the construction contract to a contractor,
called a general contractor. Assigned the responsibility for construction of the
building, this contractor may perform some, all, or none of the work. Usually, much
of the work is let out to specialists, called subcontractors. For public work, there
may be a legal requirement that bids be taken and the contract awarded to the
lowest responsible bidder. Sometimes also, separate contracts have to be awarded
for the major specialists, such as mechanical and electrical trades, and to a general
contractor, who is assigned responsibility for coordinating the work of the trades
and performance of the work. (See also Art. 1.4.)
Building design should provide for both normal and emergency conditions. The
latter includes fire, explosion, power cutoffs, hurricanes, and earthquakes. The design
should include access and facilities for disabled persons.
1.4 TRADITIONAL CONSTRUCTION
PROCEDURES
As mentioned in Art. 1.3, construction under the traditional construction procedure
is performed by contractors. While they would like to satisfy the owner and the
1.6 SECTION ONE
building designers, contractors have the main objective of making a profit. Hence,
their initial task is to prepare a bid price based on an accurate estimate of construction
costs. This requires development of a concept for performance of the work
and a construction time schedule. After a contract has been awarded, contractors
must furnish and pay for all materials, equipment, power, labor, and supervision
required for construction. The owner compensates the contractors for construction
costs and services.
A general contractor assumes overall responsibility for construction of a building.
The contractor engages subcontractors who take responsibility for the work
of the various trades required for construction. For example, a plumbing contractor
installs the plumbing, an electrical contractor installs the electrical system, a steel
erector structural steel, and an elevator contractor installs elevators. Their contracts
are with the general contractor, and they are paid by the general contractor.
Sometimes, in addition to a general contractor, the owners contracts separately
with specialty contractors, such as electrical and mechanical contractors, who perform
a substantial amount of the work required for a building. Such contractors are
called prime contractors. Their work is scheduled and coordinated by the general
contractor, but they are paid directly by the owner.
Sometimes also, the owner may use the design-build method and award a contract
to an organization for both the design and construction of a building. Such
organizations are called design-build contractors. One variation of this type of
contract is employed by developers of groups of one-family homes or low-rise
apartment buildings. The homebuilder designs and constructs the dwellings, but
the design is substantially completed before owners purchase the homes.
Administration of the construction procedure often is difficult. Consequently,
some owners seek assistance from an expert, called a professional construction
manager, with extensive construction experience, who receives a fee. The construction
manager negotiates with general contractors and helps select one to construct
the building. Managers usually also supervise selection of subcontractors. During
construction, they help control costs, expedite equipment and material deliveries,
and keep the work on schedule (see Art. 17.9). In some cases, instead, the owner
may prefer to engage a construction program manager, to assist in administrating
both design and construction.
Construction contractors employ labor that may or may not be unionized. Unionized
craftspeople are members of unions that are organized by construction
trades, such as carpenter, plumber, and electrician unions. Union members will
perform only the work assigned to their trade. On the job, groups of workers are
supervised by crew supervisors, all of whom report to a superintendent.
During construction, all work should be inspected. For this purpose, the owner,
often through the architect and consultants, engages inspectors. The field inspectors
may be placed under the control of an owner’s representative, who may be titled
clerk of the works, architect’s superintendent, engineer’s superintendent, or resident
engineer. The inspectors have the responsibility of ensuring that construction meets
the requirements of the contract documents and is performed under safe conditions.
Such inspections may be made at frequent intervals.
In addition, inspections also are made by representatives of one or more governmental
agencies. They have the responsibility of ensuring that construction meets
legal requirements and have little or no concern with detailed conformance with
the contract documents. Such legal inspections are made periodically or at the end
of certain stages of construction. One agency that will make frequent inspections
is the local or state building department, whichever has jurisdiction. The purpose
of these inspections is to ensure conformance with the local or state building code.
BUILDING SYSTEMS 1.7
During construction, standards, regulations, and procedures of the Occupational
Safety and Health Administration should be observed. These are given in detail in
‘‘Construction Industry. OSHA Safety and Health Standards (29CFR1926/1910),’’
Government Printing Office, Washington, DC 20402.
Following is a description of the basic traditional construction procedure for a
multistory building:
After the award of a construction contract to a general contractor, the owner
may ask the contractor to start a portion of the work before signing of the contract
by giving the contractor a letter of intent or after signing of the contract by issuing
a written notice to proceed. The contractor then obtains construction permits, as
required, from governmental agencies, such as the local building, water, sewer, and
highway departments.
The general contractor plans and schedules construction operations in detail and
mobilizes equipment and personnel for the project. Subcontractors are notified of
the contract award and issued letters of intent or awarded subcontracts, then are
given, at appropriate times, notices to proceed.
Before construction starts, the general contractor orders a survey to be made of
adjacent structures and terrain, both for the record and to become knowledgeable
of local conditions. A survey is then made to lay out construction.
Field offices for the contractor are erected on or near the site. If desirable for
safety reasons to protect passersby, the contractor erects a fence around the site and
an overhead protective cover, called a bridge. Structures required to be removed
from the site are demolished and the debris is carted away.
Next, the site is prepared to receive the building. This work may involve grading
the top surface to bring it to the proper elevations, excavating to required depths
for basement and foundations, and shifting of utility piping. For deep excavations,
earth sides are braced and the bottom is drained.
Major construction starts with the placement of foundations, on which the building
rests. This is followed by the erection of load-bearing walls and structural
framing. Depending on the height of the building, ladders, stairs, or elevators may
be installed to enable construction personnel to travel from floor to floor and eventually
to the roof. Also, hoists may be installed to lift materials to upper levels. If
needed, temporary flooring may be placed for use of personnel.
As the building rises, pipes, ducts, and electric conduit and wiring are installed.
Then, permanent floors, exterior walls, and windows are constructed. At the appropriate
time, permanent elevators are installed. If required, fireproofing is placed for
steel framing. Next, fixed partitions are built and the roof and its covering, or
roofing, are put in place.
Finishing operations follow. These include installation of the following: ceilings;
tile; wallboard; wall paneling; plumbing fixtures; heating furnaces; air-conditioning
equipment; heating and cooling devices for rooms; escalators; floor coverings; window
glass; movable partitions; doors; finishing hardware; electrical equipment and
apparatus, including lighting fixtures, switches, outlets, transformers, and controls;
and other items called for in the drawings and specifications. Field offices, fences,
bridges, and other temporary construction must be removed from the site. Utilities,
such as gas, electricity, and water, are hooked up to the building. The site is landscaped
and paved. Finally, the building interior is painted and cleaned.
The owner’s representatives then give the building a final inspection. If they find
that the structure conforms with the contract documents, the owner accepts the
project and gives the general contractor final payment on issuance by the building
department of a certificate of occupancy, which indicates that the completed building
meets building-code requirements.
1.8 SECTION ONE
1.5 ROLE OF THE CLIENT IN DESIGN AND
CONSTRUCTION
Article 1.4 points out that administration of building construction is difficult, as a
result of which some clients, or owners, engage a construction manager or construction
program manager to act as the owner’s authorizing agent and project
overseer. The reasons for the complexity of construction administration can be seen
from an examination of the owner’s role before and during construction.
After the owner recognizes the need for a new building, the owner establishes
project goals and determines the economic feasibility of the project. If it appears
to be feasible, the owner develops a building program (list of requirements), budget,
and time schedule for construction. Next, preliminary arrangements are made to
finance construction. Then, the owner selects a construction program manager or
an architect for design of the building. Later, a construction manager may be chosen,
if desired.
The architect may seek from the owner approval of the various consultants that
will be needed for design. If a site for the building has not been obtained at this
stage, the architect can assist in site selection. When a suitable site has been found,
the owner purchases it and arranges for surveys and subsurface explorations to
provide information for locating the building, access, foundation design and construction,
and landscaping. It is advisable at this stage for the owner to start developing
harmonious relations with the community in which the building will be
erected.
During design, the owner assists with critical design decisions; approves schematic
drawings, rough cost estimates, preliminary drawings, outline specifications,
preliminary cost estimates, contract documents, and final cost estimate; pays designers’
fees in installments as design progresses; and obtains a construction loan.
Then, the owner awards the general contract for construction and orders construction
to start. Also, the owner takes out liability, property, and other desirable insurance.
At the start of construction, the owner arranges for construction permits. As
construction proceeds, the owner’s representatives inspect the work to ensure compliance
with the contract documents. Also, the owner pays contractors in accordance
with the terms of the contract. Finally, the owner approves and accepts the completed
project.
One variation of the preceding procedure is useful when time available for construction
is short. It is called phase, or fast-track, construction. In this variation,
the owner engages a construction manager and a general contractor before design
has been completed, to get an early start on construction. Work then proceeds on
some parts of the building while other parts are still being designed. For example,
excavation and foundation construction are carried out while design of the structural
framing is being finished. The structural framing is erected, while heating, ventilation,
and air-conditioning, electrical, plumbing, wall, and finishing details are
being developed. For tall buildings, the lower portion can be constructed while the
upper part is still being designed. For large, low-rise buildings, one section can be
built while another is under design.
1.6 BUILDING COSTS
Construction cost of a building usually is a dominant design concern. One reason
is that if construction cost exceeds the owner’s budget, the owner may cancel the
BUILDING SYSTEMS 1.9
project. Another reason is that costs, such as property taxes and insurance, that
occur after completion of the building often are proportional to the initial cost.
Hence, owners usually try to keep that cost low. Designing a building to minimize
construction cost, however, may not be in the owner’s best interests. There are
many other costs that the owner incurs during the anticipated life of the building
that should be taken into account.
Before construction of a building starts, the owner generally has to make a
sizable investment in the project. The major portion of this expenditure usually
goes for purchase of the site and building design. Remaining preconstruction costs
include those for feasibility studies, site selection and evaluation, surveys, and program
definition.
The major portion of the construction cost is the sum of the payments to the
general contractor and prime contractors. Remaining construction costs usually consist
of interest on the construction loan, permit fees, and costs of materials, equipment,
and labor not covered by the construction contracts.
The initial cost to the owner is the sum of preconstruction, construction, and
occupancy costs. The latter covers costs of moving possessions into the building
and start-up of utility services, such as water, gas, electricity, and telephone.
After the building is occupied, the owner incurs costs for operation and maintenance
of the buildings. Such costs are a consequence of decisions made during
building design.
Often, preconstruction costs are permitted to be high so that initial costs can be
kept low. For example, operating the building may be expensive because the design
makes artificial lighting necessary when daylight could have been made available
or because extra heating and air conditioning are necessary because of inadequate
insulation of walls and roof. As another example, maintenance may be expensive
because of the difficulty of changing electric lamps or because cleaning the building
is time-consuming and laborious. In addition, frequent repairs may be needed because
of poor choice of materials during design. Hence, operation and maintenance
costs over a specific period of time, say 10 or 20 years, should be taken into account
in optimizing the design of a building.
Life-cycle cost is the sum of initial, operating, and maintenance costs. Generally,
it is life-cycle cost that should be minimized in building design rather than construction
cost. This would enable the owner to receive the greatest return on the
investment in the building. ASTM has promulgated a standard method for calculating
life-cycle costs of buildings, E917, Practice for Measuring Life-Cycle Costs
of Buildings and Building Systems, as well as a computer program and user’s guide
to improve accuracy and speed of calculation.
Nevertheless, a client usually establishes a construction budget independent of
life-cycle cost. This often is necessary because the client does not have adequate
capital for an optimum building and places too low a limit on construction cost.
The client hopes to have sufficient capital later to pay for the higher operating and
maintenance costs or for replacement of undesirable building materials and installed
equipment. Sometimes, the client establishes a low construction budget because the
client’s goal is a quick profit on early sale of the building, in which case the client
has little or no concern with future high operating and maintenance costs for the
building. For these reasons, construction cost frequently is a dominant concern in
design.
1.7 MAJOR BUILDING SYSTEMS
The simplest building system consists of only two components. One component is
a floor, a flat, horizontal surface on which human activities can take place. The
1.10 SECTION ONE
FIGURE 1.1 Vertical section through a one-story building with basement shows location
of some major components. (Reprinted with permission from F. S. Merritt and J. Ambrose,
‘‘Building Engineering and Systems Design,’’ 2d ed., Van Nostrand Reinhold, New York.)
other component is an enclosure that extends over the floor and generally also
around it to provide shelter from the weather for human activities.
The ground may serve as the floor in primitive buildings. In better buildings,
however, the floor may be a structural deck laid on the ground or supported above
ground on structural members, such as the joist and walls in Fig. 1.1. Use of a
deck and structural members adds at least two different types of components, or
two subsystems, to the simplest building system. Also, often, the enclosure over
the floor requires supports, such as the rafter and walls in Fig. 1.1, and the walls,
in turn, are seated on foundations in the ground. Additionally, footings are required
at the base of the foundations to spread the load over a large area of the ground,
to prevent the building from sinking (Fig. 1.2a). Consequently, even slight improvements
in a primitive building introduce numerous additional components, or subsystems,
into a building.
More advanced buildings consist of numerous subsystems, which are referred to
as systems in this book when they are major components. Major subsystems generally
include structural framing and foundations, enclosure systems, plumbing,
lighting, acoustics, safety systems, vertical-circulation elements, electric power and
signal systems, and heating, ventilation, and air conditioning (HVAC).
Structural System. The portion of a building that extends above the ground level
outside it is called the superstructure. The portion below the outside ground level
is called the substructure. The parts of the substructure that distribute building
loads to the ground are known as foundations.
Foundations may take the form of walls. When the ground under the building
is excavated for a cellar, or basement, the foundation walls have the additional task
of retaining the earth along the outside of the building (Fig. 1.1). The superstructure
in such cases is erected atop the foundation walls.
BUILDING SYSTEMS 1.11
FIGURE 1.2 Commonly used foundations:
(a) foundation wall on continuous footing; (b)
individual spread footing for a column; (c) pile
footing for a column.
The footing under a wall (Fig. 1.2a)
is called a continuous spread footing.
A slender structural member, such as a
column (Fig. 1.2b), usually is seated on
an individual spread footing. When the
soil is so weak, however, that the spread
footings for columns become very large,
it often is economical to combine the
footings into a single footing under the
whole building. Such a footing is called
a raft, or mat, footing or a floating
foundation. For very weak soils, it generally
is necessary to support the foundations
on piles (Fig. 1.2c). These are
slender structural members that are
hammered or otherwise driven through the weak soil, often until the tips seat on
rock or a strong layer of soil.
The foundation system must be designed to transmit the loads from the superstructure
structural system directly to the ground in such a manner that settlement
of the completed building as the soil deflects will be within acceptable limits. The
superstructure structural system, in turn, should be designed to transmit its loads
to the foundation system in the manner anticipated in the design of the foundations.
(See also Sec. 6.)
In most buildings, the superstructure structural system consists of floor and roof
decks, horizontal members that support them, and vertical members that support
the other components.
The horizontal members are generally known as beams, but they also are called
by different names in specific applications. For example:
Joists are closely spaced to carry light loads.
Stringers support stairs.
Headers support structural members around openings in floors, roofs, and walls.
Purlins are placed horizontally to carry level roof decks.
Rafters are placed on an incline to carry sloping roof decks.
Girts are light horizontal members that span between columns to support walls.
Lintels are light horizontal beams that support walls at floor levels in multistory
buildings or that carry the part of walls above openings for doors and windows.
Girders may be heavily loaded beams or horizontal members that support other
beams (Fig. 1.3).
Spandrels carry exterior walls and support edges of floors and roofs in multistory
buildings.
Trusses serve the same purposes as girders but consists of slender horizontal,
vertical, and inclined components with large open spaces between them. The
spaces are triangular in shape. Light beams similarly formed are called openweb
joists (Fig. 1.6d).
Floor and roof decks or the beams that support them are usually seated on loadbearing
walls or carried by columns, which carry the load downward. (The horizontal
members also may be suspended on hangers, which transmit the load to
1.12 SECTION ONE
FIGURE 1.3 Structural-steel skeleton framing for a multistory building.
(Courtesy of the American Institute of Steel Construction.)
other horizontal members at a higher level.) The system comprising decks, beams,
and bearing walls is known as load-bearing construction (Fig. 1.1). The system
composed of decks, beams, and columns is known as skeleton framing (Fig. 1.3).
Both types of systems must be designed to transmit to the foundations vertical
(gravity) loads, vertical components of inclined loads, horizontal (lateral) loads, and
horizontal components of inclined loads. Vertical walls and columns have the appropriate
alignments for carrying vertical loads downward. But acting alone, these
structural members are inadequate for resisting lateral forces.
One way to provide lateral stability is to incorporate in the system diagonal
members, called bracing (Fig. 1.3). Bracing, columns, and beams then work together
to carry the lateral loads downward. Another way is to rigidly connect beams
to columns to prevent a change in the angle between the beams and columns, thus
making them work together as a rigid frame to resist lateral movement. Still another
way is to provide long walls, known as shear walls, in two perpendicular
directions. Lateral forces on the building can be resolved into forces in each of
these directions. The walls then act like vertical beams cantilevers) in transmitting
the forces to the foundations. (See also Art. 3.2.4.)
Because of the importance of the structural system, the structural members
should be protected against damage, especially from fire. For fire protection, bracing
BUILDING SYSTEMS 1.13
FIGURE 1.4 Roofs composed of plane surfaces: (a) flat roof; (b) shed roof; (c) pitched roof;
(d) hipped roof; (e) gambrel roof; (?) mansard roof; (g) monitored roof; (h) sawtooth
roof. (Reprinted with permission from F. S. Merritt and J. Ambrose, ‘‘Building Engineering and
Systems Design,’’ 2d ed., Van Nostrand Reinhold, New York.)
may be encased in fire-resistant floors, roofs, or walls. Similarly, columns may be
encased in walls, and beams may be encased in floors. Or a fire-resistant material,
such as concrete, mineral fiber, or plaster, may be used to box in the structural
members (Fig. 1.6c).
See also Secs. 7 to 11.
Systems for Enclosing Buildings. Buildings are enclosed for privacy, to exclude
wind, rain, and snow from the interior, and to control interior temperature and
humidity. A single-enclosure type of system is one that extends continuously from
the ground to enclose the floor. Simple examples are cone-like tepees and dome
igloos. A multiple-enclosure type of system consists of a horizontal or inclined top
covering, called a roof (Fig. 1.1), and vertical or inclined side enclosures called
walls.
Roofs may have any of a wide variety of shapes. A specific shape may be
selected because of appearance, need for attic space under the roof, requirements
for height between roof and floor below, desire for minimum enclosed volume,
structural economy, or requirements for drainage of rainwater and shedding of snow.
While roofs are sometimes given curved surfaces, more often roofs are composed
of one or more plane surfaces. Some commonly used types are shown in Fig. 1.4.
The flat roof shown in Fig. 1.4a is nearly horizontal but has a slight pitch for
drainage purposes. A more sloped roof is called a shed roof (Fig. 1.4b). A pitched
roof (Fig. 1.4c) is formed by a combination of two inclined planes. Four inclined
planes may be combined to form either a hipped roof (Fig. 1.4d) or a gambrel roof
(Fig. 1.4e). A mansard roof (Fig. 1.4?) is similar to a hipped roof but, composed
of additional planes, encloses a larger volume underneath. Any of the preceding
roofs may have glazed openings, called skylights (Fig. 1.4b), for daylighting the
building interior. The roofs shown in Fig. 1.4c to ? are often used to enclose attic
space. Windows may be set in dormers that project from a sloped roof (Fig. 1.4c).
Other alternatives, often used to provide large areas free of walls or columns, include
flat-plate and arched or dome roofs.
Monitored roofs are sometimes used for daylighting and ventilating the interior.
A monitor is a row of windows installed vertically, or nearly so, above a roof (Fig.
1.14 SECTION ONE
FIGURE 1.5 Types of exterior wall construction: (a) concrete-block wall; (b) wood-framed
wall; (c) precast-concrete curtain wall.
1.4g). Figure 1.4h illustrates a variation of a monitored roof that is called a sawtooth
roof.
The basic element in a roof is a thin, waterproof covering, called roofing (Sec.
12). Because it is thin, it is usually supported on sheathing, a thin layer, or roof
deck, a thick layer, which in turn, is carried on structural members, such as beams
or trusses. The roof or space below should contain thermal insulation (Fig. 1.6c
and d).
Exterior walls enclose a building below the roof. The basis element in the walls
is a strong, durable, water-resistant facing. For added strength or lateral stability,
this facing may be supplemented on the inner side by a backing or sheathing (Fig.
1.5b). For esthetic purposes, an interior facing usually is placed on the inner side
of the backing. A layer of insulation should be incorporated in walls to resist
passage of heat.
Generally, walls may be built of unit masonry, panels, framing, or a combination
of these materials.
Unit masonry consists of small units, such as clay brick, concrete block, glass
block, or clay tile, held together by a cement such as mortar. Figure 1.5a shows a
wall built of concrete blocks.
Panel walls consist of units much larger than unit masonry. Made of metal,
concrete, glass, plastics, or preassembled bricks, a panel may extend from founBUILDING
SYSTEMS 1.15
dation to roof in single-story buildings, or from floor to floor or from window
header in one story to window sill of floor above in multistory buildings. Large
panels may incorporate one or more windows. Figure 1.5c shows a concrete panel
with a window.
Framed walls consist of slender, vertical, closely spaced structural members,
tied together with horizontal members at top and bottom, and interior and exterior
facings. Thermal insulation may be placed between the components. Figure 1.5b
shows a wood-framed exterior wall.
Combination walls are constructed of several different materials. Metal, brick,
concrete, or clay tile may be used as the exterior facing because of strength, durability,
and water and fire resistance. These materials, however, are relatively expensive.
Consequently, the exterior facing is made thin and backed up with a less
expensive material. For example, brick may be used as an exterior facing with wood
framing or concrete block as the backup.
Exterior walls may be classified as curtain walls or bearing walls. Curtain walls
serve primarily as an enclosure. Supported by the structural system, such walls
need to be strong enough to carry only their own weight and wind pressure on the
exterior face. Bearing walls, in contrast, serve not only as an enclosure but also to
transmit to the foundation loads from other building components, such as beams,
floors, roofs, and other walls (Fig. 1.5a and b). (See also Sec. 11.)
Openings are provided in exterior walls for a variety of purposes, but mainly
for windows and doors. Where openings occur, structural support must be provided
over them to carry the weight of the wall above and any other loads on that portion
of the wall. Usually, a beam called a lintel is placed over openings in masonry
walls (Fig. 1.5a) and a beam called a top header is set over openings in woodframed
walls.
A window usually consists of transparent glass or plastics (glazing) held in place
by light framing, called sash. The window is fitted into a frame secured to the
walls (Fig. 1.5a). For sliding windows, the frame carries guides in which the sash
slides. For swinging windows, stops against which the window closes are built into
the frame.
Hardware is provided to enable the window to function as required. For movable
windows, the hardware includes grips for moving them, locks, hinges for
swinging windows, and sash balances and pulleys for vertically sliding windows.
The main purposes of windows are to illuminate the building interior with daylight,
to ventilate the interior, and to give occupants a view of the outside. For retail
stores, windows may have the major purpose of giving passersby a view of items
displayed inside. (See also Sec. 11.)
Doors are installed in exterior walls to give access to or from the interior or to
prevent such access. For similar reasons, doors are also provided in interior walls
and partitions. Thus, a door may be part of a system for enclosing a building or a
component of a system for enclosing interior spaces.
Systems for Enclosing Interior Spaces. The interior of a building usually is compartmented
into spaces or rooms by horizontal dividers (floor-ceiling or roof-ceiling
systems) and vertical dividers (interior walls and partitions). (The term partitions is
generally applied to non-load-bearing walls.)
Floor-Ceiling Systems. The basic element of a floor is a load-carrying deck.
For protection against wear, esthetic reasons, foot comfort, or noise control, a floor
covering often is placed over the deck, which then may be referred to as a subfloor.
Figure 1.6a shows a concrete subfloor with a flexible-tile floor covering. A hollowcold-
formed steel deck is incorporated in the subfloor to house electric wiring.
1.16 SECTION ONE
(a)
FIGURE 1.6 Examples of floor-ceiling and roof-ceiling systems. (a) Concrete structural slab
carries hollow-steel deck, concrete fill, and flexible tile flooring. (b) Acoustical-tile ceiling
incorporating a lighting fixture with provisions for air distribution is suspended below a floor.
(c) Insulated roof and steel beams are sprayed with mineral fiber for fire protection. (d) Insulated
roof and open-web joists are protected by a fire-rated suspended ceiling.
In some cases, a subfloor may be strong and stiff enough to span, unaided, long
distances between supports provided for it. In other cases, the subfloor is closely
supported on beams. The subfloor in Fig. 1.6a, for example, is shown constructed
integrally with concrete beams, which carry the loads from the subfloor to bearing
walls or columns.
The underside of a floor or roof and of beams supporting it, including decorative
treatment when applied to that side, is called a ceiling. Often, however, a separate
BUILDING SYSTEMS 1.17
FIGURE 1.6 (Continued)
ceiling is suspended below a floor or roof for esthetic or other reasons. Figure 1.6b
shows such a ceiling. It is formed with acoustical panels and incorporates a lighting
fixture and air-conditioning inlets and outlets.
Metal and wood subfloors and beams require fire protection. Figure 1.6c shows
a roof and its steel beams protected on the underside by a sprayed-on mineral fiber.
Figure 1.6d shows a roof and open-web steel joists protected on the underside by
a continuous, suspended, fire-resistant ceiling. As an alternative to encasement in
or shielding by a fire-resistant material, wood may be made fire-resistant by treatment
with a fire-retardant chemical.
Fire Ratings. Tests have been made, usually in conformance with E119, ‘‘Standard
Methods of Tests of Building Construction and Materials,’’ developed by
ASTM, to determine the length of time specific assemblies of materials can withstand
a standard fire, specified in E119. On the basis of test results, each construction
is assigned a fire rating, which gives the time in hours that the assembly can
withstand the fire. Fire ratings for various types of construction may be obtained
from local, state, or model building codes or the ‘‘Fire Resistance Design Manual,’’
published by the Gypsum Association.
Interior Walls and Partitions. Interior space dividers do not have to withstand
such severe conditions as do exterior walls. For instance, they are not exposed to
rain, snow, and solar radiation. Bearing walls, however, must be strong enough to
1.18 SECTION ONE
FIGURE 1.7 Types of partitions: (a) non-load-bearing; (b) gypsumboard on metal studs; (c)
gypsumboard face panels laminated to a gypsum core panel; (d) concrete bearing wall, floors,
and beams. (Reprinted with permission from F. S. Merritt and J. Ambrose, ‘‘Building Engineering
and Systems Design,’’ 2d ed., Van Nostrand Reinhold, New York.)
transmit to supports below them the loads to which they are subjected. Usually,
such interior walls extend vertically from the roof to the foundations of a building
and carry floors and roof. The basic element of a bearing wall may be a solid core,
as shown in Fig. 1.7d, or closely spaced vertical framing (studs), as shown in Fig.
1.7b.
Non-load-bearing partitions do not support floors or roof. Hence, partitions may
be made of such thin materials as sheet metal (Fig. 1.7a), brittle materials as glass
(Fig. 1.7a), or weak materials as gypsum (Fig. 1.7c). Light framing may be used
to hold these materials in place. Because they are non-load-bearing, partitions may
be built and installed to be easily shifted or to be foldable, like a horizontally sliding
door. (see also Sec. 11.)
Wall Finishes. Walls are usually given a facing that meets specific architectural
requirements for the spaces enclosed. Such requirements include durability under
indoor conditions, ease of maintenance, attractive appearance, fire resistance, water
resistance, and acoustic properties appropriate to the occupancy of the space enclosed.
The finish may be the treated surface of the exposed wall material, such as
the smooth, painted face of a sheet-metal panel, or a separate material, such as
plaster, gypsumboard, plywood, or wallpaper. (See also Sec. 11.)
Doors. Openings are provided in interior walls and partitions to permit passage
of people and equipment from one space to another. Doors are installed in the
openings to provide privacy, temperature, odor and sound control, and control passage.
Usually, a door frame is set around the perimeter of the opening to hold the
door in place (Fig. 1.8). Depending on the purpose of the door, size, and other
factors, the door may be hinged to the frame at top, bottom, or either side. Or the
door may be constructed to slide vertically or horizontally or to rotate about a
vertical axis in the center of the opening (revolving door). (See also Sec. 11.)
Hardware is provided to enable the door to function as required. For example,
hinges are provided for swinging doors, and guides are installed for sliding doors.
Locks or latches are placed in or on doors to prevent them from being opened.
Knobs or pulls are attached to doors for hand control.
BUILDING SYSTEMS 1.19
FIGURE 1.8 Example of door and frame.
Builder’s Hardware. This is a general
term applied to fastenings and devices,
such as nails, screws, locks, hinges, and
pulleys. These items generally are classified
as either finishing hardware or
rough hardware (Sec. 11).
Plumbing. The major systems for conveyance
of liquids and gases in pipes
within a building are classified as
plumbing. Plumbing pipes usually are
connected to others that extend outside
the building to a supply source, such as
a public water main or utility gas main,
or to a disposal means, such as a sewer.
For health, safety, and other reasons, pipes of different types of plumbing systems
must not be interconnected, and care must be taken to prevent flow from one system
to another.
The major purposes of plumbing are: (1) to convey water and heating gas, if
desired, from sources outside a building to points inside where the fluid or gas is
needed, and (2) to collect wastewater and storm water in the building, on the roof,
or elsewhere on the site and convey the liquid to sewers outside the building.
For these purposes, plumbing requires fixtures for collecting discharged water
and wastes; pipes for supply and disposal; valves for controlling flow; drains, and
other accessories. For more details, see Sec. 14.
Heating, Ventilation, and Air-Conditioning (HVAC). Part of the environmental
control systems within buildings, along with lighting and sound control, HVAC is
often necessary for the health and comfort of building occupants. Sometimes, however,
HVAC may be needed for manufacturing processes, product storage, or operation
of equipment, such as computers. HVAC usually is used to control temperature,
humidity, air movement, and air quality in the interior of buildings.
Ventilation is required to supply clean air for breathing, to furnish air for operation
of combustion equipment, and to remove contaminated air. Ventilation, however,
also can be used for temperature control by bringing outside air into a building
when there is a desirable temperature difference between that air and the interior
air.
The simplest way to ventilate is to open windows. When this is not practicable,
mechanical ventilation is necessary. This method employs fans to draw outside air
into the building and distribute the air, often through ducts, to interior spaces. The
method, however, can usually be used only in mild weather. To maintain comfort
conditions in the interior, the fresh air may have to be heated in cold weather and
cooled in hot weather.
Heating and cooling of a building interior may be accomplished in any of a
multitude of ways. Various methods are described in Sec. 13.
Lighting. For health, safety, and comfort of occupants, a building interior should
be provided with an adequate quantity of light, good quality of illumination, and
proper color of light. The required illumination may be supplied by natural or
artificial means.
1.20 SECTION ONE
Daylight is the source of natural illumination. It enters a building through a
fenestration, such as windows in the exterior walls or monitors or skylights on the
roof.
Artificial illumination can be obtained through consumption of electrical energy
in incandescent, fluorescent, electroluminescent, or other electric lamps. The light
source is housed in a luminaire, or lighting fixture. More details are given in Sec.
15.
Acoustics. The science of sound, its production, transmission, and effects are applied
in the building design for sound and vibration control.
A major objective of acoustics is provision of an environment that enhances
communication in the building interior, whether the sound is created by speech or
music. This is accomplished by installation of enclosures with appropriate acoustic
properties around sound sources and receivers. Another important objective is reduction
or elimination of noise—unwanted sound—from building interiors. This
may be accomplished by elimination of the noise at the source, by installation of
sound barriers, or by placing sound-absorbing materials on the surfaces of enclosures.
Still another objective is reduction or elimination of vibrations that can annoy
occupants, produce noise by rattling loose objects, or crack or break parts or contents
of a building. The most effective means of preventing undesirable vibrations
is correction of the source. Otherwise, the source should be isolated from the building
structure and potential transmission paths should be interrupted with carefully
designed discontinuities.
Electric Power and Communication Systems. Electric power is generally bought
from nearby utility and often supplemented for emergency purposes by power from
batteries or a generating plant on the site. Purchased power is brought from the
power lines connected to the generating source to an entrance control point and a
meter in the building. From there, conductors distribute the electricity throughout
the building to outlets where the power can be tapped for lighting, heating, and
operating electric devices.
Two interrelated types of electrical systems are usually provided within a building.
One type is used for communications, including data, telephone, television,
background music, paging, signal and alarm systems. The second type serves the
other electrical needs of the building and its occupants. For more details, see Sec.
15 and 18.
In addition to conductors and outlets, an electrical system also incorporates devices
and apparatus for controlling electric voltage and current. Because electricity
can be hazardous, the system must be designed and installed to prevent injury to
occupants and damage to building components.
For more details, see Sec. 15.
Vertical-Circulation Elements. In multistory buildings, provision must be made
for movement of people, supplies, and equipment between the various levels. This
may be accomplished with ramps, stairs, escalators, elevators, dumbwaiters, vertical
conveyors, pneumatic tubes, mail chutes, or belt conveyors. Some of the mechanical
equipment, however, may not be used for conveyance of people.
A ramp, or sloping floor, is often used for movement of people and vehicles in
such buildings as stadiums and garages. In most buildings, however, stairs are installed
because they can be placed on a steeper slope and therefore occupy less
space than ramps. Nevertheless, federal rules require at least one handicap accessible
entrance for all new buildings.
BUILDING SYSTEMS 1.21
FIGURE 1.9 Vertical-circulation elements: (a) stairs; (b) electric traction elevator; (c) hydraulic
elevator.
A stairway consists of a series of steps and landings. Each step consists of a
horizontal platform, or tread, and a vertical separation or enclosure, called a riser
(Fig. 1.9a). Railings are placed along the sides of the stairway and floor openings
for safety reasons. Also, structural members may be provided to support the stairs
and the floor edges. Often, in addition, the stairway must be enclosed for fire
protection.
Escalators, or powered stairs, are installed in such buildings as department
stores and transportation terminals, or in the lower stories of office buildings and
hotels, where there is heavy pedestrian traffic between floors. Such powered stairs
consist basically of a conveyor belt with steps attached; an electric motor for moving
the belt, and steps, controls, and structural supports.
Elevators are installed to provide speedier vertical transportation, especially in
tall buildings. Transportation is provided in an enclosed car that moves along
guides, usually within a fire-resistant vertical shaft but sometimes unenclosed along
the exterior of a building. The shaft, or the exterior wall, has openings, protected
by doors, at each floor to provide access to the elevator car. The car may be suspended
on and moved by cables (Fig. 1.9b) or set atop a piston moved by hydraulic
pressure (Fig. 1.9c).
More information on vertical-circulation elements is given in Sec. 16.
Intelligent Buildings. In addition to incorporating the major systems previously
described, intelligent buildings, through the use of computers and communication
equipment, have the ability to control the total building environment. The equipment
and operating personnel can be stationed in a so-called control center or the
equipment can be monitored and controlled remotely via a computer, modem and
telephone line. Various sensors and communication devices, feeding information to
and from the control center, are located in key areas throughout the building for
the purposes of analyzing and adjusting the environment, delivering messages during
emergencies, and dispatching repair personnel and security guards, as needed.
To conserve energy, lighting may be operated by sensors that detected people
movement. HVAC may be adjusted in accordance with temperature changes. Ele1.22
SECTION ONE
vators may be programmed for efficient handling of variations in traffic patterns
and may be equipped with voice synthesizers to announce floor stops and give
advice in emergencies. In addition, intelligent buildings are designed for ease and
flexibility in providing for changes in space use, piping, electrical conductors, and
installed equipment. See also Arts. 3.5.12 and 3.7.2.
(F. S. Merritt and J. Ambrose, ‘‘Building Engineering and Systems Design,’’ 2nd
Ed., Van Nostrand Reinhold, New York.)
1.8 VALUE ENGINEERING
As indicated in Art. 1.3, the client in the initial design phase develops a program,
or list of requirements. The goal of the designers is to select a system that meets
these requirements. Before the designers do this, however, it is advisable for them
to question whether the requirements represent the client’s actual needs. Can the
criteria and standards affecting the design be made less stringent? After the program
has been revised to answer these questions, the designers select a system. Next, it
is advisable for the designers to question whether the system provides the best
value at the lowest cost. Value engineering is a useful procedure for answering this
question and selecting a better alternative if the answer indicates this is desirable.
Value engineering is the application of the scientific method to the study of
values of systems. The major objective of value engineering in building design and
construction is reduction of initial and life-cycle costs (Art. 1.6). Thus, value engineering
has one of the objectives of systems design, in which the overall goal is
production of an optimum building, and should be incorporated in the systemsdesign
procedure.
The scientific method, which is incorporated in the definitions of value engineering
and systems design, consists of the following steps:
1. Collection of data and observations of natural phenomena
2. Formulation of a hypothesis capable of predicting future observations
3. Testing of the hypothesis to verify the accuracy of its predictions and abandonment
or improvement of the hypothesis if it is inaccurate
Those who conduct or administer value studies are often called value engineers,
or value analysts. They generally are organized into an interdisciplinary team for
value studies for a specific project. Sometimes, however, an individual, such as an
experienced contractor, performs value engineering services for the client for a fee
or a percentage of savings achieved by the services.
Value Analysis. Value is a measure of benefits anticipated from a system or from
the contribution of a component to system performance. This measure must be
capable of serving as a guide in a choice between alternatives in evaluations of
system performance. Because generally in comparisons of systems only relative
values need be considered, value takes into account both advantages and disadvantages,
the former being considered positive and the latter negative. It is therefore
possible in comparisons of systems that the value of a component of a system may
be negative and subtracts of systems from the overall performance of the system.
System evaluations would be relatively easy if a monetary value could always
be placed on performance. Then, benefits and costs could be compared directly.
BUILDING SYSTEMS 1.23
Value, however, often must be based on a subjective decision of the client. For
example, how much extra is an owner willing to pay for beauty, prestige, or better
community relations? Will the owner accept gloom, glare, draftiness, or noise for
a savings in cost? Consequently, other values than monetary must be considered in
value analysis. Such considerations require determination of the relative importance
of the client’s requirements and weighting of values accordingly.
Value analysis is the part of the value-engineering procedure devoted to investigation
of the relation between costs and values of components and systems and
alternatives to these. The objective is to provide a rational guide for selection of
the lowest-cost system that meets the client’s actual needs.
Measurement Scales. For the purposes of value analysis, it is essential that characteristics
of a component or system on which a value is to be placed be distinguishable.
An analyst should be able to assign different numbers, not necessarily
monetary, to values that are different. These numbers may be ordinates of any one
of the following four measurement scales: ratio, interval, ordinal, nominal.
Ratio Scale. This scale has the property that, if any characteristic of a system
is assigned a value number k, any characteristic that is n times as large must be
assigned a value number nk. Absence of the characteristic is assigned the value
zero. This type of scale is commonly used in engineering, especially in cost comparisons.
For example, if a value of $10,000 is assigned to system A and of $5000
to system B, then A is said to cost twice as much as B.
Interval Scale. This scale has the property that equal intervals between assigned
values represent equal differences in the characteristic being measured. The scale
zero is assigned arbitrarily. The Celsius scale of temperature measurements is a
good example of an interval scale. Zero is arbitrarily established as the temperature
at which water freezes; the zero value does not indicate absence of heat. The boiling
point of water is arbitrarily assigned the value of 100. The scale between 0 and
100 is then divided into 100 equal intervals called degrees (
C). Despite the arbitrariness
of the selection of the zero point, the scale is useful in heat measurement.
For example, changing the temperature of an objective from 40
C to 60
C, an
increase of 20
C, requires twice as much heat as changing the temperature from
45
C to 55
C, an increase of 10
C.
Ordinal Scale. This scale has the property that the magnitude of a value number
assigned to a characteristic indicates whether a system has more, or less, of the
characteristic than another system has or is the same with respect to that characteristic.
For example, in a comparison of the privacy afforded by different types of
partitions, each may be assigned a number that ranks it in accordance with the
degree of privacy that it provides. Partitions with better privacy are given larger
numbers. Ordinal scales are commonly used when values must be based on subjective
judgments of nonquantifiable differences between systems.
Nominal Scale. This scale has the property that the value numbers assigned to
a characteristic of systems being compared merely indicate whether the systems
differ in this characteristic. But no value can be assigned to the difference. This
type of scale is often used to indicate the presence or absence of a characteristic
or component. For example, the absence of a means of access to equipment for
maintenance may be represented by zero or a blank space, whereas the presence
of such access may be denoted by 1 or X.
Weighting. In practice, construction cost usually is only one factor, perhaps the
only one with a monetary value, of several factors that must be evaluated in a
comparison of systems. In some cases, some of the other characteristics of the
system may be more important to the owner than cost. Under such circumstances,
the comparison may be made by use of an ordinal scale for ranking each characteristic
and then weighting the rankings in accordance with the importance of the
characteristic to the owner.
As an example of the use of this procedure, calculations for comparison of two
partitions are shown in Table 1.1. Alternative 1 is an all-metal partition and alternative
2 is made of glass and metal.
In Table 1.1, characteristics of concern in the comparison are listed in the first
column. The numbers in the second column indicate the relative importance of each
characteristic to the owner: 1 denotes lowest priority and 10 highest priority. These
are the weights. In addition, each of the partitions is ranked on an ordinal scale,
with 10 as the highest value, in accordance with the degree to which it possesses
each characteristic. These rankings are listed as relative values in Table 1.1. For
construction cost, for instance, the metal partition is assigned a relative value of 10
and the glass-metal partition a value of 8, because the metal partition costs a little
less than the other one. In contrast, the glass-metal partition is given a relative value
of 8 for visibility, because the upper portion is transparent, whereas the metal
partition has a value of zero, because it is opaque.
To complete the comparison, the weight of each characteristic is multiplied by
the relative value of the characteristic for each partition and entered in Table 1.1
as a weighted value. For construction cost, for example, the weighted values are
8 
 10  80 for the metal partition and 8 
 8  64 for the glass-metal partition.
The weighted values for each partition are then added, yielding 360 for alternative
1 and 397 for alternative 2. While this indicates that the glass-metal partition is
better, it may not be the best for the money. To determine whether it is, the weighted
value for each partition is divided by its cost, yielding 0.0300 for the metal partition
BUILDING SYSTEMS 1.25
and 0.0265 for the other. Thus, the metal partition appears to offer more value for
the money and would be recommended.
Economic Comparisons. In a choice between alternative systems, only the differences
between system values are significant and need to be compared.
Suppose, for example, the economic effect of adding 1 in of thermal insulation
to a building is to be investigated. In a comparison, it is not necessary to compute
the total cost of the building with and without the insulation. Generally, the value
analyst need only subtract the added cost of 1 in of insulation from the decrease
in HVAC cost to obtain the net saving or cost increase resulting from addition of
insulation. A net saving would encourage addition of insulation. Thus, a decision
can be reached without the complex computation of total building cost.
In evaluating systems, value engineers must take into account not only initial
and life-cycle costs but also the return the client wishes to make on the investment
in the building. Generally, a client would like not only to maximize profit, the
difference between revenue from use of the building and total costs, but also to
ensure that the rate of return, the ratio of profit to investment, is larger than all of
the following:
Rate of return expected from the type of business
Interest rate for borrowed money
Rate for government bonds or notes
Rate for highly rated corporate bonds
The client is concerned with interest rates because all costs represent money that
must be borrowed or that could otherwise be invested at a current interest rate. The
client also has to be concerned with time, measured from the date at which an
investment is made, because interest cost increases with time. Therefore, in economic
comparisons of systems, interest rates and time must be taken into account.
(Effects of monetary inflation can be taken into account in much the same way as
interest.)
An economic comparison usually requires evaluation of initial capital investments,
salvage values after several years, annual disbursements and annual revenues.
Because each element in such a comparison may have associated with it an
expected useful life different from that of the other elements, the different types of
costs and revenues must be made commensurable by reduction to a common basis.
This is commonly done by either:
1. Converting all costs and revenues to equivalent uniform annual costs and income
2. Converting all costs and revenues to present worth of all costs and revenues at
time zero.
Present worth is the money that, invested at time zero, would yield at later
times required costs and revenues at a specified interest rate. In economic comparisons,
the conversions should be based on a rate of return on investment that is
attractive to the client. It should not be less than the interest rate the client would
have to pay if the amount of the investment had to be borrowed. For this reason,
the desired rate of return is called interest rate in conversions. Calculations also
should be based on actual or reasonable estimates of time periods. Salvage values,
for instance, should be taken as the expected return on sale or trade-in of an item
Cost of operation, maintenance, repairs, property taxes, and insurance are included
in the annual costs. The present-worth method is used for the comparison, with
interest rate i  8%.
Conversion of all costs and revenues to present worth must be based on a common
service life, although the two units have different service lives, 10 and 20
years, respectively. For the purpose of the conversion, it may be assumed that
replacement assets will repeat the investment and annual costs predicted for the
initial asset. (Future values, however, should be corrected for monetary inflation.)
In some cases, it is convenient to select for the common service life the least
common multiple of the lives of the units being compared. In other cases, it may
be more convenient to assume that the investment and annual costs continue indefinitely.
The present worth of such annual costs is called capitalized cost.
For this example, a common service life of 20 years, the least common multiple
of 10 and 20, is selected. Hence, it is assumed that unit 1 will be replaced at the
end of the tenth period at a cost of $300,000 less the salvage value. Similarly, the
replacement unit will be assumed to have the same salvage value after 20 years.
The calculations in Table 1.2 indicate that the present worth of the net cost of
unit 2 is less than that for unit 1. If total cost during the twenty year period were
the sole consideration, purchase of unit 2 would be recommended.
ASTM has developed several standard procedures for making economic studies
of buildings and building systems, in addition to ASTM E917 for measuring lifecycle
costs, mentioned previously. For example, ASTM E964 is titled Practice for
Measuring Benefit-to-Cost and Savings-to-Investment Ratios for Buildings and
Building Systems. Other standards available present methods for measuring internal
rate of return, net benefits, and payback. ASTM also has developed computer programs
for these calculations.
Value Analysis Procedure. In building design, value analysis generally starts with
a building system or subsystem proposed by the architect and consultants. The client
or the client’s representative appoints an interdisciplinary team to study the system
or subsystem and either recommend its use or propose a more economical alternative.
The team coordinator sets goals and priorities for the study and may appoint
task groups to study parts of the building in accordance with the priorities. The
value analysts should follow a systematic, scientific procedure for accomplishing
1.28 SECTION ONE
all the necessary tasks that comprise a value analysis. The procedure should provide
an expedient format for recording the study as it progresses, assure that consideration
has been given to all information, some of which may have been overlooked
in development of the proposed system, and logically resolve the analysis into
components that can be planned, scheduled, budgeted, and appraised.
The greatest cost reduction can be achieved by analysis of every component of
a building. This, however, is not practical, because of the short time usually available
for the study and because the cost of the study increases with time. Hence, it
is advisable that the study concentrate on those building systems (or subsystems)
whose cost is a relatively large percentage of the total building (or system) cost,
because those components have possibilities for substantial cost reduction.
During the initial phase of value analysis, the analysts should obtain a complete
understanding of the building and its major systems by rigorously reviewing the
program, proposed design and all other pertinent information. They should also
define the functions, or purposes, of each building component to be studied and
estimate the cost of accomplishing the functions. Thus, the analysts should perform
a systems analysis, as indicated in Art. 1.2, answer the questions listed in Art 1.2
for the items to be studied, and estimate the initial and life-cycle costs of the items.
In the second phase of value analysis, the analysts should question the costeffectiveness
of each component to be studied. Also, by use of imagination and
creative techniques, they should generate several alternative means for accomplishing
the required functions of the component. Then, in addition to answers to the
questions in Art. 1.2, the analysts should obtain answers to the following questions:
Do the original design and each alternative meet performance requirements?
What does each cost installed and over the life cycle?
Will it be available when needed? Will skilled labor be available?
Can any components be eliminated?
What other components will be affected by adoption of an alternative? What
will the resulting changes in the other components cost? Will there be a net
saving in cost?
In investigating the possibility of elimination of a component, the analysts also
should see if any part of it can be eliminated, if two parts or more can be combined
into one, and if the number of different sizes and types of an element can be
reduced. If costs might be increased by use of a nonstandard or unavailable item,
the analysts should consider substitution of a more appropriate alternative. In addition,
consideration should be given to simplification of construction or installation
of components and to ease of maintenance and repair.
In the following phase of value analysis, the analysts should critically evaluate
the original design and alternatives. The ultimate goal should be recommendation
of the original design and alternative, whichever offers the greatest value and costsavings
potential. The analysts also should submit estimated costs for the original
design and the alternative.
In the final phase, the analysts should prepare and submit to the client or the
client’s representative who appointed them a written report on the study and resulting
recommendations. Also, they should submit a workbook containing detailed
backup information.
Value engineering should start during the conceptual phase of design. Then, it
has the greatest impact on cost control and no cost is involved in making design
changes. During later design phases, design changes involve some cost, especially
BUILDING SYSTEMS 1.29
when substitution of major subsystems is involved, but the cost is nowhere near as
great as when changes are made during construction. Such changes should be
avoided if possible. Value engineering, however, should be applied to the project
specifications and construction contract. Correction of unnecessary and overconservative
specifications and contract provisions offers considerable potential for cost
reduction.
(E. D. Heller, ‘‘Value Management: Value Engineering and Cost Reduction,’’
Addison-Wesley, Reading, Mass.; L. D. Miles, ‘‘Techniques of Value Analysis and
Engineering,’’ McGraw-Hill Publishing Co., New York; A Mudge, ‘‘Value Engineering,’’
McGraw-Hill Publishing Company, New York; M. C. Macedo, P. V. Dobrow,
and J. J. O’Rourke, ‘‘Value Management for Construction,’’ John Wiley &
Sons, Inc., New York.)
1.9 EXECUTION OF SYSTEMS DESIGN
The basic traditional design procedure (Art. 1.3), which has been widely used for
many years, and commonly used variations of it have resulted in many excellent
buildings. It needs improvement, however, because clients cannot be certain that
its use gives the best value for the money or that the required performance could
not have been attained at lower cost. The uncertainty arises because historically:
1. Actual construction costs often exceed low bids or negotiated prices, because of
design changes during construction; unanticipated delays during construction,
which increase costs; and unforeseen conditions, such as unexpectedly poor subsurface
conditions that make excavation and foundation construction more expensive.
2. Construction, operation, or maintenance costs are higher than estimated, because
of design mistakes or omissions.
3. Separation of design and construction into different specialties leads to underestimated
or overestimated construction costs and antagonistic relations between
designers and builders.
4. Construction costs are kept within the client’s budget at the expense of later
higher operating, maintenance, and repair costs.
5. Coordination of the output of architects and consultants is not sufficiently close
for production of an optimum building for the client’s actual needs.
One objective of systems design is to correct these defects. This can be done
while retaining the desirable features of traditional procedures, such as development
of building design in stages, with progressively more accurate cost estimates and
frequent client review. Systems design therefore should at least do the following:
1. Question the cost effectiveness of proposed building components and stimulate
generation of lower-cost alternatives that achieve the required performance. This
can be done by incorporating value engineering in systems design.
2. More closely coordinate the work of various design specialists and engage building
construction and operation experts to assist in design.
3. Take into account both initial and life-cycle costs.
1.30 SECTION ONE
4. Employ techniques that will reduce the number of design mistakes and omissions
that are not discovered until after construction starts.
Systems Design Procedure. Article 1.2 defines systems and explains that systems
design comprises a rational, orderly series of steps that leads to the best decision
for a given set of conditions. Article 1.2 also lists the basic components of the
procedure as analysis, synthesis, appraisal, and feedback. Following is a more formal
definition:
Systems design is the application of the scientific method to selection and assembly
of components or subsystems to form the optimum system to attain specified
goals and objectives while subject to given constraints and restrictions.
The scientific method is defined in Art. 1.8. Goals, objectives, and constraints
are discussed later.
Systems design of buildings, in addition to correcting defects in traditional design,
must provide answers to the following questions:
1. What does the client actually want the building to accomplish (goals, objectives,
and associated criteria)?
2. What conditions exist, or will exist after construction, that are beyond the designers’
control?
3. What requirements for the building or conditions affecting system performance
does design control (constraints and associated standards)?
4. What performance requirements and time and cost criteria can the client and
designers use to appraise system performance?
Collection of information necessary for design of the building starts at the inception
of design and may continue through the contract documents phase. Data
collection is an essential part of systems design but because it is continuous
throughout design it is not listed as one of the basic steps.
For illustrative purposes, the systems design procedure is shown resolved into
nine basic steps in Fig. 1.10. Because value analysis is applied in step 5, steps 4
through 8 covering synthesis, analysis, and appraisal may be repeated several times.
Each iteration should bring the design closer to the optimum.
In preparation for step 1, the designers should secure a building program and
information on existing conditions that will affect building design. In step 1, the
designers use the available information to define goals to be met by the system.
Goals. These state what the building is to accomplish, how it will affect the
environment and other systems, and how other systems and the environment will
affect the building. Goals should be generalized but brief statements, encompassing
all the design objectives. They should be sufficiently specific, however, to guide
generation of initial and alternative designs and control selection of the best alternative.
A simple example of a goal is: Design a branch post-office building with 100
employees to be constructed on a site owned by the client. The building should
harmonize with neighboring structures. Design must be completed within 90 days
and construction within 1 year. Construction cost is not to exceed $500,000.
When systems design is applied to a subsystem, goals serve the same purpose
as for a system. They indicate the required function of the subsystem and how it
affects and is affected by other systems.
Objectives. With the goals known, the designers can advance to step 2 and
define the system objectives. These are similar to goals but supply in detail the
requirements that the system must satisfy to attain the goals.
BUILDING SYSTEMS 1.31
FIGURE 1.10 Basic steps in systems design in addition to collection of necessary information.
1.32 SECTION ONE
In listing objectives, the designers may start with broad generalizations that they
later develop at more detailed levels to guide design of the system. Some objectives,
such as minimization of initial costs, life-cycle costs and construction time, should
be listed. Other objectives that apply to the design of almost every building, such
as the health, safety, and welfare objectives of the building, zoning, and Occupational
Safety and Health Administration regulations, are too numerous to list and
may be adopted by reference. Objectives should be sufficiently specific to guide
the planning of building interior spaces and selection of specific characteristics for
the building and its components: appearance, strength, durability, stiffness, operational
efficiency, maintenance, and fire resistance. Also, objectives should specify
the degree of control needed for operation of systems provided to meet the other
objectives.
At least one criterion must be associated with each objective. The criterion is a
range of values within which the performance of the system must lie for the objective
to be met. The criterion should be capable of serving as a guide in evaluations
of alternative systems. For example, for fire resistance of a wall, the criterion
might be 2-hr fire rating.
In addition to establishing criteria, the designers should weight the objectives in
accordance with the relative importance of the objectives to the client (Art. 1.8).
These weights should also serve as guides in comparisons of alternatives.
System Constraints. In step 2 of systems design, the designers should also
define constraints on the system. Constraints are restrictions on the values of design
variables that represent properties of the system and are controllable by the designers.
Designers are seldom completely free to choose any values desired for
controllable variables because of various restrictions, which may be legal ones such
as building or zoning code requirements, or may be economic, physical, chemical,
temporal, psychological, sociological, or esthetic requirements. Such restrictions
may fix the values of the controllable variables or establish a range in which they
must lie.
At least one standard must be associated with each constraint. A standard is a
value or range of values governing a property of the system. The standard specifying
a fixed value may be a minimum or maximum value.
For example, a designer may be seeking to determine the thickness of a loadbearing
brick wall. The local building code may state that such a wall may not be
less than 8 in thick. This requirement is a minimum standard. The designer may
then select a wall thickness of 8 in or more. The requirements of other systems,
however, may indicate that the wall thickness may not exceed 16 in. This is a
maximum standard. Furthermore, bricks may be available only in nominal widths
of 4 in. Hence, the constraints limit the values of the controllable variable, in this
case wall thickness, to 8, 12, or 16 in.
Synthesis. In step 3, the designers must conceive at least one system that satisfies
the objectives and constraints. For this, they rely on their past experience,
knowledge, imagination, and creative skills and on advice from consultants, including
value engineers, construction experts, and experienced operators of the type
of facilities to be designed.
In addition, the designers should select systems that are cost-effective and can
be erected speedily. To save design time in selection of a system, the designers
should investigate alternative systems in a logical sequence for potential for achieving
optimum results. The following is a possible sequence:
1. Selection of an available industrialized building, a system that is preassembled
in a factory. Such a system is likely to be low cost, because of the use of massBUILDING
SYSTEMS 1.33
production techniques and factory wages, which usually are lower than those
for field personnel. Also, the quality of materials and construction may be better
than for custom-built structures, because of assembly under controlled conditions
and close supervision.
2. Design of an industrialized building (if the client needs several of the same type
of structure).
3. Assembling a building with prefabricated components or systems. This type of
construction is similar to that used for industrialized buildings except that the
components preassembled are much smaller parts of the building system.
4. Specification of as many prefabricated and standard components as feasible.
Standard components are off-the shelf items, readily available from building
supply companies.
5. Repetition of the same component as many times as possible. This may permit
mass production of some nonstandard components. Also, repetition may speed
construction, because field personnel will work faster as they become familiar
with the components.
6. Design of components for erection so that building trades will be employed on
the site continuously. Work that compels one trade to wait for completion of
work by another trade delays construction and is costly.
Models. In step 4, the designers should represent the system by a model that
will enable them to analyze the system and evaluate its performance. The model
should be simple, consistent with the role for which it is selected, for practical
reasons. The cost of formulating and using the model should be negligible compared
with the cost of assembling and testing the actual system.
For every input to a system, there must be a known, corresponding input to the
model such that the responses (output) of the model to that input are determinable
and correspond to the response of the system to its input. The correlation may be
approximate but nevertheless close enough to serve the purposes for which the
model is to be used. For example, for cost estimates during the conceptual phase
of design, use may be made of a cost model that yields only reasonable guesses of
construction costs. The cost model used in the contract documents phase, however,
should be accurate.
Models may be classified as iconic, symbolic, or analog. The iconic type may
be the actual system or a part of it or merely bear a physical resemblance to the
actual system. This type is often used for physical tests of performance, such as
load or wind-tunnel tests or adjustments of controls. Symbolic models represent
by symbols the input and output of a system and are usually amenable to mathematical
analysis of a system. They enable relationships to be generally, yet compactly,
expressed, are less costly to develop and use than other types of models,
and are easy to manipulate. Analog models are real systems but with physical
properties different from those of the actual system. Examples include dial watches
for measuring time, thermometers for measuring heat changes, slide rules for multiplying
numbers, flow of electric current for measuring heat flow through a metal
plate, and soap membranes for measuring torsion in an elastic shaft.
Variables representing input and properties of a system may be considered independent
variables. These are of two types:
1. Variables that the designers can control or constraints: x1, x2, x3, . . .
2. Variables that are uncontrollable: y1, y2, y3, . . .
1.34 SECTION ONE
Variables representing system output or performance may be considered dependent
variables: z1, z2, z3. . . .
The dependent variables are functions of the independent variables. These functions
also contain parameters, which can be adjusted in value to calibrate the model
to the behavior of the actual system.
Step 4 of systems design then may be resolved into four steps, as indicated in
Fig. 1.10:
1. Select and calibrate a model to represent the system for optimization and appraisal.
2. Estimate values for the uncontrollable, independent variables.
3. Determine values for the controllable variables.
4. Determine the output or performance of the system from the relationship of
dependent and independent variables by use of the model.
Systems with large numbers of variables may sometimes be optimized by a
process called simulation, which involves trial and error with the actual system or
a model. In simulation, the properties of the system or model are adjusted with a
specific input or range of inputs to the system, and outputs or performance are
measured until an optimum result is obtained. When the variables are quantifiable
and models are used, the solution usually can be expedited by use of computers.
The actual system may be used when it is available and accessible and changes in
it will have little or no effect on construction costs. For example, after installation
of air ducts, an air-conditioning system may be operated for a variety of conditions
to determine the optimum damper position for control of airflow for each condition.
Suboptimization is a trial-and-error process in which designers try to optimize
a system by first optimizing its subsystems. It is suitable when components influence
each other in series. For example, consider a structural system consisting only
of roof, columns, and footings. The roof has a known load (input), exclusive of its
own weight. Design of the roof affects the columns and footings, because its output
equals the load on the columns. Design of the columns loads only the footings.
1.36 SECTION ONE
Design of the footings, however, has no effect on any of the other structural components.
Therefore, the structural components are in series and they may be designed
by suboptimization to obtain the minimum construction cost or least weight
of the system.
Suboptimization of the system may be achieved by first optimizing the footings,
for example, designing the lowest-cost footings. Next, the design of both the columns
and the footings should be optimized. (Optimization of the columns alone
will not yield an optimum structural system, because of the effect of the column
weight on the footings.) Finally, roof, columns, and footings together should be
optimized. (Optimization of the roof alone will not yield an optimum structural
system, because of the effect of its weight on columns and footings. A low-cost
roof may be very heavy, requiring costly columns and footings, whereas the cost
of a lightweight roof may be so high as to offset any savings from less-expensive
columns and footings. An alternative roof may provide optimum results.)
Appraisal. In step 5 of systems design, the designers should evaluate the results
obtained in step 4, modeling the system and applying the model. The designers
should verify that construction and life-cycle costs will be acceptable to the client
and that the proposed system satisfies all objectives and constraints.
During the preceding steps, value analysis may have been applied to parts of
the building. In step 6, however, value analysis should be applied to the whole
building system. This process may result in changes only to parts of the system,
producing a new system, or several alternatives to the original design may be proposed.
In steps 7 and 8, therefore, the new systems, or at least those with good
prospects, should be modeled and evaluated. During and after this process, completely
different alternatives may be conceived. As a result, steps 4 through 8 should
be repeated for the new concepts. Finally, in step 9, the best of the systems studied
should be selected.
(R. J. Aguilar, ‘‘Systems Analysis and Design in Engineering, Architecture Construction
and Planning,’’ Prentice-Hall, Inc., Englewood Cliffs, N.J.: R. L. Ackoff
and M. W. Saseini, ‘‘Fundamentals of Operations Research,’’ John Wiley & Sons,
Inc., New York; K. I. Majid, ‘‘Optimum Design of Structures,’’ Halsted Press/Wiley,
New York; E. J. McCormick, ‘‘Human Factors in Engineering,’’ McGraw-Hill Publishing
Company, New York; F. S. Merritt and J. A. Ambrose, ‘‘Building Engineering
and Systems Design,’’ 2nd Ed., Van Nostrand Reinhold, New York; R.
DeNeufville and J. H. Stafford, ‘‘Systems Analysis for Engineers and Managers,’’
McGraw-Hill Publishing Company, New York; L. Spunt, ‘‘Optimum Structural Design,’’
Prentice-Hall, Englewood Cliffs, N.J.)
1.10 BUILDING CODES
Many of the restrictions encountered in building design are imposed by legal regulations.
While all must be met, those in building codes are the most significant
because they affect almost every part of a building.
Building codes are established under the police powers of a state to protect the
health, welfare, and safety of communities. A code is administered by a building
official of the municipality or state that adopts it by legislation. Development of a
local code may be guided by a model code, such as those promulgated by the
International Conference of Building Officials, Inc., Building Officials and Code
Administrators International, Inc., and Southern Building Code Congress International,
Inc.
BUILDING SYSTEMS 1.37
In general, building-code requirements are the minimum needed for public protection.
Design of a building must satisfy these requirements. Often, however, architects
and engineers must design more conservatively, to meet the client’s needs,
produce a more efficient building system, or take into account conditions not covered
fully by code provisions.
Construction drawings for a building should be submitted to the building-code
administrator before construction starts. If the building will meet code requirements,
the administrator issues a building permit, on receipt of which the contractor may
commence building. During construction, the administrator sends inspectors periodically
to inspect the work. If they discover a violation, they may issue an order
to remove it or they may halt construction, depending on the seriousness of the
violation. On completion of construction, if the work conforms to code requirements,
the administrator issues to the owner a certificate of occupancy.
Forms of Codes. Codes often are classified as specifications type or performance
type. A specification-type code names specific materials for specific uses and specifies
minimum or maximum dimensions, for example, ‘‘a brick wall may not be
less than 6 in thick.’’ A performance-type code, in contrast, specifies required performance
of a construction but leaves materials, methods, and dimensions for the
designers to choose. Performance-type codes are generally preferred, because they
give designers greater design freedom in meeting clients’ needs, while satisfying
the intent of the code. Most codes, however, are neither strictly specifications nor
performance type but rather a mixture of the two. The reason for this is that insufficient
information is currently available for preparation of an entire enforceable
performance code.
The organization of building codes varies with locality. Generally, however, they
consist of two parts, one dealing with administration and enforcement and the other
specifying requirements for design and construction in detail.
Part 1 usually covers licenses, permits, fees, certificates of occupancy, safety,
projections beyond street lines, alterations, maintenance, applications, approval of
drawings, stop-work orders, and posting of buildings to indicate permissible live
loads and occupant loads.
Part 2 gives requirements for structural components, lighting, HVAC, plumbing,
gas piping and fixtures, elevators and escalators, electrical distribution, stairs, corridors,
walls, doors, and windows. This part also defines and sets limits on occupancy
and construction-type classifications. In addition, the second part contains
provisions for safety of public and property during construction operations and for
fire protection and means of egress after the building is occupied.
Many of the preceding requirements are adopted by reference in the code from
nationally recognized standards or codes of practice. These may be promulgated
by agencies of the federal government or by such organizations as the American
National Standards Institute, ASTM, American Institute of Steel Construction,
American Concrete Institute, and American Institute of Timber Construction.
Code Classifications of Buildings. Building codes usually classify a building in
accordance with the fire zone in which it is located, the type of occupancy, and the
type of construction, which is an indication of the fire protection offered.
The fire zone in which a building is located may be determined from the community’s
fire-district zoning map. The building code specifies the types of construction
and occupancy groups permitted or prohibited in each fire zone.
The occupancy group to which a building official assigns a building depends
on the use to which the building is put. Typical classifications include one- and
two-story dwellings; apartment buildings, hotels, dormitories; industrial buildings
1.38 SECTION ONE
with noncombustible, combustible, or hazardous contents; schools; hospitals and
nursing homes; and places of assembly, such as theaters, concert halls, auditoriums,
and stadiums.
Type of construction of a building is determined, in general, by the fire ratings
assigned to its components. A code usually establishes two major categories: combustible
and noncombustible construction. The combustible type may be subdivided
in accordance with the fire protection afforded major structural components and the
rate at which they will burn; for example, heavy timber construction is considered
slow-burning. The noncombustible type may be subdivided in accordance with the
fire-resistive characteristics of components.
Building codes may set allowable floor areas for fire-protection purposes. The
limitations depend on occupancy group and type of construction. The purpose is
to delay or prevent spread of fire over large portions of the building. For the same
reason, building codes also may restrict building height and number of stories. In
addition, to permit rapid and orderly egress in emergencies, such as fire, codes limit
the occupant load, or number of persons allowed in a building or room. In accordance
with permitted occupant loads, codes indicate the number of exits of adequate
capacity and fire protection that must be provided.
1.11 ZONING CODES
Like building codes, zoning codes are established under the police powers of the
state, to protect the health, welfare, and safety of the public. Zoning, however,
primarily regulates land use by controlling types of occupancy of buildings, building
height, and density and activity of population in specific parts of a jurisdiction.
Zoning codes are usually developed by a planning commission and administered
by the commission or a building department. Land-use controls adopted by the
local planning commission for current application are indicated on a zoning map.
It divides the jurisdiction into districts, shows the type of occupancy, such as commercial,
industrial, or residential, permitted in each district, and notes limitations
on building height and bulk and on population density in each district.
The planning commission usually also prepares a master plan as a guide to the
growth of the jurisdiction. A future land-use plan is an important part of the master
plan. The commission’s objective is to steer changes in the zoning map in the
direction of the future land-use plan. The commission, however, is not required to
adhere rigidly to the plans for the future. As conditions warrant, the commission
may grant variances from any of the regulations.
In addition, the planning commission may establish land subdivision regulations,
to control development of large parcels of land. While the local zoning map specifies
minimum lot area for a building and minimum frontage a lot may have along
a street, subdivision regulations, in contrast, specify the level of improvements to
be installed in new land-development projects. These regulations contain criteria
for location, grade, width, and type of pavement of streets, length of blocks, open
spaces to be provided, and right of way for utilities.
A jurisdiction may also be divided into fire zones in accordance with population
density and probable degree of danger from fire. The fire-zone map indicates the
limitations on types of construction that the zoning map would otherwise permit.
In the vicinity of airports, zoning may be applied to maintain obstruction-free
approach zones for aircraft and to provide noise-attenuating distances around the
BUILDING SYSTEMS 1.39
FIGURE 1.11 Examples of limitations placed by zoning codes on building height: (a) height
limitations for buildings constructed along lot boundaries; (b) setbacks required by a 3:1 sky
exposure plane; (c) height of a sheet tower occupying only part of a lot is limited by the total
floor area permitted. (Reprinted with permission from F. S. Merritt and J. Ambrose, ‘‘Building
Engineering and Systems Design,’’ 2d ed., Van Nostrand Reinhold, New York.)
airports. Airport zoning limits building heights in accordance with distance from
the airport.
Control of Building Height. Zoning places limitations on building dimensions to
limit population density and to protect the rights of occupants of existing buildings
to light, air, and esthetic surroundings. Various zoning ordinances achieve these
objectives in a variety of ways, including establishment of a specific maximum
height or number of stories, limitation of height in accordance with street width,
setting minimums for distances of buildings from lot lines, or relating total floor
area in a building to the lot area or to the area of the lot occupied by a building.
Applications of some of these limitations are illustrated in Fig. 1.11.
Figure 1.11a shows a case where zoning prohibits buildings from exceeding 12
stories or 150 ft in height. Figure 1.11b illustrates a case where zoning relates
building height to street width. In this case, for the specific street width, zoning
permits a building to be erected along the lot boundary to a height of six stories
or 85 ft. Greater heights are permitted, however, so long as the building does not
penetrate sky-exposure planes. For the case shown in Fig. 1.11b, these planes start
at the lot line at the 85-ft height and incline inward at a slope of 3:1. Some zoning
codes will permit the upper part of the building to penetrate the planes if the floor
area of the tower at any level does not exceed 40% of the lot area and the ratio of
floor area to lot area (floor-area ratio) of the whole building does not exceed 15.
To maximize the floor area in the building and maintain verticality of exterior walls,
designers usually set back the upper parts of a building in a series of steps (Fig.
1.11b).
Some zoning ordinances, however, permit an alternative that many designers
prefer. If the building is set back from the lot lines at the base to provide a streetlevel
plaza, which is a convenience to the public and reduces building bulk, zoning
1.40 SECTION ONE
permits the building to be erected as a sheer tower (Fig. 1.11c). The code may set
a maximum floor-area ratio of 15 or 18, depending on whether the floor area at
any level of the tower does not exceed 50 or 40%, respectively, of the lot area.
1.12 OTHER REGULATIONS
In addition to building and zoning codes, building design and construction must
comply with many other regulations. These include those of the local or state health,
labor, and fire departments; local utility companies; and local departments of highways,
streets, sewers, and water. These agencies may require that drawings for the
building be submitted for review and that a permit be granted before construction
starts.
Also, building construction and conditions in buildings after completion must
comply with regulations of the U.S. Occupational Safety and Health Administration
(OSHA) based on the Occupational Safety and Health Act originally passed by
Congress in 1970. There is, however, no provision in this law for reviewing building
plans before construction starts. OSHA usually inspects buildings only after an
accident occurs or a complaint has been received. Therefore, building owners, designers,
and contractors should be familiar with OSHA requirements and enforce
compliance with them.
Other government agencies also issue regulations affecting buildings. For example,
materials used in military construction must conform with federal specifi-
cations. Another example: Buildings must provide access and facilities for disabled
persons, in accordance with requirements of the Americans with Disabilities Act
(ADA).
[‘‘Construction Industry: OSHA Safety and Health Standards (29CFR 1926/
1910),’’ Superintendent of Documents, Government Printing Office, Washington,
D.C. 20401; ‘‘ADA Compliance Guidebook,’’ Building Owners and Managers Association
International,’’ 1201 New York Ave., N.W., Washington, D.C. 20005.]
1.13 SYSTEMS DESIGN BY TEAM
For efficient and successful execution of systems, design of buildings, a design
organization superior to that used for traditional design (Art. 1.3) is highly desirable.
For systems design, the various specialists required should form a building team,
to contribute their skills in concert.
One reason why the specialists should work closely together is that in systems
design account must be taken of the effects of each component on the performance
of the building and of the interaction of building components. Another reason is
that for cost effectiveness, unnecessary components should be eliminated and,
where possible, two or more components should be combined. When the components
are the responsibility of different specialists, these tasks can be accomplished
with facility only when the specialists are in direct and immediate communication.
In addition to the design consultants required for traditional design, the building
team should be staffed with value engineers, cost estimators, construction experts,
and building operators and users experienced in operation of the type of building
BUILDING SYSTEMS 1.41
to be constructed. Because of the diversity of skills present on such a team, it is
highly probable that all ramifications of a decision will be considered and chances
for mistakes and omissions will be reduced. See also Sec. 2.
(W. W. Caudill, ‘‘Architecture by Team,’’ and F. S. Merritt and J. Ambrose,
‘‘Building Engineering and Systems Design,’’ 2nd Ed., Van Nostrand Reinhold,
New York.)
1.14 PROJECT PEER REVIEW
The building team should make it standard practice to have the output of the various
disciplines checked at the end of each design step and especially before incorporation
in the contract documents. Checking of the work of each discipline should
be performed by a competent practitioner of that discipline other than the original
designer and reviewed by principals and other senior professionals. Checkers should
seek to ensure that calculations, drawings, and specifications are free of errors,
omissions, and conflicts between building components.
For projects that are complicated, unique, or likely to have serious effects if
failure should occur, the client or the building team may find it advisable to request
a peer review of critical elements of the project or of the whole project. In such
cases, the review should be conducted by professionals with expertise equal to or
greater than that of the original designers, that is, by peers; and they should be
independent of the building team, whether part of the same firm or an outside
organization. The review should be paid for by the organization that requests it.
The scope may include investigation of site conditions, applicable codes and governmental
regulations, environmental impact, design assumptions, calculations,
drawings, specifications, alternative designs, constructibility, and conformance with
the building program. The peers should not be considered competitors or replacements
of the original designers, and there should be a high level of respect and
communication between both groups. A report of the results of the review should
be submitted to the authorizing agency and the leader of the building team.
(‘‘The Peer Review Manual,’’ American Consulting Engineers Council, 1015
15th St., NW, Washington, D.C. 20005, and ‘‘Peer Review, a Program Guide for
Members of the Association of Soil and Foundation Engineers,’’ ASFE, Silver
Spring, MD.)
1.15 APPLICATION OF SYSTEMS DESIGN
Systems design may be used profitably in all phases of building design. Systems
design, however, is most advantageous in the early design stages. One system may
be substituted for another, and components may be eliminated or combined in those
stages with little or no cost.
Systems design should be preferably applied in the contract documents stage
only to the details being worked out then. Major changes are likely to be costly.
Value analysis, though, should be applied to the specifications and construction
contract, because such studies may achieve significant cost savings.
1.42 SECTION ONE
Systems design should be applied in the construction stage only when design is
required because of changes necessary in plans and specifications at that time. Time
available at that stage, however, may not be sufficient for thorough studies. Nevertheless,
value analysis should be applied to the extent feasible.
(F. S. Merritt and J. Ambrose, ‘‘Building Engineering and Systems Design,’’ 2nd
Ed., Van Nostrand Reinhold, New York.)
2.1
SECTION TWO
THE BUILDING TEAM—
MANAGING THE BUILDING
PROCESS
Alan D. Hinklin
Director
Skidmore, Owings & Merrill
Chicago, Illinois
Since the beginning of time, mankind has been involved in the business of building.
Technology and construction methods continually evolve: from the Egyptian post
and lintel system, the Greek pediment, the Roman arch and dome, the Byzantine
basilica, and the new Renaissance perspective to the School of the Bauhaus and
the International Style leading us into modern times and the new millennium. Over
time, societies change, construction methods change, clients change, and the architect’s
tools change; however, the excitement and energy inherent in the building
process does not change, because of one factor only—the process itself. To begin
this process, two elements are necessary: an idea and a client. Creative minds then
carry the process forward. With the idea comes the development of a building
concept. A sketch or drawing, created through personal interaction with the client,
develops the vocabulary for the physical construction of the concept. A builder and
labor force turn the concept into reality.
Many processes have been used to manage this interaction. Continual evolution
of the management process has turned it into an independent discipline which,
coupled with the computer, is a major focus of the building industry today. From
the beginning, individuals generating the concepts, preparing drawings, and building
the project were considered part of what we now call the ‘‘service industry.’’ This
section outlines the various complex components and professionals involved in the
building process with respect primarily to the architectural profession. Despite the
changes that have occurred, the basics of the building team and the building process
remain unchanged.
2.2 SECTION TWO
2.1 PROFESSIONAL AND BUSINESS
REQUIREMENTS OF ARCHITECTS AND
ENGINEERS
Management of the building process is best performed by the individuals educated
and trained in the profession, that is, architects and engineers. While the laws of
various states and foreign countries differ, they are consistent relative to the registration
requirements for practicing architecture. No individual may legally indicate
to the public that he or she is entitled to practice as an architect without a professional
certificate of registration as an architect registered in the locale in which the
project is to be constructed. This individual is the registered architect. In addition
to the requirements for individual practice of architecture, most states and countries
require a certificate of registration for a single practitioner and a certificate of authorization
for an entity such as a corporation or partnership to conduct business
in that locale.
An architect is a person who is qualified by education, training, experience, and
examination and who is registered under the laws of the locale to practice architecture
there. The practice of architecture within the meaning and intent of the law
includes:
Offering or furnishing of professional services such as environmental analysis,
feasibility studies, programming, planning, and aesthetic and structural design
Preparation of construction documents, consisting of drawings and specifications,
and other documents required in the construction process
Administration of construction contracts and project representation in connection
with the construction of building projects or addition to, alteration of, or
restoration of buildings or parts of building
All documents intended for use in construction are required to be prepared and
administered in accordance with the standards of reasonable skill and diligence of
the profession. Care must be taken to reflect the requirements of country and state
statutes and county and municipal building ordinances. Inasmuch as architects are
licensed for the protection of the public health, safety, and welfare, documents
prepared by architects must be of such quality and scope and be so administered
as to conform to professional standards.
Nothing contained in the law is intended to prevent drafters, students, project
representatives, and other employees of those lawfully practicing as registered
architects from acting under the instruction, control, or supervision of their employers,
or to prevent employment of project representatives from acting under the
immediate personal supervision of the registered architect who prepared the
construction documents.
2.2 CLIENT OBJECTIVES FOR BUILDINGS
Building types, time schedules, building attitudes, and legal and economic conditions
affect relations with the four major client types for whom an architect may
provide services. These are known as the traditional, developer, turnkey, and design/
build client base.
Traditional client is usually an individual or organization building a one-time
project with no in-house building expertise. The client, however, possesses the
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.3
innate excitement for the process of witnessing the transformation of plans into the
built environment and seeks an architect to assert control of the process. In most
cases, this includes the architect’s definition of the client’s space needs, program
and physical plant requirements. A more sophisticated traditional client might be a
large corporation, university or other institutional entity that may or may not have
an architect on staff, but still looks to a selected architect to guide the development
process. In this case, the client may have more input into the client’s program
definition based on the in-house capabilities. In both cases, the architect plays the
lead role in the management process and normally provides programming, design,
construction documents, bidding, and characteristic administration in the role of the
traditional architect.
Developer client offers building process management that reduces some of the
architect’s management role in managing the overall project and provides alternative
methods for approaching design and construction. Development processes such as
scope documentation, fast track, and bid packages are construction methodologies
resulting from the developer client’s need to accelerate the total process due to
fluctuating interest rates and the need to be first in providing space in the marketplace.
Through this client base the acceptance of a construction consultant as a
necessary part of the design team evolved. The construction consultant enables
accelerated schedules to be met, provides for the compression of time, and allows
a contractor to be selected by the client to build while the architect is still designing.
Turnkey client is interchangeable with the design/build client in concept. Both
are based on a complete project being turned over to the owner by a single entity
that is responsible for designing and constructing the project. The owner has little
input in the process until it is turned over. The turnkey developer or contractor
employs the services of an architect, or has an on-staff registered architect, who
designs the project in accordance with the owner’s program requirements. Bids are
usually taken on turnkey developer designs and cost proposals to meet these requirements.
Once a turnkey developer is selected, the owner may sell the property
to the developer or authorize its purchase from a third party under option. From
this point forward the owner has little or no participation in the project; the developer
is the turnkey client of an externally employed architect. The architect is then
working on the developer team and is not an independent voice for the real owner.
All decisions are then made by the turnkey developer relative to the architect’s
services.
Design/build client also has the architect on the developer team and not performing
services for the owner. Designers/builders offer to design and construct a
facility for a fixed lump-sum price. They bid competitively to provide this service
or provide free design services prior to commitment to the project and as a basis
for negotiation. Their design work is not primarily aimed at cost-performance tradeoffs,
but at reduced cost for acceptable quality.
The design/build approach to facilities is best employed when the owner requires
a relatively straightforward building and does not want to participate in
detailed decision making regarding the various building systems and materials. This
does not mean that the owner has no control over these items. On the contrary, the
owner is often permitted a wide range of selection. But the range of choices is
affected by the fixed-cost restraints imposed by the designer/builder and accepted
by the owner. When the facilities required are within the range of relatively standard
industry-wide prototypes, this restriction may have little significance.
A common misconception regarding design/build is that poor-quality work inevitably
results. While there is a general benefit to the builder for reductions in
material and labor costs, the more reputable designer/builder may be relied on to
deliver a building within acceptable industry standards. Facilities where higher2.4
SECTION TWO
quality systems, more sensitive design needs, or atypical technical requirements
occur deserve the services of an independent design professional.
2.3 PROGRAM DEFINITION
Usually when the term ‘‘program definition’’ is used relative to an architect, it is
understood to mean the client’s program for physical space requirements in a building.
With the decline in the office market in the late 1980s came the loss of, or
minimum use of, the traditional developer and construction management/ construction
consultant roles. As an outgrowth of the developer client era, certain developers
and construction consultants turned their emphasis to ‘‘program management.’’ In
this process, a firm is engaged by the client to manage the total development process,
acting as the client’s agent throughout the total process. The program management
approach expanded the meaning of the word ‘‘program’’ beyond that normally
associated with only the physical space program requirements. The term
‘‘program’’ in this new context defines the process of organizing and executing a
project from inception to completion. This process takes into account legal, financial,
funding, land acquisition, architecture, engineering, specialist consulting, design
administration, insurance, construction administration, and facilities operation
and/or management. The client, instead of managing portions of the process as in
the traditional client and developer client scenarios, looks to one firm for managing
the total process.
2.4 ORGANIZATION OF THE BUILDING TEAM
Architecture is a process involving multidisciplinary input by many professionals.
Comprehensive design services in the professional disciplines of planning, architecture,
landscape architecture, interior design, and civil, structural, mechanical,
electrical, plumbing, and fire protection engineering are offered within one organization
by some large architect-engineer (A/E) and engineer-architect (E/A) firms.
Smaller architectural firms retain these services by contract with consultants. Singlesource
design responsibility, coordinated via a common, integrated management
structure, is a requirement in either case for successful development of a project.
In the performance of professional A/E services on any project, a design team
charged with successful completion of the project in a dedicated professional manner
is essential. This team provides continuous service to the project from start to
finish, establishing and maintaining the quality and integrity of each design. A
project leader should be selected to coordinate and manage all the professional
disciplines and consultants involved in the project and to act as liaison with the
client. This leader should work closely with the client to provide policy direction
and set goals and objectives for the professional team. Day-to-day management and
direction of the project’s technical development should be provided by an individual,
usually identified as the architect’s project manager, who performs the key
administrative duties, establishes and maintains design services budgets and schedules,
and coordinates the entire A/E effort. A senior designer supervises daily
organization and progress of design development and directs the design efforts of
the project team. As a project’s specific needs or schedule require, additional
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.5
architects, planners, engineers, interior architects, and consultants are involved in
the project to augment the team or to provide specialized consultation.
2.4.1 Architects and Engineering Consultants
The major distinctions between architects and engineers run along generalist and
specialist lines. The generalists are ultimately responsible for the overall planning.
It is for this reason that an architect is generally employed as the prime professional
by a client. On some special projects, such as dams, power plants, wastewater
treatment, and research or industrial installations, where one of the engineering
specialties becomes the predominant feature, a client may select an engineering
professional or an E/A firm to assume responsibility for design and construction
and taken on the lead role. On certain projects, it is the unique and imaginative
contribution of the engineer that may make the most significant total impact on the
architectural design. The overall strength of a dynamic, exposed structure, the sophistication
of complex lighting systems, or the quiet efficiency of a well-designed
mechanical system may prove to be the major source of the client’s pride in a
facility. In any circumstance, the responsibilities of the professional engineer for
competence and contribution are just as important to the project as those of the
architect.
Engineers, for example, play a major role in intelligent building system design,
which involves mechanical-electrical systems. However, a building’s intelligence is
also measured by the way it responds to people, both on the inside and outside.
The systems of the building must meet the functional needs of the occupants as
well as respect the human response to temperature, humidity, airflow, noise, light,
and air quality. To achieve the multifaceted goals, an intelligent building requires
an intelligent design process with respect to design and system formulation as well
as efficient and coordinated execution of design and technical documentation within
the management structure.
An intelligent building begins with intelligent architecture—the shape, the building
enclosure, and the way the building appears and functions. Optimal building
solutions can be achieved through a design process that explores and compares
varying architectural and engineering options in concert. Sophisticated visualization
and analytical tools using three-dimensional computer modeling techniques permit
architects and engineers to rapidly evaluate numerous alternatives. Options can be
carefully studied both visually and from a performance standpoint, identifying energy
and life-cycle cost impact. This enables visualization and technical evaluation
of multiple schemes early in the design phase, setting the basis for an intelligent
building.
In all cases, the architect’s or engineer’s legal responsibilities to the client remain
firm. The prime professional is fully responsible for the services delivered. The
consultants, in turn, are responsible to the architect or engineer with whom they
contract. Following this principle, the architect or engineer is responsible to clients
for performance of each consultant. Consequently, it is wise for architects and
engineers to evaluate their expertise in supervising others before retaining consultants
in other areas of responsibility.
2.4.2 Other Consultants
A building team may require the assistance of specialists. These specialty consultants
provide skills and expertise not normally found in an architectural or engi2.6
SECTION TWO
neering firm. The prime professional should define the consultants required and
assist the client in selecting those consultants. The architect or engineer should
define and manage their services even if the specialty consultant contracts directly
with the client for liability purposes, with the understanding that the client has the
ultimate say in decision making.
While several consultants may be required, depending on the complexity of the
project, the cost for each may be minimal since their services are provided over
short periods of time during the development process, and all consultants are usually
not servicing the project at the same time. The following consultant services, most
of which are not normally provided by architects and engineers, are provided by
various firms:
• Acoustical
• Audiovisual
• Communications
• Exterior wall maintenance
• Fire and life safety
• Food service
• Geotechnical engineering and subsurface exploration
• Graphics
• Space-usage operations
• Independent research and testing
• Landscaping
• Marketing and leasing
• Materials handling
• Parking
• Preconstruction survey
• Schedule
• Security
• Site surveyor
• Special foundation systems
• Special structures
• Specialty lighting
• Telecommunications
• Traffic
• Vertical transportation
• Water features
• Wind tunnel testing
2.5 CLIENT-A/E AGREEMENT
Although verbal contracts can be considered legal, a formal written document is
the preferred way to contract for professional services to be provided by an archiTHE
BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.7
tect. Purchase orders are not an acceptable means, since they are not applicable to
a service arrangement but rather only provide a financial accounting system for
purchasing a product, which is normally required internally by a client. A purchase
order should not be used as a client-A /E agreement.
Most professionals use the AIA Standard Form of Agreement for Architect and
Owner (client). Some larger firms, however, have their own form of agreement
which augments or further defines that of the AIA. The basic elements of the
agreement establish the definition and identification of project phases and define
the specific scope and compensation for the architect’s basic services. Flexibility is
built into this agreement to accommodate supplementary services that may be considered.
In addition, the agreement should define the understandings of the two
parties as well as of any third parties that may be involved in the process and
stipulate how the third parties are to be managed and compensated.
Furthermore, the client-A /E agreement should define items considered as direct
costs that may be reimbursed under the agreement. Other items also to be addressed
include project terminology, project terms and definitions, and the architect’s status
as it relates to the profession such that the standard of care is clearly understood.
The definition of additional services, changes, and compensation for such services,
as well as the method and timing of payment, reimbursable expenses, taxes, the
responsibility for client-furnished information, project budgets, ownership of documents,
confidentiality provisions, the use of project databases, insurance requirements,
termination provisions by either party, and dispute resolution may also be
addressed. A/E agreements may also define the documents to be delivered at the
conclusion of each development phase and, in certain cases, the time estimated for
completion of each phase of service.
Compensation for Professional Services. A major concern of an architect is to
arrive at an accurate assessment of the scope of services to be performed. The
nature of the project, the degree of professional involvement, and the skills required
should be considered in arriving at an equitable fee arrangement. Types of fees that
may be used are
• Percentage of the construction cost of the project
• Cost plus fee
• Multiple of direct personnel expense
• Multiple of technical personnel hourly rates
• Stipulated or lump sum
• Billing rates for personnel classification
For a project requiring what could be described as standard services, the
percentage-of-construction-cost fee is a safe standard. Years of experience with the
relationship between the scope of architectural services required for various sizes
of standard construction contracts provide a basis for such rule-of-thumb fee agreements.
For projects where atypical services are required, other arrangements are more
suitable. For example, for projects where the scope of service is indefinite, a costplus
fee is often best. It permits services to proceed on an as-authorized basis,
without undue gambling for either party to the agreement. Under such an arrangement,
the architect is reimbursed for costs and also receives an agreed-on fee for
each unit of effort the architect expended on the project. Special studies, consultations,
investigations, and unusual design services are often performed under such
an arrangement.
2.8 SECTION TWO
TABLE 2.1 Types of Architect and Engineer Insurance
Type of insurance Coverage
Commercial general liability According to occurrence and aggregate
Commercial automobile liability Bodily injury and property damage
Workers’ compensation Statutory limits
Employer’s liability Medical care and time lost as a result of injuries
incurred during the performance of the services
Professional liability Errors and omissions
Valuable papers Loss of drawings, models, computer-produced data,
etc.
Umbrella liability Provides coverage in excess of professional
liability coverage
For projects where the scope can be clearly defined, a lump-sum fee is often
appropriate. In such cases, however, architects should know their own costs and be
able to accurately project the scope of service required to accomplish fixed tasks.
Architects should take care, for the protection of their own, their staff’s, and the
client’s interests, that fees cover the costs adequately. Otherwise, the client’s interests
will suffer, and the architect’s own financial stability may be undermined.
Fee and payment agreements should be accompanied by a well-defined understanding
in the form of a written agreement for services between architect and
client. The method of payment should also be defined in the agreement. Certain
clients may desire a billing and payment schedule while monthly billing and payment
is preferred by the architect.
2.6 A/E LIABILITY AND INSURANCE
Architecture and engineering firms normally maintain professional liability insurance.
This requires payment of annual premiums based on the coverage provided.
Architects and engineers should maintain coverage in connection with their foreign
operations as well as with their domestic operations. Various types of insurance
usually carried by architects and engineers are listed in Table 2.1.
2.6.1 ‘‘Services’’ vs. ‘‘Work’’
The building industry generally recognizes that the professional architect, engineer,
or design consultant provides service, whereas the contractor, subcontractor, or
material supplier provides work. In providing work, the contractor delivers a product
and then warrants or guarantees the work. These distinctions are important to
understand with respect to insurance. In the architect’s case, professional liability
insurance provides coverage for the judgment the professional provides while using
reasonable care and therefore does not normally have liquidated damages provisions.
Professional liability insurance does not cover the work itself or items undertaken
by the contractor in pursuit of the work but does cover negligent errors
and omissions of the architect or engineer. This insurance is a means of managing
the risk associated with the architect’s judgment; it is not product-related. Most
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.9
claims against professionals in the building industry are made by clients. Fewer
claims are made by contractors and workers.
2.6.2 Risk Management
So that the architect’s or engineer’s business goals can be accomplished, professional
liability insurance is offered through various underwriters and managed by
professionals. Such professionals should not dictate or limit architectural practice,
but rather should support it; neither should they tell architects to turn away from
risk, but instead they should help manage it.
Insurance allows the architect or engineer to transfer the risk of financial uncertainty
to an insurance company for a known premium. The professional should
calculate how much risk to assume. The risk the individual retains is the deductible.
The risk the insurance company accrues is the limit of liability over and above the
deductible. By choosing a higher deductible, the professional retains more risk but
pays a lower premium.
Professional liability protection for the architectural and engineering profession
has been designed with the help of the American Institute of Architects (AIA) and
the National Society of Professional Engineers (NSPE)/ Professional Engineers in
Private Practice (PEPP). In addition to errors and omissions coverage, the protection
incorporates liability coverage for on-time performance, cost estimating, interior
design, asbestos, and pollution.
Liability programs vary widely from company to company. In general, the insurance
industry recommends that architects and engineers:
• Select a program with flexible limits of liability and deductible options
• Carefully review the insurance coverage
• Compare competitive costs
• Consider the insurance company’s experience
• Examine the insurance company’s criteria for accepting risk
• Compare loss prevention services
• Assure that the company shares its loss information
The AIA and NSPE/PEPP can also provide architects and engineers with valuable
information on what to look for in a professional liability insurance program.
2.6.3 Project Insurance
Project insurance permits the architect to be responsive to the client who has particular
insurance demands. Suppose, for example, that the client wants 3 times the
coverage the architect carries. Project insurance can respond to this requirement.
Project insurance costs are often reimbursable costs and considered a common
element of the construction cost, similar to the cost of the contractor’s insurance
coverage and performance bonds. Project insurance can sometimes reduce the architect’s
policy costs because project billings are not included in the architect’s
billings when the architect’s practice policy premium is calculated. Project insurance
may provide long-term coverage guarantees to the day of substantial or final
completion and up to 5 years thereafter with no annual renewals. Project insurance
2.10 SECTION TWO
permits clients to take control in the design of an insurance package to protect their
investment and provides clients with stability, security, and risk management.
2.7 DEFINITION OF PROJECT PHASES
The definition of the various phases of development for a particular project from
initial studies through postconstruction should be understood by the client and outlined
thoroughly in the client-A /E agreement. The most-often-used phases of development
include the following:
Feasibility Studies. To assist the client in determining the scope of the project
and the extent of services to be performed by various parties, the architect may
enter into an interim agreement for services relating to feasibility studies, environmental
impact studies or reports, master planning, site selection, site analysis, code
and zoning review, programming, and other predesign services.
Environmental Impact Studies. Determination of environmental studies and reports
required for a project and preparation of such reports, special drawings, or
other documents that may be required for governmental approvals are normally
performed under separate agreements. Attention should be given to zoning, soils,
and the potential of hazardous materials in any form. If any impermissible hazardous
materials are encountered, clients should be advised so that they can obtain the
services of a specialty consultant to determine what course of action to take.
Programming. If the architect is required to prepare the program of space requirements
for a project, the program should be developed in consultation with the
client to help the client recognize particular needs. Space requirements, interrelationships
of spaces and project components, organization subdivision of usage, special
provision and systems, flexibility, constraints, future expansion, phasing, site
requirements, budgetary and scheduling limitations, and other pertinent data should
all be addressed.
Conceptual Design. During this phase of development, the architect evaluates the
client’s program requirements and develops alternatives for design of the project
and overall site development. A master plan may also be developed during this
phase. The plan serves as the guide and philosophy for the remainder of the development
of the project or for phasing, should the project be constructed in various
phases or of different components.
Schematic Design. During this phase the project team, including all specialty
consultants, prepares schematic design documents based on the conceptual design
alternative selected by the client. Included are schematic drawings, a written description
of the project, and other documents that can establish the general extent
and scope of the project and the interrelationships of the various project components,
sufficient for a preliminary estimate of probable construction costs to be
prepared. Renderings and finished scale models may also be prepared at this time
for promotional and marketing purposes.
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.11
Design Development. After client approval of the schematic design, the architect
and the specialty consultants prepare design development documents to define further
the size and character of the project. Included are applicable architectural, civil,
structural, mechanical, and electrical systems, materials, specialty systems, interior
development, and other such project components that can be used as a basis for
working drawing development.
Construction Documents. After approval of the design development documents,
the architectural-engineering team, together with the applicable specialty consultants,
prepares construction documents, consisting of working drawings and technical
specifications for the project components. These include architectural, structural,
mechanical, electrical, hydraulic, and civil work, together with general and
supplementary conditions of the construction contract for use in preparing a final
detailed estimate of construction costs and for bidding purposes.
Construction Phase Services. Diligent construction phase services are essential
to translate design into a finished project. The A/E team continues with the development
process by issuing clarifications of the bid documents and assisting in
contractor selection (Art. 2.20). Also, during the construction period, the team reviews
shop drawings, contractor payment requests, change-order requests, and visits
the construction site to observe the overall progress and quality of the work. Architect
and engineer personnel involved in the design of the project should be
available during construction to provide continuity in the design thought process
until project completion and occupancy.
Postconstruction Services. Follow-up with the client after construction completion
is essential to good client relations. Periodic visits to the project by the architect
through the contractor’s warranty period is considered good business.
2.8 SCHEDULING AND PERSONNEL
ASSIGNMENTS
The effective coordination of any project relies on management’s ability to organize
the project into a series of discreet efforts, with deadlines and milestones identified
in advance. The interdependence of these milestones should be clearly understood
by the client and the project team so that the project can be structured yet still be
flexible to respond to changes and unforeseen delays without suffering in overall
coordination and completion.
Experience is the basis on which architects and engineers establish major project
milestones that form the framework for project development. The critical path
method (CPM) of scheduling can be used to confirm intermediate milestones corresponding
to necessary review and approvals, program and budget reconciliation,
and interdisciplinary coordination. CPM consultants can also assist contractors in
establishing overall shop drawings and fabrication and installation schedules for
efficient phasing and coordination of construction. Schedules can be maintained in
a project management computer database. They should be updated on a regular
basis for the duration of the project, since critical path items change from time to
time depending on actual progress of construction. See also Art. 2.9.
2.12 SECTION TWO
2.9 ACCELERATED DESIGN AND
CONSTRUCTION
The traditional process of design and construction and the roles and responsibilities
of the various parties need not be changed when fast track, an accelerated design
and construction process, is required. However, this process can affect scheduling
and personnel assignments.
In the traditional process, the entire facility moves phase by phase through the
entire development process, that is, programming, design, design development, construction
documents, bid and award of contracts, construction and acceptance of
completed project (Art. 2.7). With any form of accelerated design and construction,
the final phases remain substantially the same, but the various building systems or
subsystems move through the development process at different times and result in
the release of multiple construction contracts at various times throughout the process.
For any project, basic building siting is determined early in the design process.
Therefore, at an early stage in design, a construction contract can be awarded for
demolition and excavation work. Similarly, basic structural decisions can be made
before all details of the building are established. This permits early award of foundation,
below grade utility work, and structural work contracts. Under such circumstances,
construction can be initiated early in the design process, rather than at the
conclusion of a lengthy design and contract preparation period. Months and even
years can be taken out of the traditional project schedule, depending on the scale
and complexity of the project. Purchase of preengineered, commercially available
building systems can be integrated into the accelerated design and construction
process when standard system techniques are employed, reducing time even more.
The major requirements for a project in which design and construction occur
simultaneously are
• Accurate cost management to maintain project budgets.
• Full understanding of the construction process by the client, contractor, and design
professionals so that design decisions and contract documents for each building
system or subsystem can be completed in a professional manner that addresses
the requirements of the ongoing construction process.
• Organized and efficient management of the construction process with feedback
into the design process to maintain a clear definition of the required contract
packages and schedule.
• Overall project cost control and project construction responsibilities, including
interface management of independent prime contracts, should also be established.
Often the major purpose of accelerated design and construction is to reduce the
effect of rapidly increasing construction costs and inflation over the extended project
design and construction period. For projects extending over several years, for example,
contractors and subcontractors have to quote costs for providing material
and labor that may be installed several years later. In most cases, the costs associated
with such work are uncertain. Bid prices for such work, especially when it
is of large magnitude, therefore, must be conservative. Accelerated design and construction,
however, brings all the financial benefits of a shortened project duration
and early occupancy and reduces the impact of cost escalation. Also, bid prices can
be closer to the actual costs, thus reducing bidding risk to the contractor. The
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.13
combination of phased bidding, shortened contract duration, reduced escalation,
smaller bid packages, and a greater number of bidders can produce substantial
savings in overall construction costs.
A major objection to accelerated design and construction is that project construction
is initiated before bids are obtained for the total project and assurance is
secured that the total project budget can be maintained. In this regard, the reliability
of early cost estimating becomes even more critical. It is the experience of most
clients and architects involved with multiple contracts, however, that such contracts,
bid one at a time, can be readily compared with a total budget line item or trade
breakdown and thus provide safeguards against budget overruns. The ability to
design, bid, and negotiate each contract as a separate entity provides optimum cost
control.
For accelerated design and construction programs to work effectively, services
of a professional construction manager are normally required. This cost, however,
can be offset by the overall saving in the total project cost due to the reduction in
construction time.
Normally, the client is responsible for entering into the various construction
contracts when multiple contracts are used. The construction manager acts as the
client’s agent in administration of the contracts. If the architect is to administer the
contracts, additional compensation will be required beyond that associated with one
general contractor who holds all subcontracts, as is the case in the traditional clientcontractor
relationship.
2.10 DESIGN MANAGEMENT
Architects manage all aspects of project design simultaneously, their own internal
resources, relations with the specialty consultants, the processes that deliver service
to the client, and through that service, the programs of client needs through the
development process to the creation of a built environment. The requirement that
architects be capable businesspersons is, therefore, far-reaching. The need for good
business sense and a thorough knowledge of the architect’s own cost is reinforced
by the need to manage these costs throughout the duration of the project. Allocation,
commitment, and monitoring of the expenditure of resources are of critical importance
to the financial success of every project. Only when these are properly managed
can quality services, proper advice, appropriate design, and state-of-the-art
contract documents be delivered to clients.
As a businessperson, an architect is faced with acquiring personnel, advancing
those who are outstanding, and removing those who are unacceptable. The firm
should keep records of business expenses, file tax returns, provide employee benefits,
distribute and account for profits, and keep accurate cost records for project
planning and to satisfy government requirements. The architect must meet legal
requirements for practice as an individual, partnership, or corporation. In many of
these areas, the architect will be assisted by experts. It is impossible for an architect
to practice effectively or successfully without a thorough understanding and complete
concern for the business of architecture.
Once the resources required to deliver services are assured, the architect should
provide management skills to see that these services are kept timely, wellcoordinated,
accurate, and closely related to the client’s needs. This is especially
important for work on large projects, in large design offices, or when dealing with
2.14 SECTION TWO
the architect’s employees and consultants. The best talent must be secured, appropriately
organized, directed, and coordinated to see that the project receives wellintegrated
and well-directed professional service.
The objective is to produce an appropriately designed facility the client needs,
within budget, and on schedule. While the contractor has the front-line responsibility
for budgeted construction cost and schedule, the architect’s resources and the
services provided should be helpful in managing the construction process for the
benefit of the client. The architect’s management of materials and technology and
relationship with the client and contractors will account in good measure for the
success of the project.
2.11 INTERNAL RECORD KEEPING
Part of good office management is document control and record keeping. Much
information is received, disseminated, and collated in an architect’s office. Included
are project directories, contractual correspondence, client correspondence, consultant
correspondence, minutes of meetings, insurance certifications, in-progress drawings,
drawing release for owner review, and building permit and construction issues.
Also dealt with are facsimiles, e-mail, computer tapes, calculations, shop drawings,
specifications, material samples, renderings, photography, slides, field reports, specifications
addenda, contract modifications, invoices, financial statements, audit records,
and time records. In addition, there are contractor payment requests, change
orders, personnel records, client references and more. Certain clients may have
particular formats or record-keeping controls they impose on a project in addition
to the architect’s standard procedures.
A multitude of data is transferred among many parties during the progress of
the architect’s services. The data should be maintained in an organized manner for
future reference and archival purposes. The architect should establish an office
procedure for document control, record keeping, and document storage beyond the
life of the project to ensure easy retrieval. There are many computerized systems
that can aid the architect in catalog filing and information retrieval. Record keeping
can typically be subdivided into the following categories: contractual, financial,
personnel, marketing and publicity, legal, correspondence, project documentation,
drawings, shop drawings, warehousing, and archival records. These should not only
be supervised but also controlled, inasmuch as some files require limited access for
reasons of confidentiality and legalities.
2.12 CODES AND REGULATIONS
Various statutory codes, regulations, statutes, laws, and guidelines affect design and
construction of projects. In most jurisdictions, the architect and engineer are required
by law to design to applicable building codes and regulations, which vary
from one jurisdiction to another and can vary between codes. Some jurisdictions
that do not have sophisticated codes usually follow recognized national or international
codes, which should be agreed on at the onset of a project so that the
client and architect understand the rules for design and construction. All codes are
intended for the health, welfare, and safety of the public and occupants of buildings.
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.15
Affirmative-Action Program. The objective of equal employment opportunity and
affirmative-action programs should be to ensure that individuals are recruited, hired,
and promoted for all job classifications without regard to race, color, religion, national
origin, sex, age, handicap, or veteran status. Employment decisions should
be based solely on an individual’s qualifications for the position for which the
individual is considered.
Affirmative action means more than equal employment opportunity. It means
making a concentrated effort to inform the community of the architect’s desire to
foster equal employment opportunity. It also means making a special effort to attract
individuals to the profession and to engage them in a program of professional
development. Furthermore, architects should be committed to a meaningful minority
business enterprise (MBE) and women business enterprise (WBE) participation program.
Initial contact with local MBE/WBE firms should be pursued for each applicable
project to respond to this important requirement. Architects should be prepared
to review this requirement with clients to achieve participation targets
consistent with client goals and objectives.
2.13 PERMITS
Most jurisdictions require a building permit for construction or remodeling. The
building permit, for which a fee is paid by the contractor or client, is an indication
that drawings showing the work to be done have been prepared by a registered
professional and submitted to the governing authority have jurisdiction over design
and construction of the project. Furthermore, it is an indication that this authority
stipulates that the documents meet the intent of the applicable building codes and
regulations. Issuance of a permit, however, does not relieve the governing agency
of the right to inspect the project during and after construction and to require minor
modifications. In addition, while most locales do not provide for a written permit
by the fire department, this agency is involved in the review process relative to lifesafety
provisions. It also has the right to inspect the project when constructed and
to require modifications if they are considered appropriate to meet the intent of the
code or the department’s specific requirements. Major items reviewed by both the
permit-issuing agencies relate to occupancy classifications, building population, fire
separations, exiting requirements, travel paths for exiting, areas of refuse, and other
general life safety and public health issues.
Occupancy Permits. Many jurisdictions require that a permit be obtained by the
client or tenant of a multitenant building indicating that the building or tenant space
has been reviewed by the applicable agency and fire department. This permit indicates
that the building meets the requirements of the building codes and is appropriate
for occupancy for the intended use and classification for which the building
or space was designed and constructed.
In addition, elevator usage certificates are issued by certain building authorities.
These certificates indicate that the elevators have been inspected and found to be
acceptable for use based on the size, loading, and number of occupants posted on
the certificate.
Furthermore, certain spaces within a project may have a maximum-occupancy
limitation for which a notice is posted in those spaces by the applicable building
authority. Examples of this type of usage include restaurants, ballrooms, convention
2.16 SECTION TWO
centers, and indoor sports facilities where a large number of occupants might be
gathered for the intended use.
2.14 ENERGY CONSERVATION
In response to the national need for energy conservation and in recognition of the
high consumption of energy in buildings, the U.S. Department of Energy gave a
grant to the American Society of Heating, Refrigeration, and Air-Conditioning
Engineers (ASHRAE) for development of a national energy conservation standard
for new buildings. The resulting standard, ASHRAE 90-75, establishes thermal
design requirements for exterior walls and roofs. It is incorporated in some building
codes.
Seeking greater energy-use reduction, Congress passed the Energy Conservation
Standards for New Buildings Act of 1976, mandating development of energy performance
standards for new buildings (BEPS). Accordingly, the Department of Energy
develops such standards, for adoption by federal agencies and state and local
building codes. BEPS consists of three fundamental elements:
1. Energy budget levels for different classifications of buildings in different climates,
expressed as rate of energy consumption, Btu/ ft2-yr.
2. A method for applying these energy budget levels to a specific building design
to obtain a specific annual rate of energy consumption, or design energy budget,
for the proposed building.
3. A method for calculating the estimated annual rate of energy consumption, or
design energy consumption, of the proposed building.
The design energy consumption may not exceed the design energy budget of a
new building. Even without these regulations, energy conservation for buildings
makes good sense, for a reduction in energy usage also reduces building operating
costs. It is worthwhile, therefore, to spend more on a building initially to save
energy over its service life, at least to the point where the amortized annual value
of the increased investment equals the annual savings in energy costs. As a consequence,
life-cycle cost, considered the sum of initial, operating, and maintenance
costs, may be given preference over initial cost in establishment of a cost budget
for a proposed building.
Energy use and conservation are key elements in an architect’s approach to
design. Aided by computer simulation, engineers can develop system concepts and
evaluate system performance, deriving optimal operation schedules and procedures.
During the initial design phase, the computer can be used in feasibility studies
involving energy programs, preliminary load calculations for the selection of heating,
ventilating, and air-conditioning (HVAC) systems and equipment, technical and
economic evaluation of conservation alternatives. Using solar heating and cooling
systems for new and existing facilities, modeling energy consumption levels, forecasting
probable operating costs, and developing energy recovery systems can be
investigated during the early design of a project.
2.15 THE INTERIOR ENVIRONMENT
Architects have long been leaders in building design that is sensitive to environmental
issues. Several areas of general concern for all buildings are described in
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.17
the following paragraphs; they support the basic philosophy that the environment
within buildings is as critical a concern as esthetics.
Indoor Air Quality. Many factors, such as temperature, air velocity, fresh-air ventilation
rates, relative humidity, and noise, affect indoor air quality. The fresh-air
ventilation rate has the greatest influence on indoor air quality in many buildings.
Fresh-air ventilation rates in a building is the flow of outside air brought into the
building for the well-being of the occupants and the dilution of odors and other
internally generated air pollutants. The outside air may vary in its ‘‘freshness’’
depending on the location of the building, its surrounding conditions, and the location
of the fresh-air intakes for the building. Therefore, careful studies should be
made by the architect to ensure the optimum internal air quality.
Ventilation is required to combat not only occupant-generated odors, as has been
traditionally the case, but also to provide ventilation for materials used and stored
in buildings. ASHRAE Standard 62-1989, American Society of Heating, Refrigeration,
and Air-Conditioning Engineers, recommends a rate of 20 cfm per person
as a minimum ventilation rate for office buildings. Air-handling systems for numerous
buildings provide not only this minimum recommended level but also often
increased fan capacity (available when outdoor temperatures and humidity levels
are favorable) through an air-side economizer control.
Environmental Pollution. In response to current concern for the effect of chlorofluorocarbons
(CFCs, fully halogenated refrigerants) on the earth’s ozone layer,
the refrigerant for mechanical systems should have the lowest ozone depletion potential
compatible with commercial building cooling systems.
Noise Control. The acoustical environment within a building is a result of the
noise entering the space from outdoors, or from adjacent interior areas, or most
importantly, from the mechanical, electrical, and elevator systems of the building.
This is in addition to the noise generated within the space by people and equipment.
Mechanical systems should be designed to limit equipment noise and to maintain
the transmission of noise via mechanical systems to occupied spaces within a range
necessary for efficient and enjoyable use of the building. Occupied space noise
should normally be limited to NC-35 or less if desired, through the use of stateof-
the-art-distribution equipment and appropriate use of materials within the finished
spaces.
Safe Building Materials. The technical specifications provided by the architect
should be continually updated to eliminate any materials that are potential health
hazards to occupants or construction workers, such as materials that give off gas
within the occupied spaces. In addition, requirements in local, national, and international
building codes to reduce fire and smoke hazards should be met.
Occupational Health and Safety Issues. As discussed in the preceding, architects
should exercise professional care in design and specification of all architectural and
building systems to create a state-of-the-art building offering a safe, healthy environment
for all occupants, visitors, and users.
Recycled Materials. In today’s environment, architects should understand that
their designs must consider the impact on the ecological health of our society. With
this in mind, architects should work together with the client to develop policies and
innovative solutions that will reduce waste and promote the recycling of materials.
2.18 SECTION TWO
2.16 COST ESTIMATING AND VALUE
ENGINEERING
During development of a project the client normally looks to the architect for
construction cost estimates. It is advisable to provide a probable cost of construction
at completion of the schematic design, design development, and construction document
phases. A design contingency is usually carried in cost estimates. It can be
reduced as the documents are further developed. At completion of the construction
documents, the architect prepares, or has a consultant prepare, a final and most
accurate estimate of construction cost, which can be used for comparison with the
bids submitted to perform the work.
Value engineering may be performed by consultants and construction managers
during the development of the construction documents. (This is a misnomer for
cost-reduction engineering, since value engineering should occur before a design
has been finalized and construction documents have started. To be effective, value
engineering should be undertaken prior to design of any building system.
Value engineering should address operating and maintenance costs as well as
first costs, to provide true life-cycle cost estimates for comparative analysis. This
can be accomplished as early as the conceptual design phase of the project and
should use the expertise of cost consultants, if such service is not offered directly
by the architect or engineer.
Cost analysis should be performed concurrently with technical evaluation of the
systems proposed by the architects or engineers, to provide the client with proper
information to make an informed decision. The architect and engineer should address
cost without compromising the building program, building safety, or desired
design and performance of the facility and respond to the client in a professional
manner regarding cost estimating and value engineering.
2.17 TECHNICAL SPECIFICATIONS
Specifications for a building project are written descriptions, and the drawings are
a diagrammatic presentation of the construction work required for that project. The
drawings and specifications are complementary.
Specifications are addressed to the prime contractor. Presenting a written description
of the project in an orderly and logical manner, they are organized into
divisions and sections representing, in the opinion of the specification writer, the
trades that will be involved in construction. Proper organization of the specifications
facilitates cost estimating and aids in preparation of bids. The architect should
coordinate the specification terminology with that shown on the drawings.
2.17.1 Content of Specifications
It is not practical for an architect or engineer to include sufficient notes on the
drawings to describe in complete detail all of the products and methods required
of a construction project. Detailed descriptions should be incorporated in specifi-
cations. For example, workmanship required should be stated in the specifications.
Contractors study specifications to determine details or materials required, sequence
of work, quality of workmanship, and appearance of the end product. From
this information, contractors can estimate costs of the various skills and labor reTHE
BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.19
quired. If workmanship is not determined properly, unrealistic costs will result and
quality will suffer. Good specifications expand or clarify drawing notes, define
quality of materials and workmanship, establish the scope of the work, and describe
the responsibilities of the contractor.
The terms of the contract documents should obligate each contractor to guarantee
to the client and the architect or engineer that all labor and materials furnished and
the work performed are in accordance with the requirements of the contract documents.
In addition, a guarantee should also provide that if any defects develop
from use of inferior materials, equipment, or workmanship during the guarantee
period (1 year or more from the date of final completion of the contract or final
occupancy of the building by the client, whichever is earlier), the contractor must,
as required by the contract, restore all unsatisfactory work to a satisfactory condition
or replace it with acceptable materials. Also, the contractor should repair or replace
any damage resulting from the inferior work and should restore any work or equipment
or contents disturbed in fulfilling the guarantee.
Difficult and time-consuming to prepare, technical specifications supply a written
description of the project, lacking only a portrayal of its physical shape and its
dimensions. The specifications describe in detail the material, whether concealed
or exposed, in the project and fixed equipment needed for the normal functioning
of the project. If they are properly prepared, well-organized, comprehensive, and
indexed, the applicable requirements for any type of work, kind of material, or
piece of equipment in a project can be easily located.
The technical specifications cover the major types of work—architectural, civil,
structural, mechanical, and electrical. Each of these types is further divided and
subdivided in the technical specifications and given a general title that describes
work performed by specific building trades or technicians, such as plasterers, tile
setters, plumbers, carpenters, masons, and sheet-metal workers, to name a few.
The prime contractor has the responsibility to perform all work, to furnish all
materials, and to complete the project within a schedule. The contractor, therefore,
has the right to select subcontractors or perform the work with the contractor’s own
forces. In recognition of this, each specification should contain a statement either
in the General Conditions or in the Special Conditions, that, regardless of the subdivision
of the technical specifications, the contractor shall be responsible for allocation
of the work to avoid delays due to conflict with local customs, rules, and
union jurisdictional regulations and decisions.
Standard forms for technical specifications can be obtained from the Construction
Specifications Institute (CSI). The CSI publishes a Master List of Section Titles
and Numbers, which is the generally accepted industry standard. In it, technical
specifications are organized into 16 divisions, each with titles that identify a major
class of work. Each division contains basic units of work, called sections, related
to the work described by the division title. Following is the division format developed
by CSI:
1. General Requirements
2. Site Work
3. Concrete
4. Masonry
5. Metals
6. Woods and Plastics
7. Thermal and Moisture Protection
8. Doors and Windows
2.20 SECTION TWO
9. Finishes
10. Specialties
11. Equipment
12. Furnishings
13. Special Construction
14. Conveying Systems
15. Mechanical
16. Electrical
Language should be clear and concise. Good specifications contain as few words
as necessary to describe the materials and the work. The architect or engineer
should use the term ‘‘shall’’ when specifying the contractor’s duties and responsibilities
under the contract and use the term ‘‘will’’ to specify the client’s or architect’s
responsibilities.
Phrases such as ‘‘as directed by the architect,’’ ‘‘. . . to the satisfaction of the
architect,’’ or ‘‘. . . approved by the architect’’ should be avoided. The specification
should be comprehensive and adequate in scope to eliminate the necessity of using
these phrases. ‘‘Approved by the architect’’ may be used, however, if it is accompanied
by a specification that indicates what the architect would consider in a
professional evaluation. The term ‘‘by others’’ is not clear or definite and, when
used, can result in extra costs to the client. The word ‘‘any’’ should not be used
when ‘‘all’’ is meant.
2.17.2 Types of Specifications
Technical requirements may be specified in different ways, depending on what best
meets the client’s requirements. One or more of the following types of technical
specifications may be used for a building project.
Descriptive Specifications. These describe the components of a product and how
they are assembled. The specification writer specifies the physical and chemical
properties of the materials, size of each member, size and spacing of fastening
devices, exact relationship of moving parts, sequence of assembly, and many other
requirements. The contractor has the responsibility of constructing the work in
accordance with this description. The architect or engineer assumes total responsibility
for the function and performance of the end product. Usually, architects and
engineers do not have the resources, laboratory, or technical staff capable of conducting
research on the specified materials or products. Therefore, unless the specification
writer is very sure the assembled product will function properly, descriptive
specifications should not be used.
Reference Specifications. These employ standards of recognized authorities to
specify quality. Among these authorities are ASTM, American National Standards
Institute, National Institute of Standards and Technology, Underwriters Laboratories,
Inc., American Institute of Steel Construction, American Concrete Institute,
and American Institute of Timber Construction.
An example of a reference specification is: Cement shall be portland cement
conforming to ASTM C150, ‘‘Specification for Portland Cement,’’ using Type 1 or
Type 11 for general concrete construction.
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.21
Reputable companies state in their literature that their products conform to specific
recognized standards and furnish independent laboratory reports supporting
their claims. The buyer is assured that the products conform to minimum requirements
and that the buyer will be able to use them consistently and expect the same
end result. Reference specifications generally are used in conjunction with one or
more of the other types of specifications.
Proprietary Specifications. These specify materials, equipment, and other products
by trade name, model number, and manufacturer. This type of specification
simplifies the specification writer’s task, because commercially available products
set the standard of quality acceptable to the architect or engineer.
Sometimes proprietary specifications can cause complications because manufacturers
reserve the right to change their products without notice, and the product
incorporated in the project may not be what the specifier believed would be installed.
Another disadvantage of proprietary specifications is that they may permit
use of alternative products that are not equal in every respect. Therefore, the specifier
should be familiar with the products and their past performance under similar
use and should know whether they have had a history of satisfactory service. The
specifier should also take into consideration the reputation of the manufacturers or
subcontractors for giving service and their attitude toward repair or replacement of
defective or inferior work.
Under a proprietary specification, the architect or engineer is responsible to the
client for the performance of the material or product specified and for checking the
installation to see that it conforms with the specification. The manufacturer of the
product specified by the model number has the responsibility of providing the performance
promised in its literature.
In general, the specification writer has the responsibility of maintaining competition
between manufacturers and subcontractors to help keep costs in line. Naming
only one supplier may result in a high price. Two or more names are normally
supplied for each product to enhance competition.
Use of ‘‘or equal’’ should be avoided. It is not fully satisfactory in controlling
quality of materials and equipment, though it saves time in preparing the specifi-
cation. Only one or two products need to be investigated and research time needed
to review other products is postponed.
Base-Bid Specifications. These establish acceptable materials and equipment by
naming one or more (often three) manufacturers and fabricators. The bidder is
required to prepare a proposal with prices submitted from these suppliers. Usually,
base-bid specifications permit the bidder to submit substitutions or alternatives for
the specified products. When this is done, the bidder should state in the proposal
the price to be added to, or deducted from, the base bid and include the name,
type, manufacturer, and descriptive data for the substitutions. Final selection rests
with the client. Base-bid specifications often provide the greatest control of quality
of materials and equipment, but there are many pros and cons for the various types
of specifications, and there are many variations of them.
2.17.3 Automated Specifications
For building projects, specification writers normally maintain a library of master
documents that are used as a basis for creating project specifications with a computer.
Typically, they employ the industry-standard Construction Specifications In2.22
SECTION TWO
stitute format (Art. 2.17.1). Computers are used to facilitate and speed production
of specifications and other technical documents.
Although computer systems can be complex, requiring an experienced person
for setup and maintenance, they are cost-effective, saving time and effort. For example,
one program used for preparing specifications has a point-and-click graphics
user interface with directories and files represented by icons and manipulated by a
mouse. Multiple files are viewed and edited on the screen simultaneously, and each
file is seen as a full-page display exactly as it will be printed. The graphics and
document layout capabilities of the program are suitable for producing technical
manuals and for publishing periodicals. Documents displayed on the computer permit
the architect to eliminate the editing of drafts on paper or markups. Instead,
editing is performed directly on the computer screen, thus reducing the amount of
paper filing and printing that would otherwise be required.
2.18 UPFRONT DOCUMENTS
The contract documents prepared by the architect, engineer, or client’s legal counsel
include the contract between the client and contractor; the bidding requirements,
which contain the invitation to bid, instruction to bidders, general information, bid
forms, and bid bond; the contract forms, which may include the agreement (contract)
format between the client and contractor, performance bond, and payment
bond and certificates; the contract conditions identified as the general and supplementary
conditions; the list of technical specifications; drawings; addenda; and contract
modifications. The bidding requirements, contract forms, and contract conditions
are sometimes referred to as the upfront documents.
Bidding Requirements. These explain the procedures bidders are to follow in
preparing and submitting their bid. They assist all bidders in following established
guidelines so that bids can be submitted for comparative purposes and not be disqualified
because of technicalities. The bidding requirements address all prospective
bidders, whereas the final contract documents address only the successful bidder,
who, after signing the client-contractor agreement, becomes the contractor.
Contract Forms. The agreement (contract) is the written document, signed by the
client and contractor, which is the legal instrument binding the two parties. This
contract defines the relationships and obligations that exist between the client and
contractor. It incorporates other contract documents by reference.
The contract may require a construction performance bond for financial protection
of the client in the event the contractor is unable to complete the work in
accordance with the contract. Not all clients require performance bonds, but the
architect should review its necessity with the client and prepare the bidding documents
in accordance with the client’s decision.
The contract usually requires a contractor payment bond from the contractor to
ensure that a surety will pay the labor force and material suppliers should the
contractor fail to pay them. The use of this bond precludes the need for the labor
force or suppliers to seek payment directly from the client, through liens or otherwise,
because of nonpayment by the contractor.
Certificates include those project forms that may be required for insurance, certificate
of compliance, guarantees or warranties, or compliance with applicable
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.23
laws and regulations. Contract forms vary, depending on the type and usage of the
project.
Contract Conditions. These define the rights, responsibilities, and relationships
of the various parties involved in the construction process. Two types of contract
conditions exist, General Conditions and Supplementary Conditions.
The General Conditions have general clauses that establish how the project is
to be administered. They normally contain provisions that are common practice.
Definitions of project terms, temporary provisions, site security, management process
required, and warranties and guarantees are among those items addressed in
the General Conditions.
The Supplementary Conditions modify or supplement the general conditions to
provide for requirements unique to a specific project and not normally found in
standard General Conditions.
2.19 QUALITY CONTROL FOR ARCHITECTS
AND ENGINEERS
To maintain a consistently high level of quality in design and construction documentation,
a rigorous internal review of the documents prepared by the architect or
engineer, which draws on the full depth and experience of resources available,
should be undertaken during the contract document phase. Quality control can begin
in the earliest stages of design, when criteria are established and developed as
design guidelines for use throughout the project. At each stage of development, a
coordination checklist, based on previous experience, can be utilized for the project
through an independent internal or external technical checking program.
Computer file management may be used to enable the various technical disciplines
to share graphic data and check for interference conditions, thereby enhancing
technical coordination of the documents. Quality control should also continue
throughout the construction phase with architect and engineer review of shop drawings
and on-site observation of the work.
Quality Management Program. To have a truly meaningful quality management
program, all personnel must be committed to it. To help the professional staff
understand the quality program, quality systems should be developed, updated,
maintained, and administered to assist the architect and professional staff in providing
quality service to clients. An individual in each office may be assigned to
assist in the quality management program. This person should undertake to instill
in all personnel the importance of such a program in every aspect of the daily
conduct of business.
The quality management program should set quality goals; develop professional
interaction for meeting these goals among peers and peer groups; review building
systems, specifications, and drawings to ensure quality; and see that these objectives
are known to the public. Such a program will result in a client base that will
communicate the quality level of the architect to others in the community, profession,
and international marketplace. The architect’s image is of extreme importance
in acquiring and maintaining clients, and the best quality management program
focuses on client service and dedication to the profession.
2.24 SECTION TWO
2.20 BIDDING AND CONTRACT AWARD
Competitive bidding is one method of determining the least cost for performing
work defined by the construction documents. The bid states the price that the bidder
will contract for to perform the work based on the work shown and described in
the bidding documents. Bids are prepared in confidence by each bidder. They are
usually sealed when submitted to the client (or, in the case of subcontractors, to
the bidding contractors). At a specified time and date, all bids are opened, competitively
examined, and compared. Unless there are compelling reasons to do otherwise,
the client (contractor in the case of subcontractors) usually enters into an
agreement to have the work performed by the bidder submitting the lowest price.
Before bids may be received, prospective bidders need to be identified and made
aware of the project. Sufficient data should be furnished to potential bidders to
allow preparation of their bids. The client may or may not wish to prequalify
bidders. In those cases where prequalification is required, the architect can have
meaningful input in the process based on past experience with potential bidders.
The terms bid and proposal are synonymous. Although proposal may imply an
opportunity for more consideration and discussion with the client, architect, or
engineer, bid, bidder, and bid form are preferable, to prevent misunderstanding by
the bidders.
After client approval of the construction documents and selection of a construction
bidding method, the architect may assist in the selection of contractors to bid
the work; preparation of bid forms; issuance of bidding documents for competitive
bidding; answering inquiries from bidders; and preparing and issuing any necessary
addenda to the bidding documents. Furthermore, the architect may assist in analyzing
bid proposals and making recommendations to the client as to the award of
the construction contract. The architect can also assist in preparation of the construction
contract.
Bidders may elect to change their bid on the basis of certain conditions, such
as errors in the bid, changes in product cost, changes in labor rates, or nonavailability
of labor because of other work or strikes. Each bidder is responsible for
providing for any eventuality during the period the bid is open for acceptance.
Unless provided for otherwise, bidders may withdraw their bid before acceptance
by the client, unless the client consents to a later withdrawal. If all conditions of
the instructions to bidders have been met, then after the bids have been opened,
the bids should be evaluated. The low bid especially should be analyzed to ensure
that it reflects accurately the cost of the work required by the contract documents.
The bids may be compared with the architect’s construction cost estimate that was
prepared on completion of the contract documents. The client can accept a bid and
award the contract to the selected bidder, who then becomes the contractor for the
work.
2.21 CONSTRUCTION SCHEDULING
Normally, a client asks the architect for an estimate of the construction time for the
project. The client can then incorporate this estimate in the overall development
schedule.
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.25
The contractor should prepare a detailed construction schedule for use in administering
the work of subcontractors and the contractor’s own forces. The contractor
should be requested to submit the schedule to the architect and the client
within 30 days of contract award. The schedule will also form the basis for the
contractor’s development of a shop drawing schedule.
A construction schedule can consist simply of a bar chart for each item of work
or a breakdown for the major trades on the project. Alternatively, the schedule can
be highly detailed; for example, a critical-path-method (CPM) schedule. This is
recommended for large projects for monitoring the critical-path item at any point
in time, since the critical path can change, depending on actual construction conditions.
The contractor should monitor and update the schedule monthly during the
construction phase so that the anticipated completion and move-in date can be
verified or adjusted. If the completion date cannot be adjusted and the schedule
appears to be of concern, more work time (overtime) may be required to maintain
the nonadjusted schedule. This could have an impact on cost, depending on how
the client-contract agreement was structured.
The construction schedule is an extremely meaningful tool in monitoring the
construction process. It can assist the architect’s ongoing role in quality control
during the construction phase, when the management of the building process is
transferred to, and becomes the responsibility of, the contractor. The schedule also
is a meaningful tool for use by all trades involved in the building process. The
schedule affects trades in different ways, depending on the size of the labor force,
availability of material and personnel hoisting equipment, access to the work, coordination
of subcontractors’ work with material suppliers, material testing agencies
involved, preparation of mock-ups, shop-drawing submittals, and general overall
construction coordination issues.
2.22 SHOP DRAWING REVIEW
After the construction contract is awarded, the contractor should submit a proposed
schedule for submission of shop drawings to meet the construction schedule. This
permits the architect to anticipate submissions and plan manpower requirements
accordingly, based on the number and complexity of each submission.
As an ongoing part of quality control, the architect should review the shop
drawings, product literature, and samples and observe material and mock-up testing.
This is considered part of the shop drawing submittal process. The architect should
be an independent agent and side neither with the client nor the contractor in
acceptance or rejection of a submittal. Rather, based on professional judgment, the
architect should render a decision as to whether the submittal is in general accordance
with the construction documents and design intent. All submittals should be
properly identified and recorded when received by the architect, as part of document
control. The architect should review the submittal expeditiously and return it to the
contractor with the appropriate action.
The architect’s action shown on the submittal usually records that the contractor
can proceed, proceed as noted, or not proceed. A copy of the proceed and proceedas-
noted submittal should be maintained in the architect’s and contractor’s site office
for reference. The client should also be provided with the transmittal associated
with submittals. This helps keep the client informed regarding the progress of the
work relative to the schedule for submission of shop drawings.
2.26 SECTION TWO
2.23 ROLE OF ARCHITECT OR ENGINEER
DURING CONSTRUCTION
After award of the construction contract, the architect or engineer generally continues
to assist the client in relations with the contractor.
2.23.1 Site Observation
As part of their ongoing services during construction, and depending on the scale
and complexity of the project, architects and engineers may make periodic site visits
or maintain full-time representation on site during a portion or all of the construction
period. The professional’s role is to expedite day-to-day communication and
decision making by having on-site personnel available to respond to required drawing
and specification clarifications.
Site-observation requirements for the project should be discussed with the client
at the onset of the project and be outlined in the architect-client agreement. Many
clients prefer periodic or regularly scheduled site visits by the design professional.
A provision for additional or full-time on-site representation, however, can be addressed
in the agreement, and compensation for this additional service can be outlined
in the agreement for discussion with the client later in the development process
or during the construction phase. The client and the architect and engineer
should agree on the appropriate amount of site visitation provided in the architect’s
basic services to allow adequate site-observation services based on specific project
conditions.
If periodic site observations are made, the architect should report such observations
to the client in written form. This should call attention to items observed
that do not meet the intent of the construction documents. It is normally left to the
client to reject or replace work unless such defective work involves life safety,
health, or welfare of the building occupants or is a defect involving structural integrity.
If the architect provides full-time site observation services, daily or weekly
reports should be issued to the client outlining items observed that are not in accordance
with the construction documents or design intent.
2.23.2 Site Record Keeping
Depending on contractual requirements for service during the construction phase,
the architect may establish a field office. In this event, dual record keeping is
suggested between the site and architect’s office so that records required for daily
administration of construction are readily accessible on site. Contractor correspondence,
field reports, testing and balancing reports, shop drawings, record documents,
contractor payment requests, change orders, bulletin issues, field meeting minutes,
and schedules are used continually during construction. Computer systems and electronic
mail make the communication process somewhat easy to control.
2.23.3 Inspection and Testing
Technical specifications require testing and inspection of various material and building
systems during construction to verify that the intent of the design and construcTHE
BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.27
tion documents is being fulfilled under field conditions. Testing is required where
visual observations cannot verify actual conditions. Subsurface conditions, concrete
and steel testing, welding, air infiltration, and air and water balancing of mechanical
systems are such building elements that require inspection and testing services.
Normally, these services are performed by an independent testing agency employed
directly by the client so that third-party evaluation can be obtained.
Although the architect does not become involved in the conduct of work or
determine the means or methods of construction, the architect has the general responsibility
to the client to see that the work is installed in general accordance with
the contract documents.
Other areas of inspection and testing involve establishing and checking benchmarks
for horizontal and vertical alignment, examining soils and backfill material,
compaction testing, examining subsurface retention systems, inspecting connections
to public utilities, verifying subsoil drainage, verifying structural column centerlines
and base-plate locations (if applicable), checking alignment and bracing of concrete
formwork, verifying concrete strength and quality, and other similar items.
2.23.4 Payment Requests
The contractor normally submits a consolidated payment request monthly to the
architect and client for review and certification. The payment request should be
subdivided by trade and compared with the schedule of values for each trade that
would have been submitted with the subcontractor bid if required by the instructions
to bidders and bid form. The architect should review the payment request with
respect to the percentage of completion of the pertinent work item or trade.
Some clients or lending institutions require that a partial waiver of lien be submitted
for each work item or trade with each payment request. This partial waiver
of lien can either be for the prior monthly request, which will indicate that the prior
month’s payment has been received, or in certain cases for the current monthly
request. If the latter procedure is followed, the waiver may require revision, depending
on the architect’s review, if a work-item or trade-payment request is modified.
The architect is not expected to audit the payment request or check the mathematical
calculations for accuracy.
2.23.5 Change Orders
Contractor’s change-order requests require the input of the architect, engineer, and
client and are usually acted on as part of the payment request procedure. A change
order is the instrument for amending the original contract amount and schedule, as
submitted with the bid and agreed on in the client-contractor contract. Change
orders can result from departures from the contract documents ordered during construction,
by the architect, engineer, or client; errors or omissions; field conditions;
unforeseen subsoil; or other similar conditions.
A change order outlines the nature of the change and the effect, if any, on the
contract amount and construction schedule. Change orders can occur with both a
zero cost and zero schedule change. Nevertheless, they should be documented in
writing and approved by the contractor, architect, and client to acknowledge that
the changes were made, with no impact. Change orders are also used to permit a
material substitution when a material or system not included in the contract documents
is found acceptable by the client and architect. For material substitutions
2.28 SECTION TWO
proposed by the contractor, schedule revisions are not normally recognized as a
valid change.
The sum of the change-order amounts is added or deducted from the original
contract amount. Then, the revised contract amount is carried forward on the contractor’s
consolidated application for payment after the change orders have been
signed by all parties. The normal contractor payment request procedure is then
followed, on the basis of the new contract amount. If the schedule is changed
because of a change order, the subsequent issue of the construction schedule should
indicate the revised completion or move-in date, or both, that result from the approved
change.
2.23.6 Project Closeout
Project closeout involves all parties, including subcontractors and material suppliers.
It should be addressed early in the construction phase so that the closeout can be
expedited and documented in an organized and meaningful manner. At this point
in the construction process, the attention of the contractor and architect is focused
on accomplishing the necessary paperwork and administrative functions required
for final acceptance of the work and issuance of the contractor’s final consolidated
application for payment and final waiver of lien.
The normal project closeout proceeds as follows:
1. The contractor formally notifies the architect and the client that the contracted
work is substantially complete.
2. From on-site observations and representations made by the contractor, the
architect documents substantial completion with the client and the contractor. In
some cases, this may trigger the start of certain guarantees or warranties, depending
on the provisions of the general and supplementary conditions of the contract.
3. For some projects that are phased, some but not all the building systems
may be recognized by the architect and the client as being substantially complete.
This should be well-documented, since start dates for warranty and guarantee
periods for various building systems or equipment may vary.
4. On-site visits are made by the architect and representatives of the client,
sometimes called a walk-through, and a final punchlist is developed by the architect
to document items requiring remedial work or replacement to meet the requirement
of the construction documents.
5. A complete keying schedule, with master, submaster, room, and specialty
keys, is documented by the contractor and delivered to the client.
6. The contractor submits all record drawings, as-builts, testing and balancing
reports, and other administrative paperwork required by the contract documents.
7. The contractor should submit all required guarantees, warranties, certificates,
and bonds required by the general and supplementary conditions of the contract or
technical specifications for each work item or trade outlined in the breakdown of
the contractor’s consolidated final payment request.
8. The contractor corrects all work noted on the punchlist. A final observation
of the corrected work may then be made by the architect and client.
9. If the client accepts the work, the architect sends a certificate of completion
to the contractor with a copy to the client. The certificate documents that final
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.29
completion of the work has occurred. All required operating manuals and maintenance
instructions are given to the architect for document control and forwarding
to the client.
10. The contractor submits final waivers of lien from each subcontractor or
material supplier. Also provided is an affidavit stating that all invoices have been
paid, with the exception of those amounts shown on the final waiver of lien. With
these documents, the contractor submits the final consolidated payment request,
including all change orders.
11. The architect sends a final certificate of payment to the client, with a copy
to the contractor.
12. The contractor provides any required certificate of occupancy, indicating that
the building authorities have jurisdiction over the project approve occupancy of the
space for the intended use.
13. The client makes final payment to the contractor and notifies the architect
of this.
This process is important inasmuch as it can trigger the transfer of risk from the
contractor’s insurance program during construction to the client’s insurance program
for the completed project.
2.24 TESTING AND BALANCING OF BUILDING
SYSTEMS
It is normal for projects to go through what is known as a shakedown period after
final acceptance and occupancy by the client or building tenant. The warranty and
guarantee period (normally 1 year) is the contractor’s representation and recognition
that certain building elements and systems may need adjustment or slight modifi-
cation, depending on actual occupancy conditions or normal maintenance and usage
of such systems. The heating, ventilating, air conditioning, and systems unique to
a project require testing and balancing and potential minor modifications and adjustments
during this warranty and guarantee period, even though they were tested
and balanced by the contractor’s testing agency prior to project closeout. An independent
testing and balancing contractor who was employed prior to final project
closeout normally returns on an as-needed, on-call basis to adjust, test, and balance
systems during the first year. In addition, the building engineer will become familiar
with the systems during this first year of operation and may also adjust and balance
systems.
2.25 POSTCONSTRUCTION OPERATION AND
MAINTENANCE
The technical specifications for a building project normally require that some time
be devoted prior to project closeout for instruction and training of the client’s building
operating personnel and building engineer, who will be responsible for operating
and maintaining the various building systems. Manufacturers’ operating procedures,
manuals, and inventory of spare parts and attic stock should be reviewed with the
2.30 SECTION TWO
client, building engineer, and the contractor installing the work. The building engineer
should thus gain a general understanding of the individual systems and their
interaction in the operation of the building. During the warranty and guarantee
period, the contractor or applicable subcontractor may be requested to assist the
building engineer further in operation and maintenance of a system, including testing,
balancing, and minor adjustment. After the shakedown period and when the
engineer thoroughly understands system operation, the client’s personnel assume
full responsibility and deal directly with the manufacturers of various building components
for maintenance. Or the client may subcontract maintenance, a normal
procedure for such systems as elevators and escalators where specialty expertise in
maintenance is required.
2.26 RECORD DRAWINGS
The normal procedure for submission of record drawings rests primarily with the
contractor. These are edited drawings and specifications submitted by the contractor
that describe actual installed conditions based on the contractor’s field coordination
of the work.
In some instances, the client may request that the architect revise the original
construction documents or prepare new drawings to reflect the as-built conditions.
This is normally an additional service in the architect-client agreement. It should
be made clear to the client that the architect, if brought into this process, is acting
only in a drafting role, inasmuch as the as-built documentation, including dimensions
and details, is furnished by, and is the responsibility of, the contractor.
As-built and record drawings are helpful to the client in remodeling, maintenance,
building-system modification, or making future additions to the project. The
client should retain the drawings with maintenance manuals and operations procedures.
2.27 FOLLOW-UP INTERVIEWS
It is advisable that the architect or engineer have follow-up interviews with the
client and occupants of the building or tenant spaces to help ascertain the success
of the project and learn where certain materials, details, equipment, or systems may
be improved for future use in other projects. Good client relations demand this type
of exchange. It is also helpful for the architect or engineer to disseminate the
interview results throughout the office and professional community, to improve
problem solving, design, and construction.
2.28 MANAGEMENT OF DISPUTES
Even in the best of relationships, disputes can arise between the client and architect,
client and contractor, or architect and contractor, even though the architect and
contractor do not normally have a written agreement with each other. Disputes
should be quickly addressed and resolved for the well-being of the project and to
THE BUILDING TEAM—MANAGING THE BUILDING PROCESS 2.31
minimize disruption of the design and building process. If the dispute cannot be
resolved by the parties, various methods of resolution are offered that include
settlement, mediation, arbitration, and litigation. To maintain insurance coverage
and protect appropriate interests, proper notification to insurers or involvement of
legal counsel is required.
Settlement of Disputes. Disputes between two parties should be addressed quickly
and, if at all possible, a settlement should be rendered and recorded. Settlement
can be in the form of monetary adjustments or payments, free services on behalf
of the architect to remedy or correct an error, or such other agreement between the
two parties. It is recommended that this method of dispute resolution be used whenever
possible to avoid time, cost, and anguish, which can occur as a result of
mediation, arbitration, and litigation.
Mediation. In mediation, the parties in dispute agree on a third independent party
to act as a mediator and hear each side’s position in the dispute in an attempt to
mediate a resolution. Mediation is not binding on either party but helps resolve
certain disputes due to a third party’s focus on, and question of, the issues.
Arbitration. This is a method of handling disputes in which an arbitrator or arbitration
panel, often consisting of three members, is selected to hear the positions
of the parties in the dispute and decide on a potential resolution. The resolution is
binding on the parties. Cost and time for arbitration is usually, but not always, less
than that required for litigation. The arbitrators usually consist of professionals
(architects and engineers), lawyers, contractors, or other parties involved in the
building industry.
Litigation. In the event settlement or mediation cannot resolve a dispute and the
parties do not wish to arbitrate, the only remaining course of action is to litigate
the dispute. This requires that much time and money be expended for depositions,
document and other discovery, and preparation for trial. The final results are rendered
by a group of individuals (the jury) or judge not involved in the building
industry. Therefore, a possession of a thorough knowledge and understanding of
issues affecting the architectural and engineering profession and construction industry
become the responsibility of each party’s legal counsel to establish a true
and accurate picture of each party’s position and the facts in the case. See also
Art. 17.14.
2.29 PROFESSIONAL ETHICS
The American Institute of Architects has formulated the following basic principles
for guidance of architects:
Advice and counsel constitute the service of the profession. Given in verbal, written,
or graphic form, they are normally rendered in order that buildings with their equipment
and the areas about them, in addition to being well suited to their purposes, well planned
for health, safety, and efficient operation and economical maintenance, and soundly
constructed of materials and by methods most appropriate and economical for their
particular uses, shall have a beauty and distinction that lift them above the common2.32
SECTION TWO
place. It is the purpose of the profession of architecture to render such services from
the beginning to the completion of a project.
The fulfillment of that purpose is advanced every time architects render the
highest quality of service they are capable of giving. In particular, the architect’s
drawings, specifications, and other documents should be complete, definite, and
clear concerning the architect’s intentions, the scope of the contractor’s work, the
materials to be employed, and the conditions under which the construction is to be
completed and the work paid for. The relation of architects to their clients depends
on good faith. Architects should explain the exact nature and extent of their services
and the conditional character of construction cost estimates made before final drawings
and specifications are complete.
The contractor depends on the architect to guard the contractor’s interests as
well as those of the client. The architect should reject workmanship and materials
that are determined not to be in conformity with the contract documents, but it is
also the architect’s duty to give reasonable aid toward a complete understanding of
those documents so that errors may be avoided. An exchange of information between
architects and those who supply and handle building materials should be
encouraged.
Architects, in their investments and business relations outside the profession,
should avoid financial or personal activities that tend to weaken or discredit their
standing as an unprejudiced and honest adviser, free to act in the client’s best
interests. Permitting use of free architectural or engineering services to be offered
by manufacturers; suppliers of building materials, appliances, and equipment; or
contractors may imply an obligation that can become detrimental to the best interest
of the client.
Architects may offer their services to anyone for commission, salary, or fee as
architect, consultant, adviser, or assistant, provided the architect rigidly maintains
professional integrity, disinterestedness, and freedom to act.
Architects should work together through their professional organizations to promote
the welfare of the physical environment. They should share in the interchange
of technical information and experience.
Architects should seek opportunities to be of service in civic affairs. To the best
of their ability, they should endeavor to advance the safety, health, and well-being
of the community in which they reside by promoting appreciation of good design,
good construction, proper placement of facilities, and harmonious development of
the areas surrounding the facility.
Architects should take action to advance the interests of their personnel, providing
suitable working conditions for them, requiring them to render competent and
efficient services, and paying them adequate and just compensation. Architects
should also encourage and sponsor those who are entering the profession, assisting
them to a full understanding of the functions, duties, and responsibilities of the
architectural profession.
Every architect should contribute toward justice, courtesy, and sincerity in the
profession. In the conduct of their practice, architects should maintain a totally
professional attitude toward those served, toward those who assist in the practice,
toward fellow architects, and toward the members of other professions. Daily performance
should command respect to the extent that the profession will benefit
from the example architects set to other professionals and to the public in general.
3.1
SECTION THREE
PROTECTION AGAINST
HAZARDS
David W. Mock*
Gee & Jenson
West Palm Beach, Florida
A hazard poses the threat that an unwanted event, possibly a catastrophe, may occur.
Risk is the probability that the event will occur. Inasmuch as all buildings are
subject to hazards such as hurricanes, earthquakes, flood, fire, and lightning strikes,
both during and after construction, building designers and contractors have the
responsibility of estimating the risks of these hazards and the magnitudes of the
consequences should the events be realized.
3.1 RISK MANAGEMENT
After the risk of a hazard has been assessed, the building designers and contractors,
guided by building-code, design standards, zoning-code, and health-agency speci-
fications and exercising their best judgment, should decide on an acceptable level
for the risk. With this done, they should then select a cost-effective way of avoiding
the hazard, if possible, or protecting against it so as to reduce the risk of the hazard’s
occurring to within the acceptable level.
Studies of building failures provide information that building designers should
use to prevent similar catastrophes. Many of the lessons learned from failures have
led to establishment of safety rules in building codes. These rules, however, generally
are minimum requirements and apply to ordinary structures. Building designers,
therefore, should use judgment in applying code requirements and should
adopt more stringent design criteria where conditions dictate.
Such conditions are especially likely to exist for buildings in extreme climates
or in areas exposed to natural hazards, such as high winds, earthquakes, floods,
landslides, and lightning. Stricter criteria should also be used for buildings that are
*Revised and updated from Sec. 3, ‘‘Protection Against Hazards’’ by the late Frederick S. Merritt,
Consulting Engineer.
3.2 SECTION THREE
tall and narrow, are low but very large, have irregular or unusual shapes, house
hazardous material or critical functions, or are of novel construction. Furthermore,
building codes may not contain provisions for some hazards against which building
designers nevertheless should provide protection. Examples of such hazards are
vandalism, trespass, and burglary. In addition, designers should anticipate conditions
that may exist in buildings in emergencies and provide refuge for occupants or safe
evacuation routes.
Building designers also should use judgment in determining. the degree of protection
to be provided against specific hazards. Costs of protection should be commensurate
with probable losses from an incident. In many cases, for example, it is
uneconomical to construct a building that will be immune to extreme earthquakes,
high winds of tornadoes, arson, bombs, burst dams, or professional burglars. Full
protection, however, should always be provided against hazards with a high probability
of occurrence accompanied by personal injuries or high property losses. Such
hazards include hurricanes and gales, fire, and vandals.
Structures containing extremely valuable contents or critical equipment justifying
design for even the most extreme events may require special hardened rooms
or areas.
3.1.1 Design Life of Buildings
For natural phenomena, design criteria may be based on the probability of occurrence
of extreme conditions, as determined from statistical studies of events in
specific localities. These probabilities are often expressed as mean recurrence intervals.
A mean recurrence interval of an extreme condition is the average time, in
years, between occurrences of a condition equal to or worse than the specified
extreme condition. For example, the mean recurrence interval of a wind of 60 mi/
hr or more may be recorded for Los Angeles as 50 years. Thus, after a building
has been erected in Los Angeles, chances are that in the next 50 years it will be
subjected only once to a wind of 60 mi/hr or more. Consequently, if the building
was assumed to have a 50-year life, designers might logically design it basically
for a 60-mi/hr wind, with a safety factor included in the design to protect against
low-probability faster winds. Mean recurrence intervals are the basis for minimum
design loads for high winds, snowfall, and earthquake in many building codes.
3.1.2 Safety Factors
Design of buildings for both normal and emergency conditions should always incorporate
a safety factor against failure. The magnitude of the safety factor should
be selected in accordance with the importance of a building, the extent of personal
injury or property loss that may result if a failure occurs, and the degree of uncertainty
as to the magnitude or nature of loads and the properties and behavior of
building components.
As usually incorporated in building codes, a safety factor for quantifiable system
variables is a number greater than unity. The factor may be applied in either of two
ways.
One way is to relate the maximum permissible load, or demand, on a system
under service conditions to design capacity. This system property is calculated by
PROTECTION AGAINST HAZARDS 3.3
dividing by the safety factor the ultimate capacity, or capacity at failure, for sustaining
that type of load. For example, suppose a structural member assigned a
safety factor of 2 can carry 1000 lb before failure occurs. The service load then is
1000/2 
 500 lb.
The second way in which codes apply safety factors is to relate the ultimate
capacity of a system, to a design load. This load is calculated by multiplying the
maximum load under service conditions by a safety factor, often referred to as a
load factor. For example, suppose a structural member assigned a load factor of 2
is required to carry a service load of 500 lb. Then, the member should be designed
to have a capacity for sustaining a design load of 500  2 
 1000 lb, without
failing.
While both methods achieve the objective of providing reserve capacity against
unexpected conditions, use of load factors offers the advantage of greater flexibility
in design of a system for a combination of different loadings, because a different
load factor can be assigned to each type of loading in accordance with probability
of occurrence and effects of other uncertainties.
Safety factors for various building systems are discussed in following sections
of the book. This section presents general design principles for protection of buildings
and occupants against high winds, earthquakes, water, fire, lightning, and intruders.
3.2 WIND PROTECTION
For practical design, wind and earthquakes may be treated as horizontal, or lateral,
loads. Although wind and seismic loads may have vertical components, these generally
are small and readily resisted by columns and bearing walls. Vertical earthquake
components can be important in the design of connections as in precast
concrete structures. Wind often generates significant uplift forces that require special
attention to vertical restraint and lateral support for members in reverse bending.
The variation with height of the magnitude of a wind load for a multistory
building differs from that of a seismic load. Nevertheless, provisions for resisting
either type of load are similar.
In areas where the probability of either a strong earthquake or a high wind is
small, it is nevertheless advisable to provide in buildings considerable resistance to
both types of load. In many cases, such resistance can be incorporated with little
or no increase in costs over designs that ignore either high wind or seismic resistance.
3.2.1 Wind Characteristics
Because wind loads are considered horizontal forces, wind pressure, for design
purposes, should be assumed to be applied to the gross area of the vertical projection
of that portion of the building above the average level of the adjoining ground.
Although the loads are assumed to be horizontal, they may nevertheless apply either
inward pressures or suctions to inclined and horizontal surfaces. In any case, wind
loads should be considered to act normal to the exposed building surfaces. Furthermore,
wind should be considered to be likely to come from any direction unless
3.4 SECTION THREE
it is known for a specific locality that extreme winds may come only from one
direction. As a consequence of this assumption, each wall of a rectangular building
should be considered in design to be subject to the maximum wind load.
Winds generally strike a building in gusts. Consequently, the building is subjected
to dynamic loading. Nevertheless, except for unusually tall or narrow buildings,
it is common practice to treat wind as a static loading, even though wind
pressures are not constant. High velocity winds can cause considerable vibrations,
particularly in lighter more flexible structures. Therefore, connections that tend to
loosen under heavy vibration should be avoided.
Estimation of design wind pressures is complicated by several factors. One factor
is the effect of natural and man-made obstructions along the ground. Another factor
is the variation of wind velocity with height above ground. Still another factor
complicating wind-pressure calculation is the effect of building or building component
shape or geometry (relationship of height or width to length) on pressures.
For important buildings, it is advisable to base design wind pressures on the results
of wind tunnel tests of a model of a building, neighboring buildings, and nearby
terrain.
3.2.2 Wind Pressures and Suctions
Pressures are considered positive when they tend to push a building component
toward the building interior. They are treated as negative for suctions or uplifts,
which tend to pull components outward.
Figure 3.1a illustrates wind flow over the sloping roof of a low building. For
roofs with inclines up to about 30
, the wind may create an uplift over the entire
roof (Fig. 3.1b). Also, as shown in Fig. 3.1b and c, the pressure on the external
face of the windward wall is positive and on the leeward wall, negative (suction).
If there are openings in the walls, the wind will impose internal pressures on the
walls, floors, and roof. The net pressure on any building component, therefore, is
the vector sum of the pressures acting on opposite faces of the component.
Because of the wind characteristics described in Art. 3.2.1 and the dependence
of wind pressures on building geometry, considerable uncertainty exists as to the
magnitude, direction, and duration of the maximum wind loads that may be imposed
on any portion of a specific building. Consequently, numerous assumptions, based
to some extent on statistical evidence, generally are made to determine design wind
loads for buildings. Minimum requirements for wind loads are presented in local
and model building codes.
Codes usually permit design wind loads to be determined either by mathematical
calculations in accordance with an analytical procedure specified in the code or by
wind-tunnel tests. Such tests are advisable for structures with unusual shapes, unusual
response to lateral loading, or location where channeling effects or buffeting
in the wake of upwind obstructions are likely to occur. Tests also are desirable
where wind records are not available or when more accurate information is needed.
Codes often require that the following conditions be met in execution of windtunnel
tests:
1. Air motion should be modeled to account for variation of wind speed with
elevation and the intensity of the longitudinal component of turbulence.
2. The geometric scale of the model should not be greater than 3 times that of the
longitudinal component of turbulence.
PROTECTION AGAINST HAZARDS 3.5
FIGURE 3.1 Effects of wind on a low building with pitched roof. (a) Airflow at the building. (b)
Wind applies inward pressure against the windward wall, suction on the leeward wall, and uplift
over all of a roof with slight slopes. (c) With a steep roof, inward pressure acts on the windward
side of the roof and uplift only on the leeward side. (d ) Pressure distribution along walls and roof
assumed for design of wind bracing of a building.
3. Instruments used should have response characteristics consistent with the required
accuracy of measurements to be recorded.
4. Account should be taken of the dependence of forces and pressures on the
Reynolds number of the air motion.
5. Tests for determining the dynamic response of a structure should be conducted
on a model scaled with respect to dimensions, mass distribution, stiffness, and
damping of the proposed structure.
In the analytical methods specified by building codes, maximum wind speeds
observed in a region are converted to velocity pressures. These are then multiplied
by various factors, to take into account building, site, and wind characteristics, to
obtain design static wind loads. Bear in mind, however, that, in general, code requirements
are applicable to pressures considerably smaller than those created by
tornadoes, which may have wind speeds up to 600 mi/hr. For more information on
wind loads, see Art. 5.1.2.
3.2.3 Failure Modes
Consideration of the ways in which winds may damage or destroy buildings suggests
provisions that should be made to prevent failures. Past experience with build3.6
SECTION THREE
FIGURE 3.2 Some ways in which wind may destroy a building: (a) overturning; (b) sliding
through the ground; (c) sliding off the foundations; (d ) excessive drift (sidesway).
ing damage by winds indicates buildings are likely to fail by overturning; sliding;
separation of components; excessive sway, or drift; or structural collapse. Lightweight
and open-sided structures may be subject to failure either partially, or
wholly, due to uplift.
Subjected to lateral forces W, and uplift U, a building may act as a rigid body
and overturn. It would tend to rotate about the edge of its base on the leeward side
(Fig. 3.2a). Overturning is resisted by the weight of the building M with a lever
arm e measured from the axis of rotation. Building codes usually require that
Me  1.5Wh (3.1)
where Wh is the overturning moment.
Resistance to overturning may be increased by securely anchoring buildings to
foundations. When this is done, the weight of earth atop the footings and pressing
against foundation walls may be included with the weight of the building.
In addition to the danger of overturning, there is the risk of a building being
pushed laterally by high winds. Sliding is resisted by friction at the base of the
footings and earth pressure against foundation walls (Fig. 3.2b). (Consideration
should be given to the possibility that soil that is highly resistant to building movement
when dry may become weak when wet.) Another danger is that a building
may be pushed by wind off the foundations (Fig. 3.2c). Consequently, to prevent
this, a building should be firmly anchored to its foundations.
Buildings also may be damaged by separation of other components from each
other. Therefore, it is essential that all connections between structural members and
between other components and their supports be capable of resisting design wind
loads. The possibility of separation of components by uplift or suction should not
be overlooked. Such pressures can slide a roof laterally or lift it from its supports,
tear roof coverings, rip off architectural projections, and suck out windows. Failure
of a roof diaphragm or bracing can result in failure of the entire structure.
Another hazard is drift (sway) or collapse without overturning or sliding. Excessive
drift when the wind rocks a building can cause occupant discomfort, induce
failure of structural components by fatigue, or lead to complete collapse of the
structure. The main resistance to drift usually is provided by structural components,
such as beams, columns, bracing, and walls that are also assigned the task of
supporting gravity loads. Some means must be provided to transmit wind or seismic
loads from these members to the foundations and thence to the ground. Otherwise,
the building may topple like a house of cards (Fig. 3.2d).
PROTECTION AGAINST HAZARDS 3.7
FIGURE 3.3 Some ways of restricting drift of a building: (a) shear wall; (b) pair of perpendicular
shear walls; (c) diagonal bracing; (d ) rigid frames.
Consideration should also be given to the potential for wind blown debris impacting
a structure and damaging critical lateral force resisting elements.
3.2.4 Limitation of Drift
There are no generally accepted criteria for maximum permissible lateral deflections
of buildings. Some building codes limit drift of any story of a building to a maximum
of 0.25% of the story height for wind and 0.50% of the story height for
earthquake loads. Drift of buildings of unreinforced masonry may be restricted to
half of the preceding values. The severer limitation of drift caused by wind loads
is applied principally because they are likely to occur more frequently than earthquakes
and will produce motions that will last much longer.
Three basic methods are commonly used, separately or in combination with each
other, to prevent collapse of buildings under lateral loads, limit drift and transmit
the loads to the foundations. These methods are illustrated in Fig. 3.3. One method
is to incorporate shear walls in a building. A shear wall is a vertical cantilever with
high resistance to horizontal loads parallel to its length (Fig. 3.3a). A pair of perpendicular
walls can resist wind from any direction, because any wind load can be
resolved into components in the planes of the walls (Fig. 3.3b). Diaphragms developed
from wall, floor, and roof sheating can function similar to solid shear walls
when properly attached and laterally supported.
A second method of providing resistance to lateral loads is to incorporate diagonal
structural members to carry lateral forces to the ground (Fig. 3.3c). (The
diagonals in Fig. 3.3c are called X bracing. Other types of bracing are illustrated
in Fig. 3.6.) Under lateral loads, the braced bays of a building act like cantilever
vertical trusses. The arrows in Fig. 3.3c show the paths taken by wind forces from
points of application to the ground. Note that the lateral loads impose downward
axial forces on the leeward columns, causing compression, and uplift on the windward
columns, causing tension.
A third method of providing resistance to lateral loads is to integrate the beams,
or girders, and columns into rigid frames (Fig. 3.3d). In a rigid frame, connections
between horizontal and vertical components prevent any change of angle between
the members under loads. (Drift can occur only if beams and columns bend.) Such
joints are often referred to as rigid, moment, or wind connections. They prevent
the frame from collapsing in the manner shown in Fig. 3.2d until the loads are so
3.8 SECTION THREE
FIGURE 3.4 Bracing of low buildings: (a) diagonal bracing in roofs and walls; (b) isolated pairs
of shear walls in a T pattern; (c) service-core enclosure used as shear walls; (d ) shear walls at ends
of building and rigid frames in the perpendicular direction.
large that the strength of the members and connections is exhausted. Note that in
a rigid frame, leeward columns are subjected to bending and axial compression and
windward columns are subjected to bending and axial tension.
In addition to using one or more of the preceding methods, designers can reduce
drift by proper shaping of buildings, arrangements of structural components, and
selection of members with adequate dimensions and geometry to withstand changes
in dimensions. Shape is important because low, squat buildings have less sidesway
than tall, narrow buildings, and buildings with circular or square floor plans have
less sidesway than narrow rectangular buildings with the same floor area per story.
Low Buildings. Figure 3.4a illustrates the application of diagonal bracing to a
low, industrial-type building. Bracing in the plane of the roof acts with the rafters,
ridge beam, and an edge roof beam as an inclined truss, which resists wind pressures
on the roof. Each truss transmits the wind load to the ends of the building.
Diagonals in the end walls transmit the load to the foundations. Wind pressure on
the end walls is resisted by diagonal bracing in the end panels of the longitudinal
walls. Wind pressure on the longitudinal walls, like wind on the roof, is transmitted
to the end walls.
For large buildings, rigid frames are both structurally efficient and economic.
Alternatively, for multistory buildings, shear walls may be used. Figure 3.4b
shows shear walls arranged in the shape of a T in plan, to resist wind from any
direction. Figure 3.4c illustrates the use of walls enclosing stairwells and elevator
shafts as shear walls. In apartment buildings, closet enclosures also can serve as
shear walls if designed for the purpose. Figure 3.4d shows shear walls placed at
the ends of a building to resist wind on its longitudinal walls. Wind on the shear
walls, in turn, is resisted by girders and columns in the longitudinal direction acting
as rigid frames. (See also Art. 5.12.)
Tall Buildings. For low buildings, structural members sized for gravity loads may
require little or no enlargement to also carry stresses due to lateral loads. For tall
buildings, however, structural members often have to be larger than sizes necessary
only for gravity loads. With increase in height, structural material requirements
increase rapidly. Therefore, for tall buildings, designers should select wind-bracing
systems with high structural efficiency to keep material requirements to a minimum.
PROTECTION AGAINST HAZARDS 3.9
FIGURE 3.5 Bracing of tall buildings: (a) diagonal bracing, rigid frames, or shear walls
placed in planes (bents) parallel to the lateral forces; (b) interior tube enclosing service core;
(c) perforated tube enclosing the building; (d ) tube within a tube; (e) bundled tubes.
While shear walls, diagonal bracing, and rigid frames can be used even for very
tall buildings, simple framing arrangements, such as planar systems, are not so
efficient in high structures as more sophisticated framing. For example, shear walls
or rigid frames in planes parallel to the lateral forces (Fig. 3.5a) may sway considerably
at the top if the building is tall (more than 30 stories) and slender. Resistance
to drift may be improved, however, if the shear walls are arranged in the form of
a tube within the building (Fig. 3.5b). (The space within the tube can be utilized
for stairs, elevators, and other services. This space is often referred to as the service
core.) The cantilevered tube is much more efficient in resisting lateral forces than
a series of planar, parallel shear walls containing the same amount of material.
Similarly, rigid frames and diagonal bracing may be arranged in the form of an
internal tube to improve resistance to lateral forces.
The larger the size of the cantilevered tube for a given height, the greater will
be its resistance to drift. For maximum efficiency of a simple tube, it can be arranged
to enclose the entire building (Fig. 3.5c) For the purpose, bracing or a rigid
frame may be erected behind or in the exterior wall, or the exterior wall itself may
be designed to act as a perforated tube. Floors act as horizontal diaphragms to brace
the tube and distribute the lateral forces to it.
For very tall buildings, when greater strength and drift resistance are needed
than can be provided by a simple tube, the tube around the exterior may be augmented
by an internal tube (Fig. 3.5d) or by other arrangements of interior bracing,
such as shear walls attached and perpendicular to the exterior tube. As an alternative,
a very tall building may be composed of several interconnected small tubes,
which act together in resisting lateral forces (Fig. 3.5e). Known as bundled tubes,
this type of framing offers greater flexibility in floor-area reduction at various levels
than a tube-within-tube type, because the tubes in a bundle can differ in height.
Diagonal bracing is more efficient in resisting drift than the other methods,
because the structural members carry the loads to the foundations as axial forces,
as shown in Fig. 3.3c, rather than as a combination of bending, shear, and axial
3.10 SECTION THREE
FIGURE 3.6 Some types of diagonal bracing: (a) X bracing in an interior bent; (b)
single diagonal; (c) K bracing; (d ) V bracing; (e) inverted V bracing; (?) horizontal
trusses at the roof and intermediate levels to restrict drift; (g) X bracing on the exterior
of a building.
forces. Generally, the bracing is arranged to form trusses composed of triangular
configurations, because of the stability of such arrangements. The joints between
members comprising a triangle cannot move relative to each other unless the length
of the members changes. Figure 3.6a illustrates the use of X bracing in the center
bay of a multistory building to form a vertical cantilever truss to resist lateral forces.
Other forms of bracing, however, may be used as an alternative to reduce material
requirements or to provide more space for wall penetrations, such as doors
and windows. Figure 3.6b shows how a single diagonal can be used in the center
bay to form a vertical truss. In large bays, however, the length of the diagonal may
become too long for structural efficiency. Hence, two or more diagonals may be
inserted in the bay instead, as shown in Fig. 3.6c to e. The type of bracing in Fig.
3.6c is known as K bracing; that in Fig. 3.6d, as V bracing; and that in Fig. 3.6e,
as inverted V bracing. The V type, however, has the disadvantage of restricting
deflection of the beams to which the diagonals are attached and thus compelling
the diagonals to carry gravity loads applied to the beams.
The bracing shown in Fig. 3.6a to e has the disadvantage of obstructing the bay
and interfering with placement of walls, doors, passageways, and, for bracing along
the building exterior, placement of windows. Accordingly, the inverted V type often
is converted to knee bracing, short diagonals placed near beam-to-column joints.
When knee bracing also is architecturally objectionable because of interference with
room arrangements, an alternative form of wind bracing, such as rigid frames or
shear walls, has to be adopted.
Trusses also can be placed horizontally to stiffen buildings for less drift. For
example, Fig. 3.6? shows a building with wind bracing provided basically by an
internal vertical cantilever tube. A set of horizontal trusses at the roof and a similar
set at an intermediate level tie the tube to the exterior columns. The trusses reduce
the drift at the top of the building by utilizing bending resistance of the columns.
A belt of horizontal trusses around the building exterior at the roof and the intermediate
level also helps resist drift of the building by utilizing bending resistance
of the exterior columns.
When not considered architecturally objectionable, diagonal bracing may be
placed on the building exterior to form a braced tube. The bracing may also serve
PROTECTION AGAINST HAZARDS 3.11
as columns to transmit floor and roof loads to the ground. Figure 3.6g shows how
multistory X bracing has been used to create a braced tube for a skyscraper.
See also Arts. 3.3.5, 5.18–19, and Secs. 7 through 10.
(Council on Tall Buildings and Urban Habitat, ‘‘Planning and Design of Tall
Buildings,’’ Vols. SC, SB, and CB, American Society of Civil Engineers, New York;
E. Simiu and R. H. Scanlon, ‘‘Wind Effects on Structures,’’ John Wiley & Sons,
Inc., New York; Minimum Design Loads for Tall Buildings and Other Structures
ANSI/ASCE 7-98, American Society of Civil Engineers, New York.)
3.3 PROTECTION AGAINST EARTHQUAKES
Buildings should be designed to withstand minor earthquakes without damage, because
they may occur almost everywhere. For major earthquakes, it may not be
economical to prevent all damage but collapse should be precluded.
Because an earthquake and a high wind are not likely to occur simultaneously,
building codes usually do not require that buildings be designed for a combination
of large seismic and wind loads. Thus, designers may assume that the full strength
of wind bracing is also available to resist drift caused by earthquakes.
The methods of protecting against high winds described in Art. 3.2.4 may also
be used for protecting against earthquakes. Shaking of buildings produced by temblors,
however, is likely to be much severer than that caused by winds. Consequently,
additional precautions must be taken to protect against earthquakes. Because
such protective measures will also be useful in resisting unexpectedly high
winds, such as those from tornadoes, however, it is advisable to apply aseismic
design principles to all buildings.
These principles require that collapse be avoided, oscillations of buildings
damped, and damage to both structural and nonstructural components minimized.
Nonstructural components are especially liable to damage from large drift. For
example, walls are likely to be stiffer than structural framing and therefore subject
to greater seismic forces. The walls, as a result, may crack or collapse. Also, they
may interfere with planned actions of structural components and cause additional
damage. Consequently, aseismic design of buildings should make allowance for
large drift, for example, by providing gaps between adjoining buildings and between
adjoining building components not required to be rigidly connected together and
by permitting sliding of such components. Thus, partitions and windows should be
free to move in their frames so that no damage will occur when an earthquake
wracks the frames. Heavy elements in buildings, such as water tanks, should be
firmly anchored to prevent them from damaging critical structural components.
Displacement of gas hot water heaters is a common cause of gas fires following
earthquakes.
3.3.1 Earthquake Characteristics
Earthquakes are produced by sudden release of tremendous amounts of energy
within the earth by a sudden movement at a point called the hypocenter. (The point
on the surface of the earth directly above the hypocenter is called the epicenter.)
The resulting shock sends out longitudinal, vertical, and transverse vibrations in all
3.12 SECTION THREE
directions, both through the earth’s crust and along the surface, and at different
velocities. Consequently, the shock waves arrive at distant points at different times.
As a result, the first sign of the advent of an earthquake at a distant point is
likely to be faint surface vibration of short duration as the first longitudinal waves
arrive at the point. Then, severe shocks of longer duration occur there, as other
waves arrive.
Movement at any point of the earth’s surface during a temblor may be recorded
with seismographs and plotted as seismograms, which show the variation with time
of displacements. Seismograms of past earthquakes indicate that seismic wave
forms are very complex.
Ground accelerations are also very important, because they are related to the
inertial forces that act on building components during an earthquake. Accelerations
are recorded in accelerograms, which are a plot of the variation with time of components
of the ground accelerations. Newton’s law relates acceleration to force:
W
F 
 Ma 
 a (3.2)
g
where F 
 force, lb
M 
 mass accelerated
a 
 acceleration of the mass, ft / s2
W 
 weight of building component accelerated, lb
g 
 acceleration due to gravity 
 32.2 ft / s2
3.3.2 Seismic Scales
For study of the behavior of buildings in past earthquakes and application of the
information collected to contemporary aseismic design, it is useful to have some
quantitative means for comparing earthquake severity. Two scales, the Modified
Mercalli and the Richter, are commonly used in the United States.
The Modified Mercalli scale compares earthquake intensity by assigning values
to human perceptions of the severity of oscillations and extent of damage to buildings.
The scale has 12 divisions. The severer the reported oscillations and damage,
the higher is the number assigned to the earthquake intensity (Table 3.1).
The Richter scale assigns numbers M to earthquake intensity in accordance with
the amount of energy released, as measured by the maximum amplitude of ground
motion:
100
M 
 log A  1.73 log (3.3)
D
where M 
 earthquake magnitude 100 km from epicenter
A 
 maximum amplitude of ground motion, micrometers
D 
 distance, km, from epicenter to point where A is measured
The larger the ground displacement at a given location, the higher the value of the
number assigned on the Richter scale. A Richter magnitude of 8 corresponds approximately
to a Modified Mercalli intensity of XI, and for smaller intensities,
Richter scale digits are about one unit less than corresponding Mercalli Roman
numerals.
PROTECTION AGAINST HAZARDS 3.13
TABLE 3.1 Modified Mercalli Intensity Scale (Abridged)
Intensity Definition
I Detected only by sensitive instruments.
II Felt by a few persons at rest, especially on upper floors. Delicate suspended
objects may swing.
III Felt noticeably indoors; not always recognized as an earthquake. Standing
automobiles rock slightly. Vibration similar to that caused by a passing
truck.
IV Felt indoors by many, outdoors by few; at night some awaken. Windows,
dishes, doors rattle. Standing automobiles rock noticeably.
V Felt by nearly everyone. Some breakage of plaster, windows, and dishes.
Tall objects disturbed.
VI Felt by all; many frightened and run outdoors. Falling plaster and damaged
chimneys.
VII Everyone runs outdoors. Damage of buildings negligible to slight, depending
on quality of construction. Noticeable to drivers of automobiles.
VIII Damage slight to considerable in substantial buildings, great in poorly
constructed structures. Walls thrown out of frames; walls, chimneys,
monuments fall; sand and mud ejected.
IX Considerable damage to well-designed structures; structures shifted off
foundations; buildings thrown out of plumb; underground pipes damaged.
Ground cracked conspicuously.
X Many masonry and frame structures destroyed; rails bent; water splashed
over banks; landslides; ground cracked.
XI Bridges destroyed; rails bent greatly; most masonry structures destroyed;
underground service pipes out of commission; landslides; broad fissures in
ground.
XII Total damage. Waves seen in surface level; lines of sight and level distorted;
objects thrown into air.
3.3.3 Effects of Ground Conditions
The amplitude of ground motion at a specific location during an earthquake depends
not only on distance from the epicenter but also on the types of soil at the location.
(Some soils suffer a loss of strength in an earthquake and allow large, uneven
foundation settlements, which cause severe property damage.) Ground motion usually
is much larger in alluvial soils (sands or clays deposited by flowing water) than
in rocky areas or diluvial soils (material deposited by glaciers). Reclaimed land or
earth fills generally undergo even greater displacements than alluvial soils. Consequently,
in selection of sites for structures in zones where severe earthquakes are
highly probable during the life of the structures, preference should be given to sites
with hard ground or rock to considerable depth, with sand and gravel as a less
desirable alternative and clay as a poor choice.
3.3.4 Seismic Forces
During an earthquake, the ground may move horizontally in any direction and up
and down, shifting the building foundations correspondingly. Inertial forces, or seis3.14
SECTION THREE
mic loads, on the building resist the displacements. Major damage usually is caused
by the horizontal components of these loads, inasmuch as vertical structural members
and connections generally have adequate strength to resist the vertical components.
Hence, as for wind loads, buildings should be designed to resist the maximum
probable horizontal component applied in any direction. Vertical components
of force must be considered in design of connections in high mass prefabricated
elements such as precast concrete slabs and girders.
Seismic forces vary rapidly with time. Therefore, they impose a dynamic loading
on buildings. Calculation of the building responses to such loading is complex (Art.
5.18.6) and is usually carried out only for important buildings that are very tall and
slender. For other types of buildings, building codes generally permit use of an
alternative static loading for which structural analysis is much simpler (Art. 5.19).
3.3.5 Aseismic Design
The basic methods for providing wind resistance—shear walls, diagonal bracing,
and rigid frames (Art. 3.2.4) are also suitable for resisting seismic loads. Ductile
rigid frames, however, are preferred because of large energy-absorbing capacity.
Building codes encourage their use by permitting them to be designed for smaller
seismic loads than those required for shear walls and diagonal bracing. (Ductility
is a property that enables a structural member to undergo considerable deformation
without failing. The more a member deforms, the more energy it can absorb and
therefore the greater is the resistance it can offer to dynamic loads.)
For tall, slender buildings, use of the basic methods alone in limiting drift to an
acceptable level may not be cost-effective. In such cases, improved response to the
dynamic loads may be improved by installation of heavy masses near the roof, with
their movements restricted by damping devices. Another alternative is installation
of energy-absorbing devices at key points in the structural framing, such as at the
bearings of bottom columns or the intersections of cross bracing.
Designers usually utilize floors and roofs, acting as horizontal diaphragms, to
transmit lateral forces to the resisting structural members. Horizontal bracing, however,
may be used instead. Where openings occur in floors and roofs, for example
for floors and elevators, structural framing should be provided around the openings
to bypass the lateral forces.
As for wind loads, the weight of the building and of earth adjoining foundations
are the only forces available to prevent the horizontal loads from overturning the
building. [See Eq. (3.1) in Art. 3.2.3.] Also, as for wind loads, the roof should be
firmly anchored to the superstructure framing, which, in turn, should be securely
attached to the foundations. Furthermore, individual footings, especially pile and
caisson footings, should be tied to each other to prevent relative movement.
Building codes often limit the drift per story under the equivalent static seismic
load (see Art. 5.19.3). Connections and intersections of curtain walls and partitions
with each other or with the structural framing should allow for a relative movement
of at least twice the calculated drift in each story. Such allowances for displacement
may be larger than those normally required for dimensional changes caused by
temperature variations.
See also Art. 5.19.
(N. M. Newmark and E. Rosenblueth, ‘‘Fundamentals of Earthquake Engineering,’’
and J. S. Stratta, ‘‘Manual of Seismic Design,’’ Prentice-Hall, Englewood
Cliffs, N.J.; ‘‘Standard Building Code,’’ Southern Building Code Congress International,
Inc., 900 Montclair Road, Birmingham, AL 35213-1206; ‘‘Uniform BuildPROTECTION
AGAINST HAZARDS 3.15
ing Code,’’ International Conference of Building Officials, Inc., 5360 South Workman
Mill Road, Whittier, CA 90601.)
3.4 PROTECTION AGAINST WATER
Whether thrust against and into a building by a flood, driven into the interior by a
heavy rain, leaking from plumbing, storm surge, or seeping through the exterior
enclosure, water can cause costly damage to a building. Consequently, designers
should protect buildings and their contents against water damage.
Protective measures may be divided into two classes: floodproofing and waterproofing.
Floodproofing provides protection against flowing surface water, commonly
caused by a river overflowing its banks. Waterproofing provides protection
against penetration through the exterior enclosure of buildings of groundwater, rainwater,
and melting snow. Buildings adjacent to large water bodies may also require
protection from undermining due to erosion and impact from storm driven waves.
3.4.1 Floodproofing
A flood occurs when a river rises above an elevation, called flood stage, and is not
prevented by enclosures from causing damage beyond its banks. Buildings constructed
in a flood plain, an area that can be inundated by a flood, should be
protected against a flood with a mean recurrence interval of 100 years. Maps
showing flood-hazard areas in the United States can be obtained from the Federal
Insurance Administrator, Department of Housing and Urban Development, who
administers the National Flood Insurance Program. Minimum criteria for floodproofing
are given in National Flood Insurance Rules and Regulations (Federal
Register, vol. 41, no. 207, Oct. 26, 1976).
Major objectives of floodproofing are to protect fully building and contents from
damage from a l00-year flood, reduce losses from more devastating floods, and
lower flood insurance premiums. Floodproofing, however, would be unnecessary if
buildings were not constructed in flood prone areas. Building in flood prone areas
should be avoided unless the risk to life is acceptable and construction there can
be economically and socially justified.
Some sites in flood prone areas possess some ground high enough to avoid flood
damage. If such sites must be used, buildings should be clustered on the high areas.
Where such areas are not available, it may be feasible to build up an earth fill, with
embankments protected against erosion by water, to raise structures above flood
levels. Preferably, such structures should not have basements, because they would
require costly protection against water pressure.
An alternative to elevating a building on fill is raising it on stilts (columns in
an unenclosed space). In that case, utilities and other services should be protected
against damage from flood flows. The space at ground level between the stilts may
be used for parking automobiles, if the risk of water damage to them is acceptable
or if they will be removed before flood waters reach the site.
Buildings that cannot be elevated above flood stage should be furnished with an
impervious exterior. Windows should be above flood stage, and doors should seal
tightly against their frames. Doors and other openings may also be protected with
a flood shield, such as a wall. Openings in the wall for access to the building may
3.16 SECTION THREE
be protected with a movable flood shield, which for normal conditions can be stored
out of sight and then positioned in the wall opening when a flood is imminent.
To prevent water damage to essential services for buildings in flood plains,
important mechanical and electrical equipment should be located above flood level.
Also, auxiliary electric generators to provide some emergency power are desirable.
In addition, pumps should be installed to eject water that leaks into the building.
Furthermore, unless a building is to be evacuated in case of flood, an emergency
water supply should be stored in a tank above flood level, and sewerage should be
provided with cutoff valves to prevent backflow.
3.4.2 Waterproofing*
In addition to protecting buildings against floods, designers also should adopt measures
that prevent groundwater, rainwater, snow, or melted snow from penetrating
into the interior through the exterior enclosure. Water may leak through cracks,
expansion joints or other openings in walls and roofs, or through cracks around
windows and doors. Also, water may seep through solid but porous exterior materials,
such as masonry. Leakage generally may be prevented by use of weatherstripping
around windows and doors, impervious waterstops in joints, or calking of
cracks and other openings. Methods of preventing seepage, however, depend on the
types of materials used in the exterior enclosure.
Definitions of Terms Related to Water Resistance
Permeability. Quality or state of permitting passage of water and water vapor
into, through, and from pores and interstices, without causing rupture or displacement.
Terms used in this section to describe the permeability of materials, coatings, structural
elements, and structures follow in decreasing order of permeability:
Pervious or Leaky. Cracks, crevices, leaks, or holes larger than capillary pores,
which permit a flow or leakage of water, are present. The material may or may
not contain capillary pores.
Water-resistant. Capillary pores exist that permit passage of water and water
vapor, but there are few or no openings larger than capillaries that permit leakage
of significant amounts of water.
Water-repellent. Not ‘‘wetted’’ by water; hence, not capable of transmitting water
by capillary forces alone. However, the material may allow transmission of water
under pressure and may be permeable to water vapor.
Waterproof. No openings are present that permit leakage or passage of water and
water vapor; the material is impervious to water and water vapor, whether under
pressure or not.
These terms also describe the permeability of a surface coating or a treatment
against water penetration, and they refer to the permeability of materials, structural
members, and structures whether or not they have been coated or treated.
*Excerpted with minor revisions from Sec. 12 of the third edition of this handbook, authored by Cyrus
C. Fishburn, formerly with the Division of Building Technology, National Bureau of Standards.
PROTECTION AGAINST HAZARDS 3.17
Permeability of Concrete and Masonry. Concrete contains many interconnected
voids and openings of various sizes and shapes, most of which are of capillary
dimensions. If the larger voids and openings are few in number and not directly
connected with each other, there will be little or no water penetration by leakage
and the concrete may be said to be water-resistant.
Concrete in contact with water not under pressure ordinarily will absorb it. The
water is drawn into the concrete by the surface tension of the liquid in the wetted
capillaries.
Water-resistant concrete for buildings should be a properly cured, dense, rich
concrete containing durable, well-graded aggregate. The water content of the concrete
mix should be as low as is compatible with workability and ease of placing
and handling. Resistance of concrete to penetration of water may be improved,
however, by incorporation of a water-repellent admixture in the mix during manufacture.
(See also Art. 9.9.)
Water-repellent concrete is permeable to water vapor. If a vapor-pressure gradient
is present, moisture may penetrate from the exposed face to an inner face.
The concrete is not made waterproof (in the full meaning of the term) by the use
of an integral water repellent. Note also that water repellents may not make concrete
impermeable to penetration of water under pressure. They may, however, reduce
absorption of water by the concrete.
Most masonry units also will absorb water. Some are highly pervious under
pressure. The mortar commonly used in masonry will absorb water too but usually
contains few openings permitting leakage.
Masonry walls may leak at the joints between the mortar and the units, however.
Except in single-leaf walls of highly pervious units, leakage at the joints results
from failure to fill them with mortar and poor bond between the masonry unit and
mortar. As with concrete, rate of capillary penetration through masonry walls is
small compared with the possible rate of leakage.
Capillary penetration of moisture through above-grade walls that resist leakage
of wind-driven rain is usually of minor importance. Such penetration of moisture
into well-ventilated subgrade structures may also be of minor importance if the
moisture is readily evaporated. However, long-continued capillary penetration into
some deep, confined subgrade interiors frequently results in an increase in relative
humidity, a decrease in evaporation rate, and objectionable dampness.
3.4.3 Roof Drainage
Many roof failures have been caused by excessive water accumulation. In most
cases, the overload that caused failure was not anticipated in design of those roofs,
because the designers expected rainwater to run off the roof. But because of inadequate
drainage, the water ponded instead.
On flat roofs, ponding of rainwater causes structural members to deflect. The
resulting bowing of the roof surface permits more rainwater to accumulate, and the
additional weight of this water causes additional bowing and collection of even
more water. This process can lead to roof collapse. Similar conditions also can
occur in the valleys of sloping roofs.
To avoid water accumulation, roofs should be sloped toward drains and pipes
that have adequate capacity to conduct water away from the roofs, in accordance
with local plumbing codes. Minimum roof slope for drainage should be at least 1?4
in / ft, but larger slopes are advisable.
3.18 SECTION THREE
The primary drainage system should be supplemented by a secondary drainage
system at a higher level to prevent ponding on the roof above that level. The
overflow drains should be at least as large as the primary drains and should be
connected to drain pipes independent of the primary system or scuppers through
the parapets. The roof and its structural members should be capable of sustaining
the weight of all rainwater that could accumulate on the roof if part or all of the
primary drainage system should become blocked.
3.4.4 Drainage for Subgrade Structures
Subgrade structures located above groundwater level in drained soil may be in
contact with water and wet soil for periods of indefinite duration after longcontinued
rains and spring thaws. Drainage of surface and subsurface water, however,
may greatly reduce the time during which the walls and floor of a structure
are subjected to water, may prevent leakage through openings resulting from poor
workmanship and reduce the capillary penetration of water into the structure. If
subsurface water cannot be removed by drainage, the structure must be made
waterproof or highly water-resistant.
Surface water may be diverted by grading the ground surface away from the
walls and by carrying the runoff from roofs away from the building. The slope of
the ground surface should be at least 1?4 in / ft for a minimum distance of 10 ft from
the walls. Runoff from high ground adjacent to the structure should also be diverted.
FIGURE 3.7 Drainage at the bottom of a
foundation wall.
Proper subsurface drainage of ground
water away from basement walls and
floors requires a drain of adequate size,
sloped continuously, and, where necessary,
carried around corners of the building
without breaking continuity. The
drain should lead to a storm sewer or to
a lower elevation that will not be
flooded and permit water to back up in
the drain.
Drain tile should have a minimum diameter
of 6 in and should be laid in
gravel or other kind of porous bed at
least 6 in below the basement floor. The
open joints between the tile should be
covered with a wire screen or building
paper to prevent clogging of the drain
with fine material. Gravel should be laid above the tile, filling the excavation to an
elevation well above the top of the footing. Where considerable water may be
expected in heavy soil, the gravel fill should be carried up nearly to the ground
surface and should extend from the wall a distance of at least 12 in (Fig. 3.7).
3.4.5 Concrete Floors at Grade
Floors on ground should preferably not be constructed in low-lying areas that are
wet from ground water or periodically flooded with surface water. The ground
PROTECTION AGAINST HAZARDS 3.19
FIGURE 3.8 Insulated concrete slab on ground with membrane dampproofing.
should slope away from the floor. The level of the finished floor should be at least
6 in above grade. Further protection against ground moisture and possible flooding
of the slab from heavy surface runoffs may be obtained with subsurface drains
located at the elevation of the wall footings.
All organic material and topsoil of poor bearing value should be removed in
preparation of the subgrade, which should have a uniform bearing value to prevent
unequal settlement of the floor slab. Backfill should be tamped and compacted in
layers not exceeding 6 in in depth.
Where the subgrade is well-drained, as where subsurface drains are used or are
unnecessary, floor slabs of residences should be insulated either by placing a granular
fill over the subgrade or by use of a lightweight-aggregate concrete slab covered
with a wearing surface of gravel or stone concrete. The granular fill, if used, should
have a minimum thickness of 5 in and may consist of coarse slag, gravel, or crushed
stone, preferably of 1-in minimum size. A layer of 3-, 4-, or 6-in-thick hollow
masonry building units is preferred to gravel fill for insulation and provides a
smooth, level bearing surface.
Moisture from the ground may be absorbed by the floor slab. Floor coverings,
such as oil-base paints, linoleum, and asphalt tile, acting as a vapor barrier over
the slab, may be damaged as a result. If such floor coverings are used and where
a complete barrier against the rise of moisture from the ground is desired, a twoply
bituminous membrane or other waterproofing material should be placed beneath
the slab and over the insulating concrete or granular fill (Fig. 3.8). The top of the
lightweight-aggregate concrete, if used, should be troweled or brushed to a smooth
level surface for the membrane. The top of the granular fill should be covered with
a grout coating, similarly finished. (The grout coat, 1?2 to 1 in thick, may consist
of a 1:3 or a 1:4 mix by volume of portland cement and sand. Some 3?8- or 1?2-in
maximum-sized coarse aggregate may be added to the grout if desired.) After the
top surface of the insulating concrete or grout coating has hardened and dried, it
should be mopped with hot asphalt or coal-tar pitch and covered before cooling
with a lapped layer of 15-lb bituminous saturated felt. The first ply of felt then
should be mopped with hot bitumen and a second ply of felt laid and mopped on
its top surface. Care should be exercised not to puncture the membrane, which
3.20 SECTION THREE
should preferably be covered with a coating of mortar, immediately after its completion.
If properly laid and protected from damage, the membrane may be considered
to be a waterproof barrier.
Where there is no possible danger of water reaching the underside of the floor,
a single layer of 55-lb smooth-surface asphalt roll roofing or an equivalent waterproofing
membrane may be used under the floor. Joints between the sheets should
be lapped and sealed with bituminous mastic. Great care should be taken to prevent
puncturing of the roofing layer during concreting operations. When so installed,
asphalt roll roofing provides a low-cost and adequate barrier against the movement
of excessive amounts of moisture by capillarity and in the form of vapor. In areas
with year-round warm climates, insulation can be omitted.
(‘‘A Guide to the Use of Waterproofing, Dampproofing, Protective and Decorative
Barrier Systems for Concrete,’’ ACI 515.1R, American Concrete Institute.)
3.4.6 Basement Floors
Where a basement is to be used in drained soils as living quarters or for the storage
of things that may be damaged by moisture, the floor should be insulated and should
preferably contain the membrane waterproofing described in Art. 3.4.5 In general
the design and construction of such basement floors are similar to those of floors
on ground.
If passage of moisture from the ground into the basement is unimportant or can
be satisfactorily controlled by air conditioning or ventilation, the waterproof
membrane need not be used. The concrete slab should have a minimum thickness
of 4 in and need not be reinforced, but should be laid on a granular fill or other
insulation placed on a carefully prepared subgrade. The concrete in the slab should
have a minimum compressive strength of 2000 psi and may contain an integral
water repellent.
A basement floor below the water table will be subjected to hydrostatic upward
pressures. The floor should be made heavy enough to counteract the uplift.
An appropriate sealant in the joint between the basement walls and a floor over
drained soil will prevent leakage into the basement of any water that may occasionally
accumulate under the slab. Space for the joint may be provided by use of
beveled siding strips, which are removed after the concrete has hardened. After the
slab is properly cured, it and the wall surface should be in as dry a condition as is
practicable before the joint is filled to ensure a good bond of the filler and to reduce
the effects of slab shrinkage on the permeability of the joint.
(‘‘Guide to Joint Sealants for Concrete Structures,’’ ACI 504R, American Concrete
Institute.)
3.4.7 Monolithic Concrete Basement Walls
These should have a minimum thickness of 6 in. Where insulation is desirable, as
where the basement is used for living quarters, lightweight aggregate, such as those
prepared by calcining or sintering blast-furnace slag, clay, or shale that meet the
requirements of ASTM Standard C330 may be used in the concrete. The concrete
should have a minimum compressive strength of 2000 psi.
For the forms in which concrete for basement walls is cast, form ties of an
internal-disconnecting type are preferable to twisted-wire ties. Entrance holes for
the form ties should be sealed with mortar after the forms are removed. If twistedPROTECTION
AGAINST HAZARDS 3.21
wire ties are used, they should be cut a minimum distance of 11?2 in inside the face
of the wall and the holes filled with mortar.
The resistance of the wall to capillary penetration of water in temporary contact
with the wall face may be increased by the use of a water-repellent admixture. The
water repellent may also be used in the concrete at and just above grade to reduce
the capillary rise of moisture from the ground into the superstructure wails.
Where it is desirable to make the wall resistant to passage of water vapor from
the outside and to increase its resistance to capillary penetration of water, the
exterior wall face may be treated with an impervious coating. The continuity and
the resultant effectiveness in resisting moisture penetration of such a coating is
dependent on the smoothness and regularity of the concrete surface and on the skill
and technique used in applying the coating to the dry concrete surface. Some
bituminous coatings that may be used are listed below in increasing order of their
resistance to moisture penetration:
Spray- or brush-applied asphalt emulsions
Spray- or brush-applied bituminous cutbacks
Trowel coatings of bitumen with organic solvent, applied cold
Hot-applied asphalt or coal-tar pitch, preceded by application of a suitable primer
Cementitious brush-applied paints and grouts and trowel coatings of a mortar
increase moisture resistance of monolithic concrete, especially if such coatings contain
a water repellent. However, in properly drained soil, such coatings may not be
justified unless needed to prevent leakage of water through openings in the concrete
resulting from segregation of the aggregate and bad workmanship in casting the
walls. The trowel coatings may also be used to level irregular wall surfaces in
preparation for the application of a bituminous coating. For information on other
waterproofing materials, see ‘‘A Guide to the Use of Waterproofing, Dampproofing,
Protective and Decorative Barrier Systems for Concrete,’’ ACI 515.1R, American
Concrete Institute.
3.4.8 Unit-Masonry Basement Walls
Water-resistant basement walls of masonry units should be carefully constructed of
durable materials to prevent leakage and damage due to frost and other weathering
exposure. Frost action is most severe at the grade line and may result in structural
damage and leakage of water. Where wetting followed by sudden severe freezing
may occur, the masonry units should meet the requirements of the following specifications:
Building brick (solid masonry units made from clay or shale), ASTM Standard
C62, Grade SW
Facing brick (solid masonry units made from clay or shale), ASTM Standard
C216, Grade SW
Structural clay load-bearing wall tile, ASTM Standard C34, Grade LBX
Hollow load-bearing concrete masonry units, ASTM Standard C90, Grade N
For such exposure conditions, the mortar should be a Type S mortar (Table 4.4)
having a minimum compressive strength of 1800 psi when tested in accordance
with the requirements of ASTM Standard C270. For milder freezing exposures and
3.22 SECTION THREE
where the walls may be subjected to some lateral pressure from the earth, the mortar
should have a minimum compressive strength of 1000 psi.
Leakage through an expansion joint in a concrete or masonry foundation wall
may be prevented by insertion of a waterstop in the joint. Waterstops should be of
the bellows type, made of l6-oz copper sheet, which should extend a minimum
distance of 6 in on either side of the joint. The sheet should be embedded between
wythes of masonry units or faced with a 2-in-thick cover of mortar reinforced with
welded-wire fabric. The outside face of the expansion joint should be filled flush
with the wall face with a joint sealant, as recommended in ACI 504R.
Rise of moisture, by capillarity, from the ground into the superstructure walls
may be greatly retarded by use of an integral water-repellent admixture in the
mortar. The water-repellent mortar may be used in several courses of masonry
located at and just above grade.
The use of shotcrete or trowel-applied mortar coatings, 3?4 in or more in thickness,
to the outside faces of both monolithic concrete and unit-masonry walls
greatly increases their resistance to penetration of moisture. Such plaster coatings
cover and seal construction joints and other vulnerable joints in the walls against
leakage. When applied in a thickness of 2 in or more, they may be reinforced with
welded-wire fabric to reduce the incidence of large shrinkage cracks in the coating.
However, the cementitious coatings do not protect the walls against leakage if the
walls, and subsequently the coatings, are badly cracked as a result of unequal
foundation settlement, excessive drying shrinkage, and thermal changes. (‘‘Guide
to Shotcrete,’’ ACI 506, American Concrete Institute.)
Two trowel coats of a mortar containing 1 part portland cement to 3 parts sand
by volume should be applied to the outside faces of basement walls built of hollow
masonry units. One trowel coat may suffice on the outside of all-brick and of brickfaced
walls.
The wall surface and the top of the wall footing should be cleansed of dirt and
soil, and the masonry should be thoroughly wetted with water. While still damp,
the surface should be covered with a thin scrubbed-on coating of portland cement
tempered to the consistency of thick cream. Before this prepared surface has dried,
a 3?8-in-thick trowel-applied coating of mortar should be placed on the wall and
over the top of the footing; a fillet of mortar may be placed at the juncture of the
wall and footing.
Where a second coat of mortar is to be applied, as on hollow masonry units,
the first coat should be scratched to provide a rough bonding surface. The second
coat should be applied at least 1 day after the first, and the coatings should be
cured and kept damp by wetting for at least 3 days. A water-repellent admixture
in the mortar used for the second or finish coat will reduce the rate of capillary
penetration of water through the walls. If a bituminous coating is not to be used,
the mortar coating should be kept damp until the backfill is placed.
Thin, impervious coatings may be applied to the plaster if resistance to penetration
of water vapor is desired. (See ACI 515.1R.) The plaster should be dry and
clean before the impervious coating is applied over the surfaces of the wall and the
top of the footing.
3.4.9 Impervious Membranes
These are waterproof barriers providing protection against penetration of water under
hydrostatic pressure and water vapor. To resist hydrostatic pressure, a membrane
should be made continuous in the walls and floor of a basement. It also should be
PROTECTION AGAINST HAZARDS 3.23
protected from damage during building operations and should be laid by experienced
workers under competent supervision. It usually consists of three or more
alternate layers of hot, mopped-on asphalt or coal-tar pitch and plies of treated glass
fabric, or bituminous saturated cotton or woven burlap fabric. The number of moppings
exceeds the number of plies by one.
Alternatives are cold-applied bituminous systems, liquid-applied membranes,
and sheet-applied membranes, similar to those used for roofing. In installation,
manufacturers’ recommendations should be carefully followed. See also ACI
515.1R and ‘‘The NRCA Waterproofing Manual,’’ National Roofing Manufacturers
Association.
Bituminous saturated cotton fabric is stronger and is more extensible than bituminous
saturated felt but is more expensive and more difficult to lay. At least one
or two of the plies in a membrane should be of saturated cotton fabric to provide
strength, ductility, and extensibility to the membrane. Where vibration, temperature
changes, and other conditions conducive to displacement and volume changes in
the basement are to be expected, the relative number of fabric plies may be increased.
The minimum weight of bituminous saturated felt used in a membrane should
be 13 lb per 100 ft2. The minimum weight of bituminous saturated woven cotton
fabric should be 10 oz/yd2.
Although a membrane is held rigidly in place, it is advisable to apply a suitable
primer over the surfaces receiving the membrane and to aid in the application of
the first mopped-on coat of hot asphalt or coal-tar pitch.
Materials used in the hot-applied system should meet the requirements of the
following current ASTM standards:
Creosote primer for coal-tar pitch—D43
Primer for asphalt—D41
Coal-tar pitch—D450, Type II
Asphalt—D449, Type A
Cotton fabric, bituminous saturated—D173
Woven burlap fabric, bituminous saturated—D1327
Treated glass fabric—D1668
Coal-tar saturated felt—D227
Asphalt saturated organic felt—D226
The number of plies of saturated felt or fabric should be increased with increase
in the hydrostatic head to which the membrane is to be subjected. Five plies is the
maximum commonly used in building construction, but 10 or more plies have been
recommended for pressure heads of 35 ft or greater. The thickness of the membrane
crossing the wall footings at the base of the wall should be no greater than necessary,
to keep very small the possible settlement of the wall due to plastic flow in
the membrane materials.
The amount of primer to be used may be about 1 gal per 100 ft2. The amount
of bitumen per mopping should be at least 41?2 gal per 100 ft2. The thickness of
the first and last moppings is usually slightly greater than the thickness of the
moppings between the plies.
The surfaces to which the membrane is to be applied should be smooth, dry,
and at a temperature above freezing. Air temperature should be not less than 50
F.
The temperature of coal-tar pitch should not exceed 300
F and asphalt, 350
F.
3.24 SECTION THREE
If the concrete and masonry surfaces are not sufficiently dry, they will not readily
absorb the priming coat, and the first mopping of bitumen will be accompanied by
bubbling and escape of steam. Should this occur, application of the membrane
should be stopped and the bitumen already applied to damp surfaces should be
removed.
The membrane should be built up ply by ply, the strips of fabric or felt being
laid immediately after each bed has been hot-mopped. The lap of succeeding plies
or strips over each other depends on the width of the roll and the number of plies.
In any membrane there should be a lap of the top or final ply over the first, initial
ply of at least 2 in. End laps should be staggered at least 24 in, and the laps between
succeeding rolls should be at least 12 in.
For floors, the membrane should be placed over a concrete base or subfloor
whose top surface is troweled smooth and which is level with the tops of the wall
footings. The membrane should be started at the outside face of one wall and extend
over the wall footing, which may be keyed. It should cover the floor and tops of
other footings to the outside faces of the other walls, forming a continuous horizontal
waterproof barrier. The plies should project from the edges of the floor
membrane and lap into the wall membrane.
The loose ends of felt and fabric must be protected; one method is to fasten
them to a temporary vertical wood form about 2 ft high, placed just outside the
wall face. Immediately after the floor membrane has been laid, its surface should
be protected and covered with a layer of portland-cement concrete, at least 2 in
thick.
For walls, the installed membrane should be protected against damage and held
in position by protection board or a facing of brick, tile, or concrete block. A brick
facing should have a minimum thickness of 21?2 in. Facings of asphalt plank, asphalt
block, or mortar require considerable support from the membrane itself and give
protection against abrasion of the membrane from lateral forces only. Protection
against downward forces such as may be produced by settlement of the backfill is
given only by the self-supporting masonry walls.
The kind of protective facing may have some bearing on the method of constructing
the membrane. The membrane may be applied to the exterior face of the
wall after its construction, or it may be applied to the back of the protective facing
before the main wall is built. The first of these methods is known as the outside
application; the second is known as the inside application.
For the inside application, a protective facing of considerable stiffness against
lateral forces must be built, especially if the wall and its membrane are to be used
as a form for the casting of a main wall of monolithic concrete. The inner face of
the protecting wall must be smooth or else leveled with mortar to provide a suitable
base for the membrane. The completed membrane should be covered with a 3?8-inthick
layer of mortar to protect it from damage during construction of the main
wall.
Application of wall membranes should he started at the bottom of one end of
the wall and the strips of fabric or felt laid vertically. Preparation of the surfaces
and laying of the membrane proceed much as they do with floor membranes. The
surfaces to which the membrane is attached must be dry and smooth, which may
require that the faces of masonry walls be leveled with a thin coat of grout or
mortar. The plies of the wall membrane should be lapped into those of the floor
membrane.
If the outside method of application is used and the membrane is faced with
masonry, the narrow space between the units and the membrane should be filled
PROTECTION AGAINST HAZARDS 3.25
with mortar as the units are laid. The membrane may be terminated at the grade
line by a return into the superstructure wall facing.
Waterstops in joints in walls and floors containing a bituminous membrane
should be the metal-bellows type. The membrane should be placed on the exposed
face of the joint and it may project into the joint, following the general outline of
the bellows.
The protective facing for the membrane should be broken at the expansion joint
and the space between the membrane and the line of the facing filled with a joint
sealant, as recommended in ACI 504R.
Details at pipe sleeves running through the membrane must be carefully prepared.
The membrane should be reinforced with additional plies and may be calked
at the sleeve. Steam and hot-water lines should be insulated to prevent damage to
the membrane.
3.4.10 Above-Grade Walls
The rate of moisture penetration through capillaries in above-grade walls is low
and usually of minor importance. However, such walls should not permit leakage
of wind-driven rain through openings larger than those of capillary dimension.
Precast-concrete or metal panels are usually made of dense, highly waterresistant
materials. However, walls made of these panels are vulnerable to leakage
at the joints. In such construction, edges of the panels may be recessed and the
interior of vertical joints filled with grout or other sealant after the panels are
aligned.
Calking compound is commonly used as a facing for the joints. Experience has
shown that calking compounds often weather badly; their use as a joint facing
creates a maintenance problem and does not prevent leakage of wind-driven rain
after a few years’ exposure.
The amount of movement to be expected in the vertical joints between panels
is a function of the panel dimensions and the seasonal fluctuation in temperature
and, for concrete, the moisture content of the concrete. For panel construction, it
may be more feasible to use an interlocking water-resistant joint. For concrete, the
joint may be faced on the weather side with mortar and backed with either a
compressible premolded strip or calking. See ACI 504R.
Brick walls 4 in or more in thickness can be made highly water-resistant. The
measures that need to be taken to ensure there will be no leakage of wind-driven
rain through brick facings are not extensive and do not require the use of materials
other than those commonly used in masonry walls. The main factors that need to
be controlled are the rate of suction of the brick at the time of laying and filling
of all joints with mortar (Art. 11.7).
In general, the greater the number of brick leaves, or wythes, in a wall, the more
water-resistant the wall.
Walls of hollow masonry units are usually highly permeable, and brick-faced
walls backed with hollow masonry units are greatly dependent upon the water
resistance of the brick facing to prevent leakage of wind-driven rain. For exterior
concrete masonry walls without facings of brick, protection against leakage may
be obtained by facing the walls with a cementitious coating of paint, stucco, or
shotcrete.
For wall of rough-textured units, a portland cement–sand grout provides a highly
water-resistant coating. The cement may be either white or gray.
3.26 SECTION THREE
Factory-made portland-cement paints containing a minimum of 65%, and preferably
80%, portland cement may also be used as a base coat on concrete masonry.
Application of the paint should conform with the requirements of ACI 515.1R. The
paints, stuccos, and shotcrete should be applied to dampened surfaces. Shotcrete
should conform with the requirements of ACI 506R.
Cavity walls, particularly brick-faced cavity walls, may be made highly resistant
to leakage through the wall facing. However, as usually constructed, facings are
highly permeable, and the leakage is trapped in the cavity and diverted to the
outside of the wall through conveniently located weep holes. This requires that the
inner tier of the cavity be protected against the leakage by adequate flashings, and
weep holes should be placed at the bottom of the cavities and over all wall openings.
The weep holes may be formed by the use of sash-cord head joints or 3?8-indiameter
rubber tubing, withdrawn after the wall is completed.
Flashings should preferably be hot-rolled copper sheet of 10-oz minimum
weight. They should be lapped at the ends and sealed either by solder or with
bituminous plastic cement. Mortar should not be permitted to drop into the flashings
and prevent the weep holes from functioning.
Prevention of Cracking. Shrinkage of concrete masonry because of drying and a
drop in temperature may result in cracking of a wall and its cementitious facing.
Such cracks readily permit leakage of wind-driven rain. The chief factor reducing
incidence of shrinkage cracking is the use of dry block. When laid in the wall, the
block should have a low moisture content, preferably one that is in equilibrium
with the driest condition to which the wall will be exposed.
The block should also have a low potential shrinkage. See moisture-content
requirements in ASTM C90 and method of test for drying shrinkage of concrete
block in ASTM C426.
Formation of large shrinkage cracks may be controlled by use of steel reinforcement
in the horizontal joints of the masonry and above and below wall openings.
Where there may be a considerable seasonal fluctuation in temperature and moisture
content of the wall, high-yield-strength, deformed-wire joint reinforcement should
be placed in at least 50% of all bed joints in the wall.
Use of control joints faced with calking compound has also been recommended
to control shrinkage cracking; however, this practice is marked by frequent failures
to keep the joints sealed against leakage of rain. Steel joint reinforcement strengthens
a concrete masonry wall, whereas control joints weaken it, and the calking in
the joints requires considerable maintenance.
Water-Resistant Surface Treatments for Above-Grade Walls. Experience has
shown that leakage of wind-driven rain through masonry walls, particularly those
of brick, ordinarily cannot be stopped by use of an inexpensive surface treatment
or coating that will not alter the appearance of the wall. Such protective devices
either have a low service life or fail to stop all leakage.
Both organic and cementitious pigmented coating materials, properly applied as
a continuous coating over the exposed face of the wall, do stop leakage. Many of
the organic pigmented coatings are vapor barriers and are therefore unsuitable for
use on the outside, ‘‘cold’’ face of most buildings. If vapor barriers are used on the
cold face of the wall, it is advisable to use a better vapor barrier on the warm face
to reduce condensation in the wall and behind the exterior coating.
Coatings for masonry may be divided into four groups, as follows: (1) colorless
coating materials; (2) cementitious coatings; (3) pigmented organic coatings; and
(4) bituminous coatings.
PROTECTION AGAINST HAZARDS 3.27
Colorless Coating Materials. The colorless ‘‘waterproofings’’ are often claimed
to stop leakage of wind-driven rain through permeable masonry walls. Solutions of
oils, paraffin wax, sodium silicate, chlorinated rubber, silicone resins, and salts of
fatty acids have been applied to highly permeable test walls and have been tested
at the National Institute of Standards and Technology under exposure conditions
simulating a wind-driven rain. Most of these solutions contained not more than
10% of solid matter. These treatments reduced the rate of leakage but did not stop
all leakage through the walls. The test data show that colorless coating materials
applied to permeable walls of brick or concrete masonry may not provide adequate
protection against leakage of wind-driven rain.
Solutions containing oils and waxes tended to seal the pores exposed in the faces
of the mortar joints and masonry units, thereby acting more or less as vapor barriers,
but did not seal the larger openings, particularly those in the joints.
Silicone water-repellent solutions greatly reduced leakage through the walls as
long as the treated wall faces remained water-repellent. After an exposure period
of 2 or 3 hr, the rate of leakage gradually increased as the water repellency of the
wall face diminished.
Coatings of the water-repellent, breather type, such as silicone and ‘‘soap’’
solutions, may be of value in reducing absorption of moisture into the wall surface.
They may be of special benefit in reducing the soiling and disfiguration of stucco
facings and light-colored masonry surfaces. They may be applied to precastconcrete
panels to reduce volume changes that may otherwise result from changes
in moisture content of the concretes. However, it should be noted that a waterrepellent
treatment applied to the surface may cause water, trapped in the masonry,
to evaporate beneath the surface instead of at the surface. If the masonry is not
water-resistant and contains a considerable amount of soluble salts, as evidenced
by efflorescence, application of a water repellent may cause salts to be deposited
beneath the surface, thereby causing spalling of the masonry. The water repellents
therefore should be applied only to walls having water-resistant joints. Furthermore,
application of a colorless material makes the treated face of the masonry waterrepellent
and may prevent the proper bonding of a cementitious coating that could
otherwise be used to stop leakage.
Cementitious Coatings. Coatings of portland-cement paints, grouts, and stuccos
and of pneumatically applied mortars are highly water-resistant. They are preferred
above all other types of surface coatings for use as water-resistant base coatings on
above-grade concrete masonry. They may also be applied to the exposed faces of
brick masonry walls that have not been built to be water-resistant.
The cementitious coatings absorb moisture and are of the breather type, permitting
passage of water vapor. Addition of water repellents to these coatings does
not greatly affect their water resistance but does reduce the soiling of the surface
from the absorption of dirt-laden water. If more than one coating is applied, as in
a two-coat paint or stucco facing job, the repellent is preferably added only to the
finish coat, thus avoiding the difficulty of bonding a cementitious coating to a waterrepellent
surface.
The technique used in applying the cementitious coatings is highly important.
The backing should be thoroughly dampened. Paints and grouts should be scrubbed
into place with stiff fiber brushes and the coatings should be properly cured by
wetting. Properly applied, the grouts are highly durable; some grout coatings applied
to concrete masonry test walls were found to be as water-resistant after 10
years out-of-doors exposure as when first applied to the walls.
Pigmented Organic Coatings. These include textured coatings, mastic coatings,
conventional paints, and aqueous dispersions. The thick-textured and mastic coatings
are usually spray-applied but may be applied by trowel. Conventional paints
3.28 SECTION THREE
and aqueous dispersions are usually applied by brush or spray. Most of these coatings
are vapor barriers but some textured coatings, conventional paints, and aqueous
dispersions are breathers. Except for the aqueous dispersions, all the coatings are
recommended for use with a primer.
Applied as a continuous coating, without pinholes, the pigmented organic coatings
are highly water-resistant. They are most effective when applied over a smooth
backing. When they are applied with paintbrush or spray by conventional methods
to rough-textured walls, it is difficult to level the surface and to obtain a continuous
water-resistant coating free from holes. A scrubbed-on cementitious grout used as
a base coat on such walls will prevent leakage through the masonry without the
use of a pigmented organic coating.
The pigmented organic coatings are highly decorative but may not be so waterresistant,
economical, or durable as the cementitious coatings.
Bituminous Coatings. Bituminous cutbacks, emulsions, and plastic cements are
usually vapor barriers and are sometimes applied as ‘‘dampproofers’’ on the inside
faces of masonry walls. Plaster is often applied directly over these coatings, the
bond of the plaster to the masonry being only of a mechanical nature. Tests show
that bituminous coatings applied to the inside faces of highly permeable masonry
walls, not plastered, will readily blister and permit leakage of water through the
coating. It is advisable not to depend on such coatings to prevent the leakage of
wind-driven rain unless they are incorporated in the masonry or held in place with
a rigid self-sustaining backing.
Even though the walls are resistant to wind-driven rain, but are treated on their
inner faces with a bituminous coating, water may be condensed on the warm side
of the coating and damage to the plaster may result, whether the walls are furred
or not. However, the bituminous coating may be of benefit as a vapor barrier in
furred walls, if no condensation occurs on the warm side.
See also Secs. 9 and 11.
(‘‘Admixtures for Concrete,’’ ACI 212.1R; ‘‘Guide for Use of Admixtures for
Concrete,’’ ACI 212.2R; ‘‘Guide to Joint Sealants for Concrete Structures,’’ ACI
504R; ‘‘Specification for Materials, Proportioning and Application of Shotcrete,’’
ACI 506.2; ‘‘A Guide to the Use of Waterproofing, Dampproofing, Protective and
Decorative Barrier Systems for Concrete,’’ ACI 515.1R; ‘‘Specification for Concrete
Masonry Construction,’’ ACI 531.1; ‘‘Polymers in Concrete,’’ ACI 548R; ‘‘Guide
for the Use of Polymers in Concrete,’’ ACI 548.1R, American Concrete Institute,
P.O. Box 19150, Redford Station, Detroit, MI 48219.)
3.5 PROTECTION AGAINST FIRE
There are two distinct aspects of fire protection: life safety and property protection.
Although providing for one aspect generally results in some protection for the other,
the two goals are not mutually inclusive. A program that provides for prompt notification
and evacuation of occupants meets the objectives for life safety, but provides
no protection for property. Conversely, it is possible that adequate property
protection might not be sufficient for protection of life.
Absolute safety from fire is not attainable. It is not possible to eliminate all
combustible materials or all potential ignition sources. Thus, in most cases, an
adequate fire protection plan must assume that unwanted fires will occur despite
the best efforts to prevent them. Means must be provided to minimize the losses
caused by the fires that do occur.
PROTECTION AGAINST HAZARDS 3.29
The first obligation of designers is to meet legal requirements while providing
the facilities required by the client. In particular, the requirements of the applicable
building code must be met. The building code will contain fire safety requirements,
or it will specify some recognized standard by reference. Many owners will also
require that their own insurance carrier be consulted—to obtain the most favorable
insurance rate, if for no other reason.
3.5.1 Fire-Protection Standards
The standards most widely adopted are those published by the National Fire Protection
Association (NFPA), Batterymarch Park, Quincy, MA 02269. The NFPA
‘‘National Fire Codes’’ comprise several volumes containing numerous standards,
updated annually. (These are also available separately.) The standards are supplemented
by the NFPA ‘‘Fire Protection Handbook,’’ which contains comprehensive
and detailed discussion of fire problems and much valuable statistical and engineering
data.
Underwriters Laboratories, Inc. (UL), 333 Pfingsten Road, Northbrook, IL
60062, publishes testing laboratory approvals of devices and systems in its ‘‘Fire
Protection Equipment List,’’ updated annually and by bimonthly supplements. The
publication outlines the tests that devices and systems must pass to be listed. The
UL ‘‘Building Materials List’’ describes and lists building materials, ceiling-floor
assemblies, wall and partition assemblies, beam and column protection, interior
finish materials, and other pertinent data. UL also publishes lists of ‘‘Accident
Equipment,’’ ‘‘Electrical Equipment,’’ ‘‘Electrical Construction Materials,’’ ‘‘Hazardous
Location Equipment,’’ ‘‘Gas and Oil Equipment,’’ and others.
Separate standards for application to properties insured by the Factory Mutual
System are published by the Factory Mutual Engineering Corporation (FM), Norwood,
MA 02062. FM also publishes a list of devices and systems it has tested
and approved.
The General Services Administration, acting for the federal government, has
developed many requirements that must be considered, if applicable. Also, the federal
government encourages cities to adopt some uniform code. In addition, buildings
must comply with provisions of the Americans with Disability Act (ADA).
(See Department of Justice final rules, Federal Register, 28 CFR Part 36, July 26,
1991; American National Standards Institute ‘‘Accessibility Standard,’’ ANSI
A117.1; ‘‘ADA Compliance Guidebook,’’ Building Owners and Managers Association
International, 1201 New York Ave., Washington, D.C. 20005.)
The Federal Occupational Safety and Health Act (OSHA) sets standards for
protecting the health and safety of nearly all employees. It is not necessary that a
business be engaged in interstate commerce for the law to apply. OSHA defines
employer as ‘‘a person engaged in a business affecting commerce who has employees,
but does not include the United States or any State or political subdivision
of a State.’’
An employer is required to ‘‘furnish to each of his employees employment and
a place of employment which are free from recognized hazards that are causing or
are likely to cause death or serious physical harm to his employees.’’ Employers
are also required to ‘‘comply with occupational safety and health standards promulgated
under the Act.’’
Building codes consist of a set of rules aimed at providing reasonable safety to
the community, to occupants of buildings, and to the buildings themselves. The
codes may adopt the standards mentioned previously and other standards concerned
with fire protection by reference or adapt them to the specific requirements of the
3.30 SECTION THREE
community. In the absence of a municipal or state building code, designers may
apply the provisions of the Uniform Building Code, promulgated by the International
Conference of Building Officials, or other national model code.
Many states have codes for safety to life in commercial and industrial buildings,
administered by the Department of Labor, the State Fire Marshal’s Office, the State
Education Department, or the Health Department. Some of these requirements are
drastic and must always be considered.
Obtaining optimum protection for life and property can require consultation with
the owner’s insurance carrier, municipal officials, and the fire department. If the
situation is complicated enough, it can require consultation with a specialist in all
phases of fire protection and prevention. In theory, municipal building codes are
designed for life safety and for protection of the public, whereas insurance-oriented
codes (except for NFPA 101, ‘‘Life Safety Code’’) are designed to minimize property
fire loss. Since about 70% of any building code is concerned with fire protection,
there are many circumstances that can best be resolved by a fire protection
consultant.
3.5.2 Fire-Protection Concepts
Although fires in buildings can be avoided, they nevertheless occur. Some of the
reasons for this are human error, arson, faulty electrical equipment, poor maintenance
of heating equipment, and natural causes, such as lightning. Consequently,
buildings should be designed to minimize the probability of a fire and to protect
life and limit property damage if a fire should occur. The minimum steps that should
be taken for the purpose are as follows:
1. Limit potential fire loads, with respect to both combustibility and ability to
generate smoke and toxic gases.
2. Provide means for prompt detection of fires, with warnings to occupants who
may be affected and notification of the presence of fire to fire fighters.
3. Communication of instructions to occupants as to procedures to adopt for
safety, such as to staying in place, proceeding to a designated refuge area, or
evacuating the building.
4. Provide means for early extinguishment of any fire that may occur, primarily
by automatic sprinklers but also by trained fire fighters.
5. Make available also for fire fighting an adequate water supply, appropriate
chemicals, adequate-size piping, conveniently located valves on the piping,
hoses, pumps, and other equipment necessary.
6. Prevent spread of fire from building to building, either through adequate separation
or by enclosure of the building with incombustible materials.
7. Partition the interior of the building with fire barriers, or divisions, to confine
a fire to a limited space.
8. Enclose with protective materials structural components that may be damaged
by fire (fireproofing).
9. Provide refuge areas for occupants and safe evacuation routes to outdoors.
10. Provide means for removal of heat and smoke from the building as rapidly as
possible without exposing occupants to these hazards, with the air-conditioning
PROTECTION AGAINST HAZARDS 3.31
TABLE 3.2 Relation between Weight of
Combustibles and Fire Severity*
Average weight of
combustibles, psf
Equivalent fire
severity, hr
5 1?2
71?2 3?4
10 1
15 11?2
20 2
30 3
40 41?2
50 6
60 71?2
* Based on National Institute of Standards and
Technology Report BMS92, ‘‘Classifications of
Building Constructions,’’ Government Printing Of-
fice, Washington, D.C. 20402.
system, if one is present, assisting the removal by venting the building and by
pressurizing smokeproof towers, elevator shafts, and other exits.
11. For large buildings, install standby equipment for operation in emergencies of
electrical systems and elevators.
These steps are discussed in the following articles.
3.5.3 Fire Loads and Resistance Ratings
The nature and potential magnitude of fire in a building are directly related to the
amount and physical arrangement of combustibles present, as contents of the building
or as materials used in its construction. Because of this, all codes classify
buildings by occupancy and construction, because these features are related to the
amount of combustibles.
The total amount of combustibles is called the fire load of the building. Fire
load is expressed in pounds per square foot (psf ) of floor area, with an assumed
calorific value of 7000 to 8000 Btu/ lb. (This Btu content applies to organic materials
similar to wood and paper. Where other materials are present in large proportion,
the weights must be adjusted accordingly. For example, for petroleum products,
fats, waxes, alcohol, and similar materials, the weights are taken at twice their
actual weights, because of the Btu content.)
National Institute of Standards and Technology burnout tests presented in Report
BMS92 indicate a relation between fire load and fire severity as shown in
Table 3.2.
The temperatures used in standard fire tests of building components are indicated
by the internationally recognized time-temperature curve shown in Fig. 3.9. Fire
resistance of construction materials, determined by standard fire tests, is expressed
in hours. The Underwriters Laboratories ‘‘Building Materials List’’ tabulates fire
ratings for materials and assemblies it has tested.
3.32 SECTION THREE
FIGURE 3.9 Time-temperature curve for a
standard fire test.
Every building code specifies required
fire-resistance ratings for structural
members, exterior walls, fire divisions,
fire separations, ceiling-floor
assemblies, and any other constructions
for which a fire rating is necessary. (Fire
protection for structural steel is discussed
in Arts. 7.49 to 7.53. Design for
fire resistance of steel deck in Arts.
8.21.5 and 8.22.4. Design for fire safety
with wood construction is covered in
Art. 10.28.)
Building codes also specify the ratings
required for interior finish of walls,
ceilings and floors. These are classified
as to flame spread, fuel contributed, and
smoke developed, determined in standard
tests performed according to
ASTM E84 or ASTM E119.
3.5.4 Fire and Smoke Barriers
A major consideration in building design is safety of the community. Hence, buildings
should be designed to control fires and smoke so that they will not spread
from building to building.
One way that building codes try to achieve this objective is to establish fire
zones or fire limits that restrict types of construction or occupancy that can be used.
Additional zoning regulations establish minimum distances between buildings. Another
way to achieve the objective is to specify the types of construction that can
be used for enclosing the exterior of buildings. The distance between adjoining
buildings, fire rating, and stability when exposed to fire of exterior walls, windows,
and doors, and percent of window area are some of the factors taken into account
in building codes for determination of the construction classification of a building.
To prevent spread of fire from roof to roof, building codes also often require
that exterior walls extend as a parapet at least 3 ft above the roof level. Parapets
also are useful in shielding fire fighters who may be hosing a fire from roofs of
buildings adjoining the one on fire. In addition, buildings should be topped with
roof coverings that are fire-resistant.
Fire Divisions. To prevent spread of fire vertically in building interiors, building
codes generally require that floor-ceiling and roof-ceiling assemblies be fireresistant.
The fire rating of such assemblies is one of the factors considered in
determination of the construction classification of a building. Also, openings in
floors and roofs should be fire-protected, although building codes do not usually
require this for one-story or two-story dwellings. For the purpose, an opening, such
as that for a stairway, may be protected with a fire-resistant enclosure and fire doors.
In particular, stairways and escalator and elevator shafts should be enclosed, not
only to prevent spread of fire and smoke but also to provide a protected means of
egress from the building for occupants and of approach to the fire source by fire
fighters.
To prevent spread of fire and smoke horizontally in building interiors, it is desirable
to partition interiors with fire divisions. A fire division is any construction
PROTECTION AGAINST HAZARDS 3.33
with the fire-resistance rating and structural stability under fire conditions required
for the type of occupancy and construction of the building to bar the spread of fire
between adjoining buildings or between parts of the same building on opposite
sides of the division. A fire division may be an exterior wall, fire window, fire door,
fire wall, ceiling, or firestop.
A fire wall should be built of incombustible material, have a fire rating of at
least 4 hr, and extend continuously from foundations to roof. Also, the wall should
have sufficient structural stability in a fire to allow collapse of construction on either
side without the wall collapsing. Building codes restrict the size of openings that
may be provided in a fire wall and require the openings to be fire-protected (Art.
11.55).
To prevent spread of fire through hollow spaces, such spaces should be firestopped.
A firestop is a solid or compact, tight closure set in a hollow, concealed
space in a building to retard spread of flames, smoke, or hot gases. All partitions
and walls should be firestopped at every floor level, at the top-story ceiling level,
and at the level of support for roofs. Also, very large unoccupied attics should be
subdivided by firestops into areas of 3000 ft2 or less. Similarly, any large concealed
space between a ceiling and floor or roof should be subdivided. For the purpose,
firestops extending the full depth of the space should be placed along the line of
supports of structural members and elsewhere, if necessary, to enclose areas not
exceeding 1000 ft2 when situated between a floor and ceiling or 3000 ft2 when
located between a ceiling and roof.
Openings between floors for pipes, ducts, wiring, and other services should be
sealed with the equal of positive firestops. Partitions between each floor and a
suspended ceiling above are not generally required to be extended to the slab above
unless this is necessary for required compartmentation. But smoke stops should be
provided at reasonable intervals to prevent passage of smoke to noninvolved areas.
3.5.5 Height and Area Restrictions
Limitations on heights and floor areas included between fire walls in any story of
a building are given in every building code and are directly related to occupancy
and construction. From the standpoint of fire protection, these provisions are chiefly
concerned with safety to life. They endeavor to ensure this through requirements
determining minimum number of exits, proper location of exits, and maximum
travel distance (hence escape time) necessary to reach a place of refuge. The limitations
are also aimed at limiting the size of fires.
Unlimited height and area are permitted for the most highly fire-resistant type
of construction. Permissible heights and areas are decreased with decrease in fire
resistance of construction. Area permitted between fire walls in any story reduces
to 6000 ft2 for a one-story, wood-frame building.
Installation of automatic sprinklers increases permissible heights and areas in all
classes, except those allowed unlimited heights and areas.
Permissible unlimited heights and areas in fire-resistive buildings considered
generally satisfactory in the past may actually not be safe. A series of fires involving
loss of life and considerable property damage opened the fire safety of such
construction to question. As a result, some cities have made more stringent the
building-code regulations applicable to high-rise buildings.
Many building codes prohibit floor areas of unlimited size unless the building
is sprinklered. Without automatic sprinklers, floor areas must be subdivided into
fire-wall-protected areas of from 7500 to 15,000 ft2 and the enclosing fire walls
must have 1- or 2-hr fire ratings, depending on occupancy and construction.
3.34 SECTION THREE
TABLE 3.3 Approximate Fire Loads for
Various Occupancies*
Occupancy class
Typical average
fire load including
floors and trim, psf
Assembly 10.0
Business 12.6
Educational 7.6
High hazard †
Industrial 25.0
Institutional 5.7
Mercantile 15–20
Residential 8.8
Storage 30.0
*From National Institute of Standards and Technology
Report BMS92, ‘‘Classifications of Building
Constructions,’’ Government Printing Office, Washington.
D.C. 20402.
† Special provisions are made for this class, and
hazards are treated for the specific conditions encountered,
which might not necessarily be in proportion
to the actual fire load.
(‘‘Life Safety Handbook’’ and ‘‘Fire Protection Handbook,’’ National Fire Protection
Association, Quincy, Mass.)
3.5.6 Fire-Resistance Classification of Buildings
Although building codes classify buildings by occupancy and construction, there is
no universal standard for number of classes of either occupancy or construction.
Table 3.3 lists some typical occupancy classifications and associates approximate
fire loads with them. This table should be used only as a guide. For a specific
project refer to the applicable local code. Note, however, that codes do not relate
life-safety hazards to the actual fire load, but deal with them through requirements
for exit arrangements, interior finishes, and ventilation.
Types of construction may be classified by a local building code as follows but
may have further subdivisions, depending on fire-resistance requirements:
1. Fire-resistive construction
2. Protected noncombustible construction
3. Unprotected noncombustible construction
4. Heavy-timber construction
5. Ordinary construction
6. Wood-frame construction
The required fire resistance varies from 4 hr for exterior bearing walls and interior
columns in the highest fire resistive class to 1 hr for walls and none for columns
in the wood-frame construction class.
PROTECTION AGAINST HAZARDS 3.35
Type of construction affects fire-protection-system design through requirements
that structural members as well as contents of buildings be protected.
3.5.7 Extinguishment of Fires
Design of all buildings should include provisions for prompt extinguishment of
fires. Apparatus installed for the purpose should take into account the nature and
amount of combustible and smoke-producing materials that may be involved in a
fire. Such apparatus may range from small, hand-held extinguishers for small fires
to hoses attached to a large, pressurized water supply and automatic fire sprinklers.
Also desirable are fire and smoke detectors and a protective signaling system that
sounds an alarm to alert building occupants and calls fire fighters.
Classes of Fires. For convenience in defining effectiveness of extinguishing media,
Underwriters Laboratories, Inc., has developed a classification that separates
combustible materials into four types:
1. Class A fires involve ordinary combustibles and are readily extinguishable by
water or cooling, or by coating with a suitable chemical powder.
2. Class B fires involve flammable liquids where smothering is effective and where
a cooling agent must be applied with care.
3. Class C fires are those in live electrical equipment where the extinguishing agent
must be nonconductive. Since a continuing electrical malfunction will keep the
fire source active, circuit protection must operate to cut off current flow, after
which an electrically conductive agent can be used with safety.
4. Class D fires involve metals that burn, such as magnesium, sodium, and powdered
aluminum. Special powders are necessary for such fires, as well as special
training for operators. These fires should never be attacked by untrained personnel.
Automatic Sprinklers. The most widely used apparatus for fire protection in
buildings is the automatic sprinkler system. In one or more forms, automatic sprinklers
are effective protection in all occupancy classes. Special treatment and use of
additional extinguishing agents, though, may be required in many high-hazard, industrial,
and storage occupancies.
Basically, a sprinkler system consists of a network of piping installed at the
ceiling or roof and supplied with water from a suitable source. On the piping at
systematic intervals are placed heat-sensitive heads, which discharge water when a
predetermined temperature is reached at any head. A gate valve is installed in the
main supply, and drains are provided. An alarm can be connected to the system so
that local and remote signals can be given when the water flows.
Sprinkler systems are suitable for extinguishing all Class A fires and, in many
cases, also Class B and C fires. For Class B fires, a sealed (fusible) head system
may be used if the flammable liquid is in containers or is not present in large
quantity. Sprinklers have a good record for extinguishing fires in garages, for example.
An oil-spill fire can be extinguished or contained when the water is applied
in the form of spray, as from a sprinkler head. When an oil spill or process-pipe
rupture can release flammable liquid under pressure, an open-head (deluge) system
may be required to apply a large volume of water quickly and to keep surrounding
equipment cool.
3.36 SECTION THREE
For Class C fires, water can be applied to live electrical equipment if it is done
in the form of a nonconducting foglike spray. This is usually the most economical
way to protect outdoor oil-filled transformers and oil circuit breakers.
Fire protection should be based on complete coverage of the building by the
sprinkler system. Partial coverage is rarely advisable, because extinguishing capacity
is based on detecting and extinguishing fires in their incipiency, and the system
must be available at all times in all places. Systems are not designed to cope with
fires that have gained headway after starting in unsprinklered areas.
See also Arts. 14.27 to 14.29.
Standpipes. Hoses supplied with water from standpipes are the usual means of
manual application of water to interior building fires. Standpipes are usually designed
for this use by the fire department, but they can be used by building fire
fighters also.
Standpipes are necessary in buildings higher than those that ground-based fire
department equipment can handle effectively. The Standard Building Code requires
standpipes in buildings higher than 50 ft. The Uniform Building Code requirement
starts at four stories or occupancies over 5000 ft2 in area and depends on whether
automatic sprinklers are installed.
See also Art. 14.30.
Chemical Extinguishment. Fires involving some materials may not be readily
extinguished with water alone. When such materials may be present in a building,
provision should be made for application of appropriate chemicals.
Foamed chemicals, mostly masses of air- or gas-filled bubbles, formed by
chemical or mechanical means, may be used to control fires in flammable liquids.
Foam is most useful in controlling fires in flammable liquids with low flash points
and low specific gravity, such as gasoline. The mass of bubbles forms a cohesive
blanket that extinguishes fire by excluding air and cooling the surface.
Foam clings to horizontal surfaces and can also be used on vertical surfaces of
process vessels to insulate and cool. It is useful on fuel-spill fires, to extinguish
and confine the vapors.
For fire involving water-soluble liquids, such as alcohol, a special foam concentrate
must be used. Foam is not suitable for use on fires involving compressed
gases, such as propane, nor is it practical on live electrical equipment. Because of
the water content, foam cannot be used on fires involving burning metals, such as
sodium, which reacts with water. It is not effective on oxygen-containing materials.
Three distinct types of foam are suitable for fire control: chemical foam, air
foam (mechanical foam), and high-expansion foam.
Chemical foam was the first foam developed for fire fighting. It is formed by
the reaction of water with two chemical powders, usually sodium bicarbonate and
aluminum sulfate. The reaction forms carbon dioxide, which is the content of the
bubbles. This foam is the most viscous and tenacious of the foams. It forms a
relatively tough blanket, resistant to mechanical or heat disruption. The volume of
expansion may be as much as 10 times that of the water used in the solution.
Chemical foam is sensitive to the temperature at which it is formed, and the
chemicals tend to deteriorate during long storage periods. It is not capable of being
transported through long pipe lines. For these reasons, it is not used as much as
other foams. National Fire Protection Association standard NFPA 11 covers chemical
foam.
PROTECTION AGAINST HAZARDS 3.37
Air foam (mechanical foam) is made by mechanical mixing of water and a
protein-based chemical concentrate. There are several methods of combining the
components, but essentially the foam concentrate is induced into a flowing stream
of water through a metering orifice and a suitable device, such as a venturi. The
volume of foam generated is from 16 to 33 times the volume of water used. Several
kinds of mixing apparatus are available, choice depending on volume required,
availability of water, type of hazard, and characteristics of the protected area or
equipment.
Air foam can be conducted through pipes and discharged through a fixed chamber
mounted in a bulk fuel storage tank, or it can be conducted through hoses and
discharged manually through special nozzles. This foam can also be distributed
through a sprinkler system of special design to cover small equipment, such as
process vessels, or in multisystem applications, over an entire airplane hangar. The
standard for use and installation of air foam is NFPA 11, and for foam-water sprinkler
systems, NFPA 16.
High-expansion foam was developed for use in coal mines, where its extremely
high expansion rate allowed it to be generated quickly in sufficient volume to fill
mine galleries and reach inaccessible fires. This foam can be generated in volumes
of from 100 to 1000 times the volume of water used, with the latter expansion in
most general use. The foam is formed by passage of air through a screen constantly
wetted by a solution of chemical concentrate, usually with a detergent base. The
foam can be conducted to a fire area by ducts, either fixed or portable, and can be
applied manually by small portable generators. Standard for equipment and use of
high-expansion foam is NFPA 11A.
High-expansion foam is useful for extinguishing fires by totally flooding indoor
confined spaces, as well as for local application to specific areas. It extinguishes
by displacing air from the fire and by the heat-absorbing effect of converting the
foam water content into steam. The foam forms an insulating barrier for exposed
equipment or building components.
High-expansion foam is more fragile than chemical or air foam. Also, it is not
generally reliable when used outdoors where it is subject to wind currents. Highexpansion
foam is not toxic, but it has the effect of disorienting people who may
be trapped in it.
Carbon dioxide is useful as an extinguishing agent, particularly on surface fires,
such as those involving flammable liquids in confined spaces. It is nonconductive
and is effective on live electrical equipment. Because carbon dioxide requires no
clean-up, it is desirable on equipment such as gasoline or diesel engines. The gas
can be used on Class A fires. But when a fire is deep-seated, an extended discharge
period is required to avoid rekindling.
Carbon dioxide provides its own pressure for discharge and distribution and is
nonreactive with most common industrial materials. Because its density is 11?2 times
that of air, carbon dioxide tends to drop and to build up from the base of a fire.
Extinguishment of a fire is effected by reduction of the oxygen concentration surrounding
a fire.
Carbon dioxide may be applied to concentrated areas or machines by hand-held
equipment, either carried or wheeled. Or the gas may be used to flood totally a
room containing a hazard. The minimum concentrations for total flooding for fires
involving some commercial liquids are listed in ‘‘Standard on Carbon-Dioxide
Extinguishing Systems,’’ NFPA 12.
Carbon dioxide is not effective on fires involving burning metals, such as magnesium,
nor is it effective on oxygen-containing materials, such as nitrocellulose.
3.38 SECTION THREE
Hazard to personnel is involved to the extent that a concentration of 9% will cause
suffocation in a few minutes, and concentrations of 20% can be fatal. When used
in areas where personnel are present, a time delay before discharge is necessary to
permit evacuation.
For use in total flooding systems, carbon dioxide is available in either highpressure
or low-pressure equipment. Generally, it is more economical to use lowpressure
equipment for large volumes, although there is no division point applicable
in all cases.
Halon 1301 is one of a series of halogenated hydrocarbons, bromotrifluoromethane
(CBrF2), used with varying degrees of effectiveness as a fire-extinguishing
agent and was included in the Montreal Protocol on Substances that Deplete the
Ozone Layer signed in September 16, 1987. It is currently limited to ‘‘critical uses’’
and is planned to be phased out by 2002. The types of uses currently defined as
critical are spaces where flammable liquid and/or gas release could occur in the
oil, gas, petrochemical and military sectors; manned communication centers of the
armed forces or other places essential for national security; or for the protection of
spaces where there may be a risk of dispersion of radioactive material.
Dry chemical extinguishing agents were used originally to extinguish Class B
fires. One type consisted of a sodium bicarbonate base with additives to prevent
caking and to improve fluid flow characteristics. Later, multipurpose dry chemicals
effective on Class A, B, and C fires were developed. These chemicals are distinctly
different from the dry powder extinguishing agents used on combustible metals
described below.
Dry chemicals are effective on surface fires, especially on flammable liquids.
When used on Class A fires, they do not penetrate into the burning material. So
when a fire involves porous or loosely packed material, water is used as a backup.
The major effect of dry chemicals is due almost entirely to ability to break the
chain reaction of combustion. A minor effect of smothering is obtained on Class
A fires.
Fires that are likely to rekindle are not effectively controlled by dry chemicals.
When these chemicals are applied to machinery or equipment at high temperatures,
caking can cause some difficulty in cleaning up after the fire.
Dry chemicals can be discharged in local applications by hand-held extinguishers,
wheeled portable equipment, or nozzles on hose lines. These chemicals can
also be used for extinguishing fires by total flooding, when they are distributed
through a piped system with special discharge nozzles. The expellant gas is usually
dry nitrogen.
Dry powder extinguishing agents are powders effective in putting out combustible-
metal fires. There is no universal extinguisher that can be used on all fires
involving combustible metals. Such fires should never be fought by untrained personnel.
There are several proprietary agents effective on several metals, but none should
be used without proper attention to the manufacturer’s instructions and the specific
metal involved. For requirements affecting handling and processing of combustible
metals, reference should be made to National Fire Protection Association standards
NFPA 48 and 652 for magnesium, NFPA 481 for titanium, NFPA 482M for zirconium,
and NFPA 65 and 651 for aluminum.
(‘‘The SFPE Handbook of Fire Protection Engineering,’’ and ‘‘Automatic Sprinkler
Systems Handbook,’’ National Fire Protection Association, Quincy, Mass.)
3.5.8 Fire Detection
Every fire-extinguishing activity must start with detection. To assist in this, many
types of automatic detectors are available, with a wide range of sensitivity. Also, a
PROTECTION AGAINST HAZARDS 3.39
variety of operations can be performed by the detection system. It can initiate an
alarm, local or remote, visual or audible; notify a central station; actuate an extinguishing
system; start or stop fans or processes, or perform any other operation
capable of automatic control.
There are five general types of detectors, each employing a different physical
means of operation. The types are designated fixed-temperature, rate-of-rise, photoelectric,
combustion-products, and ultraviolet or infrared detectors.
A wide variety of detectors has been tested and reported on by Underwriters
Laboratories, Inc. See Art. 3.5.1.
Fixed-Temperature Detectors. In its approval of any detection device, UL specifies
the maximum distance between detectors to be used for area coverage. This
spacing should not be used without competent judgment. In arriving at the permitted
spacing for any device, UL judges the response time in comparison with that of
automatic sprinkler heads spaced at 10-ft intervals. Thus, if a device is more sensitive
than a sprinkler head, the permitted spacing is increased until the response
times are nearly equal. If greater sensitivity is desired, the spacing must be reduced.
With fixed-temperature devices, there is a thermal lag between the time the
ambient temperature reaches rated temperature and the device itself reaches that
temperature. For thermostats having a rating of 135
F, the ambient temperature can
reach 206
F.
Disk thermostats are the cheapest and most widely used detectors. The most
common type employs the principle of unequal thermal expansion in a bimetallic
assembly to operate a snap-action disk at a preset temperature, to close electrical
contacts. These thermostats are compact. The disk, 1?2 in in diameter, is mounted
on a plastic base 13?4 in in diameter. The thermostats are self-resetting, the contacts
being disconnected when normal temperature is restored.
Thermostatic cable consists of two sheathed wires separated by a heat-sensitive
coating which melts at high temperature, allowing the wires to contact each other.
The assembly is covered by a protective sheath. When any section has functioned,
it must be replaced.
Continuous detector tubing is a more versatile assembly. This detector consists
of a small-diameter Inconel tube, of almost any length, containing a central wire,
separated from the tube by a thermistor element. At elevated temperatures, the
resistance of the thermistor drops to a point where a current passes between the
wire and the tube. The current can be monitored, and in this way temperature
changes over a wide range, up to 1000
F, can be detected. The detector can be
assembled to locate temperature changes of different magnitudes over the same
length of detector. It is self-restoring when normal temperature is restored. This
detector is useful for industrial applications, as well as for fire detection.
Fusible links are the same devices used in sprinkler heads and are made to
operate in the same temperature range. Melting or breaking at a specific temperature,
they are used to restrain operation of a fire door, electrical switch, or similar
mechanical function, such as operation of dampers. Their sensitivity is substantially
reduced when installed at a distance below a ceiling or other heat-collecting obstruction.
Rate-of-Rise Detectors. Detectors and detector systems are said to operate on the
rate-of-rise principle when they function on a rapid increase in temperature, whether
the initial temperature is high or low. The devices are designed to operate when
temperature rises at a specified number of degrees, usually 10 or 15
F, per minute.
They are not affected by normal temperature increases and are not subject to thermal
lag, as are fixed-temperature devices.
3.40 SECTION THREE
Photoelectric Detectors. These indicate a fire condition by detecting the smoke.
Sensitivity can be adjusted to operate when obscuration is as low as 0.4% per ft.
In these devices, a light source is directed so that it does not impinge on a photoelectric
cell. When sufficient smoke particles are concentrated in the chamber, their
reflected light reaches the cell, changing its resistance and initiating a signal.
These detectors are particularly useful when a potential fire is likely to generate
a substantial amount of smoke before appreciable heat and flame erupt. A fixedtemperature,
snap-action disk is usually included in the assembly.
Combustion-Products Detectors. Two physically different means, designated ionization
type and resistance-bridge type, are used to operate combustion-products
detectors.
The ionization type, most generally used, employs ionization of gases by alpha
particles emitted by a small quantity of radium or americum. The detector contains
two ionization chambers, one sealed and the other open to the atmosphere, in electrical
balance with a cold-cathode tube or transistorized amplifier. When sufficient
combustion products enter the open chamber, the electrical balance is upset, and
the resulting current operates a relay.
The resistance-bridge type of detector operates when combustion products
change the impedance of an electric bridge grid circuit deposited on a glass plate.
Combustion-products detectors are designed for extreme early warning, and are
most useful when it is desirable to have warning of impending combustion when
combustion products are still invisible. These devices are sensitive in some degree
to air currents, temperature, and humidity, and should not be used without consultation
with competent designers.
Flame Detectors. These discriminate between visible light and the light produced
by combustion reactions. Ultraviolet detectors are responsive to flame having wavelengths
up to 2850 A° . The effective distance between flame and detectors is about
10 ft for a 5-in-diam pan of gasoline, but a 12-in-square pan fire can be detected
at 30 ft.
Infrared detectors are also designed to detect flame. These are not designated
by range of wavelength because of the many similar sources at and above the
infrared range. To identify the radiation as a fire, infrared detectors usually employ
the characteristic flame flicker, and have a built-in time delay to eliminate accidental
similar phenomena.
(‘‘The SFPE Handbook of Fire Detection Engineering,’’ National Fire Protection
Association, Quincy, Mass.)
3.5.9 Smoke and Heat Venting
In extinguishment of any building fire, the heat-absorption capacity of water is the
principal medium of reducing the heat release from the fire. When, however, a fire
is well-developed, the smoke and heat must be released from confinement to make
the fire approachable for final manual action. If smoke and heat venting is not
provided in the building design, holes must be opened in the roof or building sides
by the fire department. In many cases, it has been impossible to do this, with total
property losses resulting.
Large-area, one-story buildings can be provided with venting by use of monitors,
or a distribution of smaller vents. Multistory buildings present many problems,
particularly since life safety is the principal consideration in these buildings.
PROTECTION AGAINST HAZARDS 3.41
TABLE 3.4 Minimum Ratios of Effective
Vent Area to Floor Area
Low-heat-release contents 1:150
Moderate-heat-release contents 1:100
High-heat-release contents 1:30–1:50
TABLE 3.5 Maximum Distance between
Vents, Ft
Low-heat-release contents 150
Moderate-heat-release contents 120
High-heat-release contents 75–100
Ventilation facilities should be provided in addition to the protection afforded
by automatic sprinklers and hose stations.
Large One-Story Buildings. For manufacturing purposes, low buildings are frequently
required to be many hundreds of feet in each horizontal dimension. Lack
of automatic sprinklers in such buildings has proven to be disastrous where adequate
smoke and heat venting has not been provided. Owners generally will not permit
fire division walls, because they interfere with movement and processing of materials.
With the whole content of a building subject to the same fire, fire protection
and venting are essential to prevent large losses in windowless buildings underground
structures, and buildings housing hazardous operations.
There is no accepted formula for determining the exact requirements for smoke
and heat venting. Establishment of guidelines is the nearest approach that has been
made to venting design, and these must be adapted to the case at hand. Consideration
must be given to quantity, shape, size, and combustibility of contents.
Venting Ratios. The ratio of effective vent opening to floor area should be at
least that given in Table 3.4.
Venting can be accomplished by use of monitors, continuous vents, unit-type
vents, or sawtooth skylights. In moderate-sized buildings exterior-wall windows
may be used if they are near the eaves.
Monitors must be provided with operable panels or other effective means of
providing openings at the required time.
Continuous gravity vents are continuous narrow slots provided with a weather
hood above. Movable shutters can be provided and should be equipped to open
automatically in a fire condition.
Vent Spacing. Unit-type vents are readily adapted to flat roofs, and can be
installed in any required number, size, and spacing. They are made in sizes from
4  4 ft to 10  10 ft, with a variety of frame types and means of automatic
opening. In arriving at the number and size of vents, preference should be given
to a large number of small vents, rather than a few large vents. Because it is
desirable to have a vent as near as possible to any location where a fire can start,
a limit should be placed on the distance between units. Table 3.5 lists the generally
accepted maximum distance between vents.
Releasing Methods. Roof vents should be automatically operated by means that
do not require electric power. They also should be capable of being manually operated.
Roof vents approved by Underwriters Laboratories, Inc., are available from
a number of manufacturers.
Refer to National Fire Protection Association standard NFPA 204 in designing
vents for large, one-story buildings. Tests conducted prior to publication of NFPA
231C indicated that a sprinkler system designed for adequate density of water application
will eliminate the need for roof vents, but the designers would be well
advised to consider the probable speed of fire and smoke development in making
a final decision. NFPA 231C covers the rack storage of materials as high as 20 ft.
3.42 SECTION THREE
High-Rise Buildings. Building codes vary in their definition of high-rise buildings,
but the intent is to define buildings in which fires cannot be fought successfully
by ground-based equipment and personnel. Thus, ordinarily, high-rise means buildings
100 ft or more high. In design for smoke and heat venting, however, any
multistory building presents the same problems.
Because smoke inhalation has been the cause of nearly all fatalities in high-rise
buildings, some building codes require that a smoke venting system be installed
and made to function independently of the air-conditioning system. Also, smoke
detectors must be provided to actuate exhaust fans and at the same time warn the
fire department and the building’s control center. The control center must have twoway
voice communication, selectively, with all floors and be capable of issuing
instructions for occupant movement to a place of safety.
Because the top story is the only one that can be vented through the roof, all
other stories must have the smoke conducted through upper stories to discharge
safely above the roof. A separate smoke shaft extending through all upper stories
will provide this means. It should be provided with an exhaust fan and should be
connected to return-air ducts with suitable damper control of smoke movement, so
that smoke from any story can be directed into the shaft. The fan and dampers
should be actuated by smoke detectors installed in suitable locations at each inlet
to return-air ducts. Operation of smoke detectors also should start the smoke-ventshaft
fan and stop supply-air flow. Central-station supervision (Art. 3.5.12) should
be provided for monitoring smoke-detector operation. Manual override controls
should be installed in a location accessible under all conditions.
Windows with fixed sash should be provided with means for emergency opening
by the fire department.
Pressurizing stair towers to prevent the entrance of smoke is highly desirable
but difficult to accomplish. Most standpipe connections are usually located in stair
towers, and it is necessary to open the door to the fire floor to advance the hose
stream toward the fire. A more desirable arrangement would be to locate the riser
in the stair tower, if required by code, and place the hose valve adjacent to the
door to the tower. Some codes permit this, and it is adaptable to existing buildings.
(‘‘The SFPE Handbook of Fire Protection Engineering,’’ National Fire Protection
Association, Quincy, Mass.)
3.5.10 Emergency Egress
In addition to providing means for early detection of fire, preventing its spread, and
extinguishing it speedily, building designers should also provide the appropriate
number, sizes, and arrangements of exits to permit quick evacuation of occupants
if fire or other conditions dangerous to life occur. Buildings should be designed to
preclude development of panic in emergencies, especially in confined areas where
large numbers of persons may assemble. Hence, the arrangement of exit facilities
should permit occupants to move freely toward exits that they can see clearly and
that can be reached by safe, unobstructed, uncongested paths. Redundancy is highly
desirable; there should be more than one path to safety, so that loss of a single path
will not prevent escape of occupants from a danger area. The paths should be
accessible to and usable by handicapped persons, including those in wheelchairs,
if they may be occupants.
Building codes generally contain requirements for safe, emergency egress from
buildings. Such requirements also are concisely presented in the ‘‘Life Safety Code’’
of the National Fire Protection Association.
PROTECTION AGAINST HAZARDS 3.43
Egress Components. Many building codes define an exit as a safe means of egress
from the interior of a building to an open exterior space beyond the reach of a
building fire or give an equivalent definition. Other codes consider an exterior door
or a stairway leading to access to such a door to be an exit. To prevent misunderstandings,
the ‘‘Life Safety Code’’ defines a means of egress composed of three
parts.
Accordingly, a means of egress is a continuous, unobstructed path for evacuees
from any point in a building to a public way. Its three parts are:
Exit access—that portion that leads to an entrance to an exit
Exit—the portion that is separated from all other building spaces by construction
or equipment required to provide a protected path to the exit discharge
Exit discharge—the portion that connects the termination of an exit to a public
way
Means of egress may be provided by exterior and interior doors and enclosed
horizontal and vertical passageways, including stairs and escalators. (Elevators and
exterior fire escapes are not generally recognized as reliable means of egress in a
fire.) Exit access includes the space from which evacuation starts and passageways
and doors that must be traversed to reach an exit.
Types of Exits. Building codes generally recognize the following as acceptable
exits when they meet the codes’ safety requirements:
Corridors—enclosed horizontal or slightly inclined public passageways, which
lead from interior spaces toward an exit discharge. Minimum floor-to-ceiling
height permitted is generally 80 in. Minimum width depends on type of occupancy
and passageway (Table 3.7 and Art. 3.5.11). Codes may require subdivision
of corridors into lengths not exceeding 300 ft for educational buildings
and 150 ft for institutional buildings. Subdivision should be accomplished with
noncombustible partitions incorporating smokestop doors. In addition, codes
may require the corridor enclosures to have a fire rating of 1 or 2 hr.
Exit passageways—horizontal extensions of vertical passageways. Minimum
floor-to-ceiling height is the same as for corridors. Width should be at least that
of the vertical passageways. Codes may require passageway enclosures to have
a 2-hr fire rating. A street-floor lobby may serve as an exit passageway if it is
sufficiently wide to accommodate the probable number of evacuees from all
contributing spaces at the lobby level.
Exit doors—doors providing access to streets or to stairs or exit passageways.
Those at stairs or passageways should have a fire rating of at least 3?4 hr.
Horizontal exit—passageway to a refuge area. The exit may be a fire door
through a wall with a 2-hr fire rating, a balcony providing a path around a fire
barrier, or a bridge or tunnel between two buildings. Doors in fire barriers with
3- or 4-hr fire ratings should have a 11?2-hr rated door on each face of the fire
division. Walls permitted to have a lower fire rating may incorporate a single
door with a rating of at least 11?2 hr. Balconies, bridges, and tunnels should be
at least as wide as the doors providing access to them, and enclosures or sides
of these passageways should have a fire rating of 2 hr or more. Exterior-wall
openings, below or within 30 ft of an open bridge or balcony, should have at
least 3?4-hr fire protection.
3.44 SECTION THREE
Interior stairs—stairs that are inside a building and that serve as an exit. Except
in one-story or two-story low-hazard buildings, such stairs should be built of
noncombustible materials. Stairway enclosures generally should have a 2-hr fire
rating. Building codes, however, may exempt low dwellings from this requirement.
Exterior stairs—stairs that are open to the outdoors and that serve as an exit
to ground level. Height of such stairs is often limited to 75 ft or six stories. The
stairs should be protected by a fire-resistant roof and should be built of noncombustible
materials. Wall openings within 10 ft of the stairs should have 3?4-hr fire
protection.
Smokeproof tower—a continuous fire-resistant enclosure protecting a stairway
from fire or smoke in a building. At every floor, a passageway should be provided
by vestibules or balconies directly open to the outdoors and at least 40 in
wide. Tower enclosures should have a 2-hr fire rating. Access to the vestibules
or balconies and entrances to the tower should be provided by doorways at least
40 in wide, protected by self-closing fire doors.
Escalators—moving stairs. Building codes may permit their use as exits if they
meet the safety requirements of interior stairs and if they move in the direction
of exit travel or stop gradually when an automatic fire-detection system signals
a fire.
Moving walks—horizontal or inclined conveyor belts for passengers. Building
codes may permit their use as exits if they meet the safety requirements for exit
passageways and if they move in the direction of exit travel or stop gradually
when an automatic fire-detection system signals a fire.
Refuge Areas. A refuge area is a space protected against fire and smoke. When
located within a building, the refuge should be at about the same level as the areas
served and separated from them by construction with at least a 2-hr fire rating.
Access to the refuge areas should be protected by fire doors with a fire rating of
11?2 hr or more.
A refuge area should be large enough to shelter comfortably its own occupants
plus those from other spaces served. The minimum floor area required may be
calculated by allowing 3 ft2 of unobstructed space for each ambulatory person and
30 ft2 per person for hospital or nursing-home patients. Each refuge area should be
provided with at least one horizontal or vertical exit, such as a stairway, and in
locations more than 11 stories above grade, with at least one elevator.
Location of Exits. Building codes usually require a building to have at least two
means of egress from every floor. Exits should be remote from each other, to reduce
the chance that both will be blocked in an emergency.
All exit access facilities and exits should be located so as to be clearly visible
to building occupants or signs should be installed to indicate the direction of travel
to the exits. Signs marking the locations of exits should be illuminated with at least
5 ft-c of light. Floors of means of egress should be illuminated with at least 1 ft-c
of artificial light whenever the building is occupied.
If an open floor area does not have direct access to an exit, a protected, continuous
passageway should be provided directly to an exit. The passageway should
be kept open at all times. Occupants using the passageway should not have to pass
any high-hazard areas not fully shielded.
PROTECTION AGAINST HAZARDS 3.45
To ensure that occupants will have sufficient escape time in emergencies, building
codes limit the travel distance from the most remote point in any room or space
to a door that opens to an outdoor space, stairway, or exit passageway. The maximum
travel distance permitted depends on the type of occupancy and whether the
space is sprinklered. For example, for corridors not protected by sprinklers, maximum
permitted length may range from 100 ft for storage and institutional buildings
to 150 ft for residential, mercantile, and industrial occupancies. With sprinkler protection,
permitted length may range from 150 ft for high-hazard and storage buildings
to 300 ft for commercial buildings, with 200 ft usually permitted for other
types of occupancies.
Building codes also may prohibit or limit the lengths of passageways or courts
that lead to a dead end. For example, a corridor that does not terminate at an exit
is prohibited in high-hazard buildings. For assembly, educational, and institutional
buildings, the maximum corridor length to a dead end may not exceed 30 ft,
whereas the maximum such length is 40 ft for residential buildings and 50 ft for
all other occupancies, except high-hazard.
3.5.11 Required Exit Capacity
Minimum width of a passageway for normal use is 36 in. This is large enough to
accommodate one-way travel for persons on crutches or in wheelchairs. For twoway
travel, a 60-in width is necessary. (A corridor, however, need not be 60 in
wide for its full length, if 60  60-in passing spaces, alcoves, or corridor intersections
are provided at short intervals.) Building codes, however, may require greater
widths to permit rapid passage of the anticipated number of evacuees in emergencies.
This number depends on a factor called the occupant load, but the minimum
width should be ample for safe, easy passage of handicapped persons. Running
slope should not exceed 1:20, and cross slope, 1:50.
Occupant load of a building space is the maximum number of persons that
may be in the space at any time. Building codes may specify the minimum permitted
capacity of exits in terms of occupant load, given as net floor area, square
feet, per person, for various types of occupancy (Table 3.6). The number of occupants
permitted in a space served by the exits then can be calculated by dividing
the floor area, square feet, by the specified occupant load.
The occupant load of any space should include the occupant load of other spaces
if the occupants have to pass through that space to reach an exit.
With the occupant load known, the required width for an exit or an exit door
can be determined by dividing the occupant load on the exit by the capacity of the
exit.
Capacities of exits and access facilities generally are measured in units of width
of 22 in, and the number of persons per unit of width is determined by the type of
occupancy. Thus, the number of units of exit width for a doorway is found by
dividing by 22 the clear width of the doorway when the door is in the open position.
(Projections of stops and hinge stiles may be disregarded.) Fractions of a unit of
width less than 12 in should not be credited to door capacity. If, however, 12 in or
more is added to a multiple of 22 in, one-half unit of width can be credited. Building
codes indicate the capacities in persons per unit of width that may be assumed for
various means of egress. Recommendations of the ‘‘Life Safety Code’’ of the National
Fire Protection Association, Batterymarch Park, Quincy, MA 02269, are summarized
in Table 3.7.
3.46 SECTION THREE
TABLE 3.6 Typical Occupant Load Requirements for
Types of Occupancy
Occupancy
Net floor
area per
occupant,
ft2
Auditoriums 7
Billiard rooms 50
Bowling alleys 50
Classrooms 20
Dance floors 7
Dining spaces (nonresidential) 12
Exhibition spaces 10
Garages and open parking structures 250
Gymnasiums 15
Habitable rooms 200
Industrial shops 200
In schools 50
Institutional sleeping rooms 120
Kindergartens 35
Kitchens (nonresidential) 200
Laboratories 50
Preparation rooms 100
Libraries 25
Locker rooms 12
Offices 100
Passenger terminals or platforms 1.5C*
Sales areas (retail)
First floor or basement
30
Other floors 60
Seating areas (audience) in places of assembly
Fixed seats
D†
Movable seats 10
Skating rinks 15
Stages S‡
Storage rooms 300
*C 
 capacity of all passenger vehicles that can be unloaded
simultaneously.
†D 
 number of seats or occupants for which space is to be used.
‡S 
 75 persons per unit of width of exit openings serving a stage
directly, or one person per 15 ft of performing area plus one person
per 50 ft2 of remaining area plus number of seats that may be placed
for an audience on stage.
PROTECTION AGAINST HAZARDS 3.47
TABLE 3.7 Capacities, Persons per Unit of Width, for
Means of Egress
Level egress components, including doors 100
Stairway 60
Ramps 44 in or more wide, slope not more than 10% 100
Narrower or steeper ramps
Up 60
Down 100
3.5.12 Building Operation in Emergencies
For buildings that will be occupied by large numbers of persons, provision should
be made for continuation of services essential to safe, rapid evacuation of occupants
in event of fire or other emergencies and for assisting safe movement of fire fighters,
medical personnel, or other aides.
Standby electric power, for example, should be available in all buildings to
replace the basic power source if it should fail. The standby system should be
equipped with a generator that will start automatically when normal power is cut
off. The emergency power supply should be capable of operating all emergency
electric equipment at full power within 1 min of failure of normal service. Such
equipment includes lights for exits, elevators for fire fighters’ use, escalators and
moving walks designated as exits, exhaust fans and pressurizing blowers, communication
systems, fire detectors, and controls needed for fire fighting and life
safety during evacuation of occupants.
In high-rise buildings, at least one elevator should be available for control by
fire fighters and to give them access to any floor from the street-floor lobby. Also,
elevator controls should be designed to preclude elevators from stopping automatically
at floors affected by fire.
Supervision of emergency operations can be efficiently provided by personnel
at a control center placed in a protected area. This center may include a computer,
supplemented by personnel performing scheduled maintenance, and should be capable
of continuously monitoring alarms, gate valves on automatic fire sprinklers,
temperatures, air and water pressures, and perform other pertinent functions. Also,
the center should be capable in emergencies of holding two-way conversations with
occupants and notifying police and fire departments of the nature of the emergencies.
In addition, provision should be made for the control center to dispatch investigators
to sources of potential trouble or send maintenance personnel to make
emergency repairs when necessary. Standards for such installations are NFPA 72A,
‘‘Local Protective Signaling Systems,’’ NFPA 72B, ‘‘Auxiliary Protective Signaling
Systems,’’ NFPA 72C, ‘‘Remote Station Protective Signaling Systems,’’ and NFPA
72D. ‘‘Proprietary Protective Signaling Systems.’’ See also Art. 3.7.2.
For economical building operation, the emergency control center may be made
part of a control center used for normal building operation and maintenance. Thus,
the control center may normally control HVAC to conserve energy, turn lights on
and off, and schedule building maintenance and repair. When an emergency occurs,
emergency control should be activated in accordance with prepared plans for handling
each type of emergency.
The control center need not be located within the building to be supervised nor
operated by in-house personnel. Instead, an external central station may provide the
3.48 SECTION THREE
necessary supervision. Such services are available in most cities and are arranged
by contract, usually with an installation charge and an annual maintenance charge.
Requirements for such systems are in National Fire Protection Association standard
NFPA 71.
3.5.13 Safety during Construction
Most building codes provide specific measures that must be taken for fire protection
during construction of buildings. But when they do not, fundamental fire-safety
precautions must be taken. Even those structures that will, when completed, be
noncombustible contain quantities of forming and packing materials that present a
serious fire hazard.
Multistory buildings should be provided with access stairways and, if applicable,
an elevator for fire department use. Stairs and elevator should follow as closely as
possible the upward progress of the structure and be available within one floor of
actual building height. In buildings requiring standpipes, the risers should be placed
in service as soon as possible, and as close to the construction floor as practicable.
Where there is danger of freezing, the water supply can consist of a Siamese connection
for fire department use.
In large-area buildings, required fire walls should be constructed as soon as
possible. Competent watchman service also should be provided.
The greatest source of fires during construction is portable heaters. Only the
safest kind should be used, and these safeguarded in every practical way. Fuel
supplies should be isolated and kept to a minimum.
Welding operations also are a source of fires. They should be regulated in accordance
with building-code requirements.
Control of tobacco smoking is difficult during building construction, so control
of combustible materials is necessary. Good housekeeping should be provided, and
all combustible materials not necessary for the work should be removed as soon as
possible.
Construction offices and shanties should be equipped with adequate portable
extinguishers. So should each floor in a multistory building.
3.6 LIGHTNING PROTECTION
Lightning, a high-voltage, high-current electrical discharge between clouds and the
ground, may strike and destroy life and property anywhere thunderstorms have
occurred in the past. Buildings and their occupants, however, can be protected
against this hazard by installation of a special electrical system. Because an incomplete
or poor installation can cause worse damage or injuries than no protection at
all, a lightning-protection system should be designed and installed by experts.
As an addition to other electrical systems required for a building, a lightningprotection
system increases the construction cost of a building. A building owner
therefore has to decide whether potential losses justify the added expenditure. In
doing so, the owner should take into account the importance of the building, danger
to occupants, value and nature of building contents, type of construction, proximity
of other structures or trees, type of terrain, height of building, number of days per
PROTECTION AGAINST HAZARDS 3.49
year during which thunderstorms may occur, costs of disruption of business or other
activities and the effects of loss of essential services, such as electrical and communication
systems. (Buildings housing flammable or explosive materials generally
should have lightning protection.) Also, the owner should compare the cost of
insurance to cover losses with the cost of the protection system.
3.6.1 Characteristics of Lightning
Lightning strikes are associated with thunderstorms. In such storms, the base of the
clouds generally develops a negative electrical charge, which induces a positive
charge in the earth directly below. As the clouds move, the positive charges, being
attracted by the negative charges, follow along the surface of the earth and climb
up buildings, antennas, trees, power transmission towers, and other conducting or
semiconducting objects along the path. The potential between clouds and earth may
build up to 106 to 109 V. When the voltage becomes great enough to overcome the
electrical resistance of the air between the clouds and the ground or an object on
it, current flows in the form of a lightning flash. Thus, the probability of a building
being struck by lightning depends not only on the frequency of occurrence of
thunderstorms but also on building height relative to nearby objects and the intensity
of cloud charges.
Destruction at the earth’s surface may result not only at points hit by lightning
directly but also by electrostatic induction at points several feet away. Also, lightning
striking a tall object may flash to a nearby object that offers a suitable path
to the ground.
Lightning often shatters nonconductors or sets them on fire if they are combustible.
Conductors struck may melt. Living things may be burned or electrocuted.
Also, lightning may induce overvoltages in electrical power lines, sending electrical
charges along the lines in both directions from the stricken point to ground. Directstroke
overvoltages may range up to several million volts and several hundred
thousand amperes. Induced strokes, which occur more frequently, may be on the
order of several hundred thousand volts with currents up to 2000 A. Such overvoltages
may damage not only electric equipment connected to the power lines but
also buildings served by them. Consequently, lightning protection is necessary for
outdoor conductors as well as for buildings.
3.6.2 Methods for Protecting against Lightning
Objectives of lightning protection are life safety, prevention of property damage,
and maintenance of essential services, such as electrical and communication systems.
Lightning protection usually requires installation of electrical conductors that
extend from points above the roof of a building to the ground, for the purpose of
conducting to the ground lightning that would otherwise strike the building. Such
an installation, however, possesses the potential hazard that, if not done properly,
lightning may flash from the lightning conductors to other building components.
Hence, the system must ensure that the lightning discharge is diverted away from
the building and its contents. Lightning protection systems should conform to the
standards of the American National Standards Institute, National Fire Protection
Association (NFPA 78, ‘‘Lightning Protection Code’’) and Underwriters Laboratories
(UL 96A, ‘‘Master Labeled Lightning-Protection Systems’’).
3.50 SECTION THREE
The key element in diverting lightning away from a building is an air terminal
or lightning rod, a conductor that projects into the air at least 12 in above the roof.
Air terminals should be spaced at intervals not exceeding 25 ft. Alternatively, a
continuous wire conductor or a grid of such conductors may be placed along the
highest points of a roof. If the tallest object on a roof is a metal mast, it can act
as an air terminal. A metal roof also can serve as an air terminal, but only if all
joints are made electrically continuous by soldering, welding, or interlocking. Arranged
to provide a cone of protection over the entire building, all the air terminals
should be connected by conductors to each other and, by the same or other conductors,
to the ground along at least two separated paths.
For roof and down conductors, copper, copper-clad steel, galvanized steel or a
metal alloy that is as resistant to corrosion as copper may be used. (A solid copper
conductor should be at least 1?4 in in diameter.) Direct connections between dissimilar
metals should be avoided to prevent corrosion. Metal objects and non-currentcarrying
components of electrical systems should be kept at least 6 ft away from
the lightning conductors or should be bonded to the nearest lightning conductor.
Sharp bends in the conductors are not desirable. If a 90
 bend must be used, the
conductor should be firmly anchored, because the high current in a lightning stroke
will tend to straighten the bend. If the conductor has a U bend, the high current
may induce an electric arc to leap across the loop while also exerting forces to
straighten out the bend.
In steel-frame buildings, the steel frame can be used as a down conductor. In
such cases, the top of the frame should be electrically connected to air terminals
and the base should be electrically connected to grounding electrodes. Similarly,
the reinforcing steel of a reinforced concrete building can be used as down conductors
if the reinforcing steel is bonded together from foundations to roof.
Damage to the electrical systems of buildings can be limited or prevented by
insertion of lightning arresters, safety valves that curtail overvoltages and bypass
thc current surge to a ground system, at the service entrance. Further protection
can be afforded electrical equipment, especially sensitive electronic devices, by
installing surge protectors, or spark gaps, near the equipment.
The final and equally important elements of a lightning-protection system are
grounding electrodes and the earth itself. The type and dimensions of the grounds,
or grounding electrodes, depends on the electrical resistance, or resistivity, of the
earth, which can be measured by technicians equipped with suitable instruments.
The objective of the grounding installation, which should be electrically bonded to
the down conductors, should be an earth-system resistance of 10  or less. Underground
water pipes can serve as grounds if they are available. If not, long metal
rods can be driven into the ground to serve as electrodes. Where earth resistivity
is poor, an extensive system of buried wires may be required.
(J. L. Marshall, ‘‘Lightning Protection,’’ John Wiley & Sons, Inc., New York.)
3.7 PROTECTION AGAINST INTRUDERS
Prevention of illegal entry into buildings by professional criminals determined to
break in is not practical. Hence, the prime objective of security measures is to make
illegal entry difficult. If this is done, it will take an intruder longer to gain entry or
will compel the intruder to make noise, thus increasing the chances of detection
and apprehension. Other objectives of security measures are detection of break-in
PROTECTION AGAINST HAZARDS 3.51
attempts and intruders, alarming intruders so that they leave the premises before
they cause a loss or injury, and alerting building occupants and the police of the
break-in attempt. Also, an objective is to safeguard valuable assets by placing them
in a guarded, locked, secure enclosure with access limited only to approved personnel.
Some communities have established ordinances setting minimum requirements
for security and incorporated them in the building code. (Communities that have
done this include Los Angeles, Oakland, and Concord in California; Indianapolis,
Ind.; Trenton, N.J.; Arlington Heights, Ill.; Arlington County, Va.; and Prince
George’s County, Md.) Provisions of these codes cover security measures for doors
and windows and associated hardware, accessible transoms, roof openings, safes,
lighting of parking lots, and intrusion-detection devices. For buildings requiring
unusual security measures, owners and designers should obtain the advice of a
security expert.
3.7.1 Security Measures
Basic security for a building is provided by commonly used walls and roofs with
openings protected by doors with key-operated locks or windows with latches. The
degree of protection required for a building and its occupants beyond basic security
and privacy needs depends on the costs of insurance and security measures relative
to potential losses from burglary and vandalism.
For a small building not housing small items of great value (these can be placed
in a safety deposit box in a bank), devices for detecting break-in attempts are
generally the most practical means for augmenting basic security. Bells, buzzers,
or sirens should be installed to sound an alarm and automatic telephone or wireless
dialer should be used to alert a monitoring service to notify the police when an
intruder tries to enter the locked building or a security area.
For a large building or a building requiring tight security, defense should be
provided in depth. Depending on the value of assets to be protected, protection
should start at the boundary of the property, with fences, gates, controlled access,
guard patrols, exterior illumination, alarms, or remote surveillance by closed-circuit
television. This defense should be backed up by similar measures at the perimeter
of the building and by security locks and latches on doors and windows. Openings
other than doorways or windows should be barred or made too small for human
entry and screened. Within the building, valuables should be housed in locked
rooms or a thick, steel safe, with controlled access to those areas.
For most types of occupancy, control at the entrance often may be provided by
a receptionist who records names of visitors and persons visited, notifies the latter
and can advise the police of disturbances. When necessary, the receptionist can be
augmented by a guard at the control point or in a security center and, in very large
or high-rise buildings, by a roving guard available for emergencies. If a large security
force is needed, facilities should be provided in the building for an office for
the security administrator and staff, photographic identification, and squad room
and lockers—all in or adjoining a security center.
3.7.2 Security Center
The security center may be equipped with or connected to electronic devices that
do the following:
3.52 SECTION THREE
1. Detect a break-in attempt and sound an alarm.
2. Identify the point of intrusion.
3. Turn on lights.
4. Display the intruder on closed-circuit television and record observations on
videotape.
5. Notify the police.
6. Limit entry to specific spaces only to approved personnel and only at permitted
times.
7. Change locks automatically.
In addition, the center may be provided with emergency reporting systems, security
guard tour reporting systems, fire detection and protection systems, including supervision
of automatic fire sprinklers, HVAC controls, and supervision of other life
safety measures. See also Art. 3.5.12.
(P. S. Hopf, ‘‘Handbook of Building Security Planning and Design,’’ McGraw-
Hill Publishing Company, New York.)
4.1
SECTION FOUR
BUILDING MATERIALS
David J. Akers
Civil Engineer, San Diego, California
This section describes the basic materials used in building construction and discusses
their common applications. As the world’s population increases and consumes
more of the natural resources, it is incumbent upon the civil engineer to use
building materials that contribute to sustaining development instead of satisfying
only the short-term need. Material selection should incorporate an evaluation of the
amount of energy required to produce and deliver the material to the building site.
This concept of ‘‘embodied energy’’ is evolving and variable. As an example, in
the Pacific Northwest lumber would have an ‘‘embodied energy’’ of 1, but in the
arid Southwest transportation raises the value several points. Examples of other
materials are concrete (2–3), steel (4–6), and aluminum (80). For discussion purposes,
materials used in similar applications are grouped and discussed in sequence,
for example, masonry materials, wood, metals, plastics, etc.
CEMENTITIOUS MATERIALS
Cementitious materials include the many products that are mixed with either water
or some other liquid or both to form a cementing paste that may be formed or
molded while plastic but will set into a rigid shape. When sand is added to the
paste, mortar is formed. A combination of coarse and fine aggregate (sand) added
to the paste forms concrete.
4.1 TYPES OF CEMENTITIOUS MATERIALS
There are many varieties of cements and numerous ways of classification. One of
the simplest classifications is by the chemical constituent that is responsible for the
setting or hardening of the cement. On this basis, the silicate and aluminate cements,
wherein the setting agents are calcium silicates and aluminates, constitute the most
important group of modern cements. Included in this group are the portland, aluminous,
and natural cements.
4.2 SECTION FOUR
Limes, wherein the hardening is due to the conversion of hydroxides to carbonates,
were formerly widely used as the sole cementitious material, but their slow
setting and hardening are not compatible with modern requirements. Hence, their
principal function today is to plasticize the otherwise harsh cements and add resilience
to mortars and stuccoes. Use of limes is beneficial in that their slow setting
promotes healing, the recementing of hairline cracks.
Another class of cements is composed of calcined gypsum and its related products.
The gypsum cements are widely used in interior plaster and for fabrication of
boards and blocks; but the solubility of gypsum prevents its use in construction
exposed to any but extremely dry climates.
Oxychloride cements constitute a class of specialty cements of unusual properties.
Their cost prohibits their general use in competition with the cheaper cements;
but for special uses, such as the production of sparkproof floors, they cannot be
equaled.
Masonry cements or mortar cements are widely used because of their convenience.
While they are, in general, mixtures of one of more of the above-mentioned
cements with some admixtures, they deserve special consideration because of their
economies.
Other cementitious materials, such as polymers, fly ash, and silica fume, may
be used as a cement replacement in concrete. Polymers are plastics with long-chain
molecules. Concretes made with them have many qualities much superior to those
of ordinary concrete.
Silica fume, also known as microsilica, is a waste product of electric-arc furnaces.
The silica reacts with limes in concrete to form a cementitious material. A
fume particle has a diameter only 1% of that of a cement particle.
4.2 PORTLAND CEMENTS
Portland cement, the most common of the modern cements, is made by carefully
blending selected raw materials to produce a finished material meeting the requirements
of ASTM C150 for one of eight specific cement types. Four major compounds
[lime (CaO), iron (Fe2O3), silica (SiO2), and alumina (Al2O3)] and two
minor compounds [gypsum (CaSO4 
 2H2O) and magnesia (MgO)] constitute the
raw materials. The calcareous (CaO) materials typically come from limestone, calcite,
marl, or shale. The argillaceous (SiO2 and Al2O3) materials are derived from
clay, shale, and sand. The materials used for the manufacture of any specific cement
are dependent on the manufacturing plant’s location and availability of raw materials.
Portland cement can be made of a wide variety of industrial by-products.
In the manufacture of cement, the raw materials are first mined and then ground
to a powder before blending in predetermined proportions. The blend is fed into
the upper end of a rotary kiln heated to 2600 to 3000
F by burning oil, gas, or
powdered coal. Because cement production is an energy-intensive process, reheaters
and the use of alternative fuel sources, such as old tires, are used to reduce the fuel
cost. (Burning tires provide heat to produce the clinker and the steel belts provide
the iron constituent.) Exposure to the elevated temperature chemically fuses the raw
materials together into hard nodules called cement clinker. After cooling, the clinker
is passed through a ball mill and ground to a fineness where essentially all of it
will pass a No. 200 sieve (75 m). During the grinding, gypsum is added in small
amounts to control the temperature and regulate the cement setting time. The maBUILDING
MATERIALS 4.3
terial that exits the ball mill is portland cement. It is normally sold in bags containing
94 lb of cement.
Concrete, the most common use for portland cement, is a complex material
consisting of portland cement, aggregates, water, and possibly chemical and mineral
admixtures. Only rarely is portland cement used alone, such as for a cement slurry
for filling well holes or for a fine grout. Therefore, it is important to examine the
relationship between the various portland cement properties and their potential effect
upon the finished concrete. Portland cement concrete is generally selected for
structural use because of its strength and durability. Strength is easily measured and
can be used as a general directly proportional indicator of overall durability. Specific
durability cannot be easily measured but can be specified by controlling the cement
chemistry and aggregate properties.
4.2.1 Specifications for Portland Cements
ASTM C150 defines requirements for eight types of portland cement. The pertinent
chemical and physical properties are shown in Table 4.1. The chemical composition
of portland cement is expressed in a cement-chemistry shorthand based on four
phase compounds: tricalcium silicate (C3S), dicalcium silicate (C2S), tricalcium aluminate
(C3A), and tetracalcium aluminum ferrite (C4AF). C2S and C3S are termed
the calcium silicate hydrates (CSH).
Most cements will exceed the requirements shown in Table 4.1 by a comfortable
margin. Note that the required compressive strengths are minimums. Almost without
exception, every portland cement will readily exceed these minimum values.
However, a caution must be attached to compressive strengths that significantly
exceed the minimum values. While there is not a one-to-one correlation between a
cement cube strength and the strength of concrete made with that cement (5000-
psi cement does not equate to 5000-psi concrete), variations in cube strengths will
be reflected in the tested concrete strength. It is imperative that, as the designed
concrete strength reaches 5000 psi and greater, the cement cube strength be rigorously
monitored. Any lowering of the running average will have a negative effect
on the strength of concrete if the concrete mix design is not altered.
The basic types of portland cement covered by ASTM C150 are as follows:
Type I, general-purpose cement, is the one commonly used for many structural
purposes. Chemical requirements for this type of cement are limited to magnesia
and sulfur-trioxide contents and loss on ignition, since the cement is adequately
defined by its physical characteristics.
Type II is a modified cement for use in general concrete where a moderate
exposure to sulfate attack may be anticipated or where a moderate heat of hydration
is required. These characteristics are attained by placing limitations on the C3S and
C3A content of the cement. Type II cement gains strength a little more slowly than
Type I but ultimately will achieve equal strength. It is generally available in most
sections of the country and is preferred by some engineers over Type I for general
construction. Type II cement may also be specified as a low-alkali cement for use
where alkali reactive aggregates are present. To do so requires that optional chemical
requirements (Table 4.2) be included in the purchase order. Type II low-alkali
cement is commonly specified in California.
Type III cement attains high early strength. In 7 days, strength of concrete made
with it is practically equal to that made with Type I or Type II cement at 28 days.
This high early strength is attained by finer grinding (although no minimum is
placed on the fineness by specification) and by increasing the C3S and C3A content
* Based on requirements in ‘‘Standard Specification for Portland Cement,’’ ASTM C150. See current
edition of C150 for exceptions, alternatives, and changes in requirements.
of the cement. Type III cement, however, has high heat evolution and therefore
should not be used in large masses. Because of the higher C3A content, Type III
cement also has poor sulfate resistance. Type III cement is not always available
from building materials dealers’ stocks but may be obtained by them from the
cement manufacturer on short notice. Ready-mix concrete suppliers generally do
not stock Type III cement because its shorter set time makes it more volatile to
transport and discharge, especially in hot weather.
Type IV is a low-heat cement that has been developed for mass concrete construction.
Normal Type I cement, if used in large masses that cannot lose heat by
radiation, will liberate enough heat during the hydration of the cement to raise the
temperature of the concrete as much as 50 or 60
F. This results in a relatively large
increase in dimensions while the concrete is still soft and plastic. Later, as the
concrete cools are hardening, shrinkage causes cracks to develop, weakening the
BUILDING MATERIALS 4.5
‡Low-alkali cement. This limit may be specified when cement is to be used in concrete with aggregates
that may be deleteriously reactive. See ‘‘Standard Specification for Concrete Aggregates,’’ ASTM C33.
concrete and affording points of attack for aggressive solutions. The potential-phase
compounds that make the largest contribution to the heat of hydration are C3S and
C3A; so the amounts of these are permitted to be present are limited. Since these
compounds also produce the early strength of cement, the limitation results in a
cement that gains strength relatively slowly. This is of little importance, however,
in the mass concrete for which this type of cement is designed.
Type V is a portland cement intended for use when high sulfate resistance is
required. Its resistance to sulfate attack is attained through the limitation on the
C3A content. It is particularly suitable for structures subject to attack by liquors
containing sulfates, such as liquids in wastewater treatment plants, seawaters, and
some other natural waters.
Both Type IV and Type V cements are specialty cements. They are not normally
available from dealer’s stock but are usually obtainable for use on a large job if
arrangements are made with the cement manufacturer in advance.
4.2.2 Air-Entraining Portland Cements
For use in the manufacturer of air-entraining concrete, agents may be added to the
cement by the manufacturer, thereby producing air-entraining portland cements
(‘‘Air-Entraining Additions for Use in the Manufacture of Air-Entraining Portland
Cement,’’ ASTM C226). These cements are available as Types IA, IIA, and IIIA.
4.3 ALUMINOUS CEMENTS
These are prepared by fusing a mixture of aluminous and calcareous materials
(usually bauxite and limestone) and grinding the resultant product to a fine powder.
These cements are characterized by their rapid-hardening properties and the high
strength developed at early ages. Table 4.3 shows the relative strengths of 4-in
cubes of 1:2:4 concrete made with normal portland, high-early-strength portland,
and aluminous cements.
Since a large amount of heat is liberated with rapidly by aluminous cement
during hydration, care must be taken not to use the cement in places where this
heat cannot be dissipated. It is usually not desirable to place aluminous-cement
concretes in lifts of over 12 in; otherwise the temperature rise may cause serious
weakening of the concrete.
Aluminous cements are much more resistant to the action of sulfate waters than
are portland cements. They also appear to be much more resistant to attack by
water containing aggressive carbon dioxide or weak mineral acids than the silicate
cements. Their principal use is in concretes where advantage may be taken of their
very high early strength or of their sulfate resistance, and where the extra cost of
the cement is not an important factor.
Another use of aluminous cements is in combination with firebrick to make
refractory concrete. As temperatures are increased, dehydration of the hydration
products occurs. Ultimately, these compounds create a ceramic bond with the aggregates.
4.4 NATURAL CEMENTS
Natural cements are formed by calcining a naturally occurring mixture of calcareous
and argillaceous substances at a temperature below that at which sintering takes
place. The ‘‘Specification for Natural Cement,’’ ASTM C10, requires that the temperature
be no higher than necessary to drive off the carbonic acid gas. Since natural
cements are derived from naturally occurring materials and no particular effort is
made to adjust the composition, both the composition and properties vary rather
widely. Some natural cements may be almost the equivalent of portland cement in
properties; others are much weaker. Natural cements are principally used in masonry
mortars and as an admixture in portland-cement concretes.
4.5 LIMES
These are made principally of calcium oxide (CaO), occurring naturally in limestone,
marble, chalk, coral, and shell. For building purposes, they are used chiefly
in mortars.
BUILDING MATERIALS 4.7
4.5.1 Hydraulic Limes
These are made by calcining a limestone containing silica and alumina to a temperature
short of incipient fusion so as to form sufficient free lime to permit hydration
and at the same time leave unhydrated sufficient calcium silicates to give
the dry powder its hydraulic properties (see ‘‘Specification for Hydraulic Hydrated
Lime for Structural Purposes,’’ ASTM C141).
Because of the low silicate and high lime contents, hydraulic limes are relatively
weak. They find their principal use in masonry mortars. A hydraulic lime with more
than 10% silica will set under water.
4.5.2 Quicklimes
When limestone is heated to a temperature in excess of 1700
F, the carbon dioxide
content is driven off and the remaining solid product is quicklime. It consists essentially
of calcium and magnesium oxides plus impurities such as silica, iron, and
aluminum oxides. The impurities are usually limited to less than 5%. If they exceed
10%, the product may be a hydraulic lime.
Two classes of quicklime are recognized, high-calcium and dolomitic. A highcalcium
quicklime usually contains less than 5% magnesium oxide. A dolomitic
quicklime usually contains from 35 to 40% magnesium oxide. A few quicklimes
are found that contain 5 to 35% magnesium oxide and are called magnesian limes.
The outstanding characteristic of quicklime is its ability to slake with water.
When quicklime is mixed with from two to three times its weight of water, a
chemical reaction takes place. The calcium oxide combines with water to form
calcium hydroxide, and sufficient heat is evolved to bring the entire mass to a boil.
The resulting product is a suspension of finely divided calcium hydroxide (and
magnesium hydroxide or oxide if dolomitic lime is used) in water. On cooling, the
semifluid mass stiffens to a putty of such consistency that it may be shoveled or
carried in a hod. This slaked quicklime putty, when cooled and preferably screened,
is the material used in construction. Quicklime should always be thoroughly slaked.
The yield of putty will vary, depending on the type of quicklime, its degree of
burning, and slaking conditions, and will usually be from 70 to 100 ft3 of putty per
ton of quicklime. The principal use of the putty is in masonry mortars, where it is
particularly valuable because of the high degree of plasticity or workability it imparts
to the mortar. It is used at times as an admixture in concrete to improve
workability. It also is used in some localities as finish-coat plaster where full advantage
may be taken of its high plasticity.
4.5.3 Mason’s Hydrated Lime
Hydrated limes are prepared from quicklimes by addition of a limited amount of
water. After hydration ceases to evolve heat, the resulting product is a fine, dry
powder. It is then classified by air-classification methods to remove undesirable
oversize particles and packaged in 50-lb sacks. It is always a factory-made product,
whereas quicklime putty is almost always a job-slaked product.
Mason’s hydrated limes are those hydrates suitable for use in mortars, base-coat
plasters, and concrete. They necessarily follow the composition of the quicklime.
High-calcium hydrates are composed primarily of calcium hydroxide. Normal dolomitic
hydrates are composed of calcium hydroxide plus magnesium oxide.
4.8 SECTION FOUR
Plasticity of mortars made from normal mason’s hydrated limes (Type N) is fair.
It is better than that attained with most cements, but not nearly so high as that of
mortars made with an equivalent amount of slaked putty.
The normal process of hydration of a dolomitic quicklime at atmospheric pressure
results in the hydration of the calcium fraction only, leaving the magnesiumoxide
portion substantially unchanged chemically. When dolomitic quicklime is
hydrated under pressure, the magnesium oxide is converted to magnesium hydroxide.
This results in the so-called special hydrates (Type S), which not only have
their magnesia contents substantially completely hydrated but also have a high
degree of plasticity immediately on wetting with water. Mortars made from Type
S hydrates are more workable than those made from Type N hydrates. In fact, Type
S hydrates are nearly as workable as those made from slaked quicklime putties.
The user of this type of hydrate may therefore have the convenience of a bagged
product and a high degree of workability without having the trouble and possible
hazard of slaking quicklime.
4.5.4 Finishing Hydrated Limes
Finishing hydrated limes are particularly suitable for use in the finishing coat of
plaster. They are characterized by a high degree of whiteness and plasticity. Practically
all finishing hydrated limes are produced in the Toledo district of Ohio from
dolomitic limestone. The normal hydrate is composed of calcium hydroxide and
magnesium oxide. When first wetted, it is no more plastic than Type N mason’s
hydrates. It differs from the latter, however, in that, on soaking overnight, the finishing
hydrated lime develops a very high degree of plasticity, whereas the mason’s
hydrate shows relatively little improvements in plasticity on soaking.
4.6 LOW-TEMPERATURE GYPSUM DERIVATIVES
When gypsum rock (CaSO4 
 2H2O) is heated to a relatively low temperature, about
130
C, three-fourths of the water of crystallization is driven off. The resulting product
is known by various names such as hemihydrate, calcined gypsum, and firstsettle
stucco. Its common name, however, is plaster of paris. It is a fine powder,
usually white. While it will set under water, it does not gain strength and ultimately,
on continued water exposure, will disintegrate.
Plaster of paris, with set retarded or unretarded, is used as a molding plaster or
as a gaging plaster. The molding plaster is used for preparing ornamental plaster
objects. The gaging plaster is used for finishing hydrated lime to form the smooth
white-coat finish on plaster walls. The unretarded plaster of paris is used by manufacturers
to make gypsum block, tile, and gypsumboard (wallboard, lath, backerboard,
coreboard, etc.).
When plaster of paris is retarded and mixed with fiber such as sisal, it is marketed
under the name of hardwall plaster or cement plaster. (The latter name is
misleading, since it does not contain any portland cement.) Hardwall plaster, mixed
with water and with from two to three parts of sand by weight, is widely used for
base-coat plastering. In some cases wood fiber is used in place of sand, making a
‘‘wood-fibered’’ plaster.
Special effects are obtained by combining hardwall plaster with the correct type
of aggregate. With perlite or vermiculite aggregate, a lightweight plaster is obtained.
BUILDING MATERIALS 4.9
Gypsum plasters, in general, have a strong set, gain their full strength when dry,
do not have abnormal volume changes, and have excellent fire-resistance characteristics.
They are not well adapted, however, for use under continued damp conditions
or intermittent wet conditions. See also Arts. 4.26 to 4.30.
4.7 OXYCHLORIDE CEMENTS
Lightly calcined magnesium oxide mixed with a solution of magnesium chloride
forms a cement known as magnesium oxychloride cement, or Sorel cement. It is
particularly useful in making flooring compositions in which it is mixed with colored
aggregates. Floors made of oxychloride cement are sparkproof and are more
resilient than floors of concrete.
Oxychloride cement has very strong bonding power and, because of its higher
bonding power, may be used with greater quantities of aggregate than are possible
with portland cement. Oxychloride cement also bonds well with wood and is used
in making partition block or tile with wood shavings or sawdust as aggregate. It is
moderately resistant to water but should not be used under continually wet conditions.
4.8 MASONRY CEMENTS
Masonry cements, or—as they are sometimes called—mortar cements, are intended
to be mixed with sand and used for setting unit masonry, such as brick, tile, and
stone. They may be any one of the hydraulic cements already discussed or mixtures
of them in any proportion.
Many commercial masonry cements are mixtures of portland cement and pulverized
limestone, often containing as much as 50 or 60% limestone. They are sold
in bags containing from 70 to 80 lb, each bag nominally containing a cubic foot.
Price per bag is commonly less than of portland cement, but because of the use of
the lighter bag, cost per ton is higher than that of portland cement.
Since there are no limits on chemical content and physical requirements, masonry
cement specifications are quite liberal. Some manufacturers vary the composition
widely, depending on competition, weather conditions, or availability of
materials. Resulting mortars may vary widely in properties.
4.9 FLY ASHES
Fly ash meeting the requirements of ASTM C618, ‘‘Specification for Fly Ash and
Raw or Calcined Natural Pozzolan for Use as a Mineral Admixture in Portland
Cement Concrete,’’ is generally used as a cementitious material as well as an admixture.
Natural pozzolans are derived from some diatomaceous earths, opaline cherts
and shales, and other materials. While part of a common ASTM designation with
fly ash, they are not as readily available as fly ashes and thus do not generate the
same level of interest or research.
4.10 SECTION FOUR
Fly ashes are produced by coal combustion, generally in an electrical generating
station. The ash that would normally be released through the chimney is captured
by various means, such as electrostatic precipitators. The fly ash may be sized prior
to shipment to concrete suppliers.
All fly ashes possess pozzolanic properties, the ability to react with calcium
hydroxide at ordinary temperatures to form compounds with cementitious properties.
When cement is mixed with water, a chemical reaction (hydration) occurs.
The product of this reaction is calcium silicate hydrate (CSH) and calcium hydroxide
[Ca(OH)2]. Fly ashes have high percentages of silicon dioxide (SiO2). In the
presence of moisture, the Ca(OH)2 will react with the SiO2 to form another CSH.
Type F ashes are the result of burning anthracite or bituminous coals and possess
pozzolanic properties. They have been shown by research and practice to provide
usually increased sulfate resistance and to reduce alkali-aggregate expansions. Type
C fly ashes result from burning lignite or subbituminous coals. Because of the
chemical properties of the coal, the Type C fly ashes have some cementitious properties
in addition to their pozzolanic properties. Type C fly ashes may reduce the
durability of concretes into which they are incorporated.
4.10 SILICA FUME (MICROSILICA)
Silica fume, or microsilica, is a condensed gas, the by-product of metallic silicon
or ferrosilicon alloys produced by electric arc furnaces. (While both terms are correct,
microsilica (MS) is a less confusing name.) The Canadian standard CAN/
CSA-A23.5-M86, ‘‘Supplementary Cementing Materials,’’ limits amorphous SiO2
to a maximum of 85% and oversize to 10%. Many MS contain more than 90%
SiO2.
MS has an average diameter of 0.1 to 0.2 m, a particle size of about 1% that
of portland cement. Because of this small size, it is not possible to utilize MS in
its raw form. Manufacturers supply it either densified, in a slurry (with or without
water-reducing admixtures), or pelletized. Either the densified or slurried MS can
be utilized in concrete. The pelletized materials is densified to the point that it will
not break down during mixing.
Because of its extremely small size, MS imparts several useful properties to
concrete. It greatly increases long-term strength. It very efficiently reacts with the
Ca(OH)2 and creates a beneficial material in place of a waste product. MS is generally
used in concrete with a design strength in excess of 12,000 psi. It provides
increased sulfate resistance to concrete, and it significantly reduces the permeability
of concrete. Also, its small size allows MS to physically plug microcracks and tiny
openings.
AGGREGATES
Aggregate is a broad encompassing boulders, cobbles, crushed stone, gravel, aircooled
blast furnace slag, native and manufactured sands, and manufactured and
natural lightweight aggregates. Aggregates may be further described by their respective
sizes.
BUILDING MATERIALS 4.11
4.11 NORMAL-WEIGHT AGGREGATES
These typically have specific gravities between 2.0 and 3.0. They are usually distinguished
by size as follows:
Boulders Larger than 6 in
Cobbles 6 to 3 in
Coarse aggregate 3 in to No. 4 sieve
Fine aggregate No. 4 sieve to No. 200 sieve
Mineral filler Material passing No. 200 sieve
Used in most concrete construction, normal-weight aggregates are obtained by
draining riverbeds or mining and crunching formational material. Concrete made
with normal-weight fine and coarse aggregates generally weights about 144 lb / ft3.
Boulders and cobbles are generally not used in their as-mined size but are
crushed to make various sizes of coarse aggregate and manufactured sand and
mineral filler. Gravels and naturally occurring sand are produced by the action of
water and weathering on glacial and river deposits. These materials have round,
smooth surfaces and particle-size distributions that require minimal processing.
These materials can be supplied in either coarse or fine-aggregate sizes.
Fine aggregates have 100% of their material passing the 3?8-in sieve. Coarse
aggregates have the bulk of the material retained on the No. 4 sieve.
Aggregates comprise the greatest volume percentage in portland-cement concrete,
mortar, or asphaltic concrete. In a portland-cement concrete mix, the coarse
and fine aggregates occupy about 60 to 75% of the total mix volume. For asphaltic
concrete, the aggregates represent 75 to 85% of the mix volume. Consequentially,
the aggregates are not inert filler materials. The individual aggregate properties have
demonstrable effects on the service life and durability of the material system in
which the aggregate is used, such as portland-cement concrete, asphaltic concrete,
mortar, or aggregate base.
The acceptability of a coarse or fine aggregate for use in concrete or mortar is
judged by many properties including gradation, amount of fine material passing the
No. 200 sieve, hardness, soundness, particle shape, volume stability, potential alkali
reactivity, resistance to freezing and thawing, and organic impurities. For aggregates
used in general building construction, property limits are provided in ASTM C33,
‘‘Specification for Concrete Aggregates,’’ C637, ‘‘Specification for Aggregates for
Radiation-Shielding Concrete,’’ and C330, ‘‘Specification for Lightweight Aggregates
for Structural Concrete.’’ For other types of construction, such as highways
and airports, standards written by various trade or governmental organizations are
available.
4.11.1 Gradation of Aggregates
The distribution of aggregate sizes in a concrete mix is important because it directly
influences the amount of cement required for a given strength, workability of the
mix (and amount of effort to place the mix in the forms), in-place durability, and
overall economy. ASTM C33 provides ranges of fine- and coarse-aggregate grading
limits. The latter are listed from Size 1 (31?2 to 11?2 in) to Size 8 (3?8 to No. 8). The
4.12 SECTION FOUR
National Stone Association specifies a gradation for manufactured sand that differs
from that for fine aggregate in C33 principally for the No. 100 and 200 sieves. The
NSA gradation is noticeably finer (greater percentages passing each sieve). The fine
materials, composed of angular particles, are rock fines, as opposed to silts and
clays in natural sand, and contribute to concrete workability.
The various gradations provide standard sizes for aggregate production and
quality-control testing. They are conducive to production of concrete with acceptable
properties. Caution should be exercised, however, when standard individual
grading limits are used. If the number of aggregate sizes are limited or there is not
sufficient overlap between aggregates sizes, an acceptable or economical concrete
may not be attainable with acceptably graded aggregates. The reason for this is that
the combined gradation is gap graded. The ideal situation is a dense or well-graded
size distribution that optimizes the void content of the combined aggregates (Art.
4.17). It is possible, however, to produce acceptable concrete with individual aggregates
that do not comply with the standard limits but that can be combined to
produce a dense gradation.
4.11.2 Amount of Fine Material Passing the No. 200 Sieve
The material passing the No. 200 sieve is clay, silt, or a combination of the two.
It increases the water demand of the aggregate. Large amounts of materials smaller
than No. 200 may also indicate the presence of clay coatings on the coarse aggregate
that would decrease bond of the aggregate to the cement matrix. A test method
is given in ASTM C117, ‘‘Materials Finer than 75 m Sieve in Mineral Aggregates
by Washing.’’
4.11.3 Hardness
Coarse-aggregate hardness is measured by the Los Angeles Abrasion Test, ASTM
C131 or C595. These tests break the aggregate down by impacting it with steel
balls in a steel tumbler. The resulting breakdown is not directly related to the
abrasion an aggregate receives in service, but the results can be empirically related
to concretes exhibiting service lives.
4.11.4 Soundness
Aggregate soundness is measured by ASTM C88, ‘‘Test Method for Soundness of
Aggregates by Use of Sodium Sulfate or Magneisum Sulfate.’’ This test measures
the amount of aggregate degradation when exposed to alternating cycles of wetting
and drying in a sulfate solution.
4.11.5 Particle Shape
Natural sand and gravel have a round, smooth particle shape. Crushed aggregate
(coarse and fine) may have shapes that are flat and elongated, angular, cubical, disk,
or rodlike. These shapes result from the crushing equipment employed and the
aggregate mineralogy. Extreme angularity and elongation increase the amount of
cement required to give strength, difficulty in finishing, and effort required to pump
BUILDING MATERIALS 4.13
the concrete. Flat and elongated particles also increase the amount of required
mixing water.
The bond between angular particles is greater than that between smooth particles.
Properly graded angular particles can take advantage of this property and offset the
increase in water required to produce concrete with cement content and strength
equal to that of a smooth-stone mix.
4.11.6 Potential Alkali Reactivity
Aggregates that contain certain forms of silicas or carbonates may react with the
alkalies present in portland cement (sodium oxide and potassium oxide). The reaction
product cracks the concrete or may create pop-outs at the concrete surface.
The reaction is more pronounced when the concrete is in a warm, damp environment.
Testing for potentially reactive aggregates is difficult, since the available tests
do not yield consistent answers. Tests for aggregate potential alkali reactivity can
be categorized as pre- or post-concrete and chemical or physical. Of the three preconcrete
tests, one is chemical. The standard chemical test (ASTM C289) is a
screening test that should only be used for an initial aggregate screening. Experience
has shown the test will give false positive reactions of potentially reactive aggregates.
The old mortar bar test (ASTM C227) is very slow and may be too lenient.
The rapid immersion mortar bar test (ASTM C1260) is a harsher test but can
produce results in two weeks. Potential alkali reactivity can be determined in concrete
by observation or using a uranal acetate ultraviolet light test procedure. Petrographic
analysis of aggregates and hardened concrete can be used to evaluate the
potential for alkali silica reactivity (ASR). Long-term field experience with available
aggregate sources is the best predictor of ASR.
4.11.7 Resistance to Freezing and Thawing
The pore structure, absorption, porosity, and permeability of aggregates are especially
important if they are used to make concrete exposed to repeated cycles of
freezing and thawing. Aggregates that become critically saturated and then freeze
cannot accommodate the expansion of the frozen water. Empirical data show that
freeze-thaw deterioration is caused by the coarse aggregates and not the fine. A
method prescribed in ‘‘Test Method for Resistance of Concrete to Rapid Freezing
and Thawing,’’ ASTM C666, measures concrete performance by weight changes, a
reduction in the dynamic modulus of elasticity, and increases in sample length.
4.11.8 Impurities in Aggregates
Erratic setting times and rates of hardening may be caused by organic impurities
in the aggregates, primarily the sand. The presence of these impurities can be
investigated by a method given in ‘‘Test Method for Organic Impurities in Fine
Aggregates for Concrete,’’ ASTM C40.
Pop-outs and reduced durability can be caused by soft particles, chert, clay
lumps and other friable particles, coal, lignite, or other lightweight materials in the
aggregates. Coal and lignite may also cause staining of exposed concrete surfaces.
4.14 SECTION FOUR
4.11.9 Volume Stability
Volume stability refers to susceptibility of aggregate to expansion when heated or
to cyclic expansions and contractions when saturated and dried. Aggregates that are
susceptible to volume change due to moisture should be avoided.
4.12 HEAVYWEIGHT AND LIGHTWEIGHT
AGGREGATES
Heavyweight aggregates include magnetite, with a specific gravity  of 4.3; barite,
 4.2; limonite,  3.8; ferrophosphorus,  6.3; and steel shot or punchings,
  7.6. Such heavyweight aggregates may be used instead of gravel or crushed
stone to produce a dense concrete; for example, for shielding of nuclear reactors
as specified in ASTM C637.
Lightweight Aggregates. These can be divided into two categories: structural and
nonstructural. The structural lightweight aggregates are defined by ASTM C330
and C331. They are either manufactured (expanded clay, shale, or slate, or blastfurnace
slag) or natural (scoria and pumice). These aggregates produce concretes
generally in the strength range of 3000 to 4000 psi; higher strengths are attainable
and are discussed in Art. 4.17. The air-dry unit weight of normal strength lightweight
concrete (less than 5000 psi) ranges from 100 to 115 pcf. High-performance
lightweight concrete has unit weights in the range of 120 pcf.
The common nonstructural lightweight aggregates (ASTM C332) are vermiculite
and perlite, although scoria and pumice can also be used. These materials are used
in insulating concretes for soundproofing and nonstructural floor toppings.
Lightweight aggregates produce concrete with low thermal conductivities, which
equate to good fire protection. When concrete is exposed to extreme heat, the
moisture present within the concrete rapidly changes from a liquid to steam having
a volume of up to 15 times larger. The large number and large sizes of pores within
lightweight aggregates create pressure-relief regions.
ADMIXTURES FOR CONCRETE
Admixtures are anything other than portland cement, water, and aggregates that are
added to a concrete mix to modify its properties. Included in this definition are
chemical admixtures (ASTM C494 and C260), mineral admixtures such as fly ash
(C618) and silica fume, corrosion inhibitors, colors, fibers, and miscellaneous
(pumping aids, dampproofing, gas-forming, permeability-reducing agents).
4.13 CHEMICAL AND MINERAL ADMIXTURES
Chemical admixtures used in concrete generally serve as water reducers, accelerators,
set retarders, or a combination. ASTM C494, ‘‘Standard Specification for
Chemical Admixtures for Concrete,’’ contains the following classification:
BUILDING MATERIALS 4.15
Type Property
A Water reducer
B Set retarder
C Set accelerator
D Water reducer and set retarder
E Water reducer and set accelerator
F High-range water reducer
G High-range water reducer and set retarder
High-range admixtures reduce the amount of water needed to produce a concrete
of a specific consistency by 12% or more.
4.13.1 Water-Reducing Admixtures
These decrease water requirements for a concrete mix by chemically reacting with
early hydration products to form a monomolecular layer of admixture at the cementwater
interface. This layer isolates individual particles of cement and reduces the
energy required to cause the mix to flow. Thus, the mix is ‘‘lubricated’’ and exposes
more cement particles for hydration.
The Type A admixture allows the amount of mixing water to be reduced while
maintaining the same mix slump. Or at a constant water-cement ratio, this admixture
allows the cement content to be decreased without loss of strength. If the amount
of water is not reduced, slump of the mix will be increased and also strength will
be increased because more of the cement surface area will be exposed for hydration.
Similar effects occur for Type D and E admixtures. Typically, a reduction in mixing
water of 5 to 10% can be expected.
Type F and G admixtures are used where there is a need for high-workability
concrete. A concrete without an admixture typically has a slump of 2 to 3 in. After
the admixture is added, the slump may be in the range of 8 to 10 in without
segregation of mix components. These admixtures are especially useful for mixes
with a low water-cement ratio. Their 12 to 30% reduction in water allows a corresponding
reduction in cementitious material.
The water-reducing admixtures are commonly manufactured from lignosulfonic
acids and their salts, hydroxylated carboxylic acids and their salts, or polymers of
derivatives of melamines or naphthalenes or sulfonated hydrocarbons. The combination
of admixtures used in a concrete mix should be carefully evaluated and tested
to ensure that the desired properties are achieved. For example, depending on the
dosage of admixture and chemistry of the cement, it is possible that a retarding
admixture will accelerate the set. Note also that all normal-set admixtures will retard
the set if the dosage is excessive. Furthermore, because of differences in percentage
of solids between products from different companies, there is not always a direct
correspondence in dosage between admixtures of the same class. Therefore, it is
important to consider the chemical composition carefully when evaluating competing
admixtures.
Superplasticizers are high-range water-reducing admixtures that meet the requirements
of ASTM C494 Type F or G. They are often used to achieve highstrength
concrete by use of a low water-cement ratio with good workability and
low segregation. They also may be used to produce concrete of specified strengths
4.16 SECTION FOUR
with less cement at constant water-cement ratio. And they may be used to produce
self-compacting, self-leveling flowing concretes, for such applications as longdistance
pumping of concrete from mixer to formwork or placing concrete in forms
congested with reinforcing steel. For these concretes, the cement content or watercement
ratio is not reduced, but the slump is increased substantially without causing
segregation. For example, an initial slump of 3 to 4 in for an ordinary concrete mix
may be increased to 7 to 8 in without addition of water and decrease in strength.
Superplasticizers may be classified as sulfonated melamine-formaldehyde condensates,
sulfonated naphthaline-formaldehyde condensates, modified lignosulfonates,
or synthetic polymers.
4.13.2 Air-Entraining Admixtures
These create numerous microscopic air spaces within concrete to protect it from
degradation due to repeated freezing and thawing or exposure to aggressive chemicals.
For concrete exposed to repeated cycles of freezing and thawing, the air gaps
provide room for expansion of external and internal water, which otherwise would
damage the concrete.
Since air-entrained concrete bleeds to a lesser extent than non-air-entrained, there
are fewer capillaries extending from the concrete matrix to the surface. Therefore,
there are fewer avenues available for ingress of aggressive chemicals into the concrete.
The ‘‘Standard Specification for Air-Entraining Admixtures for Concrete,’’
ASTM C260, covers materials for use of air-entraining admixtures to be added to
concrete in the field. Air entrainment may also be achieved by use of Types IIA
and IIIA portland cements (Art. 4.2.2).
4.13.3 Set-Accelerating Admixtures
These are used to decrease the time from the start of addition of water to cement
to initial set and to increase the rate of strength gain of concrete. The most commonly
used set-accelerating admixture is calcium chloride. Its use, however, is
controversial in cases where reinforcing or prestressing steel is present. The reason
is that there is a possibility that the accelerator will introduce free chloride ions
into the concrete, thus contributing to corrosion of the steel. An alternative is use
of one of many admixtures not containing chloride that are available.
4.13.4 Retarding Admixtures
To some extent, all normal water-reducing admixtures retard the initial set of concrete.
A Type B or D admixture will allow transport of concrete for a longer time
before initial set occurs. Final set also is delayed. Hence, precautions should be
taken if retarded concrete is to be used in walls.
Depending on the dosage and type of base chemicals in the admixture, initial
set can be retarded for several hours to several days. A beneficial side effect of
retardation of initial and final sets is an increase in the compressive strength of the
concrete. A commonly used Type D admixture provides higher 7- and 28-day
strengths than a Type A when used in the same mix design.
BUILDING MATERIALS 4.17
4.13.5 Mineral Admixtures
Fly ashes, pozzolans, and microsilicates are included in the mineral admixture classification
(Arts. 4.9 and 4.10). Natural cement (Art. 4.4) is sometimes used as an
admixture.
4.13.6 Corrosion Inhibitors
Reinforcing steel in concrete usually is protected against corrosion by the high
alkalinity of the concrete, which creates a passivating layer at the steel surface.
This layer is composed of ferric oxide, a stable compound. Within and at the surface
of the ferric oxide, however, are ferrous-oxide compounds, which are more reactive.
When the ferrous-oxide compounds come into contact with aggressive substances,
such as chloride ions, they react with oxygen to form solid, iron-oxide corrosion
products. These produce a fourfold increase in volume and create an expansion
force greater than the concrete tensile strength. The result is deterioration of the
concrete.
For corrosion to occur, chloride in the range of 1.0 to 1.5 lb /yd3 must be present.
If there is a possibility that chlorides may be introduced from outside the concrete
matrix, for example, by deicing salts, the concrete can be protected by lowering
the water-cement ratio, or increasing the amount of cover over the reinforcing steel,
or entraining air in the concrete, or adding a calcium-nitrate admixture, or adding
an internal-barrier admixture, or cathodic protection, or a combination of these
methods.
To inhibit corrosion, calcium-nitrate admixtures are added to the concrete at the
time of batching. They do not create a physical barrier to chloride ion ingress.
Rather, they modify the concrete chemistry near the steel surface. The nitrite ions
oxidize ferrous oxide present, converting it to ferric oxide. The nitrite is also absorbed
at the steel surface and fortifies the ferric-oxide passivating layer. For a
calcium-nitrite admixture to be effective, the dosage should be adjusted in accordance
with the exposure condition of the concrete to corrosive agents. The greater
the exposure, the larger should be the dosage. The correct dosage can only be
determined on a project-by-project basis with data for the specific admixture proposed.
Internal-barrier admixtures come in two groups. One comprises waterproofing
and dampproofing compounds (Art. 4.15). The second consists of agents that create
an organic film around the reinforcing steel, supplementing the passivating layer.
This type of admixture is promoted for addition at a fixed rate regardless of expected
chloride exposure.
4.13.7 Coloring Admixtures
Colors are added to concrete for architectural reasons. They may be mineral oxides
or manufactured pigments. Raw carbon black, a commonly used material for black
color, greatly reduces the amount of entrained air in a mix. Therefore, if black
concrete is desired for concrete requiring air-entrainment (for freeze-thaw or aggressive
chemical exposure), either the carbon black should be modified to entrain
air or an additional air-entraining agent may be incorporated in the mix. The mix
design should be tested under field conditions prior to its use in construction. Use
4.18 SECTION FOUR
of color requires careful control of materials, batching, and water addition in order
to maintain a consistent color at the jobsite.
4.14 FIBERS FOR CONCRETE MIXES
As used in concrete, fibers are discontinuous, discrete units. They may be described
by their aspect ratio, the ratio of length to equivalent diameter. Fibers find their
greatest use in crack control of concrete flatwork, especially slabs on grade.
The most commonly used types of fibers in concrete are synthetics, which include
polypropylene, nylon, polyester, and polyethylene materials. Specialty synthetics
include aramid, carbon, and acrylic fibers. Glass-fiber-reinforced concrete is
made using E-glass and alkali-resistant (AR) glass fibers. Steel fibers are chopped
high-tensile or stainless steel.
Fibers should be dispersed uniformly throughout a mix. Orientation of the fibers
in concrete generally is random. Conventional reinforcement, in contrast, typically
is oriented in one or two directions, generally in planes parallel to the surface.
Further, welded-wire fabric or reinforcing steel bars must be held in position as
concrete is placed. Regardless of the type, fibers are effective in crack control
because they provide omnidirectional reinforcement to the concrete matrix. With
steel fibers, impact strength and toughness of concrete may be greatly improved
and flexural and fatigue strengths enhanced.
Synthetic fibers are typically used to replace welded-wire fabric as secondary
reinforcing for crack control in concrete flatwork. Depending on the fiber length,
the fiber can limit the size and spread of plastic shrinkage cracks or both plastic
and drying shrinkage cracks. Although synthetic fibers are not designed to provide
structural properties, slabs tested in accordance with ASTM E72, ‘‘Standard Methods
of Conducting Strength Tests of Panels for Building Construction,’’ showed that
test slabs reinforced with synthetic fibers carried greater uniform loads than slabs
containing welded wire fabric. While much of the research for synthetic fibers has
used reinforcement ratios greater than 2%, the common field practice is to use 0.1%
(1.5 lb /yd3). This dosage provides more cross-sectional area than 10-gage weldedwire
fabric. The empirical results indicate that cracking is significantly reduced and
is controlled. A further benefit of fibers is that after the initial cracking, the fibers
tend to hold the concrete together.
Aramid, carbon, and acrylic fibers have been studied for structural applications,
such as wrapping concrete columns to provide additional strength. Other possible
uses are for corrosion-resistance structures. The higher costs of the specialty synthetics
limit their use in general construction.
Glass-fiber-reinforced concrete (GFRC) is used to construct many types of building
elements, including architectural wall panels, roofing tiles, and water tanks. The
full potential of GFRC has not been attained because the E-glass fibers are alkali
reactive and the AR-glass fibers are subject to embrittlement, possibly from infiltration
of calcium-hydroxide particles.
Steel fibers can be used as a structural material and replace conventional reinforcing
steel. The volume of steel fiber in a mix ranges from 0.5 to 2%. Much
work has been done to develop rapid repair methods using thin panels of densely
packed steel fibers and a cement paste squeegeed into the steel matrix. American
Concrete Institute Committee 544 states in ‘‘Guide for Specifying, Mixing, Placing,
and Finishing Steel Fiber Reinforced Concrete,’’ ACI 544.3R, that, in structural
BUILDING MATERIALS 4.19
members such as beams, columns, and floors not on grade, reinforcing steel should
be provided to support the total tensile load. In other cases, fibers can be used to
reduce section thickness or improve performance. See also ACI 344.1R and 344.2R.
4.15 MISCELLANEOUS ADMIXTURES
There are many miscellaneous concrete additives for use as pumping aids and as
dampproofing, permeability-reducing, gas-forming agents.
Pumping aids are used to decrease the viscosity of harsh or marginally pumpable
mixes. Organic and synthetic polymers, fly ash, bentonite, or hydrated lime
may be used for this purpose. Results depend on concrete mix, including the effects
of increased water demand and the potential for lower strength resulting from the
increased water-cement ratio. If sand makes the mix marginally pumpable, fly ash
is the preferred pumping additive. It generally will not increase the water demand
and it will react with the calcium hydroxide in cement to provide some strength
increase.
Dampproofing admixtures include soaps, stearates, and other petroleum products.
They are intended to reduce passage of water and water vapor through concrete.
Caution should be exercised when using these materials inasmuch as they
may increase water demand for the mix, thus increasing the permeability of the
concrete. If dense, low-permeable concrete is desired, the water-cement ratio should
be kept to a maximum of 0.50 and the concrete should be well vibrated and damp
cured.
Permeability of concrete can be decreased by the use of fly ash and silica fume
as admixtures. Also, use of a high-range water-reducing admixture and a watercement
ratio less than 0.50 will greatly reduce permeability.
Gas-forming admixtures are used to form lightweight concrete. They are also
used in masonry grout where it is desirable for the grout to expand and bond to
the concrete masonry unit. They are typically an aluminum powder.
MORTARS AND CONCRETES
4.16 MORTARS
Mortars are composed of a cementitious material, fine aggregate, sand, and water.
They are used for bedding unit masonry, for plasters and stuccoes, and with the
addition of coarse aggregate, for concrete. Here consideration is given primarily to
those mortars used for unit masonry and plasters.
Properties of mortars vary greatly, being dependent on the properties of the
cementitious material used, ratio of cementitious material to sand, characteristics
and grading of the sand, and ratio of water to solids.
4.16.1 Packaging and Proportioning of Mortar
Mortars are usually proportioned by volume. A common specification is that not
more than 3 ft3 of sand be used with 1 ft3 of cementitious material. Difficulty is
sometimes encountered, however, in determining just how much material constitutes
a cubic foot: a bag of cement (94 lb) by agreement is called a cubic foot in proportioning
mortars or concretes, but an actual cubic foot of lime putty may be used
in proportioning mortars. Since hydrated limes are sold in 50-lb bags (Art. 4.5.3),
each of which makes somewhat more than a cubic foot of putty, weights of 40, 42,
and 45 lb of hydrated lime have been used as a cubic foot in laboratory studies;
but on the job, a bag is frequently used as a cubic foot. Masonry cements are sold
in bags containing 70 to 80 lb (Art. 4.8), and a bag is considered a cubic foot.
4.16.2 Properties of Mortars
Table 4.4 lists types of mortars as a guide in selection for unit masonry.
Workability is an important property of mortars, particularly of those used in
conjunction with unit masonry of high absorption. Workability is controlled by the
character of the cement and amount of sand. For example, a mortar made from 3
parts sand and 1 part slaked lime putty will be more workable than one made from
2 parts sand and 1 part portland cement. But the 3:1 mortar has lower strength. By
proper selection or mixing of cementitious materials, a satisfactory compromise
may usually be obtained, producing a mortar of adequate strength and workability.
Water retention—the ratio of the flow after 1-min standard suction to the flow
before suction—is used as an index of the workability of mortars. A high value of
water retention is considered desirable for most purposes. There is, however, a wide
variation in water retention of mortars made with varying proportions of cement
and lime and with varying limes. The ‘‘Standard Specification for Mortar for Unit
Masonry,’’ ASTM C270, requires mortar mixed to an initial flow of 100 to 115, as
determined by the test method of ASTM C109, to have a flow after suction of at
least 75%.
Strength of mortar is frequently used as a specification requirement, even though
it has little relation to the strength of masonry. (See, for example, ASTM C270,
BUILDING MATERIALS 4.21
C780, and C476). The strength of mortar is affected primarily by the amount of
cement in the matrix. Other factors of importance are the ratio of sand to cementing
material, curing conditions, and age when tested.
Volume change of mortars constitutes another important property. Normal volume
change (as distinguished from unsoundness) may be considered as the shrinkage
during early hardening, shrinkage on drying, expansion on wetting, and changes
due to temperature.
After drying, mortars expand again when wetted. Alternate wetting and drying
produces alternate expansion and contraction, which apparently continues indefi-
nitely with portland-cement mortars.
Coefficients of thermal expansion of several mortars, reported in ‘‘Volume
Changes in Brick Masonry Materials,’’ Journal of Research of the National Bureau
of Standards, Vol. 6, p. 1003, ranged from 0.38  105 to 0.60  105 for masonrycement
mortars; from 0.41  105 to 0.53  105 for lime mortars, and from
0.42  105 to 0.61  105 for cement mortars. Composition of the cementitious
material apparently has little effect on the coefficient of thermal expansion of a
mortar.
4.16.3 High-Bond Mortars
When polymeric materials, such as styrene-butadiene and polyvinylidene chloride,
are added to mortar, greatly increased bonding, compressive, and shear strengths
result. To obtain high strength, the other materials, including sand, water, Type I
or III portland cement, and a workability additive, such as pulverized ground limestone
or marble dust, must be of quality equal to that of the ingredients of standard
mortar. The high strength of the mortar enables masonry to withstand appreciable
bending and tensile stresses. This makes possible thinner walls and prelaying of
single-wythe panels that can be hoisted into place.
4.17 PORTLAND-CEMENT CONCRETE
Portland-cement concrete is a mixture of portland cement, water, coarse and fine
aggregates, and admixtures proportioned to form a plastic mass capable of being
cast, placed, or molded into forms that will harden to a solid mass. The desirable
properties of plastic concrete are that it be workable, placeable and nonsegregating,
and that it set in the desired time. The hardened concrete should provide the desired
service properties:
1. Strength (compressive and flexural)
2. Durability (lack of cracks, resistance to freezing and thawing and to chemical
attacks, abrasion resistance, and air content)
3. Appearance (color, lack of surface imperfections)
Each of these properties affects the final cost of the mix design and the cost of
the in-place concrete. These properties are available from normal-weight, lightweight,
and heavyweight concretes.
4.22 SECTION FOUR
4.17.1 Normal-Weight Concrete
The nominal weight of normal concrete is 144 lb / ft3 for non-air-entrained concrete,
but is less the air-entrained concrete. (The weight of concrete plus steel reinforcement
is often assumed as 150 lb / ft3.)
Strength for normal-weight concrete ranges from 2000 to 20,000 psi. It is generally
measured using a standard test cylinder 6 in in diameter by 12 in high. The
strength of a concrete is defined as the average strength of two cylinders taken from
the same load and tested at the same age. Flexural beams 6  6  20 in may be
used for concrete paving mixes. The strength gains of air-entrained and non-airentrained
concretes are graphically shown in Fig. 9.2.
As illustrated in Fig. 9.2, the strength of a given mix is determined by the watercement
ratio (W/ C), and whether or not air entraining is used. Other factors are
the maximum-size aggregate and the desired fluidity (slump) of the concrete at the
point of placement. When no historical record is available for the aggregates and
cements to be used, the water-cement ratios in Table 9.2 can provide guidance for
the initial designs.
Each combination of coarse and fine aggregates has a specific water demand for
a given mix fluidity, or slump. Two general guidelines are:
1. For a constant slump, the water demand increases with increase in maximumsize
aggregate.
2. For a constant maximum-size aggregate, as the slump increases, the water demand
increases.
There are many different methods for designing a normal-weight concrete mix.
A standard method is given in ACI 211, ‘‘Standard Practice for Selecting Proportions
for Normal, Heavyweight, and Mass Concrete.’’ See also Art. 9.10.
Workability of a concrete is the property most important to contractors who
must place the concrete into forms and finish it. Workability includes the properties
of cohesiveness, plasticity, and nonsegregation. It is greatly influenced by aggregate
shape and gradation. Mixes that are hard to pump, place, and finish include those
deficient in fines, those with flat and elongated aggregates, and those with an excessive
amount of fines (sand and cement). If the sand is deficient in fines, workability
can be increased by addition of 30 to 50 lb /yd3 of fly ash. The most effective
method of producing workable concrete is to employ a well graded, combined
aggregate gradation.
Modulus of elasticity of normal-weight concrete is between 2,000,000 and
6,000,000 psi. An estimate of the modulus of elasticity for normal-weight concrete
with compressive strengths between 3000 and 5000 psi can be obtained by ?c
multiplying the square root of by 57,000. Above 5000 psi, the modulus should ?c
be determined using the procedure of ASTM C469. [See also Eq. (4.1) in Art.
4.17.2.]
Volume changes occur as either drying shrinkage, creep, or expansion due to
external thermal sources. Drying shrinkage causes the most problems, because it
produces cracks in the concrete surface. The primary cause of drying shrinkage
cracks is an excessive amount of water in the mix. The water has two effects. First,
it increases the water-cement ratio (W/ C), weakening the concrete. Second, additional
water beyond that needed for hydration of the cement creates an excessive
number of bleed channels to exposed surfaces. When the cement paste undergoes
its normal drying shrinkage, these channels cannot provide any resistance to penetration
of water or aggressive chemicals.
BUILDING MATERIALS 4.23
Creep is a time-dependent deformation of concrete that occurs after an external
load is applied to the concrete. It is an important consideration in design of prestressed
concrete.
Concrete expands when heated and contracts when cooled. Coefficients of thermal
expansion range from 3.2 to 7.0 millionths per 
F. The most notable result of
the response of concrete to thermal changes is the movement of external walls,
which may bow because of temperature differentials.
Normal-weight concrete that is not designed for fire exposure expands on being
heated. A side effect is some strength loss and a reduction in the modulus of
elasticity.
Resistance to freezing and thawing can be accomplished by proper air entrainment
in the concrete, use of a mix with a minimum water content, and proper
curing of the concrete. Table 9.3 provides guidelines for the amount of air to use
based upon exposure and maximum aggregate size.
Chemical attack may be internal (alkali-aggregate reaction) or external (sulfate
attack or an aggressive service environment). In either case, the basic concerns are
the characteristics of the available materials and the environment in which the
concrete will be used. Alkali-reactive aggregates should be avoided, but if they
must be used, a low-alkali cement complying with ASTM C150 Type II Modified
should be selected. If sulfate attack is a concern, a low W/C (0.45 maximum) and
air entrainment should be used with either a C150 Type V cement or a C150 Type
II cement with C618 Type F fly ash. For protection from attack by other chemicals,
a low W/C (0.45 maximum), more concrete cover over the reinforcing steel, a
corrosion-protection additive, or a latex-modified concrete should be used. The
American Concrete Institute ‘‘Building Code Requirements for Reinforced Concrete,’’
ACI 318, contains requirements for special exposure conditions.
Abrasion resistance is a concern with pavements and hydraulic structures. Both
require use of sound, durable, hard-rock aggregates, low W/C, and well-cured concrete.
Acceptable appearance depends on good workmanship and a supply of consistent
materials. The formwork should be watertight and properly oiled before
concrete placement. Forms should not be made of wood that will release sugars
into the concrete and create a retarded surface finish. During concrete placement,
the concrete should have consistent workability. The forms should be uniformly
and consistently vibrated to consolidate the concrete.
(‘‘Standard Practice for Selecting Proportions for Normal Heavyweight, and
Mass Concrete,’’ ACI 211.1, and ‘‘Guide for Use of Normal Weight Aggregates in
Concrete,’’ ACI 221.)
4.17.2 Lightweight Concrete
Concrete weighing considerably less than the 144 lb / ft3 of normal-weight concrete
may be produced by use of lightweight aggregates or by expanding or foaming the
concrete. Lightweight concrete is used principally to reduce the dead load of a
structure and lower the cost of foundations. The light weight of the aggregates used
for this type of concrete derives from the cellular structure of the particles. Hence,
lightweight-aggregate concrete as well as foamed and expanded concretes have
excellent fire-protection capabilities because of the internal voids in the aggregates
or the concrete itself. When lightweight aggregates are used, they may be both fine
and coarse, or lightweight coarse and normal-weight fine (sand), or normal-weight
coarse and lightweight fine. The last combination is the least often used. Unit
weights range from 90 lb / ft3 (all aggregates lightweight) to 115 lb / ft3 (sand lightweight).
Typically, compressive strengths range from 2500 to 4000 psi. Highstrength
lightweight concretes, however, have been produced with maximum unit
weights of 125 lb / ft3 and strengths from 6000 to 9000 psi. Structural lightweight
concretes are defined by the ACI as concretes with a 28-day compressive strength
more than 2500 psi and air-dry unit weight of 115 lb / ft3 or less.
The variable amount of water absorbed in the voids of lightweight aggregates
makes use of W/C difficult in design of a lightweight-aggregate mix (Table 4.5).
Air entrainment of 4 to 6% is desirable to prevent segregation. Maximum size of
the coarse aggregate should not exceed half the depth of cover over the reinforcing
steel.
Lightweight-aggregate concrete exposed to sulfates should have a compressive
strength ranging from 3750 to 4750 psi (see ACI 318). For marine structures, the
W/C should not exceed 0.40 and at least seven bags of cement should be used per
cubic yard of concrete.
The modulus of elasticity Ec of lightweight concrete generally ranges from
1,500,000 to 3,000,000 psi. It may be estimated from
1.5 E  w 
? (4.1) c c
where w  unit weight of concrete, lb / ft3
 ?c 28-day compressive strength of concrete, psi
Volume changes occur in lightweight concrete as in normal-weight concrete,
but lightweight concrete is stabler when exposed to heat. Drying shrinkage causes
the most undesirable volume changes, because it produces cracks in the surfaces
of the concrete. The primary cause of drying-shrinkage cracks is excessive water
in the mix. The water has two effects. First, it increases the W/C and weakens the
concrete. Second, the additional water beyond that needed for hydration of the
cement creates an excessive number of bleed channels to the exposed surfaces.
When the cement paste undergoes normal drying shrinkage, these channels cannot
provide any resistance to ingress of aggressive chemicals.
Creep is an important concern for lightweight concrete, as it is for normal-weight
concrete, especially for prestressed concrete.
(‘‘Standard Practice for Selecting Proportions for Structural Lightweight Concrete,’’
ACI 211.2, and ‘‘Guide for Structural Lightweight Aggregate Concrete,’’
ACI 213.)
BUILDING MATERIALS 4.25
4.17.3 Heavyweight Concrete
Concretes made with heavyweight aggregates are used for shielding and structural
purposes in construction of nuclear reactors and other structures exposed to highintensity
radiation (see Art. 4.12). Heavyweight aggregates are used where heavyweight
is needed, such as ship’s ballast and encasement of underwater pipes, and
for making shielding concretes because absorption of such radiation is proportional
to density, and consequently, these aggregates have greater capacity for absorption
than those ordinarily used for normal concrete. With such aggregates, concrete
weighing up to about 385 lb / ft3 can be produced.
Concrete made with limonite or magnetite can develop densities of 210 to 224
lb/ft3 and compressive strengths of 3200 to 5700 psi. With barite, concrete may
weigh 230 lb / ft3 and have a strength of 6000 psi. With steel punchings and sheared
bars as coarse aggregate and steel shot as fine aggregate, densities of 250 to 288
lb/ft3 and strengths of about 5600 psi can be attained. Generally, grading of aggregates
and mix proportions are similar to those used for normal concrete.
The properties of heavyweight concrete are similar to those of normal-weight
concrete. Mixing and placing operations, however, are more difficult than those for
normal-weight concrete, because of segregation. Good grading, high cement content,
low W/C, and air entrainment should be employed to prevent segregation.
Sometimes, heavyweight aggregates are grouted in place to avoid segregation.
Heavyweight concretes usually do not have good resistance to weathering or abrasion.
(‘‘Recommended Practice for Selecting Proportions for Normal, Heavyweight,
and Mass Concrete,’’ ACI 211.1.)
4.17.4 High-Performance Concretes
These concretes either have a high design strength (more than 6000 psi for normalweight
concrete and 5000 psi for lightweight concrete) or will be subjected to severe
service environments. The differences between high-performance concretes and
normal-weight concretes is that the former have lower W/C and smaller maximum
aggregate size. ACI 318 specifies the W/C and compressive strengths for concrete
in severe exposures and the maximum chloride-ion content of concrete. Highperformance
concrete is defined by either durability or strength-performance characteristics.
Durability characteristics are resistance to freeze-thaw, scaling, abrasion,
and chloride permeability. The strength characteristics have been defined in four
grades as shown in Table 4.6. (See also Art. 4.17.1)
High-strength, portland-cement concretes generally incorporate in the mix fly
ash, silica fume, or superplasticizers, or a combination of these admixtures. A retarder
is often beneficial in controlling early hydration. The W/C may be as small
as 0.25. The maximum size of aggregate should generally be limited to 1?2 in.
With superplasticizers, relatively high strengths can be achieved at early ages,
such as 7-day strengths of normal concrete in 3 days and 28-day strengths in 7
days. Compressive strengths exceeding 10,000 psi can be achieved in 90 days.
Aside from reduction in W/C, the use of superplasticizers in production of highstrength
concretes does not require significant changes in mix proportioning. An
increase in the range of sand content of about 5%, however, may help avoid a harsh
mix. Curing is very important, because strength gain halts when water is no longer
available for hydration. Also, it is important that proper quantities of air-entraining
admixtures be determined by trial. Some air loss may result when melamine- or
naphthalene-based superplasticizers are used, whereas lignosulfonate-based water
reducers may actually increase air content. Larger amounts of air-entraining agent
may be needed for high-strength concretes, especially for low-slump mixes with
high cement content and mixes with large amounts of some types of fly ash. Furthermore,
some types of superplasticizers and air-entraining admixtures may not be
compatible with each other.
(‘‘State-of-the-Art Report on High-Strength Concrete,’’ ACI 363.)
4.17.5 Nonstructural or Foamed Cellular Concretes
These are formed by the use of admixtures that generate or liberate gas bubbles in
concrete in the plastic stage. Aluminum powder, which reacts with the alkalies in
cement to release hydrogen, is generally used for this purpose, although hydrogen
peroxide, which generates oxygen, or activated carbon, which liberates absorbed
air, can be used. These foaming agents create stable, uniformly dispersed air spaces
within the concrete when it sets. Perlite and vermiculite are most frequently used
as aggregates. The resulting concrete may weigh 50 lb / ft3 or less and have a compressive
strength up to 2500 psi. Applications of such lightweight concretes include
topping and soundproofing barriers over structural concrete slabs.
The effectiveness of the admixture is controlled by the duration of mixing, handling,
and placing of the mix relative to the gas-generation rate. The amount of
unpolished aluminum powder to be added to a mix may range from 0.005 to 0.02%
by weight of cement under normal conditions. Larger quantities, however, may be
used to produce lower-strength concretes. More aluminum may be needed at low
temperatures to achieve the same amount of concrete expansion, for example, twice
as much as 40
F as at 70
F. Furthermore, at low temperatures, to speed up gas
generation, it may be necessary to add to the mix alkalies such as sodium hydroxide,
hydrated lime, or trisodium phosphate. Also, to prevent the powder from floating
on the surface of mixing water, the aluminum may be premixed with sand or
combined with other admixtures.
Curing is very important. If good curing practices and jointing are not followed,
extensive drying shrinkage may result.
4.18 POLYMER CONCRETES
Plastics with long-chain molecules, called polymers, are used in several ways to
enhance concrete properties: replacement of portland cement, incorporation in a
mix as an admixture, and impregnating hardened concrete.
BUILDING MATERIALS 4.27
Polymer concretes, such as methyl methacrylate and unsaturated polyester, in
which a polymer replaces portland cement may have more than double the strength
and modulus of elasticity of portland-cement concrete. Creep is less and resistance
to freezing and thawing cycles is higher with the polymer concretes. After curing
for a very short time, for example, overnight at room temperature, polymer concretes
are ready for use, whereas ordinary concrete may have to cure for about a
week before exposure to service loads.
Monomers and polymers may be used as admixtures for restoring and resurfacing
deteriorated concrete surfaces. Latexes of methyl methacrylate, polyester, styrene,
epoxy-styrene, furans, styrene-butadiene, and vinylidene chloride have been
employed for these purposes. The resulting concrete hardens more rapidly than
normal concrete. A polymer admixture may also be used to improve the bonding
properties of portland cement. Inserted in a mix as an emulsion for this purpose,
the admixture supplies a significant amount of water to the mix, which becomes
available for hydration of the cement. The release of the water also sets the emulsion.
Hence, moist curing is not desirable, inasmuch as the emulsion needs to dry
to develop the desired strength. A grout or mortar containing the bonding admixture
develops a higher bond strength when applied as a thin layer than as a thick one
and the bond may be stronger than materials being joined.
Impregnation of concrete with polymers is sometimes used to harden surfaces
exposed to heavy traffic. Strength and other properties of the impregnated concrete
are similar to those of concrete in which polymers replace portland cement. Impregnation
is achieved by first drying the concrete surface with heat and then soaking
the surface with a monomer, such as methyl methacrylate, styrene, acrylonitrile,
or tert-butyl styrene. It is subsequently cured with heat.
Slab Toppings. At least partly because of excellent adhesion, epoxies are formulated
with sand and other fillers to provide surfacing materials for concrete.
Unlike standard concrete topping, epoxy-based surfacing materials can be thin.
They are especially useful for smoothing uneven, irregular surfaces. The epoxy
cures quickly, allowing use of the surface in a short time.
Grout. Cracked concrete can be repaired with an epoxy grout. The grout is forced
into cracks under pressure for deep penetration. Because of its good bonding
strength, the epoxy grout can largely restore strength, while, at the same time,
sealing the crack against penetration by liquids.
(‘‘Polymers in Concrete,’’ ACI 548; ‘‘Guide for the Use of Polymers in Concrete,’’
ACI 548.1; and ‘‘Polymer Modified Concrete,’’ SP-99, American Concrete
Institute.)
4.19 CONCRETE MASONRY UNITS
A wide variety of manufactured products are produced from concrete and used in
building construction. These include such items as concrete brick, concrete block
or tile, concrete floor and roof slabs, precast wall panels, precast beams, and cast
stone. These items are made both from normal dense concrete mixes and from
mixes with lightweight aggregates. Concrete blocks are made with holes through
them to reduce their weight and to enable masons to grip them.
Nominal size (actual dimensions plus width of mortar joint) of hollow concrete
block usually is 8  8  16 in. Solid blocks often are available with nominal size
4.28 SECTION FOUR
of 4  8  16 in or 4  21?2  8 in. For a list of modular sizes, see ‘‘Standard
Sizes of Clay and Concrete Modular Units,’’ ANSI A62.3.
Properties of the units vary tremendously—from strong, dense, load-bearing
units used under exposed conditions to light, relatively weak, insulating units used
for roof and fire-resistant construction.
Many types of concrete units have not been covered by adequate standard specifications.
For these units, reliance must be placed upon the manufacturer’s speci-
fications. Requirements for strength and absorption of concrete brick and block
established by ASTM for Type I, Grades N-I and S-I (moisture-controlled), and
Type II, Grades N-II and S-II (non-moisture-controlled), units are summarized in
Table 4.7.
Manufactured concrete units have the advantage (or sometimes disadvantage)
that curing is under the control of the manufacturer. Many methods of curing are
used, from simply stacking the units in a more or less exposed location to curing
under high-pressure steam. The latter method appears to have considerable merit
in reducing ultimate shrinkage of the block. Shrinkage may be as small as 1?4 to 3?8
in per 100 ft for concrete units cured with high-pressure steam. These values are
about one-half as great as those obtained with normal atmospheric curing. Tests for
moisture movement in blocks cured with high-pressure and high-temperature steam
indicate expansions of from 1?4 to 1?2 in per 100 ft after saturation of previously
dried specimens.
BURNED-CLAY UNITS
Use of burned-clay structural units dates from prehistoric times. Hence durability
of well-burned units has been adequately established through centuries of exposure
in all types of climate.
Modern burned-clay units are made in a wide variety of sizes, shapes, colors,
and textures to suit the requirements of modern architecture. They include such
widely diverse units as common and face brick; hollow clay tile in numerous
shapes, sizes, and designs for special purposes; ceramic tile for decorative and
sanitary finishes, and architectural terra cotta for ornamentation.
Properties of burned-clay units vary with the type of clay or shale used as raw
material, method of fabrication of the units, and temperature of burning. As a
consequence, some units, such as salmon brick, are underburned, highly porous,
and of poor strength. But others are almost glass hard, have been pressed and burned
to almost eliminate porosity, and are very strong. Between these extremes lie most
of the units used for construction.
4.20 BRICK—CLAY OR SHALE
Brick have been made in a wide range of sizes and shapes, from the old Greek
brick, which was practically a 23-in cube of 12,650 in3 volume, to the small Belgian
brick, about 13?4  33?8  41?2 in with a total volume of only 27 in3. The present
common nominal sizes in the United States are 4 or 6 in thick by 22?3 or 4 in high
by 8 or 12 in long. For a list of modular sizes, see ‘‘Standard Sizes of Clay and
Concrete Modular Masonry Units,’’ ANSI A62.3. Actual dimensions are smaller,
BUILDING MATERIALS 4.29
Structural clay tiles are hollow burned-clay masonry units with parallel cells. Such
units have multitude of uses: as a facing tile for interior and exterior unplastered
walls, partitions, or columns; as load-bearing tile in masonry constructions designed
to carry superimposed loads; as partition tile for interior partitions carrying no
superimposed load; as fireproofing tile for protection of structural members against
fire; as furring tile for lining the inside of exterior walls; as floor tile in floor and
roof construction; and as header tiles, which are designed to provide recesses for
header units in brick or stone-faced walls. Units are available with the following
ranges in nominal dimensions: 8 to 16 in in length, 4 in for facing tile to 12 in for
load-bearing tile in height, and 2 in for facing tile to 12 in for load-bearing tile in
thickness.
Two general types of tile are available—side-construction tile, designed to receive
its principal stress at right angles to the axis of the cells, and end-construction
tile designed to receive its principal stress parallel to the axis of the cells.
Tiles are also available in a number of surface finishes, such as opaque glazed
tile, clear ceramic-glazed tile, nonlustrous glazed tile, and scored, combed, or
roughened finishes designed to receive mortar, plaster, or stucco.
Requirements of the appropriate ASTM specifications for absorption and
strength of several types of tile are given in Table 4.9 (see ASTM C34, C56, C57,
C212, and C126 for details pertaining to size, color, texture, defects, etc.). Strength
and absorption of tile made from similar clays but from different sources and manufacturers
vary widely. The modulus of elasticity of tile may range from 1,620,000
to 6,059,000 psi.
Tile suitable for general use in masonry construction and adapted for use in masonry exposed to
weathering. They may also be considered suitable for direct application of stucco.
LB. Tile suitable for general use in masonry where not exposed to frost action, or in exposed masonry
where protected with a facing of 3 in or more of stone, brick, terra cotta, or other masonry.
NB. Non-load-bearing tile made from surface clay, shale, or fired clay.
FT 1 and FT 2. Tile suitable for use in flat or segmental panels or in combination tile and concrete
ribbed-slab construction.
FTX. Smooth-face tile suitable for general use in exposed exterior and interior masonry walls and
partitions, and adapted for use where tiles low in absorption, easily cleaned, and resistant to staining are
required and where a high degree of mechanical perfection, narrow color range, and minimum variation in
face dimensions are required.
FTS. Smooth or rough-texture face tile suitable for general use in exposed exterior and interior masonry
walls and partitions and adapted for use where tile of moderate absorption, moderate variation in face
dimensions, and medium color range may be used, and where minor defects in surface finish, including
small handling chips, are not objectionable.
Standard. Tile suitable for general use in exterior or interior masonry walls and partitions.
Special duty. Tile suitable for general use in exterior or interior masonry walls and partitions and
designed to have superior resistance to impact and moisture transmission, and to support greater lateral and
compressive loads than standard tile construction.
Glazed units. Ceramic-glazed structural clay tile with a glossy or stain-mat finish of either an opaque
or clear gaze, produced by the application of a coating prior to firing and subsequently made vitreous by
firing.
4.32 SECTION FOUR
4.22 CERAMIC TILES
Ceramic tile is a burned-clay product used primarily for decorative and sanitary
effects. It is composed of a clay body on which is superimposed a decorative glaze.
The tiles are usually flat but vary in size from about 1?2 in square to more than
6 in. Their shape is also widely variable—squares, rectangles, and hexagons are
the predominating forms, to which must be added coved moldings and other decorative
forms. These tiles are not dependent on the color of the clay for their final
color, since they are usually glazed. Hence, they are available in a complete color
gradation from pure whites through pastels of varying hue to deep solid colors and
jet blacks.
Properties of the base vary somewhat. In particular, absorption ranges from almost
zero to about 15%. The glaze is required to be impervious to liquids and
should not stain, crack, or craze.
Ceramic tiles are applied on a solid backing by means of a mortar or adhesive.
They are usually applied with the thinnest possible mortar joint; consequently accuracy
of dimensions is of greatest importance. Since color, size, and shape of tile
are important, selection of tile should be based on the current literature of the
manufacturer.
4.23 ARCHITECTURAL TERRA COTTA
The term ‘‘terra cotta’’ has been applied for centuries to decorative molded-clay
objects whose properties are similar to brick. The molded shapes are fired in a
manner similar to brick.
Terra cotta is frequently glazed to produce a desired color or finish. This introduces
the problem of cracking or crazing of the glaze, particularly over large areas.
Structural properties of terra cotta are similar to those of clay or shale brick.
BUILDING STONES
Principal building stones generally used in the United States are limestones, marbles,
granites, and sandstones. Other stones such as serpentine and quartzite are
used locally but to a much lesser extent. Stone, in general, makes an excellent
building material, if properly selected on the basis of experience; but the cost may
be relatively high.
Properties of stone depend on what nature has provided. Therefore, the designer
does not have the choice of properties and color available in some of the manufactured
building units. The most the stone producer can do for purchasers is to
avoid quarrying certain stone beds that have been proved by experience to have
poor strength or poor durability.
4.24 PROPERTIES OF BUILDING STONES
Data on the strength of building stones are presented in Table 4.10, summarized
from U.S. National Bureau of Standards Technical Papers, No. 123, B. S. Vol. 12;
4.33
Data on the true specific gravity, bulk specific gravity, unit weights, porosity,
and absorption of various stones are given in Table 4.11.
Permeability of stones varies with types of stone, thickness, and driving pressure
that forces water through the stone. Table 4.12 represents data for the more common
stones at three different pressures, as reported in ‘‘Permeability of Stone,’’ U.S.
National Bureau of Standards Technical Papers, No. 305, Vol. 20, p. 191. The units
of measurement of permeability are cubic inches of water that will flow through a
square foot of a specimen 1?2 in thick in 1 hr.
Data on thermal expansion of building stones as given in Table 4.13 show that
limestones have a wide range of expansion as compared with granites and slates.
Marble loses strength after repeated heating and cooling. A marble that had an
original strength of 9174 psi had a strength after 50 heatings to 150
C of 8998
psi—a loss of 1.9%. After 100 heatings to 150
C, the strength was only 8507 psi,
or a loss of 7.3%. The latter loss in strength was identical with that obtained on
freezing and thawing the same marble for 30 cycles. Also, marble retains a permanent
expansion after repeated heating.
4.25 FREEZING AND THAWING OF STONE
In freezing and thawing tests of 89 different marbles (‘‘Physical and Chemical Tests
of Commercial Marbles of U.S.,’’ U.S. National Bureau of Standards Technical
Papers, No. 123, Vol. 12), after 30 cycles, 66 marbles showed loss of strength
ranging from 1.2 to 62.1% and averaging 12.3% loss. The other 23 marbles showed
increases in strength ranging from 0.5 to 43.9% and averaging 11.2% increase.
Weight change was also determined in this investigation to afford another index
of durability. Of 86 possible comparisons after 30 cycles of freezing and thawing,
16 showed no change in weight, 64 showed decreases in weight ranging from 0.01
to 0.28% and averaging 0.04% loss, while 6 showed increases in weight ranging
from 0.01 to 0.08% and averaging 0.04%.
GYPSUM PRODUCTS
Gypsum is a cementitious material composed of at least 70% of CaSO4 
 2H2O by
weight (Art. 4.6). It is a main ingredient of many building products.
4.26 GYPSUMBOARD
This product consists of a core of set gypsum surfaced with specifically manufactured
paper firmly bonded to the core. It is designed to be used without addition
of plaster for walls, ceilings, or partitions and provides a surface suitable to receive
either paint or paper (see also Sec. 11). Gypsumboard is extensively used in ‘‘drywall’’
construction, where plaster is eliminated. It is also available with one surface
covered with aluminum or other heat-reflecting type of foil, or with imitation woodgrain
or other patterns on the exposed surface so that no additional decoration is
required.
The types of gypsumboard generally available include wallboard, backing board,
coreboard, fire-resistant gypsumboard, water-resistant gypsumboard, gypsum
sheathing, and gypsum formboard.
4.36 SECTION FOUR
Gypsum Wallboard. This type is used for the surface layer on interior walls and
ceilings. Regular gypsum wallboard comes with gray liner paper on the back and
a special paper covering, usually cream-colored, on facing side and edges. This
covering provides a smooth surface suitable for decoration. Foil-backed gypsum
wallboard has aluminum foil bonded to the liner paper to serve as a vapor barrier
and, when contiguous to an airspace, as thermal insulation. Predecorated gypsum
wallboard does not require decorative treatment after installation because it comes
with a finished surface, often a decorative vinyl or paper sheet. Wallboard should
conform with ASTM C36.
Wallboard usually is available 4 ft wide in the following thicknesses and lengths:
1?4 in—for covering and rehabilitating old walls and ceilings, 4 to 12 ft long
5?16 in—where thickness greater than 1?4 in is desired, 4 to 14 ft long.
3?8 in—mainly for the outer face in two-layer wall systems, 4 to 16 ft long
1?2 in—for single-layer new construction with supports 16 to 24 in c to c, 4 to
16 ft long
5?8 in—for better fire resistance and sound control than 1?2 in provides, 4 to 16
ft long
Standard edges are rounded, beveled, tapered, or square.
Backing Board. This type is used as a base layer in multi-ply construction, where
several layers of gypsumboard are desired for high fire resistance, sound control,
and strength in walls. It has gray liner paper on front and back faces. Also available
is backing board with aluminum foil bonded to the back face. Gypsum backing
board should conform with ASTM C442. The boards come 16 to 48 in wide, 4 to
16 ft long, and 1?4 to 1 in thick.
Gypsum Coreboard. To save space, this type is used as a base in multi-ply construction
of self-supporting (studless) gypsum walls. Coreboard may be supplied as
1-in-thick, solid backing board or as two factory-laminated, 1?2-in-thick layers of
backing board. Coreboard too should conform with C442.
Type X Gypsumboard. For use in fire-rated assemblies, Type X may be gypsum
wallboard, backing board, or coreboard with core made more fire resistant by addition
of glass fiber or other reinforcing materials.
Water-Resistant Gypsum Backing Board. This type comes with a water-resistant
gypsum core and water-repellant face paper. It may be used as a base for wall tile
in baths, showers, and other areas subject to wetting. The board should conform
with ASTM C630.
Gypsum Sheathing. This type is used as fire protection and bracing of exterior
frame walls. It must be protected from the weather by an exterior facing. Sheathing
should conform with ASTM C79. It comes 24 to 48 in wide, 6 to 12 ft long, and
3?8, 4?10, 1?2, and 5?8 in thick.
Gypsum Formboard. This type is used as a permanent form in the casting of
gypsum-concrete roof decks.
(‘‘Architect Data Book—Construction Products and Systems,’’ Gold Bond Building
Products, a National Gypsum Division, 2001 Rexford Road, Charlotte, NC
BUILDING MATERIALS 4.37
28211; ‘‘Gypsum Products Design Data,’’ Gypsum Association, 1603 Orrington
Ave., Evanston, IL 60201; ‘‘Gypsum Construction Handbook,’’ United States Gypsum,
101 South Wacker Drive, Chicago, IL 60606.)
4.27 GYPSUM LATH
Gypsum lath is similar to gypsumboard in that it consists of a core of set gypsum
surfaced with paper. The paper for gypsumboard, however, is produced so that it
is ready to receive paint or paper, while that for gypsum lath is specially designed
or treated so that plaster will bond tightly to the paper. In addition, some lath
provides perforations or other mechanical keying to assist in holding the plaster
firmly on the lath. It is also available with reflective foil backing (see also Art.
11.25.5).
Gypsum lath should conform with ASTM C37. It comes in 16-, 161?2-, 24-, and
32-in widths, lengths of 32, 36, and 48 in, and 3?8- and 1?2-in widths.
Veneers plasters, special proprietary compositions for thin plaster surfaces, are
best applied over veneer plaster base, similar to gypsum lath, but produced to
accommodate the veneer plaster compositions. Both gypsum lath and veneer base
are made as regular, X-rated (fire-retardant), and insulating (foil-backed) types.
These bases should conform with ASTM G588. They come 48 in wide, 6 to 16 ft
long, and 3?8, 1?2, and 5?8 in thick.
4.28 GYPSUM SHEATHING BOARD
Gypsum sheathing boards are similar in construction to gypsumboard (Art. 4.26),
except that they are provided with a water-repellent paper surface. They are commonly
made 3?4 to 5?8 in thick, 6 to 12 ft long, and with a nominal width of 24 or
48 in in conformance with ASTM C79. They are made with either square edges or
with V tongue-and-groove edges. Sheathing boards also are available with a waterrepellent
core or fire-resistant Type X.
4.29 GYPSUM PARTITION TILE OR BLOCK
Gypsum tiles or blocks are used for non-load-bearing partition walls and for protection
of columns, elevator shafts, etc., against fire. They have been essentially
replaced by dry-wall systems.
4.30 GYPSUM PLANK
A precast gypsum product used particularly for roof construction is composed of a
core of gypsum cast in the form of a plank, with wire-fabric reinforcement and
usually with tongue-and-groove metal edges and ends. The planks are available in
4.38 SECTION FOUR
two thicknesses—a 2-in plank, which is 15 in wide and 10 ft long, and a 3-in plank
which is 12 in wide and 30 in long. (See ASTM C377.)
GLASS AND GLASS BLOCK
Glass is so widely used for decorative and utilitarian purposes in modern construction
that it would require an encyclopedia to list all the varieties available. Clear
glass for windows and doors is made in varying thicknesses or strengths, also in
double layers to obtain additional thermal insulation. Safety glass, laminated from
sheets of glass and plastic, or made with embedded wire reinforcement, is available
for locations where breakage might be hazardous. For ornamental work, glass is
available in a wide range of textures, colors, finishes, and shapes.
4.31 WINDOW GLASS
Various types and grades of glass are used for glazing:
Clear Window Glass. This is the most extensively used type for windows in all
classes of buildings. A range of grades, as established by Federal Government
Standard DD-G-451c, classifies quality according to defects. The more commonly
used grades are A and B. A is used for the better class of buildings where appearance
is important, and B is used for industrial buildings, some low-cost residences,
basements, etc.
With respect to thickness, clear window glass is classified as ‘‘single-strength’’
about 3?32 in thick; ‘‘double-strength,’’ about 1?8 in thick; and ‘‘heavy-sheet,’’ up to
7?32 in thick. Maximum sizes are as follows: single-strength, 40  50 in; doublestrength,
60  80 in; and heavy sheet, 76  120 in. Because of flexibility, single
strength and double strength should never be used in areas exceeding 12 ft2, and
for appearance’s sake areas should not exceed 7 ft2.
Plate and Float Glass. These have, in general, the same performance characteristics.
They are of superior quality, more expensive, and have better appearance,
with no distortion of vision at any angle. Showcase windows, picture windows, and
exposed windows in offices and commercial buildings are usually glazed with polished
plate or float glass. Thicknesses range from 1?8 to 7?8 in. There are two standard
qualities, silvering and glazing, the latter being employed for quality glazing.
Processed Glass and Rolled Figured Sheet. These are general classifications of
obscure glass. There are many patterns and varying characteristics. Some provide
true obscurity with a uniform diffusion and pleasing appearance, while others may
give a maximum transmission of light or a smoother surface for greater cleanliness.
The more popular types include a clear, polished surface on one side with a pattern
for obscurity on the other side.
Obscure Wired Glass. This usually is specified for its fire-retarding properties,
although it is also used in doors or windows where breakage is a problem. It should
not be used in pieces over 720 in2 in area (check local building code).
BUILDING MATERIALS 4.39
Polished Wired Glass. More expensive than obscure wired glass, polished wired
glass is used where clear vision is desired, such as in school or institutional doors.
There are also many special glasses for specific purposes:
Heat-Absorbing Glass. This reduces heat, glare, and a large percentage of ultraviolet
rays, which bleach colored fabrics. It often is used for comfort and reduction
of air-conditioning loads where large areas of glass have a severe sun exposure.
Because of differential temperature stresses and expansion induced by heat absorption
under severe sun exposure, special attention should be given to edge conditions.
Glass having clean-cut edges is particularly desirable, because these affect the edge
strength, which, in turn must resist the central-area expansion. A resilient glazing
material should be used.
Corrugated Glass, Wired Glass, and Plastic Panels. These are used for decorative
treatments, diffusing light, or as translucent structural panels with color.
Laminated Glass. This consists of two or more layers of glass laminated together
by one or more coatings or a transparent plastic. This construction adds strength.
Some types of laminated glass also provide a degree of security, sound isolation,
heat absorption, and glare reduction. Where color and privacy are desired, fadeproof
opaque colors can be included. When fractured, a laminated glass tends to
adhere to the inner layer of plastic and, therefore, shatters into small splinters, thus
minimizing the hazard of flying glass.
Bullet-Resisting Glass. This is made of three or more layers of plate glass laminated
under heat and pressure. Thicknesses of this glass vary from 3?4 to 3 in. The
more common thicknesses are 13?16 in, to resist medium-powered small arms: 11?2
in, to resist high-powered small arms; and 2 in, to resist rifles and submachine guns.
(Underwriters Laboratories lists materials having the required properties for various
degrees of protection.) Greater thicknesses are used for protection against armorpiercing
projectiles. Uses of bullet-resisting glass include cashier windows, bank
teller cages, toll-bridge booths, peepholes, and many industrial and military applications.
Transparent plastics also are used as bullet-resistant materials, and some
of these materials have been tested by the Underwriters Laboratories. Thicknesses
of 11?4 in or more have met UL standards for resisting medium-powered small arms.
Tempered Glass. This is produced by a process of reheating and sudden cooling
that greatly increases strength. All cutting and fabricating must be done before
tempering. Doors of 1?2- and 3?4-in-thick tempered glass are commonly used for
commercial building. Other uses, with thicknesses from 1?8 to 7?8 in, include backboards
for basketball, showcases, balustrades, sterilizing ovens, and windows,
doors, and mirrors in institutions. Although tempered glass is 41?2 to 5 times as
strong as annealed glass of the same thickness, it is breakable, and when broken,
disrupts into innumerable small fragments of more or less cubical shape.
Tinted and Coated Glasses. These are available in several types and for varied
uses. As well as decor, these uses can provide for light and heat reflection, lower
light transmission, greater safety, sound reduction, reduced glare, and increased
privacy.
4.40 SECTION FOUR
Transparent Mirror Glass. This appears as a mirror when viewed from a brightly
lighted side, and is transparent to a viewer on the darker opposite side. This oneway-
vision glass is available as a laminate, plate or float, tinted, and in tempered
quality.
Plastic Window Glazing. Made of such plastics as acrylic or polycarbonate, plastic
glazing is used for urban school buildings and in areas where high vandalism
might be anticipated. These plastics have substantially higher impact strength than
glass or tempered glass. Allowance should be made in the framing and installation
for expansion and contraction of plastics, which may be about 8 times as much as
that of glass. Note also that the modulus of elasticity (stiffness) of plastics is about
one-twentieth that of glass. Standard sash, however, usually will accommodate the
additional thickness of plastic and have sufficient rabbet depth.
Suspended Glazing. This utilizes metal clamps bonded to tempered plate glass at
the top edge, with vertical glass supports at right angles for resistance to wind
pressure (Fig. 4.1). These vertical supports, called stabilizers, have their exposed
edges polished. The joints between the large plates and the stabilizers are sealed
with a bonding cement. The bottom edge or sill is held in position by a metal
channel, and sealed with resilient waterproofing. Suspended glazing offers much
greater latitude in use of glass and virtually eliminates visual barriers.
Safety Glazing. A governmental specification Z-97, adopted by many states, requires
entrance-way doors and appurtenances glazed with tempered, laminated, or
plastic material.
4.32 GLASS BLOCK
Glass blocks are made by first pressing or shaping half blocks to the desired form,
then fusing the half blocks to form a complete block. A block is usually 37?8 in
thick and 53?4, 73?4, or 113?4 in square. The center of the block is hollow and is
under a partial vacuum, which adds to the insulating properties of the block. Corner
and radial blocks are also available to produce desired architectural effects.
Glass block is commonly laid up in a cement or a cement-lime mortar. Since
there is no absorption by the block to facilitate bond of mortar, various devices are
employed to obtain a mechanical bond. One such device is to coat the sides of the
block with a plastic and embed therein particles of sand. The difficulty in obtaining
permanent and complete bond sometimes leads to the opening up of mortar joints.
A wall of glass block, exposed to the weather, may leak badly in a rainstorm unless
unusual precautions have been taken during the setting of the block to obtain full
and complete bond.
Glass blocks have a coefficient of thermal expansion that is from 11?2 to 2 times
that of other masonry. For this reason, large areas of block may expand against
solid masonry and develop sufficient stress so that the block will crack. Manufacturers
usually recommend an expansion joint every 10 ft or so, to prevent building
up of pressure sufficient to crack the block. With adequate protection against expansion
and with good workmanship, or with walls built in protected locations,
BUILDING MATERIALS 4.41
FIGURE 4.1 Typical details of suspended glazing. (F. H. Sparks, Co., Inc., New
York.)
glass-block walls are ornamental, sanitary, excellent light transmitters, and have
rather low thermal conductivity.
WOOD
Wood is a building material made from trees. It is a natural polymer composed of
cells in the shape of long, thin tubes with tapered ends. The cell wall consists of
cellulose crystals, which are bonded together by a complex amorphous lignin composed
of carbohydrates. Most of the cells in a tree trunk are oriented vertically.
Consequently, properties of wood in the direction of cell axes, usually referred to
4.42
4.33 MECHANICAL PROPERTIES OF WOOD
Because of its structure, wood has different strength properties parallel and perpendicular
to the grain. Tensile, bending, and compressive strengths are greatest
parallel to the grain and least across the grain, whereas shear strength is least
parallel to the grain and greatest across the grain. Except in plywood, the shearing
strength of wood is usually governed by the parallel-to-grain direction.
The compressive strength of wood at an angle other than parallel or perpendicular
to the grain is given by the following formula:
C C 2 2 C  (4.2) 	 2 2 C sin 	 C cos 	 1 2
in which C	 is the strength at the desired angle 	 with the grain, C1 is the compressive
strength parallel to grain, and C2 is the compressive strength perpendicular
to the grain.
Increasing moisture content reduces all strength properties except impact bending,
in which green wood is stronger than dry wood. The differences are brought
out in Table 4.14. In practice, no differentiation is made between the strength of
green and dry wood in engineering timbers, because of seasoning defects that may
occur in timbers as they dry and because large timbers normally are put into service
without having been dried. This is not true of laminated timber, in which dry wood
must be employed to obtain good glued joints. For laminated timber, higher stresses
can be employed than for ordinary lumber. In general, compression and bending
parallel to the grain are affected most severely by moisture, whereas modulus of
elasticity, shear, and tensile strength are affected less. In practice, tensile strength
parallel to the grain is taken equal to the bending strength of wood.
In Table 4.14 are summarized also the principal mechanical properties of the
most important American commercial species.
Values given in the table are average ultimate strengths. To obtain working
stresses from these, the following must be considered: (1) Individual pieces may
vary 25% above and below the average. (2) Values given are for standard tests that
are completed in a few minutes. Over a period of years, however, wood may fail
under a continuous load about 9?16 that sustained in a standard test. (3) The modulus
of rupture of a standard 2-in-deep flexural-test specimen is greater than that of a
deep beam. In deriving working stresses, therefore, variability, probable duration
of load, and size are considered, and reduction factors are applied to the average
ultimate strengths to provide basic stresses, or working stresses, for blemishless
lumber. These stresses are still further reduced to account for such blemishes as
knots, wane, slope of grain, shakes, and checks, to provide working stresses for
classes of commercial engineering timbers. (See Sec. 10 for engineering design in
timber.)
4.34 EFFECTS OF HYGROSCOPIC PROPERTIES
OF WOOD
Because of its nature, wood tends to absorb moisture from the air when the relative
humidity is high, and to lose it when the relative humidity is low. Moisture imbibed
BUILDING MATERIALS 4.45
into the cell walls causes the wood to shrink and swell as the moisture content
changes with the relative humidity of the surrounding air. The maximum amount
of imbibed moisture the cell walls can hold is known as the fiber-saturation point,
and for most species is in the vicinity of 25 to 30% of the oven-dry weight of the
wood. Free water held in the cell cavities above the fiber-saturation point has no
effect upon shrinkage or other properties of the wood. Changes in moisture content
below the fiber-saturation point cause negligible shrinkage or swelling along the
grain, and such shrinkage and swelling are normally ignored; but across the grain,
considerable shrinkage and swelling occur in both the radial and tangential direction.
Tangential shrinkage (as in flat-cut material) is normally approximately 50%
greater than radial shrinkage (as in edge-grain material). See also Art. 10.1.
Separation of grain, or checking, is the result of rapid lowering of surface moisture
content combined with a difference in moisture content between inner and
outer portions of the piece. As wood loses moisture to the surrounding atmosphere,
the outer cells of the member lose at a more rapid rate than the inner cells. As the
outer cells try to shrink, they are restrained by the inner portion of the member.
The more rapid the drying, the greater will be the differential in shrinkage between
outer and inner fibers, and the greater the shrinkage stresses. As a result, checks
may develop into splits.
Checks are radial cracks caused by nonuniform drying of wood. A split is a
crack that results from complete separation of the wood fibers across the thickness
of a member and extends parallel to the grain. (Shakes are another type of defect.
Usually parallel to an annular ring, they develop in standing trees, whereas checks
and splits are seasoning defects.) Lumber grading rules limit these types of defects.
Checks affect the horizontal shear strength of timber. A large reduction factor
is applied to test values in establishing design values, in recognition of stress concentrations
at the ends of checks. Design values for horizontal shear are adjusted
for permissible checking in the various stress grades at the time of the grading.
Since strength properties of wood increase with dryness, checks may enlarge with
increasing dryness after shipment, without appreciably reducing shear strength.
Cross-grain checks and splits that tend to run out the side of a piece, or excessive
checks and splits that tend to enter connection areas, may be serious and may
require servicing. Provisions for controlling the effects of checking in connection
areas may be incorporated in design details.
To avoid excessive splitting between rows of bolts caused by shrinkage during
seasoning of solid-sawn timbers, rows should not be spaced more than 5 in apart,
or a saw kerf, terminating in a bored hole, should be provided between lines of
bolts. Whenever possible, maximum end distances for connections should be specified
to minimize the effect of checks running into the joint area. Some designers
requires stitch bolts in members, with multiple connections loaded at an angle to
the grain. Stitch bolts, kept tight, will reinforce pieces where checking is excessive.
One of the principal advantages of glued-laminated timber construction is relative
freedom from checking. Seasoning checks may, however, occur in laminated
members for the same reasons that they exist in solid-sawn members. When laminated
members are glued within the typical range of moisture contents of 7 to 16%
for the laminating lumber at the time of gluing, they will approximate the moisture
content in normal-use conditions, thereby minimizing checking. Moisture content
of the lumber at the time of gluing is thus of great importance to the control of
checking in service. However, rapid changes in moisture content of large wood
sections after gluing will result in shrinkage or swelling of the wood, and during
shrinking, checking may develop in both glued joints and wood.
Differentials in shrinkage rates of individual laminations tend to concentrate
shrinkage stresses at or near the glue line. For this reason, when checking occurs,
4.46 SECTION FOUR
it is usually at or near glue lines. The presence of wood-fiber separation indicates
adequate glue bonds, and not delamination.
In general, checks have very little effect on the strength of glued-laminated
members. Laminations in such members are thin enough to season readily in kiln
drying without developing checks. Since checks lie in a radial plane, and the majority
of laminations are essentially flat grain, checks are so positioned in horizontally
laminated members that they will not materially affect shear strength. When
members are designed with laminations vertical (with wide face parallel to the
direction of load application), and when checks may affect the shear strength, the
effect of checks may be evaluated in the same manner as for checks in solid-sawn
members.
Seasoning checks in bending members affect only the horizontal shear strength
(Art. 10.5.13). They are usually not of structural importance unless the checks are
significant in depth and occur in the midheight of the member near the support,
and then only if shear governs the design of the members. The reduction in shear
strength is nearly directly proportional to the ratio of depth of check to width of
beam. Checks in columns are not of structural importance unless the check develops
into a split, thereby increasing the slenderness ratio of columns.
Minor checking may be disregarded, since there is ample safety factor in allowable
design values. The final decision as to whether shrinkage checks are detrimental
to the strength requirements of any particular design or structural member
should be made by a competent engineer experienced in timber construction.
4.35 COMMERCIAL GRADES OF WOOD
Lumber is graded by the various associations of lumber manufacturers having jurisdiction
over various species. Two principal sets of grading rules are employed:
(1) for softwoods, and (2) for hardwoods.
Softwoods. Softwood lumber is classified as dry, moisture content 19% or less;
and green, moisture content above 19%.
According to the American Softwood Lumber Standard, softwoods are classified
according to use as:
Yard Lumber. Lumber of grades, sizes, and patterns generally intended for ordinary
construction and general building purposes.
Structural Lumber. Lumber 2 in or more nominal thickness and width for use
where working stresses are required.
Factory and Shop Lumber. Lumber produced or selected primarily for manufacturing
purposes.
Softwoods are classified according to extent of manufacture as:
Rough Lumber. Lumber that has not been dressed (surfaced) but has been
sawed, edged, and trimmed.
Dressed (Surfaced) Lumber. Lumber that has been dressed by a planning machine
(for the purpose of attaining smoothness of surface and uniformity of size)
on one side (S1S), two sides (S2S), one edge (S1E), two edges (S2E), or a combination
of sides and edges (S1S1E, S1S2, S2S1E, S4S).
Worked Lumber. Lumber that, in addition to being dressed, has been matched,
shiplapped or patterned:
Matched Lumber. Lumber that has been worked with a tongue on one edge of
each piece and a groove on the opposite edge.
BUILDING MATERIALS 4.47
Shiplapped Lumber. Lumber that has been worked or rabbeted on both edges,
to permit formation of a close-lapped joint.
Patterned Lumber. Lumber that is shaped to a pattern or to a molded form.
Softwoods are also classified according to nominal size:
Boards. Lumber less than 2 in in nominal thickness and 2 in or more in nominal
width. Boards less than 6 in in nominal width may be classified as strips.
Dimension. Lumber from 2 in to, but not including, 5 in in nominal thickness,
and 2 in or more in nominal width. Dimension may be classified as framing, joists,
planks, rafters, studs, small timbers, etc.
Timbers. Lumber 5 in or more nominally in least dimension. Timber may be
classified as beams, stringers, posts, caps, sills, girders, purlins, etc.
Actual sizes of lumber are less than the nominal sizes, because of shrinkage and
dressing. In general, dimensions of dry boards, dimension lumber, and timber less
than 2 in wide or thick are 1?4 in less than nominal; from 2 to 7 in wide or thick,
1?2 in less, and above 6 in wide or thick, 3?4 in less. Green-lumber less than 2 in
wide or thick is 1?32 in more than dry; from 2 to 4 in wide or thick, 1?16 in more, 5
and 6 in wide or thick, 1?8 in more, and 8 in or above in width and thickness, 1?4
in more than dry lumber. There are exceptions, however.
Yard lumber is classified on the basis of quality as:
Appearance. Lumber is good appearance and finishing qualities, often called
select.
Suitable for natural finishes
Practically clear
Generally clear and of high quality
Suitable for paint finishes
Adapted to high-quality paint finishes
Intermediate between high-finishing grades and common grades, and partaking
somewhat of the nature of both
Common. Lumber suitable for general construction and utility purposes, often
given various commercial designations.
For standard construction use
Suitable for better-type construction purposes
Well adapted for good standard construction
Designed for low-cost temporary construction
For less exacting purposes
Low quality, but usable
Structural lumber is assigned modulus of elasticity values and working stresses
in bending, compression parallel to grain, compression perpendicular to grain, and
horizontal shear in accordance with ASTM procedures. These values take into account
such factors as sizes and locations of knots, slope of grain, wane, and shakes
or checks, as well as such other pertinent features as rate of growth and proportions
of summerwood.
Factory and shop lumber is graded with reference to its use for doors and sash,
or on the basis of characteristics affecting its use for general cut-up purposes, or
on the basis of size of cutting. The grade of factory and shop lumber is determined
by the percentage of the area of each board or plank available in cuttings of spec4.48
SECTION FOUR
ified or of given minimum sizes and qualities. The grade of factory and shop lumber
is determined from the poor face, although the quality of both sides of each cutting
must be considered.
Hardwoods. Because of the great diversity of applications for hardwood both in
and outside the construction industry, hardwood grading rules are based on the
proportion of a given piece that can be cut into smaller pieces of material clear on
one or both sides and not less than a specified size. Grade classifications are therefore
based on the amount of clear usable lumber in a piece.
Special grading rules of interest in the construction industry cover hardwood
interior trim and moldings, in which one face must be practically free of imperfections
and in which Grade A may further limit the amount of sapwood as well as
stain. Hardwood dimension rules, in addition, cover clears, which must be clear
both faces; clear one face; paint quality, which can be covered with pain; core,
which must be sound on both faces and suitable for cores of glued-up panels; and
sound, which is a general-utility grade.
Hardwood flooring is graded under two separate sets of rules: (1) for maple,
birch, and beech; and (2) for red and white oak and pecan. In both sets of rules,
color and quality classifications range from top-quality to the lower utility grades.
Oak may be further subclassified as quarter-sawed and plain-sawed. In all grades,
top-quality material must be uniformed in color, whereas other grades place no
limitation on color.
Shingles are graded under special rules, usually into three classes: Number 1,
2, and 3. Number 1 must be all edge grain and strictly clear, containing no sapwood.
Numbers 2 and 3 must be clear to a distance far enough away from the butt to be
well covered by the next course of shingles.
4.36 DESTROYERS AND PRESERVATIVES
The principal destroyers of wood are decay, caused by fungus, and attack by a
number of animal organisms of which termites, carpenter ants, grubs of a wide
variety of beetles, teredo, and limnoria are the principal offenders. In addition, fire
annually causes widespread destruction of wood structures.
Decay will not occur if wood is kept well ventilated and air-dry or, conversely,
if it is kept continuously submerged so that air is excluded.
Most termites in the United States are subterranean and require contact with the
soil. The drywood and dampwood termites found along the southern fringes of the
country and along the west coast, however, do not require direct soil contact and
are more difficult to control.
Teredo, limnoria, and other water-borne wood destroyers are found only in salt
or brackish waters.
Various wood species vary in natural durability and resistance to decay and
insect attack. The sapwood of all species is relatively vulnerable; only the heartwood
can be considered to be resistant. Table 4.15 lists the common species in
accordance with heartwood resistance. Such a list is only approximate, and individual
pieces deviate considerably.
Preservatives employed to combat the various destructive agencies may be subdivided
into oily, water-soluble salts, and solvent-soluble organic materials. The
principal oily preservatives are coal-tar creosote and creosote mixed with petroleum.
BUILDING MATERIALS 4.49
From U.S. Forest Products Laboratory.
The most commonly employed water-soluble salts are acid copper chromate, chromated
copper arsenate and arsenite, fluor chrome arsenate phenol, chromated zinc
chloride, and other materials that are often sold under various proprietary names.
The principal solvent-soluble organic materials are chlorinated phenols, such as
pentachlorphenol, and copper naphthenate.
Preservatives may be applied in a variety of ways, including brushing and dipping,
but for maximum treatment, pressure is required to provide deep side-grain
penetration. Butts of poles and other parts are sometimes placed in a hot boiling
creosote or salt solution, and after the water in the wood has been converted to
steam, they are quickly transferred to a cold vat of the same preservative. As the
steam condenses, it produces a partial vacuum, which draws the preservative fairly
deeply into the surface.
Pressure treatments may be classified as full-cell and empty-cell. In the full-cell
treatment, a partial vacuum is first drawn in the pressure-treating tank to withdraw
most of the air in the cells of the wood. The preservative is then let in without
breaking the vacuum, after which pressure is applied to the hot solution. After
treatment is completed, the individual cells are presumably filled with preservative.
In the empty-cell method, no initial vacuum is drawn, but the preservative is
4.50 SECTION FOUR
pumped in under pressure against the back pressure of the compressed air in the
wood. When the pressure is released, the air in the wood expands and forces out
excess preservative, leaving only a coating of preservative on the cell walls.
Retentions of preservative depend on the application. For teredo-infestation, fullcell
creosote treatment to refusal may be specified, ranging from 16 to 20 lb per
cubic foot of wood. For ordinary decay conditions and resistance to termites and
other destroyers of a similar nature, the empty-cell method may be employed with
retentions in the vicinity of 6 to 8 lb of creosote per cubic foot of wood. Salt
retentions generally range in the vicinity of 11?2 to 3 lb of dry salt retained per
cubic food of wood.
Solvent-soluble organic materials, such as pentachlorphenol, are commonly employed
for the treatment of sash and door parts to impart greater resistance to decay.
This is commonly done by simply dipping the parts in the solution and then allowing
them to dry. As the organic solvent evaporates, it leaves the water-insoluble
preservative behind in the wood.
These organic materials are also employed for general preservative treatment,
including fence posts and structural lumber. The water-soluble salts and solventsoluble
organic architects leave the wood clean and paintable. Creosote in general
cannot be painted over, although partial success can be achieved with top-quality
aluminum-flake pigment paints.
Treatment against fire consists generally of applying salts containing ammonium
and phosphates, of which monoammonium phosphate and diammonium phosphate
are widely employed. At retentions of 3 to 5 lb of dry salt per cubic foot, the wood
does not support its own combustion, and the afterglow when fire is removed is
short. A variety of surface treatments is also available, most of which depend on
the formation of a blanket of inert-gas bubbles over the surface of the wood in the
presence of flame or other sources of heat. The blanket of bubbles insulates the
wood beneath and retards combustion.
See also Art. 10.6.
4.37 GLUES AND ADHESIVES FOR WOOD
A variety of adhesives is now available for use with wood, depending on the final
application. The older adhesives include animal glue, casein glue, and a variety of
vegetable glues, of which soybean is today the most important. Animal glues provide
strong, tough, easily made joints, which, however, are not moisture-resistant.
Casein mixed with cold water, when properly formulated, provides highly moistureresistant
glue joints, although they cannot be called waterproof. The vegetable glues
have good dry strength but are not moisture-resistant.
The principal high-strength glues today are synthetic resins, of which phenol
formaldehyde, urea formaldehyde, resorcinol formaldehyde, melamine formaldehyde,
and epoxy are the most important. Phenol, resorcinol, and melamine provide
glue joints that are completely waterproof and will not separate when properly made
even on boiling. Urea formaldehyde provides a glue joint of high moisture resistance,
although not quite so good as the other three. Phenol and melamine require
application of heat, as well as pressure, to cure the adhesive. Urea and resorcinol,
however, can be formulated to be mixed with water at ordinary temperatures and
hardened without application of heat above room temperature. Waterproof plywood
is commonly made in hot-plate presses with phenolic or melamine adhesive. ReBUILDING
MATERIALS 4.51
sorcinol is employed where heat cannot be applied, as in a variety of assembly
operations and the manufacture of laminated parts like ships’ keels, which must
have the maximum in waterproof qualities. Epoxide resins provide strong joints.
Adhesives containing an elastomeric material, such as natural or synthetic rubber,
may be classified as contact or mastic. The former, applied to both mating surfaces
and allowed to partly dry, permit adhesion on contact. Mastics are very viscous and
applied with a trowel or putty knife. They may be used to set wood-block flooring.
An emulsion of polyvinyl acetate serves as a general-purpose adhesive, for general
assembly operations where maximum strength and heat or moisture resistance
are not required. This emulsion is merely applied to the surfaces to be bonded,
after which they are pressed together and the adhesive is allowed to harden.
4.38 PLYWOOD AND OTHER FABRICATED
WOOD BOARDS
As ordinarily made, plywood consists of thin sheets, or veneers, of wood glued
together. The grain is oriented at right angles in adjacent plies. To obtain plywood
with balance—that is, which will not warp, shrink, or twist unduly—the plies must
be carefully selected and arranged to be mirror images of each other with respect
to the central plane. The outside plies or faces are parallel to each other and are of
species that have the same shrinkage characteristics. The same holds true of the
cross bands. As a consequence, plywood has an odd number of plies, the minimum
being three.
Principal advantages of plywood over lumber are its more nearly equal strength
properties in length and width, greater resistance to checking, greatly reduced
shrinkage and swelling, and resistance to splitting.
The approach to equalization of strength of plywood in the various directions is
obtained at the expense of strength in the parallel-to-grain direction; i.e., plywood
is not so strong in the direction parallel to its face plies as lumber is parallel to the
grain. But plywood is considerably stronger in the direction perpendicular to its
face plies than wood is perpendicular to the grain. Furthermore, the shearing
strength of plywood in a plane perpendicular to the plane of the plywood is very
much greater than that of ordinary wood parallel to the grain. In a direction parallel
to the plane of the plywood, however, the shearing strength of plywood is less than
that of ordinary wood parallel to the grain, because in this direction rolling shear
occurs in the plywood; i.e., the fibers in one ply tend to roll rather than to slide.
Depending on whether plywood is to be used for general utility or for decorative
purposes, the veneers employed may be cut by peeling from the log, by slicing, or
today very rarely, by sawing. Sawing and slicing give the greatest freedom and
versatility in the selection of grain. Peeling provides the greatest volume and the
most rapid production, because logs are merely rotated against a flat knife and the
veneer is peeled off in a long continuous sheet.
Plywood is classified as interior or exterior, depending on the type of adhesive
employed. Interior-grade plywood must have a reasonable degree of moisture resistance
but is not considered to be waterproof. Exterior-grade plywood must be
completely waterproof and capable of withstanding immersion in water or prolonged
exposure to outdoor conditions.
In addition to these classifications, plywood is further subclassified in a variety
of ways depending on the quality of the surface ply. Top quality is clear on one or
4.52 SECTION FOUR
both faces, except for occasional patches. Lower qualities permit sound defects,
such as knots and similar blemishes, which do not detract from the general utility
of the plywood but detract from its finished appearance.
Particle Board. Wood chips, sawdust, and flakes are pressed with a binder (ureaformaldehyde
or phenol-formaldehyde) to form boards (sheathing, underlayment,
corestock), having uniform strength and low shrinkage in the plane of the board.
Hardboard. Wood chips (exploded by high-pressure steam into wood fibers) and
lignin are pressed to form boards of various densities. Additives may add weather
resistance and other properties.
4.39 WOOD BIBLIOGRAPHY
Forest Products Laboratory, Forest Service, U.S. Department of Agriculture: ‘‘Wood
Handbook,’’ Government Printing Office, Washington, D.C.
National Hardwood Lumber Association, Chicago, Ill.: ‘‘Rules for the Measurement
and Inspection of Hardwood Lumber, Cypress, Veneer, and Thin Lumber.’’
American Forest and Paper Association, Washington, D.C.: ‘‘National Design
Specification for Wood Construction.’’
U.S. Department of Commerce, National Bureau of Standards, Washington,
D.C.: American Softwood Lumber Standard, Voluntary Practice Standard PS20;
Douglas Fir Plywood, Commercial Standard CS 45; Hardwood Plywood, Commercial
Standard CS 35.
Western Wood Products Association, Portland, Ore.: ‘‘Western Woods Use
Book.’’
K. F. Faherty and T. G. Williamson, ‘‘Wood Engineering and Construction Handbook,’’
McGraw-Hill Publishing Company, New York.
STEEL AND STEEL ALLOYS
Iron and its alloys are generally referred to as ferrous metals. Even small amounts
of alloy change the properties of ferrous metals significantly. Also, the properties
can be changed considerably by changing the atomic structure of these metals by
heating and cooling.
4.40 TYPES OF IRONS AND STEELS
Steel is a solution of carbon in iron. Various types of steel are produced by varying
the percentage of carbon added to molten iron and controlling the cooling, which
affects the atomic structure of the product, and hence its properties. Some of the
structural changes can be explained with the aid of an iron-carbon equilibrium
diagram (Fig. 4.2).
4.40.1 Iron-Carbon Equilibrium Diagram
The iron-carbon equilibrium diagram in Fig. 4.2 shows that, under equilibrium
conditions (slow cooling) if not more than 2.0% carbon is present, a solid solution
of carbon in gamma iron exists at elevated temperatures. This is called austenite.
If the carbon content is less than 0.8%, cooling below the A3 temperature line causes
transformation of some of the austenite to ferrite, which is substantially pure alpha
iron (containing less than 0.01% carbon in solution). Still further cooling to below
the A1 line causes the remaining austenite to transform to pearlite—the eutectoid
mixture of fine plates, or lamellas, of ferrite and cementite (iron carbide) whose
iridescent appearance under the microscope gives it its name.
If the carbon content is 0.8%, no transformation on cooling the austenite occurs
until the A1 temperature is reached. At that point, all the austenite transforms to
pearlite, with its typical ‘‘thumbprint’’ microstructure.
At carbon contents between 0.80 and 2.0%, cooling below the Acm temperature
line causes iron carbide, or cementite, to form in the temperature range between
Acm and A1,3. Below A1,3, the remaining austenite transforms to pearlite.
4.40.2 Types of Irons
Metals containing substantially no carbon (several hundredths of 1%) are called
irons, of which wrought iron, electrolytic iron, and ‘‘ingot’’ iron are examples.
Wrought iron, whether made by the traditional puddling method or by mixing
very low carbon iron and slag, contains a substantial amount of slag. Because it
contains very little carbon, it is soft, ductile, and tough and, like low-carbon ferrous
metals generally, is relatively resistant to corrosion. It is easily worked. When broken,
it shows a fibrous fracture because of the slag inclusions. ‘‘Ingot’’ iron is a
very low carbon iron containing no slag, which is also soft, ductile, and tough.
When the silicon content is kept low, and the metal is cooled rapidly, white cast
iron results. It is hard and brittle because of the high cementite content. White cast
iron as such has little use; but when it is reheated and held a long time in the
vicinity of the transformation temperature, then cooled slowly, the cementite decomposes
to ferrite and nodular or temper carbon. The result is black-heart malleable
iron. If the carbon is removed during malleabilization, white-heart malleable
iron results.
If the silicon content is raised, and the metal is cooled relatively slowly, gray
cast iron results. It contains cementite, pearlite, ferrite, and some free carbon, which
gives it its gray color. Gray iron is considerably softer and tougher than white cast
iron and is generally used for castings of all kinds. Often, it is alloyed with elements
like nickel, chromium, copper, and molybdenum.
At 5.0% carbon, the end products is hard, brittle iron carbide or cementite.
4.40.3 Types of Carbon Steels
Most of the steel used for construction is low- to medium-carbon, relatively mild,
tough, and strong, fairly easy to work by cutting, punching, riveting, and welding.
Table 4.16 summarizes the most important carbon steels and low-alloy steels used
in construction as specified by ASTM.
The plain iron-carbon metals with less than 0.8% carbon content consist of
ferrite and pearlite and provide the low-carbon (0.06 to 0.30%), medium-carbon
(0.30 to 0.50%), and high-carbon (0.50 to 0.80%) steels called hypoeutectoid steels.
The higher-carbon or hypereutectoid tool steels contain 0.8 to 2.0% carbon and
consist of pearlite and cementite. The eutectoid steels occurring in the vicinity of
0.8% carbon are essentially all pearlite.
The American Iron and Steel Institute and the Society of Automotive Engineers
have designated standard compositions for various steels including plain carbon
steels and alloy steels. AISI and SAE numbers and compositions for several representative
hot-rolled carbon-steel bars are given in Table 4.17.
Prestressed concrete imposes special requirements for reinforcing steel. It must
be of high strength with a high yield point and minimum creep in the working
range. Table 4.16 and 4.18 give ASTM specification requirements for bars, wires,
and strands.
4.40.4 Types of Structural Steels
Structural steels are low- to medium-carbon steels used in elements 1?4 in thick or
more to form structural framing. The American Institute of Steel Construction
(AISC) ‘‘Code of Standard Practice for Steel Buildings and Bridges’’ lists the elements
that are included in the scope of the work in contract documents for structural
steel. The list includes flexural members, columns, trusses, bearings and bearing
plates, bracing, hangers, bolts and nuts, shear connectors, wedges, and shims.
The AISC ‘‘Specification for Structural Steel Buildings’’ (ASD and LRFD) tabulates
the types of structural steel that are approved for use in buildings. These steels are
given in Table 4.16.
BUILDING MATERIALS 4.57
In accordance with present practice, the steels described in this section and in
Sec. 7 are given the names of the corresponding ASTM specifications for the steels.
For example, all steels conforming with ASTM A588, ‘‘Specification for High-
Strength Low-Alloy Structural Steel,’’ are called A588 steel. Further identification
may be given by a grade, which usually indicates the steel yield strength.
Structural steels may be classified as carbon steels; high-strength, low-alloy
steels; heat-treated, high-strength carbon steels; or heat-treated, constructional alloy
steels.
Carbon steels satisfy all of the following requirements:
1. The maximum content specified for alloying elements does not exceed the following:
manganese, 1.65%; silicon, 0.60%; copper, 0.60%.
2. The specified minimum for copper does not exceed 0.40%.
3. No minimum content is specified for other elements added to obtain a desired
alloying effect.
A36 and A529 steels are included in this category.
4.58 SECTION FOUR
FIGURE 4.3 Typical stress-strain curves for
structural steels.
High-strength, low-alloy steels have specified minimum yield strengths larger
than 40 ksi, which are attained without heat treatment. A242, A572, and A588
steels are included in this category. A242 and A572 steel are often referred to as
weathering steels, because they have higher resistance to corrosion than carbon
steels. On exposure to ordinary atmospheric conditions, they develop a protective
oxide surface.
Heat-treated, high-strength carbon steels are heat-treated to achieve specified
high strength and toughness. A633, A678, and A852 steels are included in this
category.
Heat-treated, constructional alloy steels contain alloying elements in excess
of the limits for carbon steels and are heat-treated to obtain a combination of high
strength and toughness. These are the strongest steels in general structural use. The
various grades of A514 steel, with yield strengths up to 100 ksi, are in this category.
4.41 PROPERTIES OF STRUCTURAL STEELS
Figure 4.3 shows a typical stress-strain curve for each classification of structural
steels defined in Art. 4.40.4. The diagram illustrates the higher-strength levels
achieved with heat treatment and addition of alloys.
4.41.1 Tensile Properties of Structural Steels
The curves in Fig. 4.3 were derived from tensile tests. The yield points, strengths,
and modulus of elasticity obtained from compression tests would be about the same.
The initial portion of the curves in Fig. 4.3 is shown to a magnified scale in
Fig. 4.4. It indicates that there is an initial elastic range for the structural steels in
which there is no permanent deformation on removal of the load. The modulus of
elasticity E, which is given by the slope of the curves, is nearly a constant 29,000
ksi for all the steels. For carbon and high-strength, low-alloy steels, the inelastic
range, where strains exceed those in the elastic range, consists of two parts: Initially,
a plastic range occurs in which the steels yield; that is, strain increases with no
increase in stress. Then follows a strain-hardening range in which increase in strain
is accompanied by a significant increase in stress.
The curves in Fig. 4.4 also show an upper and lower yield point for the carbon
and high-strength, low-alloy steels. The upper yield point is the one specified in
standard specifications for the steels. In contrast, the curves do not indicate a yield
point for the heat-treated steels. For these steels, ASTM 370, ‘‘Mechanical Testing
of Steel Products,’’ recognizes two ways of indicating the stress at which there is
a significant deviation from the proportionality of stress to strain. One way, applicable
to steels with a specified yield point of 80 ksi or less, is to define the yield
point as the stress at which a test specimen reaches a 0.5% extension under load
(0.5% EUL). The second way is to define the yield strength as the stress at which
a test specimen reaches a strain (offset) 0.2% greater than that for elastic behavior.
Yield point and yield strength are often referred to as yield stress.
Ductility is measured in tension tests by percent elongation over a given gage
length—usually 2 or 8 in—or percent reduction of cross-sectional area. Ductility
is an important property because it permits redistribution of stresses in continuous
members and at points of high local stresses.
Poisson’s ratio, the ratio of transverse to axial strain, also is measured in tension
tests. It may be taken as 0.30 in the elastic range and 0.50 in the plastic range for
structural steels.
Cold working of structural steels, that is, forming plates or structural shapes
into other shapes at room temperature, changes several properties of the steels. The
resulting strains are in the strain-hardening range. Yield strength increases but ductility
decreases. (Some steels are cold rolled to obtain higher strengths.) If a steel
4.60 SECTION FOUR
element is strained into the strain-hardening range, then unloaded and allowed to
age at room or moderately elevated temperatures (a process called strain aging),
yield and tensile strengths are increased, whereas ductility is decreased. Heat treatment
can be used to modify the effects of cold working and strain aging.
Residual stresses remain in structural elements after they are rolled or fabricated.
They also result from uneven cooling after rolling. In a welded member,
tensile residual stresses develop near the weld and compressive stresses elsewhere.
Plates with rolled edges have compressive residual stresses at the edges, whereas
flame-cut edges have tensile residual stresses. When loads are applied to such members,
some yielding may take place where the residual stresses occur. Because of
the ductility of steel, however, the effect on tensile strength is not significant but
the buckling strength of columns may be lowered.
Strain rate also changes the tensile properties of structural steels. In the ordinary
tensile test, load is applied slowly. The resulting data are appropriate for design of
structures for static loads. For design for rapid application of loads, such as impact
loads, data from rapid tension tests are needed. Such tests indicate that yield and
tensile strengths increase but ductility and the ratio of tensile strength to yield
strength decrease.
High temperatures too affect properties of structural steels. As temperatures
increase, the stress-strain curve typically becomes more rounded and tensile and
yield strengths, under the action of strain aging, decrease. Poisson’s ratio is not
significantly affected but the modulus of elasticity decreases. Ductility is lowered
until a minimum value is reached. Then, it rises with increase in temperature and
becomes larger than the ductility at room temperature.
Low temperatures in combination with tensile stress and especially with geometric
discontinuities, such as notches, bolt holes, and welds, may cause a brittle
failure. This is a failure that occurs by cleavage, with little indication of plastic
deformation. A ductile failure, in contrast, occurs mainly by shear, usually preceded
by large plastic deformation. One of the most commonly used tests for rating steels
on their resistance to brittle fracture is the Charpy V-notch test. It evaluates notch
toughness at specific temperatures.
Toughness is defined as the capacity of a steel to absorb energy; the greater the
capacity, the greater the toughness. Determined by the area under the stress-strain
curve, toughness depends on both strength and ductility of the metal. Notch toughness
is the toughness in the region of notches or other stress concentrations. A
quantitative measure of notch toughness is fracture toughness, which is determined
by fracture mechanics from relationships between stress and flaw size.
4.41.2 Shear Properties of Structural Steels
The shear modulus of elasticity G is the ratio of shear stress to shear strain during
initial elastic behavior. It can be computed from Eq. (5.25) from values of modulus
of elasticity and Poisson’s ratio developed in tension stress-strain tests. Thus G for
structural steels is generally taken as 11,000 ksi.
The shear strength, or shear stress at failure in pure shear, ranges from 0.67Ft
to 0.75Ft for structural steels, where Ft is the tensile strength. The yield strength
in shear is about 0.57Ft.
4.41.3 Creep and Relaxation
Creep, a gradual change in strain under constant stress, is usually not significant
for structural steel framing in buildings, except in fires. Creep usually occurs under
high temperatures or relatively high stresses, or both.
BUILDING MATERIALS 4.61
Relaxation, a gradual decrease in load or stress under a constant strain, is a
significant concern in the application of steel tendons to prestressing (Art. 9.104).
With steel wire or strand, relaxation can occur at room temperature. To reduce
relaxation substantially, stabilized, or low-relaxation, strand may be used. This is
produced by pretensioning strain at a temperature of about 600
F. A permanent
elongation of about 1% remains and yield strength increases to about 5% over
stress-relieved (heat-treated but not tensioned) strain.
4.41.4 Hardness of Structural Steels
Hardness is used in production of steels to estimate tensile strength and to check
the uniformity of tensile strength in various products. Hardness is determined as a
number related to resistance to indentation. Any of several tests may be used, the
resulting hardness numbers being dependent on the type of penetrator and load.
These should be indicated when a hardness number is given. Commonly used hardness
tests are the Brinell, Rockwell, Knoop, and Vickers. ASTM A370, ‘‘Mechanical
Testing of Steel Products,’’ contains tables that relate hardness numbers from
the different tests to each other and to the corresponding approximate tensile
strength.
4.41.5 Fatigue of Structural Steels
Under cyclic loading, especially when stress reversal occurs, a structural member
may eventually fail because cracks form and propagate. Known as a fatigue failure,
this can take place at stress levels well below the yield stress. Fatigue resistance
may be determined by a rotating-beam test, flexure test, or axial-load test. In these
tests, specimens are subjected to stresses that vary, usually in a constant stress range
between maximum and minimum stresses until failure occurs. Results of the tests
are plotted on an S-N diagram, where S is the maximum stress (fatigue strength)
and N is the number of cycles to failure (fatigue life). Such diagrams indicate that
the failure strength of a structural steel decreases with increase in the number of
cycles until a minimum value is reached, the fatigue limit. Presumably, if the
maximum stress does not exceed the fatigue limit, an unlimited number of cycles
of that ratio of maximum to minimum stress can be applied without failure. With
tension considered positive and compression, negative, tests also show that as the
ratio of maximum to minimum stress is increased, fatigue strength is lowered significantly.
Since the tests are made on polished specimens and steel received from mills
has a rough surface, fatigue data for design should be obtained from tests made on
as-received material.
Tests further indicate that steels with about the same tensile strength have about
the same fatigue strength. Hence the S-N diagram obtained for one steel may be
used for other steels with about the same tensile strength.
4.42 HEAT TREATMENT AND HARDENING OF
STEELS
Heat-treated and hardened steels are sometimes required in building operations. The
most familiar heat treatment is annealing, a reheating operation in which the metal
4.62 SECTION FOUR
is usually heated to the austenitic range (Fig. 4.2) and cooled slowly to obtain the
softest, most ductile state. Cold working is often preceded by annealing. Annealing
may be only partial, just sufficient to relieve internal stresses that might cause
deformation or cracking, but not enough to reduce markedly the increased strength
and yield point brought about by the cold working, for example.
Another type of heat treatment that may be used is normalizing. It requires
heating steel to 100 to 150
F above the A3 temperature line in Fig. 4.2. Then, the
steel is allowed to cool in still air. (The rate of cooling is much more rapid than
that used in annealing.) Normalizing may be used to refine steel grain size, which
depends on the finishing temperature during hot rolling, or to obtain greater notch
toughness.
Thick plates have a coarser grain structure than thin plates and thus can benefit
more from normalizing. This grain structure results from the fewer rolling passes
required for production of thick plates, consequent higher finishing temperature,
and slower cooling.
Sometimes, a hard surface is required on a soft, tough core. Two principal casehardening
methods are employed. For case carburizing, a low- to medium-carbon
steel is packed in carbonaceous materials and heated to the austenite range. Carbon
diffuses into the surface, providing a hard, high-carbon case when the part is cooled.
For nitriding, the part is exposed to ammonia gas or a cyanide at moderately
elevated temperatures. Extremely hard nitrides are formed in the case and provide
a hard surface.
4.43 EFFECTS OF GRAIN SIZE
When a low-carbon steel is heated above the A3 temperature line (Fig. 4.2), for
example, to hot rolling and forging temperatures, the steel may grow coarse grains.
For some applications, this structure may be desirable; for example, it permits
relatively deep hardening, and if the steel is to be used in elevated-temperature
service, it will have higher load-carrying capacity and higher creep strength than if
the steel had fine grains.
Fine grains, however, enhance many steel properties: notch toughness, bendability,
and ductility. In quenched and tempered steels, higher yield strengths are
obtained. Furthermore, fine-grain, heat-treated steels have less distortion, less
quench cracking, and smaller internal stresses.
During the production of a steel, grain growth may be inhibited by an appropriate
dispersion of nonmetallic inclusions or by carbides that dissolve slowly or remain
undissolved during cooling. The usual method of making fine-grain steel employs
aluminum deoxidation. In such steels, the inhibiting agent may be a submicroscopic
dispersion of aluminum nitride or aluminum oxide. Fine grains also may be produced
by hot working rolled or forged products, which otherwise would have a
coarse-grain structure. The temperature at the final stage of hot working determines
the final grain size. If the finishing temperature is relatively high and the grains
after air-cooling are coarse, the size may be reduced by normalizing (Art. 4.42).
Fine- or coarse-grain steels may be heat treated to be coarse- or fine-grain.
4.44 STEEL ALLOYS
Plain carbon steels can be given a great range of properties by heat treatment and
by working; but addition of alloying elements greatly extends those properties or
BUILDING MATERIALS 4.63
makes the heat-treating operations easier and simpler. For example, combined high
tensile strength and toughness, corrosion resistance, high-speed cutting, and many
other specialized purposes require alloy steels. However, the most important effect
of alloying is the influence on hardenability.
4.44.1 Effects of Alloying Elements
Important alloying elements from the standpoint of building, and their principal
effects, are summarized below:
Aluminum restricts grain growth during heat treatment and promotes surface
hardening by nitriding.
Chromium is a hardener, promotes corrosion resistance (see Art. 4.44.2), and
promotes wear resistance.
Copper promotes resistance to atmospheric corrosion and is sometimes combined
with molybdenum for this purpose in low-carbon steels and irons. It strengthens
steel and increases the yield point without unduly changing elongation or reduction
of area.
Manganese in low concentrations promotes hardenability and nondeforming,
nonshrinking characteristics for tool steels. In high concentrations, the steel is austenitic
under ordinary conditions, is extremely tough, and work-hardens readily. It
is therefore used for teeth of power-shovel dippers, railroad frogs, rock crushers,
and similar applications.
Molybdenum is usually associated with other elements, especially chromium
and nickel. It increases corrosion resistance, raises tensile strength and elastic limit
without reducing ductility, promotes casehardening, and improves impact resistance.
Nickel boosts tensile strength and yield point without reducing ductility; increases
low-temperature toughness, whereas ordinary carbon steels become brittle;
promotes casehardening; and in high concentrations improves corrosion resistance
under severe conditions. It is often used with chromium (see Art. 4.44.2). Invar
contains 36% nickel.
Silicon strengthens low-alloy steels; improves oxidation resistance; with low
carbon yields transformer steel, because of low hysteresis loss and high permeability;
in high concentrations provides hard, brittle castings, resistant to corrosive
chemicals, useful in plumbing lines for chemical laboratories.
Sulfur promotes free machining, especially in mild steels.
Titanium prevents intergranular corrosion of stainless steels by preventing grainboundary
depletion of chromium during such operations as welding and heat treatment.
Tungsten, vanadium, and cobalt are all used in high-speed tool steels, because
they promote hardness and abrasion resistance. Tungsten and cobalt also increase
high-temperature hardness.
The principal effects of alloying elements are summarized in Table 4.19.
4.68 SECTION FOUR
strength of 75 ksi and yield point of 30 ksi when annealed. Cold-finished steels
may have a tensile strength as high as 125 ksi with a yield point of 100 ksi.
Austenitic stainless steels are tough, strong, and shock-resistant, but work-harden
readily; so some difficulty on this score may be experienced with cold working and
machining. These steels can be welded readily but may have to be stabilized (e.g.,
AISI Types 321 and 347) against carbide precipitation and intergranular corrosion
due to welding unless special precautions are taken. These steels have the best
high-temperature strength and resistance to scaling of all the stainless steels.
Types 303 and 304 are the familiar 18-8 stainless steels widely used for building
applications. These and Types 302 and 316 are the most commonly employed
stainless steels. Where maximum resistance to corrosion is required, such as resistance
to pitting by seawater and chemicals, the molybdenum-containing Types 316
and 317 are best.
For resistance to ordinary atmospheric corrosion, some of the martensitic and
ferritic stainless steels, containing 15 to 20% chromium and no nickel, are employed.
The martensitic steels, in general, range from about 12 to 18% chromium
and from 0.08 to 1.10% carbon. Their response to heat treatment is similar to that
of the plain carbon steels. When chromium content ranges from 15 to 30% and
carbon content is below 0.35%, the steels are ferritic and nonhardenable. The highchromium
steels are resistant to oxidizing corrosion and are useful in chemical
plants.
4.45 WELDING FERROUS METALS
General welding characteristics of the various types of ferrous metals are as follows:
Wrought iron is ideally forged but may be welded by other methods if the base
metal is thoroughly fused. Slag melts first and may confuse unwary operators.
Low-carbon iron and steels (0.30%C or less) are readily welded and require
no preheating or subsequent annealing unless residual stresses are to be removed.
Medium-carbon steels (0.30 to 0.50%C) can be welded by the various fusion
processes. In some cases, especially in steel with more than 0.40% carbon, preheating
and subsequent heat treatment may be necessary.
High-carbon steels (0.50 to 0.90%C) are more difficult to weld and, especially
in arc welding, may have to be preheated to at least 500
F and subsequently heated
between 1200 and 1450
F. For gas welding, a carburizing flame is often used. Care
must be taken not to destroy the heat treatment to which high-carbon steels may
have been subjected.
Tool steels (0.80 to 1.50%C) are difficult to weld. Preheating, postannealing,
heat treatment, special welding rods, and great care are necessary for successful
welding.
Welding of structural steels is governed by the American Welding Society
‘‘Structural Welding Code,’’ AWS D1.1, the American Institute of Steel Construction
Specification for the Design, Fabrication and Erection of Structural Steel for
Buildings, or a local building code. AWS D1.1 specifies tests to be used in qualifying
welders and types of welds. The AISC Specification and many building codes
require, in general, that only qualified welds be used and that they be made only
by qualified welders.
Structural steels may be welded by shielded metal arc, submerged arc, gas metal
arc, flux-cored arc, electroslag, electrogas, or stud-welding processes.
BUILDING MATERIALS 4.69
Shielded-metal-arc welding fuses parts to be joined by the heat of an electric
arc struck between a coated metal electrode and the material being joined, or base
metal. The electrode supplies filler material for making the weld, gas for shielding
the molten metal from the air, and flux for refining this metal.
Submerged-arc welding fuses the parts to be joined by the heat of an electric
arc struck between a bare metal electrode and base metal. The weld is shielded
from the air by flux. The electrode or a supplementary welding rod supplies metal
filler for making the weld.
Gas-metal-arc welding produces fusion by the heat of an electric arc struck
between a filler-metal electrode and base metal, while the molten metal is shielded
by a gas or mixture of gas and flux. For structural steels, the gas may be argon,
argon with oxygen, or carbon dioxide.
Electroslag welding uses a molten slag to melt filler metal and surfaces of the
base metal and thus make a weld. The slag, electrically conductive, is maintained
molten by its resistance to an electric current that flows between an electrode and
the base metal. The process is suitable only for welding in the vertical position.
Moving, water-cooled shoes are used to contain and shape the weld surface. The
slag shields the molten metal.
Electrogas welding is similar to the electroslag process. The electrogas process,
however, maintains an electric arc continuously, uses an inert gas for shielding, and
the electrode provides flux.
Stud welding is used to fuse metal studs or similar parts to other steel parts by
the heat of an electric arc. A welding gun is usually used to establish and control
the arc, and to apply pressure to the parts to be joined. At the end to be welded,
the stud is equipped with a ceramic ferrule, which contains flux and which also
partly shields the weld when molten.
Preheating before welding reduces the risk of brittle failure. Initially, its main
effect is to lower the temperature gradient between the weld and adjoining base
metal. This makes cracking during cooling less likely and gives entrapped hydrogen,
a possible source of embrittlement, a chance to escape. A later effect of preheating
is improved ductility and notch toughness of base and weld metals and
lower transition temperature of weld. When, however, welding processes that deposit
weld metal low in hydrogen are used and suitable moisture control is maintained,
the need for preheat can be eliminated. Such processes include use of lowhydrogen
electrodes and inert-arc and submerged-arc welding.
Rapid cooling of a weld can have an adverse effect. One reason that arc strikes
that do not deposit weld metal are dangerous is that the heated metal cools very
fast. This causes severe embrittlement. Such arc strikes should be completely removed.
The material should be preheated, to prevent local hardening, and weld
metal should be deposited to fill the depression.
Pronounced segregation in base metal may cause welds to crack under certain
fabricating conditions. These include use of high-heat-input electrodes, such as the
1?4-in E6020, and deposition of large beads at slow speeds, as in automatic welding.
Cracking due to segregation, however, is rare with the degree of segregation normally
occurring in hot-rolled carbon-steel plates.
Welds sometimes are peened to prevent cracking or distortion, though there are
better ways of achieving these objectives. Specifications often prohibit peening of
the first and last weld passes. Peening of the first pass may crack or punch through
the weld. Peening of the last pass makes inspection for cracks difficult. But peening
is undesirable because it considerably reduces toughness and impact properties of
the weld metal. (The adverse effects, however, are eliminated by a covering weld
layer.) The effectiveness of peening in preventing cracking is open to question. And
4.70 SECTION FOUR
for preventing distortion, special welding sequences and procedures are simpler and
easier.
Failures in service rarely, if ever, occur in properly made welds of adequate
design. If a fracture occurs, it is initiated at a notchlike defect. Notches occur for
various reasons. The toe of a weld may from a natural notch. The weld may contain
flaws that act as notches. A welding-arc strike in the base metal may have an
embrittling effect, especially if weld metal is not deposited. A crack started at such
notches will propagate along a path determined by local stresses and notch toughness
of adjacent material.
Weldability of structural steels is influenced by their chemical content. Carbon,
manganese, silicon, nickel, chromium, and copper, for example, tend to have an
adverse effect, whereas molybdenum and vanadium may be beneficial. To relate
the influence of chemical content on structural steel properties to weldability, the
use of a carbon equivalent has been proposed. One formula suggested is
Mn Si
C  C  (4.3) eq 4 4
where C  carbon content, %
Mn  manganese content, %
Si  silicon content, %
Another proposed formula includes more elements:
Mn Ni Cr Mo V Cu
C  C      (4.4) eq 6 20 10 50 10 40
where Ni  nickel content, %
Cr  chromium content, %
Mo  molybdenum content, %
V  vanadium content, %
Cu  copper content, %
Carbon equivalent appears to be related to the maximum rate at which a weld
and adjacent base metal may be cooled after welding without underbead cracking
occurring. The higher the carbon equivalent, the lower will be the allowable cooling
rate. Also, the higher the carbon equivalent, the more important use of lowhydrogen
electrodes and preheating becomes.
4.46 EFFECTS OF STEEL PRODUCTION
METHODS
The processing of steels after conversion of pig iron to steel in a furnace has an
important influence on the characteristics of the final products. The general procedure
is as follows: The molten steel at about 2900
F is fed into a steel ladle, a
refractory-lined open-top vessel. Alloying materials and deoxidizers may be added
during the tapping of the heat or to the ladle. From the ladle, the liquid steel is
poured into molds, where it solidifies. These castings, called ingots, then are placed
in special furnaces, called soaking pits. There, the ingots are held at the desired
temperature for rolling until the temperature is uniform throughout each casting.
BUILDING MATERIALS 4.71
Ideally, an ingot should be homogeneous, with a fine, equiaxial crystal structure.
It should not contain nonmetallic inclusions or cavities and should be free of chemical
segregation. In practice, however, because of uneven cooling and release of
gases in the mold, an ingot may develop any of a number of internal and external
defects. Some of these may be eliminated or minimized during the rolling operation.
Prevention or elimination of the others often adds to the cost of steels.
Steel cools unevenly in a mold, because the liquid at the mold walls solidifies
first and cools more rapidly than metal in the interior of the ingot. Gases, chiefly
oxygen, dissolved in the liquid, are released as the liquid cools. Four types of ingot
may result—killed, semikilled, capped, and rimmed—depending on the amount of
gases dissolved in the liquid, the carbon content of the steel, and the amount of
deoxidizers added to the steel.
A fully killed ingot develops no gas; the molten steel lies dead in the mold. The
top surface solidifies relatively fast. Pipe, an intermittently bridged shrinkage cavity,
forms below the top. Fully killed steels usually are poured in big-end-up molds
with ‘‘hot tops’’ to confine the pipe to the hot top, which is later discarded. A
semikilled ingot develops a slight amount of gas. The gas, trapped when the metal
solidifies, forms blowholes in the upper portion of the ingot. A capped ingot develops
rimming action, a boiling caused by evolution of gas, forcing the steel to
rise. The action is stopped by a metal cap secured to the mold. Strong upward
currents along the sides of the mold sweep away bubbles that otherwise would form
blowholes in the upper portion of the ingot. Blowholes do form, however, in the
lower portion, separated by a thick solid skin from the mold walls. A rimmed ingot
develops a violent rimming action, confining blowholes to only the bottom quarter
of the ingot.
Rimmed or capped steels cannot be produced if too much carbon is present
(0.30% or more), because insufficient oxygen will be dissolved in the steels to
cause the rimming action. Killed and semikilled steels require additional costs for
deoxidizers if carbon content is low, and the deoxidation products form nonmetallic
inclusions in the ingot. Hence, it often is advantageous for steel producers to make
low-carbon steels by rimmed or capped practice, and high-carbon steels by killed
or semikilled practice.
Pipe, or shrinkage cavities, generally is small enough in most steels to be eliminated
by rolling. Blowholes in the interior of an ingot, small voids formed by
entrapped gases, also usually are eliminated during rolling. If they extend to the
surface, they may be oxidized and form seams when the ingot is rolled, because
the oxidized metal cannot be welded together. Properly made ingots have a thick
enough skin over blowholes to prevent oxidation.
Segregation in ingots depends on the chemical composition and on turbulence
from gas evolution and convection currents in the molten metal. Killed steels have
less segregation than semikilled steels, and these types of steels have less segregation
than capped or rimmed steels. In rimmed steels, the effects of segregation
are so marked that interior and outer regions differ enough in chemical composition
to appear to be different steels. The boundary between these regions is sharp.
Rimmed steels are made without additions of deoxidizers to the furnace and
with only small additions to the ladle, to ensure sufficient evolution of gas. When
properly made, rimmed ingots have little pipe and a good surface. Such steels are
preferred where surface finish is important and the effects of segregation will not
be harmful.
Capped steels are made much like rimmed steels but with less rimming action.
Capped steels have less segregation. They are used to make sheet, strip, skelp,
tinplate, wire, and bars.
4.72 SECTION FOUR
Semikilled steel is deoxidized less than killed steel. Most deoxidation is accomplished
with additions of a deoxidizer to the ladle. Semikilled steels are used in
structural shapes and plates.
Killed steels usually are deoxidized by additions to both furnace and ladle. Generally,
silicon compounds are added to the furnace to lower the oxygen content of
the liquid metal and stop oxidation of carbon (block the heat). This also permits
addition of alloying elements that are susceptible to oxidation. Silicon or other
deoxidizers, such as aluminum, vanadium, and titanium, may be added to the ladle
to complete deoxidation. Aluminum, vanadium, and titanium have the additional
beneficial effect of inhibiting grain growth when the steel is normalized. (In the
hot-rolled conditions, such steels have about the same ferrite grain size as semikilled
steels.) Killed steels deoxidized with aluminum and silicon (made to fine-grain
practice) often are specified for construction applications because of better notch
toughness and lower transition temperatures than semikilled steels of the same composition.
4.47 EFFECTS OF HOT ROLLING
While plates and shapes for construction applications can be obtained from processes
other than casting and rolling of ingots, such as continuous casting, most
plates and shapes are made by hot-rolling ingots (Art. 4.46). But usually, the final
products are not rolled directly from ingots. First, the ingots are generally reduced
in cross section by rolling into billets, slabs, and blooms. These forms permit correction
of defects before finish rolling, shearing into convenient lengths for final
rolling, reheating for further rolling, and transfer to other mills, if desired, for that
processing.
Plates produced from slabs or directly from ingots, are distinguished from sheet,
strip, and flat bars by size limitations in ASTM A6. Generally, plates are heavier,
per linear foot, than these other products. Sheared plates, or sheared mill plates,
are made with straight horizontal rolls and later trimmed on all edges. Universal
plates, or universal mill plates, are formed between vertical and horizontal rolls and
are trimmed on the ends only.
Some of the plates may be heat-treated, depending on grade of steel and intended
use. For carbon steel, the treatment may be annealing, normalizing, or stress relieving.
Plates of high-strength, low-alloy constructional steels may be quenched
and tempered. See Art. 4.42.
Shapes are rolled from blooms that first are reheated to 2250
F. Rolls gradually
reduce the plastic blooms to the desired shapes and sizes. The shapes then are cut
to length for convenient handling with a hot saw.
ASTM A6 requires that material for delivery ‘‘shall be free from injurious defects
and shall have a workmanlike finish.’’ The specification permits manufacturers
to condition plates and shapes ‘‘for the removal of injurious surface imperfections
or surface depressions by grinding, or chipping and grinding. . . .’’
Internal structure and many properties of plates and shapes are determined
largely by the chemistry of the steel, rolling practice, cooling conditions after rolling,
and heat treatment, where used. The interior of ingots consists of large crystals,
called dendrites, characterized by a branching structure. Growth of individual dendrites
occurs principally along their longitudinal axes perpendicular to the ingot
surfaces. Heating for rolling tends to eliminate dendritic segregation, so that the
BUILDING MATERIALS 4.73
rolled products are more homogeneous than ingots. Furthermore, during rolling,
the dendritic structure is broken up. Also, recrystallization occurs. The final austenitic
grain size is determined by the temperature of the steel during the last passes
through the rolls (Art. 4.43). In addition, dendrites and inclusions are reoriented in
the direction of rolling. As a result, ductility and bendability are much better in the
longitudinal direction than in the transverse, and these properties are poorest in the
thickness direction. The cooling rate after rolling determines the distribution of
ferrite and the grain size of the ferrite.
In addition to the preceding effects, rolling also may induce residual stresses in
plates and shapes (Art. 4.41.1). Still other effects are a consequence of the final
thickness of the hot-rolled material.
Thicker material requires less rolling, the finish rolling temperature is higher,
and the cooling rate is slower than for thin material. As a consequence, thin material
has a superior microstructure. Furthermore, thicker material can have a more unfavorable
state of stress because of stress raisers, such as tiny cracks and inclusions,
and residual stresses. Consequently, thin material develops higher tensile and yield
strengths than thick material of the same steel. ASTM specifications for structural
steels recognize this usually by setting lower yield points for thicker material. A36
steel, however, has the same yield point for all thicknesses. To achieve this, the
chemistry is varied for plates and shapes and for thin and thick plates. Thicker
plates contain more carbon and manganese to raise the yield point. This cannot be
done for high-strength steels because of the adverse effect on notch toughness,
ductility, and weldability.
Thin material has greater ductility than thick material of the same steel. Since
normalizing refines the grain structure, thick material improves relatively more with
normalizing than does thin material. The improvement is even greater with siliconaluminum-
killed steels.
4.48 EFFECTS OF PUNCHING AND SHEARING
Punching holes and shearing during fabrication are cold-working operations that
can cause brittle failure. Bolt holes, for example, may be formed by drilling, punching,
or punching followed by reaming. Drilling is preferable to punching, because
punching drastically cold-works the material at the edge of a hole. This makes the
steel less ductile and raises the transition temperature. The degree of embrittlement
depends on type of steel and plate thickness. Furthermore, there is a possibility that
punching can produce short cracks extending radially from the hole. Consequently,
brittle failure can be initiated at the hole when the member is stressed.
Should the material around the hole become heated, an additional risk of failure
is introduced. Heat, for example, may be supplied by an adjacent welding operation.
If the temperature should rise to the 400 to 850
F range, strain aging will occur in
material susceptible to it. The result will be a loss in ductility.
Reaming a hole after punching can eliminate the short radial cracks and the risks
of embrittlement. For the purpose, the hole diameter should be increased by 1?16 to
1?4 in by reaming, depending on material thickness and hole diameter.
Shearing has about the same effects as punching. If sheared edges are to be left
exposed, 1?16 in or more material, depending on thickness, should be trimmed by
gas cutting. Note also that rough machining, for example, with edge planers making
a deep cut, can produce the same effects as shearing or punching.
4.74 SECTION FOUR
4.49 CORROSION OF IRON AND STEEL
Corrosion of ferrous metals is caused by the tendency of iron (anode) to go into
solution in water as ferrous hydroxide and displace hydrogen, which in turn combines
with dissolved oxygen to form more water. At the same time, the dissolved
ferrous hydroxide is converted by more oxygen to the insoluble ferric hydroxide,
thereby allowing more iron to go into solution. Corrosion, therefore, requires liquid
water (as in damp air) and oxygen (which is normally present dissolved in the
water).
Alloying elements can increase the resistance of steel considerably. For example,
addition of copper to structural steels A36 and A529 can about double their corrosion
resistance. Other steels, such as A242 and A588, are called weathering steels,
because they have three to four times the resistance of A36 steel (Art. 4.40.4).
Protection against corrosion takes a variety of forms:
Deaeration. If oxygen is removed from water, corrosion stops. In hot-water heating
systems, therefore, no fresh water should be added. Boiler feedwater is sometimes
deaerated to retard corrosion.
Coatings
1. Paints. Most paints are based on oxidizing oil and a variety of pigments, of
which oxides of iron, zinc sulfate, graphite, aluminum, and various hydrocarbons
are a few. No one paint is best for all applications. Other paints are coatings of
asphalt and tar. The AISC ‘‘Specification for Structural Steel Buildings’’ (ASD
and LRFD) states that, in general, steelwork to be concealed within a building
need not be painted and that steel to be encased in concrete should not be
painted. Inspections of old buildings have revealed that concealed steelwork
withstands corrosion virtually to the same degree whether or not it is painted.
2. Metallic. Zinc is applied by hot dipping (galvanizing) or powder (sherardizing),
hot tin drip, hot aluminum dip, and electrolytic plates of tin, copper, nickel,
chromium, cadmium, and zinc. A mixture of lead and tin is called terneplate.
Zinc is anodic to iron and protects, even after the coating is broken, by sacrificial
protection. Tin and copper are cathodic and protect as long as the coating is
unbroken but may hasten corrosion by pitting and other localized action once
the coating is pierced.
3. Chemical. Insoluble phosphates, such as iron or zinc phosphate, are formed on
the surface of the metal by treatment with phosphate solutions. These have some
protective action and also form good bases for paints. Black oxide coatings are
formed by treating the surface with various strong salt solutions. These coatings
are good for indoor use but have limited life outdoors. They provide a good
base for rust-inhibiting oils.
Cathodic Protection. As corrosion proceeds, electric currents are produced as the
metal at the anode goes into solution. If a sufficient countercurrent is produced, the
metal at the anode will not dissolve. This is accomplished in various ways, such
as connecting the iron to a more active metal like magnesium (rods suspended in
domestic water heaters) or connecting the part to be protected to buried scrap iron
and providing an external current source such as a battery or rectified current from
a power line (protection of buried pipe lines).
BUILDING MATERIALS 4.75
4.50 STEEL AND STEEL ALLOY BIBLIOGRAPHY
American Iron and Steel Institute, 1000 16th St., N.W., Washington, DC 20036:
‘‘Carbon Steels, Chemical Composition Limits,’’ ‘‘Constructional Alloys, Chemical
Composition Limits’’; ‘‘Steel Products Manuals.’’
American Society for Testing and Materials, Philadelphia, Pa.: ‘‘Standards.’’
American Society for Metals, Cleveland, Ohio: ‘‘Metals Handbook.’’
M. E. Shank, ‘‘Control of Steel Construction to Avoid Brittle Failure,’’Welding
Research Council, New York.
R. L. Brockenbrough and F. S. Merritt, ‘‘Structural Steel Designers Handbook,’’
2nd ed., McGraw-Hill, Inc., New York.
ALUMINUM AND ALUMINUM-BASED ALLOYS
Pure aluminum and aluminum alloys are used in buildings in various forms. Highpurity
aluminum (at least 99% pure) is soft and ductile but weak. It has excellent
corrosion resistance and is used in buildings for such applications as bright foil for
heat insulation, roofing, flashing, gutters and downspouts, exterior and interior architectural
trim, and as pigment in aluminum-based paints. Its high heat conductivity
recommends it for cooking utensils. The electrical conductivity of the electrical
grade is 61% of that of pure copper on an equal-volume basis and 201% on an
equal-weight basis.
Aluminum alloys are generally harder and stronger than the pure metal. Furthermore,
pure aluminum is difficult to cast satisfactorily, whereas many of the
alloys are readily cast.
Pure aluminum is generally more corrosion resistant than its alloys. Furthermore,
its various forms—pure and alloy—have different solution potentials; that is, they
are anodic or cathodic to each other, depending on their relative solution potentials.
A number of alloys are therefore made with centers or ‘‘cores’’ of aluminum alloys,
overlaid with layers of metal, either pure aluminum or alloys, which are anodic to
the core. If galvanic corrosion conditions are encountered, the cladding metal protects
the core sacrifically.
4.51 ALUMINUM-ALLOY DESIGNATIONS
The alloys may be classified: (1) as cast and wrought, and (2) as heat-treatable and
non-heat-treatable. Wrought alloys can be worked mechanically by such processes
as rolling, extruding, drawing, or forging. Alloys are heat-treatable if the dissolved
constituents are less soluble in the solid state at ordinary temperatures than at
elevated temperatures, thereby making age-hardening possible. When heat-treated
to obtain complete solution, the product may be unstable and tend to age spontaneously.
It may also be treated to produce stable tempers of varying degree. Cold
working or strain hardening is also possible, and combinations of tempering and
strain hardening can also be obtained.
Because of these various possible combinations, a system of letter and number
designations has been worked out by the producers of aluminum and aluminum
4.76 SECTION FOUR
TABLE 4.20 Aluminum Association
Designations for Wrought
Aluminum Alloys
Copper 2xxx
Manganese 3xxx
Silicon 4xxx
Magnesium 5xxx
Magnesium and silicon 6xxx
Zinc 7xxx
Other elements 8xxx
Unused series 9xxx
alloys to indicate the compositions and the tempers of the various metals. Wrought
alloys are designated by a four-digit index system. 1xxx is for 99.00% aluminum
minimum. The last two digits indicate the minimum aluminum percentage. The
second digit represents impurity limits. (EC is a special designation for electrical
conductors.) 2xxx to 8xxx represent alloy groups in which the first number indicates
the principal alloying constituent, and the last two digits are identifying numbers
in the group. The second digit indicates modification of the basic alloy. The alloy
groups are listed in Table 4.20.
For cast alloys, a similar designation system is used. The first two digits identify
the alloy or its purity. The last digit, preceded by a decimal point, indicates the
form of the material; for example, casting or ingot. Casting alloys may be sand or
permanent-mold alloys.
Among the wrought alloys, the letter F, O, H, W, and T indicate various basic
temper designations. These letters in turn may be followed by numerals to indicate
various degrees of treatment. Temper designations are summarized in Table 4.21.
The structural alloys general employed in building fall in the 2xxx, 5xxx, and
6xxx categories. Architectural alloys often used include 3xxx, 5xxx, and 6xxx
groups.
4.52 FINISHES FOR ALUMINUM
Almost all finishes used on aluminum may be divided into three major categories
in the system recommended by the The Aluminum Association: mechanical finishes,
chemical finishes, and coatings. The last may be subdivided into anodic
coatings, resinous and other organic coatings, vitreous coatings, electroplated and
other metallic coatings, and laminated coatings.
In The Aluminum Association system, mechanical and chemical finishes are
designated by M and C, respectively, and each of the five classes of coating is also
designated by a letter. The various finishes in each category are designated by twodigit
numbers after a letter. The principal finishes are summarized in Table 4.22.
4.53 STRUCTURAL ALUMINUM
Structural aluminum shapes are produced by extrusion. Angles, I beams, and channels
are available in standard sizes and in lengths up to 85 ft. Plates up to 6 in
thick and 200 in wide also may be obtained.
BUILDING MATERIALS 4.77
TABLE 4.21 Basic Temper Designations for Wrought Aluminum Alloys*

F As fabricated. This designation applies to the products of shaping processes in
which no special control over thermal conditions or strain hardening is
employed. For wrought products, there are no mechanical property limits.

O Annealed. This designation applies to wrought products annealed to obtain the
lowest-strength temper, and to cast products annealed to improve ductility and
dimensional stability.

H† Strain hardened (wrought products only). This designation applies to products
that have their strength increased by strain hardening, with or without
supplementary thermal treatments to produce some reduction in strengths. The H
is always followed by two or more digits.

W Solution heat treated. An unstable temper applicable only to alloys that
spontaneously age at room temperature after solution heat treatment. This
designation is specific only when the period of natural aging is indicated: for
example W 1?2 hr.

T‡ Thermally treated to produce stable tempers other than F, O, or H. This
designation applies to products that are thermally treated, with or without
supplementary strain hardening, to produce stable tempers. The T is always
followed by one or more digits.
*Recommended by the Aluminum Association.
†A digit after H represents a specific combination of basic operations, such as H1—strain hardened
only. H2—strain hardened and partly annealed, and H3—strain hardened and stabilized. A second digit
indicates the degree of strain hardening, which ranges from 0 for annealing to 9 in the order of increasing
tensile strength.
‡A digit after T indicates a type of heat treatment, which may include cooling, cold working, and aging.
There are economic advantages in selecting structural aluminum shapes more
efficient for specific purposes than the customary ones. For example, sections such
as hollow tubes, shapes with stiffening lips on outstanding flanges, and stiffened
panels can be formed by extrusion.
Aluminum alloys generally weigh about 170 lb / ft3, about one-third that of structural
steel. The modulus of elasticity in tension is about 10,000 ksi, compared with
29,000 ksi for structural steel. Poisson’s ratio may be taken as 0.50. The coefficient
of thermal expansion in the 68 to 212
F range is about 0.000013 in / in 
 
F, about
double that of structural steel.
Alloy 6061-T6 is often used for structural shapes and plates. ASTM B308 specifies
a minimum tensile strength of 38 ksi, minimum tensile yield strength of 35
ksi, and minimum elongation in 2 in of 10%, but 8% when the thickness is less
than 1?4 in.
The preceding data indicate that, because of the low modulus of elasticity, aluminum
members have good energy absorption. Where stiffness is important, however,
the effect of the low modulus should be taken into account. Specific data for
an application should be obtained from the producers.
4.54 WELDING AND BRAZING OF ALUMINUM
Weldability and brazing properties of aluminum alloys depend heavily on their
composition and heat treatment. Most of the wrought alloys can be brazed and
welded, but sometimes only by special processes. The strength of some alloys
4.78 SECTION FOUR
Brazing is done by furnace, torch, or dip methods. Successful brazing is done
with special fluxes.
Inert-gas shielded-arc welding is usually used for welding aluminum alloys. The
inert gas, argon or helium, inhibits oxide formation during welding. The electrode
used may be consumable metal or tungsten. The gas metal arc is generally preferred
for structural welding, because of the higher speeds that can be used. The gas
tungsten arc is preferred for thicknesses less than 1?2 in.
Butt-welded joints of annealed aluminum alloys and non-heat-treatable alloys
have nearly the same strength as the parent metal. This is not true for strainhardened
or heat-tempered alloys. In these conditions, the heat of welding weakens
the metal in the vicinity of the weld. The tensile strength of a butt weld of alloy
6061-T6 may be reduced to 24 ksi, about two-thirds that of the parent metal. Tensile
yield strength of such butt welds may be only 15 to 20 ksi, depending on metal
thickness and type of filler wire used in welding.
Fillet welds similarly weaken heat-treated alloys. The shear strength of alloy
6061-T6 decreases from about 27 ksi to 17 ksi or less for a fillet weld.
Welds should be made to meet the requirements of the American Welding Society,
‘‘Structural Welding Code—Aluminum,’’ AWS D1.2.
BUILDING MATERIALS 4.79
4.55 BOLTED AND RIVETED ALUMINUM
CONNECTIONS
Aluminum connections also may be bolted or riveted. Bolted connections are bearing
type. Slip-critical connections, which depend on the frictional resistance of
joined parts created by bolt tension, are not usually employed because of the relatively
low friction and the potential relaxation of the bolt tension over time.
Bolts may be aluminum or steel. Bolts made of aluminum alloy 7075-T73 have
a minimum expected shear strength of 40 ksi. Cost per bolt, however, is higher
than that of 2024-T4 or 6061-T6, with tensile strengths of 37 and 27 ksi, respectively.
Steel bolts may be used if the bolt material is selected to prevent galvanic
corrosion or the steel is insulated from the aluminum. One option is use of stainless
steel. Another alternative is to galvanize, aluminize, or cadmium plate the steel
bolts.
Rivets typically are made of aluminum alloys. They are usually driven cold by
squeeze-type riveters. Alloy 6053-T61, with a shear strength of 20 ksi, is preferred
for joining relatively soft alloys, such as 6063-T5, Alloy 6061-T6, with a shear
strength of 26 ksi, is usually used for joining 6061-T6 and other relatively hard
alloys.
4.56 PREVENTION OF CORROSION OF
ALUMINUM
Although aluminum ranks high in the electromotive series of the metals, it is highly
corrosion resistant because of the tough, transparent, tenacious film of aluminum
oxide that rapidly forms on any exposed surface. It is this corrosion resistance that
recommends aluminum for building applications. For most exposures, including
industrial and seacoast atmospheres, the alloys normally recommended are adequate,
particularly if used in usual thicknesses and if mild pitting is not objectionable.
Pure aluminum is the most corrosion resistant of all and is used alone or as
cladding on strong-alloy cores where maximum resistance is wanted. Of the alloys,
those containing magnesium, manganese, chromium, or magnesium and silicon in
the form of MgSi2 are highly resistant to corrosion. The alloys containing substantial
proportions of copper are more susceptible to corrosion, depending markedly
on the heat treatment.
Certain precautions should be taken in building. Aluminum is subject to attack
by alkalies, and it should therefore be protected from contact with wet concrete,
mortar, and plaster. Clear methacrylate lacquers or strippable plastic coatings are
recommended for interiors and methacrylate lacquer for exterior protection during
construction. Strong alkaline and acid cleaners should be avoided and muriatic acid
should not be used on masonry surfaces adjacent to aluminum. If aluminum must
be contiguous to concrete and mortar outdoors, or where it will be wet, it should
be insulated from direct contact by asphalts, bitumens, felts, or other means. As is
true of other metals, atmospheric-deposited dirt must be removed to maintain good
appearance.
Electrolytic action between aluminum and less active metals should be avoided,
because the aluminum then becomes anodic. If aluminum must be in touch with
4.80 SECTION FOUR
other metals, the faying surfaces should be insulated by painting with asphaltic or
similar paints, or by gasketing. Steel rivets and bolts, for example, should be insulated.
Drainage from copper-alloy surfaces onto aluminum must be avoided. Frequently,
steel surfaces can be galvanized or cadmium-coated where contact is expected
with aluminum. The zinc or cadmium coating is anodic to the aluminum
and helps to protect it.
4.57 ALUMINUM BIBLIOGRAPHY
‘‘Aluminum Standards and Data,’’ ‘‘Engineering Data for Aluminum Structures,’’
‘‘Designation Systems for Aluminum Finishes,’’ and ‘‘Specifications for Aluminum
Structures,’’ The Aluminum Association, Washington, D.C.
E. H. Gaylord, Jr., and C. N. Gaylord, ‘‘Structural Engineering Handbook,’’ 3rd
ed., McGraw-Hill Publishing Company, New York.
COPPER AND COPPER-BASED ALLOYS
Copper and its alloys are widely used in the building industry for a large variety
of purposes, particularly applications requiring corrosion resistance, high electrical
conductivity, strength, ductility, impact resistance, fatigue resistance, or other special
characteristics possessed by copper or its alloys. Some of the special characteristics
of importance to building are ability to be formed into complex shapes,
appearance, and high thermal conductivity, although many of the alloys have low
thermal conductivity and low electrical conductivity as compared with the pure
metal.
4.58 COPPER
The excellent corrosion resistance of copper makes it suitable for such applications
as roofing, flashing, cornices, gutters, downspouts, leaders, fly screens, and similar
applications. For roofing and flashing, soft-annealed copper is employed, because
it is ductile and can easily be bent into various shapes. For gutters, leaders, downspouts,
and similar applications, cold-rolled hard copper is employed, because its
greater hardness and stiffness permit it to stand without large numbers of intermediate
supports.
Copper and copper-based alloys, particularly the brasses, are employed for water
pipe in buildings, because of their corrosion resistance. Electrolytic tough-pitch
copper is usually employed for electrical conductors, but for maximum electrical
conductivity and weldability, oxygen-free high-conductivity copper is used.
When arsenic is added to copper, it appears to form a tenacious adherent film,
which is particularly resistant to pitting corrosion. Phosphorus is a powerful deoxidizer
and is particularly useful for copper to be used for refrigerator tubing and
other applications where flaring, flanging, and spinning are required. Arsenic and
phosphorus both reduce the electrical conductivity of the copper.
BUILDING MATERIALS 4.81
For flashing, copper is frequently coated with lead to avoid the green patina
formed on copper that is sometimes objectionable when it is washed down over
adjacent surfaces, such as ornamental stone. The patina is formed particularly in
industrial atmospheres. In rural atmospheres, where industrial gases are absent, the
copper normally turns to a deep brown color.
Principal types of copper and typical uses are:
Electrolytic tough pitch (99.90% copper) is used for electrical conductors—
bus bars, commutators, etc.; building products—roofing, gutters, etc.; process
equipment—kettles, vats, distillery equipment; forgings. General properties are high
electrical conductivity, high thermal conductivity, and excellent working ability.
Deoxidized (99.90% copper and 0.025% phosphorus) is used, in tube form, for
water and refrigeration service, oil burners, etc.; in sheet and plate form, for welded
construction. General properties include higher forming and bending qualities than
electrolytic copper. They are preferred for coppersmithing and welding (because of
resistance to embrittlement at high temperatures).
4.59 BRASS
A considerable range of brasses is obtainable for a large variety of end uses. The
high ductility and malleability of the copper-zinc alloys, or brasses, make them
suitable for operations like deep drawing, bending, and swaging. They have a wide
range of colors. They are generally less expensive than the high-copper alloys.
Grain size of the metal has a marked effect upon its mechanical properties. For
deep drawing and other heavy working operations, a large grain size is required,
but for highly finished polished surfaces, the grain size must be small.
Like copper, brass is hardened by cold working. Hardnesses are sometimes expressed
as quarter hard, half hard, hard, extra hard, spring, and extra spring, corresponding
to reductions in cross section during cold working ranging from approximately
11 to 69%. Hardness is strongly influenced by alloy composition,
original grain size, and form (strip, rod, tube, wire).
4.59.1 Plain Brass
Brass compositions range from higher copper content to zinc contents as high as
40% or more. Brasses with less than 36% zinc are plain alpha solid solutions; but
Muntz metal, with 40% zinc, contains both alpha and beta phases.
The principal plain brasses of interest in building, and their properties are:
Commercial bronze, 90% (90.0% copper, 10.0% zinc). Typical uses are forgings,
screws, weatherstripping, and stamped hardware. General properties include
excellent cold working and high ductility.
Red brass, 85% (85.0% copper, 15.0% zinc). Typical uses are dials, hardware,
etched parts, automobile radiators, and tube and pipe for plumbing. General properties
are higher strength and ductility than copper, and excellent corrosion resistance.
Cartridge brass, 70% (70.0% copper, 30.0% zinc). Typical uses are deep drawing,
stamping, spinning, etching, rolling—for practically all fabricating processes—
cartridge cases, pins, rivets, eyelets, heating units, lamp bodies and reflectors, elec4.82
SECTION FOUR
trical sockets, drawn shapes, etc. General properties are best combination of ductility
and strength of any brass, and excellent cold-working properties.
Muntz metal (60.0% copper, 40.0% zinc). Typical uses are sheet form, perforated
metal, architectural work, condenser tubes, valve stems, and brazing rods.
General properties are high strength combined with low ductility.
4.59.2 Leaded Brass
Lead is added to brass to improve its machinability, particularly in such applications
as automatic screw machines where a freely chipping metal is required. Leaded
brasses cannot easily be cold-worked by such operations as flaring, upsetting, or
cold heading. Several leaded brasses of importance in the building field are the
following:
High-leaded brass (64.0% copper, 34.0% zinc, 2.0% lead). Typical uses are
engraving plates, machined parts, instruments (professional and scientific), nameplates,
keys, lock parts, and tumblers. General properties are free machining and
good blanking.
Forging brass (60.0% copper, 38.0% zinc, 2.0% lead). Typical uses are hot
forging, hardware, and plumbing goods. General properties are extreme plasticity
when hot and a combination of good corrosion resistance with excellent mechanical
properties.
Architectural bronze (56.5% copper, 41.25% zinc, 2.25% lead). Typical uses
are handrails, decorative moldings, grilles, revolving door parts, miscellaneous architectural
trim, industrial extruded shapes (hinges, lock bodies, automotive parts).
General properties are excellent forging and free-machining properties.
4.59.3 Tin Brass
Tin is added to a variety of basic brasses to obtain hardness, strength, and other
properties that would otherwise not be available. Two important alloys are:
Admiralty (71.0% copper, 28.0% zinc, 1.0% tin, 0.05% arsenic). Typical uses
are condenser and heat-exchanger plates and tubes, steam-power-plant equipment,
chemical and process equipment, and marine uses. General properties are excellent
corrosion resistance, combined with strength and ductility.
Manganese bronze (58.5% copper, 39.0% zinc, 1.4% iron, 1.0% tin, 0.1% manganese).
Typical uses are forgings, condenser plates, valve stems, and coal screens.
General properties are high strength combined with excellent wear resistance.
4.60 NICKEL SILVERS
These are alloys of copper, nickel, and zinc. Depending on the composition, they
range in color from a definite to slight pink cast through yellow, green, whitish
green, whitish blue, to blue. A wide range of nickel silvers is made, of which only
one typical composition will be described. Those that fall in the combined alphabeta
phase of metals are readily hot-worked and therefore are fabricated without
difficulty into such intricate shapes as plumbing fixtures, stair rails, architectural
shapes, and escalator parts. Lead may be added to improve machining.
BUILDING MATERIALS 4.83
Nickel, silver, 18% (A) (65.0% copper, 17.0% zinc, 18.0% nickel). Typical uses
are hardware, architectural panels, lighting, electrical and plumbing fixtures. General
properties are high resistance to corrosion and tarnish, malleable, and ductile.
Color: silver-blue-white.
4.61 CUPRONICKEL
Copper and nickel are alloyed in a variety of compositions of which the highcopper
alloys are called the cupronickels. Typical commercial types of cupronickel
contain 10 or 30% nickel (Table 4.15):
Cupronickel, 10% (88.5% copper, 10% nickel, 1.5% iron). Recommended for
applications requiring corrosion resistance, especially to salt water, as in tubing for
condensers, heat exchangers, and formed sheets.
Cupronickel, 30% (70.0% copper, 30.0% nickel). Typical uses are condenser
tubes and plates, tanks, vats, vessels, process equipment, automotive parts, meters,
refrigerator pump valves. General properties are high strength and ductility and
resistance to corrosion and erosion. Color: white-silver.
4.62 BRONZE
Originally, the bronzes were all alloys of copper and tin. Today, the term bronze is
generally applied to engineering metals having high mechanical properties and the
term brass to other metals. The commercial wrought bronzes do not usually contain
more than 10% tin because the metal becomes extremely hard and brittle. When
phosphorus is added as a deoxidizer, to obtain sound, dense castings, the alloys are
known as phosphor bronzes. The two most commonly used tin bronzes contain 5
or 8% tin. Both have excellent cold-working properties.
4.62.1 Silicon Bronze
These are high-copper alloys containing percentages of silicon ranging from about
1% to slightly more than 3%. In addition, they generally contain one or more of
the four elements, tin, manganese, zinc, and iron. A typical one is high-silicon
bronze, type A.
High-silicon bronze, A (96.0% copper, 3.0% silicon, 1.0% manganese). Typical
users are tanks—pressure vessels, vats; weatherstrips, forgings. General properties
are corrosion resistance of copper and mechanical properties of mild steel.
4.62.2 Aluminum Bronze
Like aluminum, these bronzes form an aluminum oxide skin on the surface, which
materially improves resistance to corrosion, particularly under acid conditions.
Since the color of the 5% aluminum bronze is similar to that of 18-carat gold, it
is used for costume jewelry and other decorative purposes. Aluminum-silicon
bronzes are used in applications requiring high tensile properties in combination
4.84 SECTION FOUR
with good corrosion resistance in such parts as valves, stems, air pumps, condenser
bolts, and similar applications. Their wear-resisting properties are good; consequently,
they are used in slide liners and bushings.
4.63 COPPER BIBLIOGRAPHY
‘‘Alloy Data,’’ Copper Development Association, New York, N.Y.
G. S. Brady and H. R. Clauser, ‘‘Materials Handbook,’’ 13th ed., and J. H.
Callender, ‘‘Time-Saver Standards for Architectural Design Data,’’ 6th ed.,
McGraw-Hill Publishing Company, New York.
LEAD AND LEAD-BASED ALLOYS
Lead is used primarily for its corrosion resistance. Lead roofs 2000 years old are
still intact.
4.64 APPLICATIONS OF LEAD
Exposure tests indicate corrosion penetrations of sheet lead ranging from less than
0.0001 in to less than 0.0003 in in 10 years in atmospheres ranging from mild rural
to severe industrial and seacoast locations. Sheet lead is therefore used for roofing,
flashing, spandrels, gutters, and downspouts.
Because the green patina found on copper may wash away sufficiently to stain
the surrounding structure, lead-coated copper is frequently employed. ASTM B101-
78 covers two classes, defined by the weight of coating.
Lead pipe should not be used for the transport of drinking water. Distilled and
very soft waters slowly dissolve lead and may cause cumulative lead poisoning.
Hard waters apparently deposit a protective coating on the wall of the pipe and
little or no lead is subsequently dissolved in the water.
Principal alloying elements used with building leads are antimony (for hardness
and strength) and tin. But copper, arsenic, bismuth, nickel, zinc, silver, iron, and
manganese are also added in varying proportions.
Soft solders consist of varying percentages of lead and tin. For greater hardness,
antimony is added, and for higher-temperature solders, silver is added in small
amounts. ASTM Standard B32 specifies properties of soft solders.
Low-melting alloys and many bearing metals are alloys of lead, bismuth, tin,
cadmium, and other metals including silver, zinc, indium, and antimony. The fusible
links used in sprinkler heads and fire-door closures, made of such alloys, have a
low melting point, usually lower than the boiling point of water. Yield (softening)
temperatures range from 73 to 160
F and melting points from about 80 to 480
F,
depending on the composition.
BUILDING MATERIALS 4.85
TABLE 4.23 Composition of Nickel Alloys
Content
Nickel
alloy,
lowcarbon
NO2201
ASTM
B160
Nickel
alloy
NO2200
ASTM
B160
Monel
NO4400
ASTM
B127
Inconel
NO6600
ASTM
B168
70–30
cupronickel
C71500
ASTM
B171
90–10
cupronickel
C70600
ASTM
B171
Carbon 0.02 0.15 0.2 0.15 max
Manganese 0.35 0.35 2.00 max 1.0 max 1.0 max 1.0 max
Sulfur 0.01 0.01 0.024 max 0.015 max
Silicon 0.35 0.35 0.5 0.5 max
Chromium 14–17
Nickel 99 min 99 min 63–70 72 min 29–33 9–11
Copper 0.25 0.25 Remainder 0.5 max 65 min 86.5 min
Iron 0.40 max 0.40 max 2.5 max 6–10 0.40–1.0 1.0–1.8
Lead 0.05 max 0.05 max
Zinc 1.0 1.0
4.65 LEAD BIBLIOGRAPHY
American Society for Metals, Cleveland, Ohio: ‘‘Metals Handbook.’’
NICKEL AND NICKEL-BASED ALLOYS
Nickel is used mostly as an alloying element with other metals, but it finds use in
its own right, largely as electroplate or as cladding metal. Among the principal
high-nickel alloys are Monel and Inconel. The nominal compositions of these metals
are given in Table 4.23
4.66 PROPERTIES OF NICKEL AND ITS ALLOYS
Nickel is resistant to alkaline corrosion under nonoxidizing conditions but is corroded
by oxidizing acids and oxidizing salts. It is resistant to fatty acids, other
mildly acid conditions, such as food processing and beverages, and resists oxidation
at temperatures as high as 1600
F.
Monel is widely used in kitchen equipment. It is better than nickel in reducing
conditions like warm unaerated acids, and better than copper under oxidizing conditions,
such as aerated acids, alkalies, and salt solutions. It is widely used for
handling chlorides of many kinds.
Inconel is almost completely resistant to corrosion by food products, pharmaceuticals,
biologicals, and dilute organic acids. It is superior to nickel and Monel
4.86 SECTION FOUR
in resisting oxidizing acid salts like chromates and nitrates but is not resistant to
ferric, cupric, or mercuric chlorides. It resists scaling and oxidation in air and
furnace atmospheres at temperatures up to 2000
F.
4.67 NICKEL BIBLIOGRAPHY
International Nickel Co., New York: ‘‘Nickel and Nickel Alloys.’’
Albert Hoerson, Jr.: ‘‘Nonferrous-clad Plate Steels,’’ Chap. 13 in A. G. H. Dietz,
‘‘Composite Engineering Laminates,’’ M.I.T. Press, Cambridge, Mass.
PLASTICS
The synonymous terms plastics and synthetic resins denote synthetic organic high
polymers, all of which are plastic at some stage in their manufacture. Plastics fall
into two large categories—thermoplastic and thermosetting materials.
4.68 GENERAL PROPERTIES OF PLASTICS
Thermoplastics may be softened by heating and hardened by cooling any number
of times. Thermosetting materials are either originally soft or liquid, or they soften
FIGURE 4.5 Stress-strain diagram shows the
influence of temperature, plasticizer, and rate of
loading on behavior of plastics.
once upon heating; but upon further
heating, they harden permanently. Some
thermosetting materials harden by an interlinking
mechanism in which water or
other by-product is given off, by a process
called condensation; but others,
like the unsaturated polyesters, harden
by a direct interlinking of the basic molecules
without release of a by-product.
Most plastics are modified with plasticizers,
fillers, or other ingredients.
Consequently, each base material forms
the nucleus for a large number of products
having a wide variety of properties.
This section can only indicate generally
the range of properties to be expected.
Because plastics are quite different in
their composition and structure from
other materials, such as metals, their behavior
under stress and under other conditions
is likely to be different from
other materials. Just as steel and lead are
markedly different and are used for different
applications, so the various plastics
materials—some hard and brittle, others soft and extensible—must be designed
BUILDING MATERIALS 4.87
on different bases and used in different ways. Some plastics show no yield point,
because they fail before a yield point can be reached. Others have a moderately
high elastic range, followed by a highly plastic range. Still others are highly extensible
and are employed at stresses far beyond the yield point.
More than many other materials, plastics are sensitive to temperature and to the
rate and time of application of load. How these parameters influence the properties
is indicated in a general way in Fig. 4.5, which shows that for many plastics in
increase in temperature, increase in plasticizer content, and decrease in rate of load
application mean an increase in strain to fracture, accompanied by a decrease in
maximum stress. This viscoelastic behavior, combining elastic and viscous or plastic
reaction to stress, is unlike the behavior of materials which are traditionally
considered to behave only elastically.
4.69 FILLERS AND PLASTICIZERS
Fillers are commonly added, particularly to the thermosetting plastics, to alter their
basic characteristics. For example, wood flour converts a hard, brittle resin, difficult
to handle, into a cheaper, more easily molded material for general purposes. Asbestos
fibers provide better heat resistance; mica gives better electrical properties;
and a variety of fibrous materials, such as chopped fibers, chopped fabric, and
chopped tire cords, increase the strength and impact properties.
Plasticizers are added to many thermoplastics, primarily to transform hard and
rigid materials into a variety of forms having varying degrees of softness, flexibility,
and strength. In addition, dyes or pigments, stabilizers, and other products may be
added.
4.70 MOLDING AND FABRICATING METHODS
FOR PLASTICS
Both thermosetting and thermoplastic molding materials are formed into final shape
by a variety of molding and fabricating methods.
Thermosetting materials are commonly formed by placing molding powder or
molded preform in heated dies and compressing under heat and pressure into the
final infusible shape. Or they are formed by forcing heat-softened material into a
heated die for final forming into the hard infusible shape.
Thermoplastics are commonly formed by injection molding, that is, by forcing
soft, hot plastic into a cold die, where it hardens by cooling. Continuous profiles
of thermoplastic materials are made by extrusion. Thermoplastic sheets, especially
transparent acrylics, are frequently formed into final shape by heating and then
blowing to final form under compressed air or by drawing a partial vacuum against
the softened sheet.
Foamed plastics are employed for thermal insulation in refrigerators, buildings,
and many other applications. In buildings, plastics are either prefoamed into slabs,
blocks, or other appropriate shapes, or they are foamed in place.
Prefoamed materials, such as polystyrene, are made by adding a blowing agent
and extruding the mixture under pressure and at elevated temperatures. As the
material emerges from the extruder, it expands into a large ‘‘log’’ that can be cut
4.88 SECTION FOUR
into desired shapes. The cells are ‘‘closed’’; that is, they are not interconnecting
and are quite impermeable.
Foamed-in-place plastics are made with pellets or liquids. The pellets, made, for
example, of polystyrene, are poured into the space to be occupied, such as a mold,
and heated, whereupon they expand and occupy the space. The resulting mass may
be permeable between pellets. Liquid-based foams, exemplified by polyurethane,
are made by mixing liquid ingredients and immediately casting the mixture into
the space to be occupied. A quick reaction results in a foam that rises and hardens
by a thermosetting reaction. When blown with fluorocarbon gases, such forms have
exceptionally low thermal conductivities.
All the plastics can be machined, if proper allowance is made for the properties
of the materials.
Plastics are often combined with sheet or mat stocks, such as paper, cotton
muslin, glass fabric, glass filament mats, nylon fabric, and other fabrics, to provide
laminated materials in which the properties of the combined plastic and sheet stock
are quite different from the properties of either constituent by itself. Two principal
varieties of laminates are commonly made: (1) High-pressure laminates employing
condensation-type thermosetting materials, which are formed at elevated temperatures
and pressures. (2) Reinforced plastics employing unsaturated polyesters and
epoxides, from which no by-products are given off, and consequently, either low
pressures or none at all may be required to form combinations of these materials
with a variety of reinforcing agents, like glass fabric or mat.
4.71 THERMOSETTING PLASTICS
General properties of thermosetting plastics are described in Art. 4.68. Following
are properties of several thermosetting plastics used in buildings:
Phenol Formaldehyde. These materials provide the greatest variety of thermosetting
molded plastic articles. They are used for chemical, decorative, electrical,
mechanical, and thermal applications of all kinds. Hard and rigid, they change
slightly, if at all, on aging indoors but, on outdoor exposure, lose their bright surface
gloss. However, the outdoor-exposure characteristics of the more durable formulations
are otherwise generally good. Phenol formaldehydes have good electrical
properties, do not burn readily, and do not support combustion. They are strong,
light in weight, and generally pleasant to the eye and touch, although light colors
by and large are not obtainable because of the fairly dark-brown basic color of the
resin. They have low water absorption and good resistance to attack by most commonly
found chemicals.
Epoxy and Polyester Casting Resins. These are used for a large variety of purposes.
For example, electronic parts with delicate components are sometimes cast
completely in these materials to give them complete and continuous support, and
resistance to thermal and mechanical shock. Some varieties must be cured at elevated
temperatures; others can be formulated to be cured at room temperatures.
One of the outstanding attributes of the epoxies is their excellent adhesion to a
variety of materials, including such metals as copper, brass, steel, and aluminum.
BUILDING MATERIALS 4.89
Polyester Molding Materials. When compounded with fibers, particularly glass
fibers, or with various mineral fillers, including clay, the polyesters can be formulated
into putties or premixes that are easily compression- or transfer-molded into
parts having high impact resistance. Polyesters are often used in geotextiles (Art.
6.11.2).
Melamine Formaldehyde. These materials are unaffected by common organic solvents,
greases, and oils, as well as most weak acids and alkalies. Their water absorption
is low. They are insensitive to heat and are highly flame-resistant, depending
on the filler. Electrical properties are particularly good, especially resistance to
arcing. Unfilled materials are highly translucent and have unlimited color possibilities.
Principal fillers are alpha cellulose for general-purpose compounding; minerals
to improve electrical properties, particularly at elevated temperatures; chopped fabric
to afford high shock resistance and flexural strength; and cellulose, mainly for
electrical purposes.
Cellulose Acetate Butyrate. The butyrate copolymer is inherently softer and more
flexible than cellulose acetate and consequently requires less plasticizer to achieve
a given degree of softness and flexibility. It is made in the form of clear transparent
sheet and film, or in the form of molding powders, which can be molded by standard
injection-molding procedures into a wide variety of applications. Like the other
cellulosics, this material is inherently tough and has good impact resistance. It has
infinite colorability, like the other cellulosics. Cellulose acetate butyrate tubing is
used for such applications as irrigation and gas lines.
Cellulose Nitrate. One of the toughest of the plastics, cellulose nitrate is widely
used for tool handles and similar applications requiring high impact strength. The
high flammability requires great caution, particularly in the form of film. Most
commercial photographic film is cellulose nitrate as opposed to safety film.
Polyurethane. This plastic is used in several ways in building. As thermal insulation,
it is used in the form of foam, either prefoamed or foamed in place. The
latter is particularly useful in irregular spaces. When blown with fluorocarbons, the
foam has an exceptionally low K-factor and is, therefore, widely used in thin-walled
refrigerators. Other uses include field-applied or baked-on clear or colored coatings
and finishes for floors, walls, furniture, and casework generally. The rubbery form
is employed for sprayed or troweled-on roofing, and for gaskets and calking compounds.
Urea Formaldehyde. Like the melamines, these offer unlimited translucent to
opaque color possibilities, light-fastness, good mechanical and electrical properties,
and resistance to organic solvents as well as mild acids and alkalies. Although there
is no swelling or change in appearance, the water absorption of urea formaldehyde
is relatively high, and it is therefore not recommended for applications involving
long exposure to water. Occasional exposure to water is without deleterious effect.
Strength properties are good, although special shock-resistant grades are not made.
Silicones. Unlike other plastics, silicones are based on silicon rather than carbon.
As a consequence, their inertness and durability under a wide variety of conditions
are outstanding. As compared with the phenolics, their mechanical properties are
poor, and consequently glass fibers are added. Molding is more difficult than with
4.90 SECTION FOUR
other thermosetting materials. Unlike most other resins, they may be used in continuous
operations at 400
F; they have very low water absorption; their dielectric
properties are excellent over an extremely wide variety of chemical attack; and
under outdoor conditions their durability is particularly outstanding. In liquid solutions,
silicones are used to impart moisture resistance to masonry walls and to
fabrics. They also form the basis for a variety of paints and other coatings capable
of maintaining flexibility and inertness to attack at high temperatures in the presence
of ultraviolet sunlight and ozone. Silicone rubbers maintain their flexibility at much
lower temperatures than other rubbers.
4.72 THERMOPLASTIC RESINS
Materials under this heading in general can be softened by heating and hardened
by cooling.
Acrylics. In the form of large transparent sheets, these are used in aircraft enclosures
and building construction. Although not so hard as glass, they have perfect
clarity and transparency. Among the most resistant of the transparent plastics to
sunlight and outdoor weathering, they possess an optimum combination of flexibility
and sufficient rigidity with resistance to shattering. A wide variety of transparent,
translucent, and opaque colors can be produced. The sheets are readily
formed to complex shapes. They are used for such applications as transparent windows,
outdoor and indoor signs, parts of lighting equipment, decorative and functional
automotive parts, reflectors, household-appliance parts, and similar applications.
They can be used as large sheets, molded from molding powders, or cast
from the liquid monomer.
Acrylonitrile-Butadiene-Styrene (ABS). This three-way copolymer provides a
family of tough, hard, chemically resistant resins with many grades and varieties,
depending on variations in constituents. The greatest use is for pipes and fittings,
especially drain-waste-vent (DWV). Other uses include buried sewer and water
lines, mine pipe, well casings, conduit, and appliance housings.
Polyethylene. In its unmodified form, this is a flexible, waxy, translucent plastic.
It maintain flexibility at very low temperatures, in contrast with many other thermoplastic
materials.
Polyethylene may be provided as low-density, or standard, or as high-density or
linear material. High-density polyethylene has greater strength and stiffness, withstands
somewhat higher temperatures, and has a more sharply defined softening
temperature range. The heat-distortion point of the low-density polyethylenes is
low; these plastics are not recommended for uses above 150
F. Unlike most plastics,
polyethylene is partly crystalline. It is highly inert to solvents and corrosive chemicals
of all kinds at ordinary temperatures. Usually low moisture permeability and
absorption are combined with excellent electrical properties. Its density is lower
than that of any other commercially available nonporous plastic. It is widely used
as a primary insulating material on wire and cable and has been used as a replacement
for the lead jacket in communication cables and other cables. It is widely
used also in geogrids, geonets, and geomembranes (Art. 6.11) and as corrosionproof
lining for tanks and other chemical equipment.
BUILDING MATERIALS 4.91
Polypropylene. This polyolefin is similar in many ways to its counterpart, polyethylene,
but is generally harder, stronger, and more temperature-resistant. It finds
a great many uses, among them piping, geotextiles, and geogrids (Art. 6.11), and
complete water cisterns for water closets in plumbing systems.
Polycarbonate. Excellent transparency, high impact resistance, and good resistance
to weathering combine to recommend this plastic for safety glazing and for
general illumination and shatter-resistant fixtures. It is available in large, clear,
tinted, and opaque sheets that can be formed into shells, domes, globes, and other
forms. It can be processed by standard molding methods.
Polytetrafluorethylene. This is a highly crystalline liner-type polymer, unique
among organic compounds in its chemical inertness and resistance to change at
high and low temperatures. Its electrical properties are excellent. Its outstanding
property is extreme resistance to attack by corrosive agents and solvents of all kinds.
Waxy and self-lubricating, polytetrafluoroethylene is used in buildings where resistance
to extreme conditions or low friction is desired. In steam lines, for example,
supporting pads of this plastic permit the lines to slide easily over the pads. The
temperatures involved have little or no effect. Other low-friction applications include,
for example, bearings for girders and trusses. Mechanical properties are only
moderately high, and reinforcement may be necessary to prevent creep and squeezeout
under heavy loads. These fluorocarbons are difficult to wet; consequently, they
are often used as parting agents, or where sticky materials must be handled.
Polyvinylfluoride. This has much of the superior inertness to chemical and weathering
attack typical of the fluorocarbons. Among other uses, it is used as thin-film
overlays for building boards to be exposed outdoors.
Polyvinyl Formal and Polyvinyl Butyral. Polyvinyl formal resins are principally
used as a base for tough, water-resistant insulating enamel for electric wire. Polyvinyl
butyral is the tough interlayer in safety glass. In its cross-linked and plasticized
form, polyvinyl butyral is extensively used in coating fabrics for raincoats,
upholstery, and other heavy-duty moisture-resistant applications.
Vinyl Chloride Polymers and Copolymers. Polyvinyl chloride is naturally hard
and rigid but can be plasticized to any required degree of flexibility as in raincoats
and shower curtains. Copolymers, including vinyl chloride plus vinyl acetate, are
naturally flexible without plasticizers. Nonrigid vinyl plastics are widely used as
insulation and jacketing for electric wire and cable because of their electrical properties
and their resistance to oil and water. Thin films are used in geomembranes
(Art. 6.11). Vinyl chlorides also are used for floor coverings in the form of tile and
sheet because of their abrasion resistance and relatively low water absorption. The
rigid materials are used for tubing, pipe, and many other applications where their
resistance to corrosion and action of many chemicals, especially acids and alkalies,
recommends them. They are attacked by a variety of organic solvents, however.
Like all thermoplastics, they soften at elevated temperatures.
Vinylidene Chloride. This material is highly resistant to most inorganic chemicals
and to organic solvents generally. It is impervious to water on prolonged immersion,
and its films are highly resistant to moisture-vapor transmission. It can be sterilized,
if not under load, in boiling water. It is used as pipe for transporting chemicals and
geomembranes (Art. 6.11).
4.92 SECTION FOUR
Nylon. Molded nylon is used in increasing quantities for impact and high resistance
to abrasion. It is employed in small gears, cams, and other machine parts,
because even when unlubricated they are highly resistant to wear. Its chemical
resistance, except to phenols and mineral acids, is excellent. Extruded nylon is
coated onto electric wire, cable, and rope for abrasion resistance. Applications like
hammerheads indicate its impact resistance.
Polystyrene. This is one of the lightest of the presently available commercial
plastics. It is relatively inexpensive, easily molded, has good dimensional stability,
and good stability at low temperatures; it is brilliantly clear when transparent and
has an infinite range of colors. Water absorption is negligible even after long immersion.
Electrical characteristics are excellent. It is resistant to most corrosive
chemicals, such as acids, and to a variety of organic solvents, although it is attacked
by others. Polystyrenes as a class are considerably more brittle and less extensible
than many other thermoplastic materials, but these properties are markedly improved
in copolymers. Under some conditions, they have a tendency to develop
fine cracks, known as craze marks, on exposure, particularly outdoors. This is true
of many other thermoplastics, especially when highly stressed. It is widely used in
synthetic rubbers.
4.73 ELASTOMERS, OR SYNTHETIC RUBBERS
Rubber for construction purposes is both natural and synthetic. Natural rubber, often
called crude rubber in its unvulcanized form, is composed of large complex molecules
of isoprene. Synthetic rubbers, also known as elastomers, are generally
rubber-like only in their high elasticity. The principal synthetic rubbers are the
following:
GR-S is the one most nearly like crude rubber and is the product of styrene and
butadiene copolymerization. It is the most widely used of the synthetic rubbers. It
is not oil-resistant but is widely used for tires and similar applications.
Nitril is a copolymer of acrylonitrile and butadiene. Its excellent resistance to
oils and solvents makes it useful for fuel and solvent hoses, hydraulic-equipment
parts, and similar applications.
Butyl is made by the copolymerization of isobutylene with a small proportion
of isoprene or butadiene. It has the lowest gas permeability of all the rubbers and
consequently is widely used for making inner tubes for tires and other applications
in which gases must be held with a minimum of diffusion. It is used for gaskets
in buildings.
Neoprene is made by the polymerization of chloroprene. It has very good mechanical
properties and is particularly resistant to sunlight, heat, aging, and oil; it
is therefore used for making machine belts, gaskets, oil hose, insulation on wire
cable, and other applications to be used for outdoor exposure, such as roofing, and
gaskets for building and glazing.
Sulfide rubbers—the polysulfides of high molecular weight—have rubbery
properties, and articles made from them, such as hose and tank linings and glazing
compounds, exhibit good resistance to solvents, oils, ozone, low temperature, and
outdoor exposure.
Silicone rubber, which also is discussed in Art. 4.71, when made in rubbery
consistency forms a material exhibiting exceptional inertness and temperature reBUILDING
MATERIALS 4.93
sistance. It is therefore used in making gaskets, electrical insulation, and similar
products that maintain their properties at both high and low temperatures.
Additional elastomers include polyethylene, cyclized rubber, plasticized polyvinyl
chloride, and polybutene. A great variety of materials enters into various
rubber compounds and therefore provide a wide range of properties. In addition,
many elastomeric products are laminated structures of rubber-like compounds combined
with materials like fabric and metals (Art. 4.76).
COMBINATIONS OF PLASTICS AND OTHER
MATERIALS
Plastics often are used as part of a composite construction with other materials. The
composites may be in the form of laminates, matrix systems, sandwich structures,
or combinations of these.
4.74 HIGH-PRESSURE LAMINATES
Laminated thermosetting products consist of fibrous sheet materials combined with
a thermosetting resin, usually phenol formaldehyde or melamine formaldehyde. The
commonly used sheet materials are paper, cotton fabric, asbestos paper or fabric,
nylon fabric, and glass fabric. The usual form is flat sheet, but a variety of rolled
tubes and rods is made.
Decorative Laminates. These high-pressure laminates consist of a base of phenolic
resin-impregnated kraft paper over which a decorative overlay, such as printed
paper, is applied. Over all this is laid a thin sheet of melamine resin. When the
entire assemblage is pressed in a hot-plate press at elevated temperatures and pressures,
the various layers are fused together and the melamine provides a completely
transparent finish, resistant to alcohol, water, and common solvents. This material
is widely used for tabletops, counter fronts, wainscots, and similar building applications.
It is customarily bonded to a core of plywood to develop the necessary
thickness and strength. In this case, a backup sheet consisting of phenolic resin and
paper alone, without the decorative surface, is employed to provide balance to the
entire sandwich.
4.75 REINFORCED PLASTICS
These are commonly made with phenolic, polyester, and epoxide resins combined
with various types of reinforcing agents, of which glass fibers in the form of mats
or fabrics are the most common. Because little or no pressure is required to form
large complex parts, rather simple molds can be employed for the manufacture of
such things as boat hulls and similar large parts. In buildings, reinforced plastics
have been rather widely used in the form of corrugated sheet for skylights and side
lighting of buildings, and as molded shells, concrete forms, sandwiches, and similar
applications.
4.94 SECTION FOUR
These materials may be formulated to cure at ordinary temperatures, or they
may require moderate temperatures to cure the resins. Customarily, parts are made
by laying up successive layers of the glass fabric or the glass mat and applying the
liquid resin to them. The entire combination is allowed to harden at ordinary temperatures,
or it is placed in a heated chamber for final hardening. It may be placed
inside a rubber bag and a vacuum drawn to apply moderate pressure, or it may be
placed between a pair of matching molds and cured under moderate pressure in the
molds.
The high impact resistance of these materials combined with good strength properties
and good durability recommends them for building applications. When the
quantity of reinforcing agent is kept relatively low, a high degree of translucence
may be achieved, although it is less than that of the acrylics and the other transparent
thermoplastic materials.
Fabrics for Air-Supported Roofs. Principal requirements for fabrics and coatings
for air-supported structures are high strip tensile strength in both warp and fill
directions, high tear resistance, good coating adhesion, maximum weathering resistance,
maximum joint strength, good flexing resistance, and good flame resistance.
Translucency may or may not be important, depending on the application. The most
commonly used fabrics are nylon, polyester, and glass. Neoprene and Hypalon have
commonly been employed for military and other applications where opacity is desired.
For translucent application, vinyl chloride and fluorocarbon polymers are
more common. Careful analysis of loads and stresses, especially dynamic wind
loads, and means of joining sections and attaching to anchorage is required.
4.76 LAMINATED RUBBER
Rubber is often combined with various textiles, fabrics, filaments, and metal wire
to obtain strength, stability, abrasion resistance, and flexibility. Among the laminated
materials are the following:
V Belts. These consist of a combination of fabric and rubber, frequently combined
with reinforcing grommets of cotton, rayon, steel, or other high-strength material
extending around the central portion.
Flat Rubber Belting. This laminate is a combination of several plies of cotton
fabric or cord, all bonded together by a soft-rubber compound.
Conveyor Belts. These, in effect, are moving highways used for transporting such
material as crushed rock, dirt, sand, gravel, slag, and similar materials. When the
belt operates at a steep angle, it is equipped with buckets or similar devices and
becomes an elevator belt. A typical conveyor belt consists of cotton duct plies
alternated with thin rubber plies; the assembly is wrapped in a rubber cover, and
all elements are united into a single structure by vulcanization. A conveyor belt to
withstand extreme conditions is made with some textile or metal cords instead of
the woven fabric. Some conveyor belts are especially arranged to assume a trough
form and made to stretch less than similar all-fabric belts.
BUILDING MATERIALS 4.95
Rubber-Lined Pipes, Tanks, and Similar Equipment. The lining materials include
all the natural and synthetic rubbers in various degrees of hardness, depending
on the application. Frequently, latex rubber is deposited directly from the latex
solution onto the metal surface to be covered. The deposited layer is subsequently
vulcanized. Rubber linings can be bonded to ordinary steel, stainless steel, brass,
aluminum, concrete, and wood. Adhesion to aluminum is inferior to adhesion to
steel. Covering for brass must be compounded according to the composition of the
metal.
Rubber Hose. Nearly all rubber hose is laminated and composed of layers of
rubber combined with reinforcing materials like cotton duck, textile cords, and
metal wire. Typical hose consists of an inner rubber lining, a number of intermediate
layers consisting of braided cord or cotton duck impregnated with rubber, and
outside that, several more layers of fabric, spirally wound cord, spirally wound
metal, or in some cases, spirally wound flat steel ribbon. Outside of all this is
another layer of rubber to provide resistance to abrasion. Hose for transporting oil,
water, wet concrete under pressure, and for dredging purposes is made of heavyduty
laminated rubber.
Vibration Insulators. These usually consist of a layer of soft rubber bonded between
two layers of metal. Another type of insulated consists of a rubber tube or
cylinder vulcanized to two concentric metal tubes, the rubber being deflected in
shear. A variant of this consists of a cylinder of soft rubber vulcanized to a tubular
or solid steel core and a steel outer shell, the entire combination being placed in
torsion to act as a spring. Heavy-duty mounts of this type are employed on trucks,
buses, and other applications calling for rugged construction.
4.77 PLASTICS BIBLIOGRAPHY
American Concrete Institute, ‘‘Polymer Modified Concrete,’’ SP-99; ‘‘Polymers in
Concrete,’’ ACI 548; and Guide for the Use of Polymers in Concrete,’’ ACI 548.1.
American Society of Civil Engineers, ‘‘Structural Plastics Design Manual,’’ and
‘‘Structural Plastics Selection Manual.’’
‘‘Modern Plastics Encyclopedia,’’ Plastics Catalog Corp., New York.
A. G. H. Dietz, ‘‘Plastics for Architects and Engineers,’’ M.I.T. Press, Cambridge,
Mass.
C. A. Harper, ‘‘Handbook of Plastics and Elastomers,’’ McGraw-Hill Publishing
Company, New York.
R. M. Koerner, ‘‘Designing with Geosynthetics,’’ 2nd ed., Prentice-Hall, Englewoods
Cliffs, N.J.
I. Skeist, ‘‘Plastics in Building,’’ Van Nostrand Reinhold, New York.
PORCELAIN-ENAMELED PRODUCTS
Porcelain enamel, also known as vitreous enamel, is an aluminum-silicate glass,
which is fused to metal under high heat. Porcelain-enameled metal is used for
4.96 SECTION FOUR
indoor and outdoor applications because of its hardness, durability, washability, and
color possibilities. For building purposes, porcelain enamel is applied to sheet metal
and cast iron, the former for a variety of purposes including trim, plumbing, and
kitchen fixtures, and the latter almost entirely for plumbing fixtures. Most sheet
metal used for porcelain enameling is steel—low in carbon, manganese, and other
elements. Aluminum is also used for vitreous enamel.
4.78 PORCELAIN ENAMEL ON METAL
Low-temperature softening glasses must be employed, especially with sheet metal,
to avoid the warping and distortion that would occur at high temperatures. To obtain
lower softening temperatures than would be attainable with high-silica glasses, boron
is commonly added. Fluorine may replace some of the oxygen, and lead may
also be added to produce easy-flowing brilliant enamels; but lead presents an occupational
health hazard.
Composition of the enamel is carefully controlled to provide a coefficient of
thermal expansion as near that of the base metal as possible. If the coefficient of
the enamel is greater than that of the metal, cracking and crazing are likely to
occur, but if the coefficient of the enamel is slightly less, it is lightly compressed
upon cooling, a desirable condition because glass is strong in compression.
To obtain good adhesion between enamel and metal, one of the so-called transition
elements used in glass formulation must be employed. Cobalt is favored.
Apparently, the transition elements promote growth of iron crystals from base metal
into the enamel, encourage formation of an adherent oxide coating on the iron,
which fuses to the enamel, or develop polar chemical bonds between metal and
glass.
Usually, white or colored opaque enamels are desired. Opacity is promoted by
mixing in, but not dissolving, finely divided materials possessing refractive indexes
widely different from the glass. Tin oxide, formerly widely used, has been largely
displaced by less expensive and more effective titanium and zirconium compounds.
Clay adds to opacity. Various oxides are included to impart color.
Most enameling consists of a ground coat and one or two cover coats fired on
at slightly lower temperatures; but one-coat enameling of somewhat inferior quality
can be accomplished by first treating the iron surface with soluble nickel salts.
The usual high-soda glasses used to obtain low-temperature softening enamels
are not highly acid-resistant and therefore stain readily and deeply when ironcontaining
water drips on them. Enamels highly resistant to severe staining conditions
must be considerably harder; i.e., have higher softening temperatures and
therefore require special techniques to avoid warping and distorting of the metal
base.
Interiors of refrigerators are often made of porcelain-enameled steel sheets for
resistance to staining by spilled foods, whereas the exteriors are commonly bakedon
synthetic-resin finishes.
4.79 PORCELAIN BIBLIOGRAPHY
F. H. Norton, ‘‘Elements of Ceramics,’’ Addison-Wesley Publishing Company, Cambridge,
Mass.
BUILDING MATERIALS 4.97
W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, ‘‘Introduction to Ceramics,’’
John Wiley & Sons, Inc., New York.
G. S. Brady and H. R. Clauser, ‘‘Materials Handbook,’’ 13th ed., and J. H.
Callender, ‘‘Time-Saver Standards for Architectural Design Data,’’ McGraw-Hill
Publishing Company, New York.
ASPHALT AND BITUMINOUS PRODUCTS
Asphalt, because of its water-resistant qualities and good durability, is used for
many building applications to exclude water, provide a cushion against vibration
and expansion, and serve as pavement.
4.80 ASPHALTS FOR DAMPPROOFING AND
WATERPROOFING
Dampproofing is generally only a mopped-on coating, whereas waterproofing usually
is a built-up coating of one or more plies. Bituminous systems used for dampproofing
and waterproofing may be hot applied or cold applied.
ASTM D449, ‘‘Asphalt Used in Dampproofing and Waterproofing,’’ specifies
three types of asphalt. Type I, a soft, adhesive, easy-flowing, self-healing bitumen,
is intended for use for underground construction, such as foundations, or where
similar moderate temperature conditions exist. The softening point of Type I may
range from 115 to 140
F. Type II may be used above ground; for example, on
retaining walls or where temperatures will not exceed 122
F. The softening point
of Type II may range from 145 to 170
F.
D449 asphalts are suitable for use with an asphalt primer meeting the requirements
of ASTM D41. In construction of membrane waterproofing systems with
these asphalts, felts should conform to ASTM D226 or D250, fabrics to D173,
D1327, or D1668, and asphalt-impregnated glass mats to D2178.
For cold-applied systems, asphalt emulsions or cut-back asphalt mastic reinforced
with glass fabric may be used. ASTM D1187 specifies asphalt-based emulsions
for protective coatings for metal. D491 contains requirements for asphalt
mastic for use in waterproofing building floors but not intended as pavement. The
mastic is a mixture of asphalt cement, mineral filler, and mineral aggregate. D1668
covers glass fabric for roofing and waterproofing membranes.
4.81 BITUMINOUS ROOFING
Hot asphalt or coal tar are used for conventional built-up roofing. The bitumens are
heated to a high enough temperature to fuse with saturant bitumen in roofing felts,
thus welding the plies together. The optimum temperature at the point of application
for achieving complete fusion, optimum mopping properties, and the desirable interply
mopping weight is called the equiviscous temperature (EVT). Information
on EVT should be obtained from the manufacturer.
4.98 SECTION FOUR
4.81.1 Built-Up Roofing
For constructing built-up roofing, four grades of asphalt are recognized (ASTM
D312): Type I, for inclines up to 1?2 in / ft; Type II, for inclines up to 11?2 in / ft;
Type III, for inclines up to 3 in/ ft; and Type IV, suited for inclines up to 6 in/ ft,
generally in areas with relatively high year-round temperatures. Types I through IV
may be either smooth or surfaced with slag or gravel. Softening ranges are 135 to
150
F, 158 to 176
F, 180 to 200
F and 210 to 225
F, respectively. Heating of the
asphalts should not exceed the flash point, the finished blowing temperature, or
475
F for Type I, 500
F for Type II, 525
F for Types III and IV.
Coal-tar pitches for roofing, dampproofing, and waterproofing are of three types
(ASTM D450): Type I, for built-up roofing systems; Type II, for dampproofing and
membranes waterproofing systems; Type III, for built-up roofing, but containing
less volatiles than Type I. Softening ranges are 126 to 140
F, 106 to 126
F, and
133 to 147
F, respectively.
4.81.2 Roofing Felts
For built-up waterproofing and roofing, types of membranes employed include felt
(ASTM D226, D227) and cotton fabrics (ASTM D173). Felts are felted sheets of
inorganic or organic fibers saturated with asphalt or coal tar conforming to ASTM
D312 and D450.
Standard asphalt felts weigh 15, 20, or 30 lb per square (100 ft2), and standard
coal-tar felts weigh 13 lb per square.
Cotton fabrics are open-weave materials weighing at least 31?2 oz/yd2 before
saturation, with thread counts of 24 to 32 per inch. The saturants are either asphalts
or coal tars. The saturated fabrics must weigh at least 10 oz/yd2.
4.81.3 Roll Roofing
Asphalt roll roofing, shingles, and siding consist basically of roofing felt, first uniformly
impregnated with hot asphaltic saturant and then coated on each side with
at least one layer of a hot asphaltic coating and compounded with a water-insoluble
mineral filler. The bottom or reverse side, in each instance, is covered with some
suitable material, like powdered mica, to prevent sticking in the package or roll.
Granule-surfaced roll roofing (ASTM D249) is covered uniformly on the weather
side with crushed mineral granules, such as slate. Minimum weight of the finished
roofing should be 81 to 83 lb per square (100 ft2), and the granular coating should
weigh at least 18.5 lb per square.
Roll roofing (ASTM 224), surfaced with powdered talc or mica, is made in two
grades, 39.8 and 54.6 lb per square, of which at least 18 lb must be the surfacing
material.
4.82 ASPHALT SHINGLES
There are three standard types: Type I, uniform or nonuniform thickness; Type II,
thick butt; and Type III, uniform or nonuniform thickness (ASTM D225). Average
BUILDING MATERIALS 4.99
weights must be 95 lb per square (100 ft2). For types I and III, the weather-side
coating must weigh 23.0 lb per square; for Type II, 30.0 lb per square. The material
in these shingles is similar to that in granule-surfaced roll roofing.
4.83 ASPHALT MASTICS AND GROUTS
Asphalt mastics used for waterproofing floors and similar structures, but not intended
for pavement, consist of mixtures of asphalt cement, mineral filler, and
mineral aggregate, which can be heated at about 400
F to a sufficiently soft condition
to be poured and troweled into place. The raw ingredients may be mixed on
the job or may be premixed, formed into cakes, and merely heated on the job
(ASTM D491).
Bituminous grouts are suitable for waterproofing above or below ground level
as protective coatings. They also can be used for membrane waterproofing or for
bedding and filling the joints of brickwork. Either asphaltic or coal-tar pitch materials
of dampproofing and waterproofing grade are used, together with mineral
aggregates as coarse as sand.
4.84 BITUMINOUS PAVEMENTS
Asphalts for pavement (ASTM D946) contain petroleum asphalt cement, derived
by the distillation of asphaltic petroleum. Various grades are designated as 40–50,
60–70, 85–100, 120–150, and 200–300, depending upon the depth of penetration
of a standard needle in a standard test (ASTM D5).
Emulsions range from low to high viscosity and quick- to slow-setting (ASTM
D977).
4.85 ASPHALT BIBLIOGRAPHY
‘‘The NRCA Roofing and Waterproofing Manual,’’ National Roofing Contractors
Association, Rosemont, IL 60018-5607.
JOINT SEALS
Calking compounds, sealants, and gaskets are employed to seal the points of contact
between similar and dissimilar building materials that cannot otherwise be made
completely tight. Such points include glazing, the joints between windows and
walls, the many joints occurring in the increasing use of panelized construction,
the copings of parapets, and similar spots.
The requirements of a good joint seal are: (1) good adhesion to or tight contact
with the surrounding materials, (2) good cohesive strength, (3) elasticity to allow
for compression and extension as surrounding materials retract or approach each
4.100 SECTION FOUR
other because of changes in moisture content or temperature, (4) good durability
or the ability to maintain their properties over a long-period of time without marked
deterioration, and (5) no staining of surrounding materials such as stone.
4.86 CALKING COMPOUNDS
These sealers are used mostly with traditional materials such as masonry, with
relatively small windows, and at other points where motion of building components
is relatively small. They are typically composed of elastomeric polymers or bodied
linseed or soy oil, or both, combined with calcium carbonate (ground marble or
limestone), tinting pigments, a gelling agent, drier, and mineral spirits (thinners).
Two types of commonly employed, gun grade and knife grade. Gun grades are
viscous semiliquids suitable for application by hand or air-operated calking guns.
Knife grades are stiffer and are applied by knife, spatula, or mason’s pointing tools.
Because calking compounds are based on drying oils that eventually harden in
contact with the air, the best joints are generally thick and deep, with a relatively
small portion exposed to the air. The exposed surface is expected to form a tough
protective skin for the soft mass underneath, which in turn provides the cohesiveness,
adhesiveness, and elasticity required. Thin shallow beads cannot be expected
to have the durability of thick joints with small exposed surface areas.
4.87 SEALANTS
For joints and other points where large movements of building components are
expected, elastomeric materials may be used as sealants. Whereas traditional calking
compounds should not be used where movements of more than 5% of joint
width or at most 10% are expected, larger movements, typically 10 to 25%, can be
accommodated by the rubbery sealants.
Some elastomeric sealants consist of two components, mixed just before application.
Polymerization occurs, leading to conversion of the viscous material to a
rubbery consistency. The working time or pot life before this occurs varies, depending
upon formulation and temperature, from a fraction of an hour to several
hours or a day. Other formulations are single-component and require no mixing.
They harden upon exposure to moisture in the air.
Various curing agents, accelerators, plasticizers, fillers, thickeners, and other
agents may be added, depending on the basic material and the end-use requirements.
Among the polymeric materials employed are:
Acrylics: solvent-release type, water-release type, latex
Butyls: skinning and nonskinning
Polysulfide: two-part and one-part
Silicone: one-part
Polyurethane: two-part and one-part
Chlorosulfonated polyethylene: one-part
Polyurethane-polyepoxide: two-part
BUILDING MATERIALS 4.101
Characteristics of the preceding formulations vary. Hence, the proper choice of
materials depends upon the application. A sealant with the appropriate hardness,
extensibility, useful temperature ranges, expected life, dirt pickup, staining, colorability,
rate of cure to tack-free condition, toxicity, resistance to ultraviolet light,
and other attributes should be chosen for the specific end use.
In many joints, such as those between building panels, it is necessary to provide
backup; that is, a foundation against which the compound can be applied. This
serves to limit the thickness of the joint, to provide the proper ratio of thickness to
width, and to force the compound into intimate contact with the substrate, thereby
promoting adhesion. For the purpose, any of various compressible materials, such
as polyethylene or polyurethane rope, or oakum, may be employed.
To promote adhesion to the substrate, various primers may be needed. (To prevent
adhesion of the compound to parts of the substrate where adhesion is not
wanted, any of various liquid and tape bond-breakers may be employed.) Generally,
good adhesion requires dry, clean surfaces free of grease and other deleterious
materials.
4.88 GASKETS
Joint seals described in Arts. 4.86 and 4.87 are formed in place; that is, soft masses
are put into the joints and conform to their geometry. A gasket, on the other hand,
is preformed and placed into a joint whose geometry must conform with the gasket
in such a way as to seal the joint by compression of the gasket. Gaskets, however,
are cured under shop-controlled conditions, whereas sealants cure under variable
and not always favorable field conditions.
Rubbery materials most commonly employed for gaskets are cellular or noncellular
(dense) neoprene, EPDM (ethylene-propylene polymers and terpolymers),
and polyvinylchloride polymers.
Gaskets are generally compression types or lock-strip (zipper) types. The former
are forced into the joint and remain tight by being kept under compression. With
lock-strip gaskets, a groove in the gasket permits a lip to be opened and admit glass
or other panel, after which a strip is forced into the groove, tightening the gasket
in place. If the strip is separable from the gasket, its composition is often harder
than the gasket itself.
For setting large sheets of glass and similar units, setting or supporting spacer
blocks of rubber are often combined with gaskets of materials such as vulcanized
synthetic rubber and are finally sealed with the elastomeric rubber-based sealants
or glazing compounds.
4.89 JOINT SEALS BIBLIOGRAPHY
‘‘Building Seals and Sealants,’’ STP 606, ASTM, Philadelphia, Pa.
J. P. Cook, ‘‘Construction Sealants and Adhesives,’’ John Wiley & Sons, Inc.,
New York.
A. Damusis, ‘‘Sealants,’’ Van Nostrand Reinhold Company, New York.
4.102 SECTION FOUR
PAINTS AND OTHER COATINGS
Protective and decorative coatings generally employed in building are the following:
Oil Paint. Drying-oil vehicles or binders plus opaque and extender pigments.
Water Paint. Pigments plus vehicles based on water, casein, protein, oil emulsions,
and rubber or resin latexes, separately or in combination.
Calcimine. Water and glue, with or without casein, plus powdered calcium carbonate
and any desired colored pigments.
Varnish. Transparent combination of drying oil and natural or synthetic resins.
Enamel. Varnish vehicle plus pigments.
Lacquer. Synthetic-resin film former, usually nitrocellulose, plus plasticizers, volatile
solvents, and other resins.
Shellac. Exudations of the lac insect, dissolved in alcohol.
Japan. Solutions of metallic salts in drying oils, or varnishes containing asphalt
and opaque pigments.
Aluminum Paint. Fine metallic aluminum flakes suspended in drying oil plus
resin, or in nitrocellulose.
4.90 VEHICLES OR BINDERS
Following are descriptions of the most commonly used vehicles and binders for
paint:
Natural Drying Oils. Drying oils harden by absorbing oxygen. The most important
natural oils are linseed from flax seed (for many years the standard paint
vehicle), tung oil (faster drying, good compatibility with varnish), oiticica oil (similar
to tung), safflower (best nonyellowing oil), soybean (flexible films), dehydrated
caster (good adhesion, fast drying), and fish oil (considered inferior but cheap).
Alkyds. These, the most widely used paint vehicles, are synthetic resins that are
modified with various vegetable oils to produce clear resins that are harder than
natural oils. Properties of the film depend on relative proportions of oil and resin.
The film is both air drying and heat hardening.
Latexes. Latex paints are based on emulsions of various polymers including acrylics,
polyvinyl acetate, styrene-butadiene, polyvinyl chloride, and rubber. They are
easy to apply, dry quickly, have no solvent odor, and application tools are easily
cleaned with soap and water. The films adhere well to various surfaces, have good
color retention, and have varying degrees of flexibility.
BUILDING MATERIALS 4.103
Epoxy and Epoxy-Polyester. Catalyzed two-part, all-epoxy coatings are formed
by addition of a catalyst to the liquid epoxy just before application (pot life a few
minutes to a day). Films are as hard as many baked-on coatings and are resistant
to solvents and traffic. Oil-modified epoxy esters, in contrast, harden on oxidation
without a catalyst. They are less hard and chemically resistant than catalyzed epoxies,
but dry fast and are easily applied. Epoxy-polyesters mixed just before use
produce smooth finishes suitable for many interior surfaces and are chemically
resistant.
Polyurethanes. These produce especially abrasion-treatment, fast-hardening coatings.
Two-component formulations, of variable pot life, are mixed just before use.
One-component formulations cure by evaporation and reaction with moisture in air
(30 to 90% relative humidity). Oils and alkyds may be added.
Vinyl Solutions. Solutions of polyvinyl chloride and vinyl esters dry rapidly and
are built up by successive, sprayed thin coatings. They characteristically have low
gloss, high flexibility, and inertness to water but are sensitive to some solvents.
Adhesion may be a problem. Weather resistance is excellent.
Dryers. These are catalysts that hasten the hardening of drying oils. Most dryers
are salts of heavy metals, especially cobalt, manganese, and lead, to which salts of
zinc and calcium may be added. Iron salts, usable only in dark coatings, accelerate
hardening at high temperatures. Dryers are normally added to paints to hasten
hardening, but they must not be used too liberally or they cause rapid deterioration
of the oil by overoxidation.
Thinners. These are volatile constituents added to coatings to promote their
spreading qualities by reducing viscosity. They should not react with the other
constituents and should evaporate completely. Commonly used thinners are turpentine
and mineral spirits, i.e., derivatives of petroleum and coal tar.
4.91 PIGMENTS FOR PAINTS
Pigments may be classified as white and colored, or as opaque and extender pigments.
The hiding power of pigments depends on the difference in index of refraction
of the pigment and the surrounding medium—usually the vehicle of a protective
coating. In opaque pigments, these indexes are markedly different from those
of the vehicles (oil or other); in extender pigments, they are nearly the same. The
comparative hiding efficiencies of various pigments must be evaluated on the basis
of hiding power per pound and cost per pound.
Principal white pigments, in descending order of relative hiding power per
pound, are approximately as follows: rutile titanium dioxide, anatase titanium dioxide,
zinc sulfide, titanium-calcium, titanium-barium, zinc sulfide-barium, titanated
lithopone, lithopone, antimony oxide, zinc oxide.
Zinc oxide is widely used by itself or in combination with other pigments. Its
color is unaffected by many industrial and chemical atmospheres. It imparts gloss
and reduces chalking but tends to crack and alligator instead.
Zinc sulfide is a highly opaque pigment widely used in combination with other
pigments.
4.104 SECTION FOUR
Titanium dioxide and extended titanium pigments have high opacity and generally
excellent properties. Various forms of the pigments have different properties.
For example, anatase titanium dioxide promotes chalking, whereas rutile inhibits
it.
Colored pigments for building use are largely inorganic materials, especially
for outdoor use, where the brilliant but fugitive organic pigments soon fade. The
principal inorganic colored pigments are:
Metallic. Aluminum flake or ground particle, copper bronze, gold leaf, zinc dust
Black. Carbon black, lampblack, graphite, vegetable black, and animal blacks
Earth colors. Yellow ocher, raw and burnt umber, raw and burnt sienna; reds
and maroons
Blue. Ultramarine, iron ferrocyanide (Prussian, Chinese, Milori)
Brown. Mixed ferrous and ferric oxide
Green. Chromium oxide, hydrated chromium oxide, chrome greens
Orange. Molybdated chrome orange
Red. Iron oxide, cadmium red, vermilion
Yellow. Zinc chromate, cadmium yellows, hydrated iron oxide
Extender pigments are added to extend the opaque pigments, increase durability,
provide better spreading characteristics, and reduce cost. The principal extender
pigments are silica, china clay, talc, mica, barium sulfate, calcium sulfate, calcium
carbonate, and such materials as magnesium oxide, magnesium carbonate, barium
carbonate, and others used for specific purposes.
4.92 RESINS FOR PAINTS
Natural and synthetic resins are used in a large variety of air-drying and baked
finishes. The natural resins include both fossil resins, which are harder and usually
superior in quality, and recent resins tapped from a variety of resin-exuding trees.
The most important fossil resins are amber (semiprecious jewelry), Kauri, Congo,
Boea Manila, and Pontianak. Recent resins include Damar, East India, Batu, Manila,
and rosin. Shellac, the product of the lac insect, may be considered to be in this
class of resins.
The synthetic resins, in addition to the ones discussed in Art. 4.90, are used for
applications requiring maximum durability. Among them are phenol formaldehyde,
melamine formaldehyde, urea formaldehyde, silicones, fluorocarbons, and cellulose
acetate-butyrate.
Phenolics in varnishes are used for outdoor and other severe applications on
wood and metals. They are especially durable when baked.
Melamine and urea find their way into a large variety of industrial finishes, such
as automobile and refrigerator finishes.
Silicones are used when higher temperatures are encountered that can be borne
by the other finishes.
Fluorocarbons are costly but provide high-performance coatings, industrial siding,
and curtain walls with excellent gloss retention, stain resistance, and weather
resistance. Cellulose acetate-butyrate provides shop-applied, high-gloss finishes.
BUILDING MATERIALS 4.105
4.93 COATINGS BIBLIOGRAPHY
A. Banov, ‘‘Paints and Coatings Handbook.’’ Structures Publishing Company, Farmington,
Mich.
R. M. Burns and W. Bradley, ‘‘Protective Coatings for Metals,’’ Van Nostrand
Reinhold Company, New York.
C. R. Martens, ‘‘The Technology of Paints, Varnishes and Lacquers,’’ Van Nostrand
Reinhold Company, New York.
W. C. Golton, ‘‘Analysis of Paints and Related Materials: Current Techniques
for Solving Coatings Problems,’’ STP 1119, ASTM, Philadelphia, Pa.
5.1
SECTION FIVE
STRUCTURAL THEORY
Akbar Tamboli, Michael Xing, Mohsin Ahmed
Thornton-Tomasetti Engineers, Newark, New Jersey
STRUCTURAL THEORY CREATES IDEALIZATION
OF STRUCTURE FOR PURPOSES OF ANALYSIS
Structural modeling is an essential and important tool in structural engineering.
Over the past 200 years, many of the most significant contributions to the understanding
of the structures have been made by Scientist Engineers while working on
mathematical models, which were used for real structures.
Application of mathematical model of any sort to any real structural system
must be idealized in some fashion; that is, an analytical model must be developed.
There has never been an analytical model, which is a precise representation of the
physical system. While the performance of the structure is the result of natural
effects, the development and thus the performance of the model is entirely under
the control of the analyst. The validity of the results obtained from applying mathematical
theory to the study of the model therefore rests on the accuracy of the
model. While this is true, it does not mean that all analytical models must be
elaborate, conceptually sophisticated devices. In some cases very simple models
give surprisingly accurate results. While in some other cases they may yield answers,
which deviate markedly from the true physical behavior of the model, yet
be completely satisfactory for the problem at hand.
Structure design is the application of structural theory to ensure that buildings
and other structures are built to support all loads and resist all constraining forces
that may be reasonably expected to be imposed on them during their expected
service life, without hazard to occupants or users and preferably without dangerous
deformations, excessive sideways (drift), or annoying vibrations. In addition, good
design requires that this objective be achieved economically.
Provision should be made in application of structural theory to design for abnormal
as well as normal service conditions. Abnormal conditions may arise as a
result of accidents, fire, explosions, tornadoes, severer-than-anticipated earthquakes,
floods, and inadvertent or even deliberate overloading of building components. Under
such conditions, parts of a building may be damaged. The structural system,
however, should be so designed that the damage will be limited in extent and
undamaged portions of the building will remain stable. For the purpose, structural
elements should be proportioned and arranged to form a stable system under normal
5.2 SECTION FIVE
service conditions. In addition, the system should have sufficient continuity and
ductility, or energy-absorption capacity, so that if any small portion of it should
sustain damage, other parts will transfer loads (at least until repairs can be made)
to remaining structural components capable of transmitting the loads to the ground.
(‘‘Steel Design Handbook, LRFD Method’’, Akbar R. Tamboli Ed., McGraw-
Hill 1997. ‘‘Design Methods for Reducing the Risk of Progressive Collapse in
Buildings’’. NBS Buildings Science Series 98, National Institute of Standards and
Technology, 1997. ‘‘Handbook of Structural Steel Connection Design and Details’’,
Akbar R. Tamboli Ed., McGraw-Hill 1999’’).
5.1 DESIGN LOADS
Loads are the external forces acting on a structure. Stresses are the internal forces
that resist them. Depending on that manner in which the loads are applied, they
tend to deform the structure and its components—tensile forces tend to stretch,
compressive forces to squeeze together, torsional forces to twist, and shearing forces
to slide parts of the structure past each other.
5.1.1 Types of Loads
External loads on a structure may be classified in several different ways. In one
classification, they may be considered as static or dynamic.
Static loads are forces that are applied slowly and then remain nearly constant.
One example is the weight, or dead load, of a floor or roof system.
Dynamic loads vary with time. They include repeated and impact loads.
Repeated loads are forces that are applied a number of times, causing a variation
in the magnitude, and sometimes also in the sense, of the internal forces. A good
example is an off-balance motor.
Impact loads are forces that require a structure or its components to absorb
energy in a short interval of time. An example is the dropping of a heavy weight
on a floor slab, or the shock wave from an explosion striking the walls and roof of
a building.
External forces may also be classified as distributed and concentrated.
Uniformly distributed loads are forces that are, or for practical purposes may
be considered, constant over a surface area of the supporting member. Dead weight
of a rolled-steel I beam is a good example.
Concentrated loads are forces that have such a small contact area as to be
negligible compared with the entire surface area of the supporting member. A beam
supported on a girder, for example, may be considered, for all practical purposes,
a concentrated load on the girder.
Another common classification for external forces labels them axial, eccentric,
and torsional.
An axial load is a force whose resultant passes through the centroid of a section
under consideration and is perpendicular to the plane of the section.
An eccentric load is a force perpendicular to the plane of the section under
consideration but not passing through the centroid of the section, thus bending the
supporting member (see Arts. 5.4.2, 5.5.17, and 5.5.19).
STRUCTURAL THEORY 5.3
Torsional loads are forces that are offset from the shear center of the section
under consideration and are inclined to or in the plane of the section, thus twisting
the supporting member (see Arts. 5.4.2 and 5.5.19).
Also, building codes classify loads in accordance with the nature of the source.
For example:
Dead loads include materials, equipment, constructions, or other elements of
weight supported in, on, or by a building, including its own weight, that are intended
to remain permanently in place.
Live loads include all occupants, materials, equipment, constructions, or other
elements of weight supported in, on, or by a building and that will or are likely to
be moved or relocated during the expected life of the building.
Impact loads are a fraction of the live loads used to account for additional
stresses and deflections resulting from movement of the live loads.
Wind loads are maximum forces that may be applied to a building by wind in
a mean recurrence interval, or a set of forces that will produce equivalent stresses.
Snow loads are maximum forces that may be applied by snow accumulation in
a mean recurrence interval.
Seismic loads are forces that produce maximum stresses or deformations in a
building during an earthquake.
5.1.2 Service Loads
In designing structural members, designers should use whichever is larger of the
following:
1. Loadings specified in the local or state building code.
2. Probable maximum loads, based not only on current site conditions and original
usage of proposed building spaces but also on possible future events. Loads that
are of uncertain magnitude and that may be treated as statistical variables should
be selected in accordance with a specific probability that the chosen magnitudes
will not be exceeded during the life of the building or in accordance with the
corresponding mean recurrence interval. The mean recurrence interval generally
used for ordinary permanent buildings is 50 years. The interval, however, may
be set at 25 years for structures with no occupants or offering negligible risk to
life, or at 100 years for permanent buildings with a high degree of sensitivity
to the loads and an unusually high degree of hazard to life and property in case
of failure.
In the absence of a local or state building code, designers can be guided by
loads specified in a national model building code or by the following data:
Loads applied to structural members may consist of the following, alone or in
combination: dead, live, impact, earth pressure, hydrostatic pressure, snow, ice, rain,
wind, or earthquake loads; constraining forces, such as those resulting from restriction
of thermal, shrinkage, or moisture-change movements; or forces caused by
displacements or deformations of members, such as those caused by creep, plastic
flow, differential settlement, or sideways (drift).
Dead Loads. Actual weights of materials and installed equipment should be used.
See Tables 5.1 and 5.2c.
5.4 TABLE 5.1 Minimum Design Dead Loads
Walls
Clay brick
High-absorption, per 4-in wythe
Medium-absorption, per 4-in wythe
Low-absorption, per 4-in wythe
Sand-lime brick, per 4-in wythe
Concrete brick
4-in, with heavy aggregate
4-in, with light aggregate
Concrete block, hollow
8-in, with heavy aggregate
lb/ft2
34
39
46
38
46
33
55
Floor Finishes lb/ft2
Asphalt block, 2-in 24
Cement, 1-in 12
Ceramic or quarry tile, 1-in 12
Hardwood flooring, 7?8-in 4
Plywood subflooring, 1?2-in 1.5
Resilient flooring, such as asphalt tile and linoleum 2
Slate, 1-in 15
Softwood subflooring, per in of thickness 3
Terrazzo, 1-in 13
Wood block, 3-in 4
8-in, with light aggregate
12-in, with heavy aggregate
12-in, with light aggregate
Clay tile, loadbearing
4-in
8-in
12-in
Clay tile, nonloadbearing
2-in
4-in
8-in
Furring tile
35
85
55
24
42
58
11
18
34
Wood joists, double wood floor, joist size
2 
 6
2 
 8
2 
 10
2 
 12
3 
 6
3 
 8
3 
 10
3 
 12
3 
 14
lb/ft2
12-in spacing
6
6
7
8
7
8
9
11
12
16-in spacing
5
6
6
7
6
7
8
9
10
11?2-in
2-in
Glass block, 4-in
Gypsum block, hollow
2-in
4-in
6-in
8
10
18
9.5
12.5
18.5
Concrete Slabs lb/ft2
Stone aggregate, reinforced, per in of thickness 12.5
Slag, reinforced, per in of thickness 11.5
Lightweight aggregate, reinforced, per in of thickness 6 to 10
5.5
TABLE 5.1 Minimum Design Dead Loads (Continued )
Masonry
Cast-stone masonry
Concrete, stone aggregate, reinforced
Ashlar:
Granite
Limestone, crystalline
Limestone, oo?litic
Marble
Sandstone
Roof and Wall Coverings
Clay tile shingles
Asphalt shingles
Composition:
3-ply ready roofing
4-ply felt and gravel
5-ply felt and gravel
Copper or tin
Corrugated steel
Sheathing (gypsum), 1?2-in
Sheathing (wood), per in thickness
Slate, 1?4-in
Wood shingles
Waterproofing
Five-ply membrane
Ceilings
Plaster (on tile or concrete)
Suspended metal lath and gypsum plaster
Suspended metal lath and cement plaster
Suspended steel channel supports
Gypsumboard per 1?4-in thickness
lb/ft3
144
150
165
165
135
173
144
lb/ft2
9 to 14
2
1
5.5
6
1
2
2
3
10
2
lb/ft2
5
lb/ft2
5
10
15
2
1.1
Floor Fill lb/ft2
Cinders, no cement, per in of thickness 5
Cinders, with cement, per in of thickness 9
Sand, per in of thickness 8
Partitions lb/ft2
Plaster on masonry
Gypsum, with sand, per in of thickness 8.5
Gypsum, with lightweight aggregate, per in 4
Cement, with sand, per in of thickness 10
Cement, with lightweight aggregate, per in 5
Plaster, 2-in solid 20
Metal studs
Plastered two sides 18
Gypsumboard each side 6
Wood studs, 2 
 4-in
Unplastered 3
Plastered one side 11
Plastered two sides 19
Gypsumboard each side 7
Glass lb/ft2
Single-strength 1.2
Double-strength 1.6
Plate, 1?8-in 1.6
Insulation lb/ft2
Cork, per in of thickness 1.0
Foamed glass, per in of thickness 0.8
Glass-fiber bats, per in of thickness 0.06
Polystyrene, per in of thickness 0.2
Urethane 0.17
Vermiculite, loose fill, per in of thickness 0.5
5.6 SECTION FIVE
TABLE 5.2 Minimum Design Live Loads
a. Uniformly distributed live loads, lb / ft2, impact includeda
Occupancy or use Load Occupancy or use Load
Assembly spaces:
Auditoriumsb with fixed seats
Auditoriumsb with movable seats
Ballrooms and dance halls
Bowling alleys, poolrooms,
similar recreational areas
Conference and card rooms
Dining rooms, restaurants
Drill rooms
Grandstand and reviewing-stand
seating areas
Gymnasiums
Lobbies, first-floor
Roof gardens, terraces
Skating rinks
Stadium and arenas bleachers
Bakeries
Balconies (exterior)
Up to 100 ft2 on one- and twofamily
houses
Bowling alleys, alleys only
Broadcasting studios
Catwalks
Corridors:
Areas of public assembly, first-
floor lobbies
Other floors same as occupancy
served, except as indicated
elsewhere in this table
Fire escapes:
Single-family dwellings only
Others
Garages:
Passenger cars
Trucks and buses
Hospitals:
Operating rooms, laboratories,
service areas
Patients’ rooms, wards,
personnel areas
Corridors above first floor
Kitchens other than domestic
Laboratories, scientific
Libraries:
Corridors above first floor
Reading rooms
Stack rooms, books and
shelving at 65 lb / ft3, but at
least
Manufacturing and repair areas:
Heavy
Light
60
100
100
75
50
100
150
100
100
100
100
100
100
150
100
60
40
100
40
100
40
100
50
60
40
80
150
100
80
60
150
250
125
Marques
Morgue
Office buildings:
Corridors above first floor
Files
Offices
Penal institutions:
Cell blocks
Corridors
Residential:
Dormitories
Nonpartitioned
Partitioned
Dwellings, multifamily:
Apartments
Corridors
Hotels:
Guest rooms, private cooridors
Public corridors
Housing, one- and two-family:
First floor
Storage attics
Uninhabitable attics
Upper floors, habitable attics
Schools:
Classrooms
Corridors above first floor
First floor corridors
Shops with light equipment
Stairs and exitways
Handrails, vertical and horizontal
thrust, lb / lin ft
Storage warehouse:
Heavy
Light
Stores:
Retail:
Basement and first floor
Upper floors
Wholesale
Telephone equipment rooms
Theaters:
Aisles, corridors, lobbies
Dressing rooms
Projection rooms
Stage floors
Toilet areas
75
125
80
125
50
40
100
60
40
40
80
40
100
40
80
20
30
40
80
100
60
100
50
250
125
100
75
125
80
100
40
100
150
60
a See Eqs. (5.1) and (5.2).
b Including churches, schools, theaters, courthouses, and lecture halls.
c Use American Association of State Highway and Transportation Officials highway lane loadings.
STRUCTURAL THEORY 5.7
TABLE 5.2 Minimum Design Live Loads (Continued)
b. Concentrated live loadsd
Location Load, lb
Elevator machine room grating (on 4-in2 area) 300
Finish, light floor-plate construction (on 1-in2 area) 200
Garages:
Passenger cars:
Manual parking (on 20-in2 area) 2,000
Mechanical parking (no slab), per wheel 1,500
Trucks, buses (on 20-in2 area), per wheel 16,000
Manufacturing
Light 2,000
Heavy 3,000
Office floors (on area 2.5 ft square) 2,000
Scuttles, skylight ribs, and accessible ceilings (on area 2.5 ft square) 200
Sidewalks (on area 2.5 ft square) 8,000
Stair treads (on 4-in2 area at center of tread) 300
Libraries (on area 2.5 ft square) 1,500
Hospitals (on area 2.5 ft square) 1,000
Schools (on area 2.5 ft square) 1,000
Stores (on area 2.5 ft square) 3,000
d Use instead of uniformly distributed live load, except for roof trusses, if concentrated loads produce
greater stresses or deflections. Add impact factor for machinery and moving loads: 100% for elevators, 20%
for light machines, 50% for reciprocating machines, 33% for floor or balcony hangers. For craneways, and
a vertical force equal to 25% of maximum wheel load; a lateral force equal to 10% of the weight of trolley
and lifted load, at the top of each rail; and a longitudinal force equal to 10% of maximum wheel loads,
acting at top of rail.
Live Loads. These may be concentrated or distributed loads and should be considered
placed on the building to produce maximum effects on the structural member
being designed. Minimum live loads to be used in building design are listed in
Table 5.2. These include an allowance for impact, except as noted in the footnote
of Table 5.2b.
Partitions generally are considered to be live loads, because they may be installed
at any time, almost anywhere, to subdivide interior spaces, or may be shifted from
original places to other places in the future. Consequently, unless a floor is designed
for a large live load, for example, 80 lb / ft2, the weight of partitions should be
added to other live loads, whether or not partitions are shown on the working
drawings for building construction.
Because of the low probability that a large floor area contributing load to a
specific structural member will be completely loaded with maximum design live
loads, building codes generally permit these loads to be reduced for certain types
of occupancy. Usually, however, codes do not permit any reduction for places of
public assembly, dwellings, garages for trucks and buses, or one-way slabs. For
areas with a minimum required live load exceeding 100 lb / ft2 and for passengercar
garages, live loads on columns supporting more than one floor may be decreased
20%. Except for the preceding cases, a reduced live load L, lb/ft2, may be computed
from
5.8 SECTION FIVE
TABLE 5.2 Minimum Design Live Loads (Continued)
c. Minimum design loads for materials
Material
Load,
lb/ft3 Material
Load,
lb/ft3
Aluminum, cast
Bituminous products:
Asphalt
Petroleum, gasoline
Pitch
Tar
Brass, cast
Bronze, 8 to 14% tin
Cement, portland, loose
Cement, portland, set
Cinders, dry, in bulk
Coal, anthracite, piled
Coal, bituminous or lignite, piled
Coal, peat, dry, piled
Charcoal
Copper
Earth (not submerged):
Clay, dry
Clay, damp
Clay and gravel, dry
Silt, moist, loose
Silt, moist, packed
Sand and gravel, dry, loose
Sand and gravel, dry, packed
Sand and gravel, wet
Gold, solid
165
81
42
69
75
534
509
90
183
45
52
47
23
12
556
63
110
100
78
96
100
110
120
1205
Gravel, dry
Gypspum, loose
Ice
Iron, cast
Lead
Lime, hydrated, loose
Lime, hydrated, compacted
Magnesium alloys
Mortar, hardened;
Cement
Lime
Riprap (not submerged):
Limestone
Sandstone
Sand, clean and dry
Sand, river, dry
Silver
Steel
Stone, ashlar:
Basalt, granite, gneiss
Limestone, marble, quartz
Sandstone
Shale, slate
Tin, cast
Water, fresh
Water, sea
104
70
57.2
450
710
32
45
112
130
110
83
90
90
106
656
490
165
160
140
155
459
62.4
64
15
L  0.25  L (5.1) 
 o AI
where Lo  unreduced live load, lb / ft2 (see Table 5.1a)
AI  influence area, or floor area over which the influence surface for structural
effects is significantly different from zero
 area of four surrounding bays for an interior column, plus similar area
from supported floors above, if any
 area of two adjoining bays for an interior girder or for an edge column,
plus similar areas from supported floors above, if any
 area of one bay for an edge girder or for a corner column, plus similar
areas from supported floors above, if any
The reduced live load L, however, should not be less than 0.5Lo for members
supporting one floor or 0.4Lo for members supporting two or ore floors.
Roofs used for promenades should be designed for a minimum life load of 60
lb/ft2, and those used for gardens or assembly, for 100 lb / ft2. Ordinary roofs should
be designed for a minimum live load L, lb/ft2, computed from
STRUCTURAL THEORY 5.9
L  20R R 
 12 (5.2) 1 2
where R1  1.2  0.001At but not less than 0.6 or more than 1.0
At  tributary area, ft2, for structural member being designed
R2  1.2  0.05r but not less than 0.6 or more than 1.0
r  rise of roof in 12 in for a pitched roof or 32 times the ratio of rise to
span for an arch or dome
This minimum live load need not be combined with snow load for design of a roof
but should be designed for the larger of the two.
Subgrade Pressures. Walls below grade should be designed for lateral soil pressures
and the hydrostatic pressure of subgrade water, plus the load from surcharges
at ground level. Design pressures should take into account the reduced weight of
soil because of buoyancy when water is present. In design of floors at or below
grade, uplift due to hydrostatic pressures on the underside should be considered.
Wind Loads. Horizontal pressures produced by wind are assumed to act normal
to the faces of buildings for design purposes and may be directed toward the interior
of the buildings or outward (Arts. 3.2.1 and 3.2.2). These forces are called velocity
pressures because they are primarily a function of the velocity of the wind striking
the buildings. Building codes usually permit wind pressures to be either calculated
or determined by tests on models of buildings and terrain if the tests meet specified
requirements (see Art. 3.2.2). Codes also specify procedures for calculating wind
loads, such as the following:
Velocity pressures due to wind to be used in building design vary with type of
terrain, distance above ground level, importance of building, likelihood of hurricanes,
and basic wind speed recorded near the building site. The wind pressures
are assumed to act normal to the building facades.
The basic wind speed used in design is the fastest-mile wind speed recorded at
a height of 10 m (32.8 ft) above open, level terrain with a 50-year mean recurrence
interval.
Unusual wind conditions often occur over rough terrain and around ocean promontories.
Basic wind speeds applicable to such regions should be selected with the
aid of meteorologists and the application of extreme-value statistical analysis to
anemometer readings taken at or near the site of the proposed building. Generally,
however, minimum basic wind velocities are specified in local building codes and
in national model building codes but should be used with discretion, because actual
velocities at a specific sites and on a specific building may be significantly larger.
In the absence of code specifications and reliable data, basic wind speed at a height
of 10 m above grade may be approximated for preliminary design from the following:
Coastal areas, northwestern and southeastern
United States and mountainous area 110 mph
Northern and central United States 90 mph
Other parts of the contiguous states 80 mph
For design purposes, wind pressures should be determined in accordance with
the degree to which terrain surrounding the proposed building exposes it to the
wind. Exposures may be classified as follows:
5.10 SECTION FIVE
Exposure A applies to centers of large cities, where for at least one-half mile
upwind from the building the majority of structures are over 70 ft high and lower
buildings extend at least one more mile upwind.
Exposure B applies to wooded or suburban terrain or to urban areas with closely
spaced buildings mostly less than 70 ft high, where such conditions prevail upwind
for a distance from the building of at least 1500 ft or 10 times the building height.
Exposure C exists for flat, open country or exposed terrain with obstructions
less than 30 ft high.
Exposure D applies to flat unobstructed areas exposed to wind blowing over a
large expanse of water with a shoreline at a distance from the building or not more
than 1500 ft or 10 times the building height.
For design purposes also, the following formulas may be used to determine, for
heights z (in feet) greater than 15 ft above ground, a pressure coefficient K for
converting wind speeds to pressures.
For Exposure A, for heights up to 1500 ft above ground level,
2 / 3 z
K  0.000517 (5.3) 
  32.8
For z less than 15 ft, K  0.00031.
For Exposure B, for heights up to 1200 ft above ground level,
4 / 9 z
K  0.00133 (5.4) 
  32.8
For z less than 15 ft, K  0.00095.
For Exposure C, for heights up to 900 ft above ground level,
2 / 7 z
K  0.00256 (5.5) 
  32.8
For z less than 15 ft, K  0.0020.
For Exposure D, for heights up to 700 ft above ground level,
1 / 5 z
K  0.00357 (5.6) 
  32.8
For z less than 15 ft, K  0.0031.
For ordinary buildings not subject to hurricanes, the velocity pressure qz, psf, at
height z may be calculated from
2 q  KV (5.7) z
where V  basic wind speed, mi/hr, but not less than 70 mi/hr.
For important buildings, such as hospitals and communication buildings, for
buildings sensitive to wind, such as slender skyscrapers, and for buildings presenting
a high degree of hazard to life and property, such as auditoriums, qz computed
from Eq. (5.7) should be increased 15%.
To allow for hurricanes, qz should be increased 10% for ordinary buildings and
20% for important, wind-sensitive or high-risk buildings along coastlines. These
increases may be assumed to reduce uniformly with distance from the shore to zero
for ordinary buildings and 15% for the more important or sensitive buildings at
points 100 mi inland.
STRUCTURAL THEORY 5.11
Wind pressures on low buildings are different at a specific elevation from those
on tall buildings. Hence, building codes may give different formulas for pressures
for the two types of construction. In any case, however, design wind pressure should
be a minimum of 10 psf.
Multistory Buildings. For design of the main wind-force resisting system of ordinary,
rectangular, multistory buildings, the design pressure at any height z, ft,
above ground may be computed from
p  G C q (5.8) zw o pw z
where pzw  design wind pressure, psf, on windward wall
Go  gust response factor
Cpw  external pressure coefficient
qz  velocity pressure computed from Eq. (5.7) and modified for hurricanes
and building importance, risks, and wind sensitivity
For windward walls, Cpw may be taken as 0.8. For side walls, Cpw may be assumed
as 0.7 (suction). For roofs and leeward walls, the design pressure at elevation z
is
p  G C q (5.9) zl o p h
where pzl  design pressure, psf, on roof or leeward wall
Cp  external pressure coefficient for roof or leeward wall
qh  velocity pressure at mean roof height h (see Fig. 3.1d)
In these equations, the gust response factor may be taken approximately as
8.58D
G  0.65  
 1 (5.10) o n (h/30)
where D  0.16 for Exposure A, 0.10 for Exposure B, 0.07 for Exposure C, and
0.05 for Exposure D
n  1?3 for Exposure A, 2?9 for Exposure B, 1?7 for Exposure C, and 0.1 for
Exposure D
h  mean roof height, ft
For leeward walls, subjected to suction, Cp depends on the ratio of the depth d
to width b of the building and may be assumed as follows:
d/b  1 or less 2 4 or more
C  0.5 0.3 0.2 p
The negative sign indicates suction. Table 5.3 lists values of Cp for pressures on
roofs.
Flexible Buildings. These are structures with a fundamental natural frequency
less than 1 Hz or with a ratio of height to least horizontal dimension (measured at
mid-height for buildings with tapers or setbacks) exceeding 5. For such buildings,
the main wind-force resisting system should be designed for a pressure on windward
walls at any height z, ft, above ground computed from
5.12 SECTION FIVE
TABLE 5.3 External Pressure Coefficients Cp for Roofs*
Flat roofs 0.7
Wind parallel to ridge of sloping roof
h/b or h/d  2.5 0.7
h/b or h/.d  2.5 0.8
Wind perpendicular to ridge of sloping roof, at angle  with horizontal
Leeward side 0.7
Windward side
h/ s
Slope of roof , deg
10 20 30 40 50 60 or more
0.3 or less 0.2 0.2 0.3 0.4 0.5
0.5 0.9 0.75 0.2 0.3 0.5 0.01 
1.0 0.9 0.75 0.2 0.3 0.5
1.5 or more 0.9 0.9 0.9 0.35 0.21
* h  height of building, ft: d  depth, ft, of building in direction of wind: b  width, ft, of building
transverse to wind.
Based on data in ANSI A58.1-1981.
p  G C q (5.11) zw ? pw z
where G  gust response factor determined by analysis of the system taking into ?
account its dynamic properties. For leeward walls of flexible buildings,
p  G C q (5.12) zl ? p h
Requiring a knowledge of the fundamental frequency, structural damping characteristics,
and type of exposure of the building, the formula for G is complicated, ?
but computations may be simplified somewhat by use of tables and charts in the
ASCE 7-98 standard.
One-Story Buildings. For design of the main wind-force resisting system of rectangular,
one-story buildings, the design pressure at any height z, ft, above ground
may be computed for windward walls from
p  (G C  C )q (5.13) zw o p pI z
where Cp1  0.75 is the percentage of openings in one wall exceeds that of other
walls by 10% or more
 0.25 for all other cases
For roofs and leeward walls, the design pressure at elevation z is
p  G C q  C q (5.14) zl o p h p2 z
where Cp2  0.75 or 0.25 if the percentage of openings in one wall exceeds
that of other walls by 10% or more
 
0.25 for all other cases
(Positive signs indicate pressures acting toward a wall; negative signs indicate pressures
acting away from the wall.)
STRUCTURAL THEORY 5.13
In ASCE-7-95 and 98, the basic wind speed changed from fast mile wind to 3-
second gust wind speed in miles per hour. The wind speed values on the basic
wind speed map has changed. This change should not have any big impact on the
wind pressure. However, confusion is easily created because all the major building
codes including the IBC 2000 are still using old basic wind speed map based on
fast mile wind, and they repeatedly refer to ASCE-7 95 or 98. It is to be noted that
the reference from the building codes to the ASCE-7 are either adoption of ASCE-
7 as an alternative approach or for certain factors that are not related to the basic
wind pressure.
In ASCE-7-95 and 98, new factors such as wind directionality factor, topographic
factor were introduced, and gust effect factors were updated for rigid structures
as well as for flexible /dynamically sensitive structures. The calculation became
much more complicated than the approach in this book and the results should
be more accurate. We suggest that for complicated structures it is necessary to use
ASCE-7-98 method to check the results.
Snow, Ice, and Rain Loads. These, in effect, are nonuniformly distributed, vertical,
live loads that are imposed by nature and hence are generally uncertain in
magnitude and duration. They may occur alone or in combination. Design snow
loads preferably should be determined for the site of the proposed building with
the advice of meteorologists and application of extreme-value statistical analysis to
rain and snow records for the locality.
Rain loads depend on drainage and may become large enough to cause roof
failure when drainage is blocked (see Art. 3.4.3).
Ice loads are created when snow melts, then freezes, or when rain follows a
snow storm and freezes. These loads should be considered in determining the design
snow load. Snow loads may consist of pure snow or a mixture of snow, ice, and
water.
Design snow loads on roofs may be assumed to be proportional to the maximum
ground snow load pg, lb/ft2, measured in the vicinity of the building with a 50-
year mean recurrence interval. Determination of the constant of proportionality
should take into account:
1. Appropriate mean recurrence interval.
2. Roof exposure. Wind may blow snow off the roof or onto the roof from nearby
higher roofs or create nonuniform distribution of snow.
3. Roof thermal conditions. Heat escaping through the roof melts the snow. If the
water can drain off, the snow load decreases. Also, for sloped roofs, if they are
warm, there is a tendency for snow to slide off. Insulated roofs, however, restrict
heat loss from the interior and therefore are subjected to larger snow loads.
4. Type of occupancy and uses of building. More conservative loading should be
used for public-assembly buildings, because of the risk of great loss of life and
injury to occupants if overloads should cause the roof to collapse.
5. Roof slope. The steeper a roof, the greater is the likelihood of good drainage
and that show will slide off.
In addition, roof design should take into account not only the design snow load
uniformly distributed over the whole roof area but also possible unbalanced loading.
Snow may be blown off part of the roof, and snow drifts may pile up over a portion
of the roof.
5.14 SECTION FIVE
For flat roofs, in the absence of building-code requirements, the basic snow load
when the ground snow load pg is 20 lb / ft2 or less may be taken as
P  p (5.15) min g
When pg is between 20 and 25 lb / ft2, the minimum allowable design load is pmin 
20 lb / ft2, and when pg exceeds 25 lb / ft2, the basic snow load may be taken as
p  0.8p (5.16) ? g
where p?  design snow load, lb / ft2, for a flat roof that may have unheated space
underneath and that may be located where the wind cannot be relied
on to blow snow off, because of nearby higher structures or trees
pg  ground snow load, lb / ft2
For roofs sheltered from the wind, increase p? computed from Eq. (5.16) by 20%,
and for windy sites, reduce p? 10%. For a poorly insulated roof with heated space
underneath, decrease p? by 30%.
Increase p? 10% for large office buildings and public-assembly buildings, such
as auditoriums, schools, factories. Increase p? 20% for essential buildings, such as
hospitals, communication buildings, police and fire stations, power plants, and for
structures housing expensive objects or equipment. Decrease p.? 20% for structures
with low human occupancy, such as farm buildings.
The ground snow load pg should be determined from an analysis of snow depths
recorded at or near the site of the proposed building. For a rough estimate in the
absence of building-code requirements, pg may be taken as follows for the United
States, except for mountainous regions:
0–5 lb/ ft2—southern states from about latitude N32 southward
10–15 lb/ ft2—Pacific coast between latitudes N32 and N40 and other states
between latitudes N32 and N37
20–30 lb/ ft2—Pacific coast from latitude N40 northward and other states between
latitudes N37 and N40
40–50 lb/ ft2—north Atlantic and central states between latitudes N40 and N43
60–80 lb/ ft2—northern New England between latitudes N43 and N45 and central
states from N43 northward
80–120 lb / ft2—Maine above latitude N45
For sloping roofs, the snow load depends on whether the roof will be warm or
cold. In either case, the load may be assumed to be zero for roofs making an angle
 of 70 or more with the horizontal. Also, for any slope, the load need not be
taken greater than p? given by Eq. (5.16). For slopes , deg, between 0 and 70,
the snow load, lb / ft2, acting vertically on the projection of the roof on a horizontal
plane, may be computed for warm roofs from
70  
p  p  p (5.17) 
  s ? ? 40
and for cold roofs from
70  
p  p  p (5.18) 
  s ? ? 25
Hip and gable roofs should be designed for the condition of the whole roof
STRUCTURAL THEORY 5.15
loaded with ps, and also with the windward wide unloaded and the leeward side
carrying 1.5ps.
For curved roofs, the snow load on the portion that is steeper than 70p may
be taken as zero. For the less-steep portion, the load ps may be computed as for a
sloped roof, with  taken as the angle with the horizontal of a line from the crown
to points on the roof where the slope starts to exceed 70. Curved roofs should be
designed with the whole area fully loaded with ps. They also should be designed
for the case of snow only on the leeward side, with the load varying uniformly
from 0.5ps at the crown to 2ps at points where the roof slope starts to exceed 30
and then decreasing to zero at points where the slope starts to exceed 70.
Multiple folded-plate, sawtooth, and barrel-vault roofs similarly should be
designed for unbalanced loads increasing from 0.5ps at ridges to 3ps in valleys.
Snow drifts may form on a roof near a higher roof that is less than 20 ft
horizontally away. The reason for this is that wind may blow snow from the higher
roof onto the lower roof. Drifts also may accumulate at projections above roofs,
such as at parapets, solar collectors, and penthouse walls. Drift loads accordingly
should be taken into account when:
1. The ground snow load pg exceeds 10 lb / ft2.
2. A higher roof exists (or may be built in the future) within 20 ft of the building,
if the height differential, ft, exceeds 1.2p? / , where p? is computed from Eq.
(5.16) and  is the snow density, lb/ ft3.
3. A projection extends a distance, ft, exceeding 1.2p? /  above the roof and is
more than 15 ft long.
In computation of drift loads, the snow density , lb/ft3, may be taken as follows:
p  11–30 31–60 60 or more g
 15 20 25
The drift may be assumed to be a triangular prism with maximum height, located
adjacent to a higher roof or along a projection, taken as hd  2pg / , modified by
factors for risk and exposure, described for flat roofs. Width of the prism should
be at least 10 ft and may be taken as 3hd for projections up to 50 ft long and as
4hd for projections more than 50 ft long. Accordingly, the load varies uniformly
with distance from a projection, from hd  at the projection to zero. For drifts due
to snow load from a higher roof at a horizontal distance S, fit, away horizontally
(S  20 ft), the maximum drift intensity may be taken as hd (20  S) / 20.
Rain-Snow Load Combination. In roof design, account should be taken of the
combination of the design snow load with a temporary water load from an intense
rainstorm, including the effects of roof deflection on ponding. The added water load
depends on the drainage characteristics of the roof, which, in turn, depend on the
roof slope. For a flat roof, the rain surcharge may be taken as 8 lb/ ft2 for slopes
less 1?4 in / ft and as 5 lb/ ft2 for steeper slopes, except where the minimum allowable
design snow load p exceeds p computed from Eq. (5.16). In such cases, these min ?
water surcharges may be reduced by p  p . min ?
(W. Tobiasson and R. Redfield, ‘‘Snow Loads for the United States,’’ Part II,
and S. C. Colbeck, ‘‘Snow Loads Resulting from Rain on Snow,’’ U.S. Army Cold
Regions Research and Engineering Laboratory, Hanover, N.H.)
5.16 SECTION FIVE
Seismic Loads. These are the result of horizontal and vertical movements imposed
on a building by earth vibrations during an earthquake. Changing accelerations of
the building mass during the temblor create changing inertial forces. These are
assumed in building design to act as seismic loads at the various floor and roof
levels in proportion to the portion of the building mass at those levels. Because
analysis of building response to such dynamic loading generally is very complex,
building codes permit, for design of ordinary buildings, substitution of equivalent
static loading for the dynamic loading (see Art. 5.18.6).
(‘‘Minimum Design Loads for Buildings and Other Structures,’’ ASCE 7-98,
American Society of Civil Engineers, 345 E. 47th St., New York, NY 10164-0619;
‘‘International Building Code 2000,’’ 1998.)
5.1.3 Factored Loads
Structural members must be designed with sufficient capacity to sustain without
excessive deformation or failure those combinations of service loads that will produce
the most unfavorable effects. Also, the effects of such conditions as ponding
of water on roofs, saturation of soils, settlement, and dimensional changes must be
included. In determination of the structural capacity of a member or structure, a
safety margin must be provided and the possibility of variations of material properties
from assumed design values and of inexactness of capacity calculations must
be taken into account.
Building codes may permit either of two methods, allowable-stress design or
load–and–resistance factor design (also known as ultimate-strength design), to be
used for a structural material. In both methods, design loads, which determine the
required structural capacity, are calculated by multiplying combinations of service
loads by factors. Different factors are applied to the various possible load combinations
in accordance with the probability of occurrence of the loads.
In allowable-stress design, required capacity is usually determined by the load
combination that causes severe cracking or excessive deformation. For the purpose,
dead, live, wind, seismic, snow, and other loads that may be imposed simultaneously
are added together, then multiplied by a factor equal to or less than 1. Load
combinations usually considered in allowable-stress design are
(1) D  L  (Lr or S or R)
(2) D  L  (W or E/ 1.4)
(3) D  L  W  S/2
(4) D  L  S  W/2
(5) D  L  S  E/ 1.4
(6) 0.9D  E/ 1.4
where D  dead load
L  live loads due to intended use of occupancy, including partitions
Lr  roof live loads
S  snow loads
R  rain loads
W  wind loads
E  seismic loads
STRUCTURAL THEORY 5.17
Building codes usually permit a smaller factor when the probability is small that
combinations of extreme loads, such as dead load plus maximum live load plus
maximum wind or seismic forces, will occur. Generally, for example, a factor of
0.75 is applied to load-combination sums (2) to (6). Such factors are equivalent to
permitting higher allowable unit stresses for the applicable loading conditions than
for load combination (1). The allowable stress is obtained by dividing the unit stress
causing excessive deformation or failure by a factor greater than 1.
In load–and–resistance factor design, the various types of loads are each multiplied
by a load factor, the value of which is selected in accordance with the
probability of occurrence of each type of load. The factored loads are then added
to obtain the total load a member or system must sustain. A structural member is
selected to provide a load-carrying capacity exceeding that sum. This capacity is
determined by multiplying the ultimate-load capacity by a resistance factor, the
value of which reflects the reliability of the estimate of capacity. Load criteria
generally used are as follows:
1. 1.4D
2. 1.2D  1.6L  0.5(Lr or S or R)
3. 1.2D  1.6(Lr or S or R)  (0.5L or 0.8W)
4. 1.2D  1.3W  0.5 (Lr or S or R)
5. 1.2D  1.0E  (0.5L or 0.2S)
6. 0.9D 
 (1.3W or 1.0E)
For garages, places of public assembly, and areas for which live loads exceed 100
lb/ft2, the load factor usually is taken as unit for L in combinations 3, 4, and 5.
For roof configurations that do not shed snow off the structure, the load factor
should be taken as 0.7 for snow loads in combination 5.
For concrete structures where load combinations do not include seismic forces,
the factored load combinations of ACI 318 Section 9.2 shall be used.
For both allowable stress design and strength design methods, elements and
components shall be designed to resist the forces due to special seismic load combinations
a) 1.2D  0.5L  Em
b) 0.9D  Em
For floors in places of public assembly, for live load in excess of 100 psf, and for
parking garage live load, the load factor is taken as 1.0 for L. Em is the maximum
seismic effect of horizontal and vertical forces.
5.2 STRESS AND STRAIN
Structural capacity, or ultimate strength, is that property of a structural member that
serves as a measure of is ability to support all potential loads without severe cracking
or excessive deformations. To indicate when the limit on load-carrying usefulness
has been reached, design specifications for the various structural materials
establish allowable unit stresses or design strengths that may not be exceeded under
5.18 SECTION FIVE
FIGURE 5.1 Truss in equilibrium under load.
Upward acting forces equal those acting downward.
FIGURE 5.2 Portion of a truss is held in equilibrium
by stresses in its components.
maximum loading. Structural theory provides methods for calculating unit stresses
and for estimating deformations. Many of these methods are presented in the rest
of this section.
5.2.1 Static Equilibrium
If a structure and its components are so supported that, after a very small deformation
occurs, no further motion is possible, they are said to be in equilibrium.
Under such circumstances, internal forces, or stresses, exactly counteract the loads.
Several useful conclusions may be drawn from the state of static equilibrium:
Since there is no translatory motion, the sum of the external forces must be zero;
and since there is no rotation, the sum of the moments of the external forces about
any point must be zero.
For the same reason, if we consider any portion of the structure and the loads
on it, the sum of the external and internal forces on the boundaries of that section
must be zero. Also, the sum of the moments of these forces must be zero.
In Fig. 5.1, for example, the sum of the forces RL and RR needed to support the
roof truss is equal to be the 20-kip load on the truss (1 kip  1 kilopound  1000
lb  0.5 ton). Also, the sum of moments of the external forces is zero about any
point. About the right end, for instance, it is 40 
 15  30 
 20  600  600.
In Fig. 5.2 is shown the portion of the truss to the left of section AA. The internal
forces at the cut members balance the external load and hold this piece of the truss
in equilibrium.
Generally, it is convenient to decompose the forces acting on a structure into
components parallel to a set of perpendicular axes that will simplify computations.
For example, for forces in a single plane—a condition commonly encountered in
building design—the most useful technique is to resolve all forces into horizontal
and vertical components. Then, for a structure in equilibrium, if H represents the
horizontal components, V the vertical components, and M the moments of the components
about any point in the plane,
H  0 V  0 and M  0 (5.19)
These three equations may be used to evaluate three unknowns in any nonconcurrent
coplanar force system, such as the roof truss in Figs. 5.1 and 5.2. They
may determine the magnitude of three forces for which the direction and point of
application already are known, or the magnitude, direction, and point of application
of a single force.
STRUCTURAL THEORY 5.19
Suppose, for the truss in Fig. 5.1, the reactions at the supports are to be computed.
Taking moments about the right end and equating to zero yields 40 Rl  30

 20  0, from which left reaction RL  600/40  15 kips. Equating the sum of
the vertical forces to zero gives 20  15  RR  0, from which the right reaction
RR  5 kips.
5.2.2 Unit Stress and Strain
To ascertain whether a structural member has adequate load-carrying capacity, the
designer generally has to compute the maximum unit stress produced by design
loads in the member for each type of internal force—tensile, compressive, or shearing—
and compare it with the corresponding allowable unit stress.
When the loading is such that the unit stress is constant over a section under
consideration, the stress may be obtained by dividing the force by the area of the
section. But in general, the unit stress varies from point to point. In that case, the
unit stress at any point in the section is the limiting value of the ratio of the internal
force on any small area to that area, as the area is taken smaller and smaller.
Sometimes in the design of a structure, unit stress may not be the prime consideration.
The designer may be more interested in limiting the deformation or
strain.
Deformation in any direction is the total change in the dimension of a member
in that direction.
Unit strain in any direction is the deformation per unit of length in that direction.
When the loading is such that the unit strain is constant over a portion of a
member, it may be obtained by dividing the deformation by the original length of
that portion. In general, however, the unit strain varies from point to point in a
member. Like a varying unit stress, it represents the limiting value of a ratio.
5.2.3 Hooke’s Law
For many materials, unit strain is proportional to unit stress, until a certain stress,
the proportional limit, is exceeded. Known as Hooke’s law, this relationship may
be written as
?
?  E  or  (5.20)
E
where ?  unit stress
 unit strain
E  modulus of elasticity
Hence, when the unit stress and modulus of elasticity of a material are known, the
unit strain can be computed. Conversely, when the unit strain has been found, the
unit stress can be calculated.
When a member is loaded and the unit stress does ot exceed the proportional
limit, the member will return to its original dimensions when the load is removed.
The elastic limit is the largest unit stress that can be developed without a permanent
deformation remaining after removal of the load.
Some materials possess one or two yield points. These are unit stresses in the
region of which there appears to be an increase in strain with no increase or a small
5.20 SECTION FIVE
FIGURE 5.5 Bracket in shear. FIGURE 5.6 Bearing load and pressure.
FIGURE 5.3 Tension member. FIGURE 5.4 Compression member.
decrease in stress. Thus, the materials exhibit plastic deformation. For materials
that do not have a well-defined yield point, the offset yield strength is used as a
measure of the beginning of plastic deformation.
The offset yield strength, or proof stress as it is sometimes referred to, is
defined as the unit stress corresponding to a permanent deformation, usually 0.01%
(0.0001 in / in) or 0.20% (0.002 in / in).
5.2.4 Constant Unit Stress
The simplest cases of stress and strain are those in which the unit stress and strain
are constant. Stresses due to an axial tension or compression load or a centrally
applied shearing force are examples; also an evenly applied bearing load. These
loading conditions are illustrated in Figs. 5.3 to 5.6.
For the axial tension and compression loadings, we take a section normal to the
centroidal axis (and to the applied forces). For the shearing load, the section is
taken along a plane of sliding. And for the bearing load, it is chosen through the
plane of contact between the two members.
STRUCTURAL THEORY 5.21
Since for these loading conditions, the unit stress is constant across the section,
the equation of equilibrium may be written
P  A? (5.21)
where P  load
?  a tensile, compressive, shearing, or bearing unit stress
A  cross-sectional area for tensile or compressive forces, or area on which
sliding may occur for shearing forces, or contact area for bearing loads
For torsional stresses, see Art. 5.4.2.
The unit strain for the axial tensile and compressive loads is given by the equation
e
 (5.22)
L
where  unit strain
e  total lengthening or shortening of the member
L  original length of the member
Applying Hooke’s law and Eq. (5.22) to Eq. (5.21) yield a convenient formula for
the deformation:
PL
e  (5.23)
AE
where P  load on the member
A  its cross-sectional area
E  modulus of elasticity of the material
[Since long compression members tend to buckle, Eqs. (5.21) to (5.23) are applicable
only to short members.]
While tension and compression strains represent a simple stretching or shortening
of a member, shearing strain represents a distortion due to a small rotation.
The load on the small rectangular portion of the member in Fig. 5.5 tends to distort
it into a parallelogram. The unit shearing strain is the change in the right angle,
measured in radians.
Modulus of rigidity, or shearing modulus of elasticity, is defined by
v
G  (5.24)

where G  modulus of rigidity
v  unit shearing stress
 unit shearing strain
It is related to the modulus of elasticity in tension and compression E by the
equation
E
G  (5.25)
2 (1  	)
where 	 is a constant known as Poisson’s ratio.
5.22 SECTION FIVE
5.2.5 Poisson’s Ratio
Within the elastic limit, when a material is subjected to axial loads, it deforms not
only longitudinally but also laterally. Under tension, the cross section of a member
decreases, and under compression, it increases. The ratio of the unit lateral strain
to the unit longitudinal strain is called Poisson’s ratio.
For many materials, this ratio can be taken equal to 0.25. For structural steel, it
is usually assumed to be 0.3.
Assume, for example, that a steel hanger with an area of 2 in2 carries a 40-kip
(40,000-lb) load. The unit stress is 40,000/2, or 20,000 psi. The unit tensile strain,
taking the modulus of elasticity of the steel as 30,000,000 psi, is 20,000/
30,000,000, or 0.00067 in / in. With Poisson’s ratio as 0.3, the unit lateral strain is
0.3 
 0.00067, or a shortening of 0.00020 in / in.
5.2.6 Thermal Stresses
When the temperature of a body changes, its dimensions also change. Forces are
required to prevent such dimensional changes, and stresses are set up in the body
by these forces.
If  is the coefficient of expansion of the material and T the change in temperature,
the unit strain in a bar restrained by external forces from expanding or contracting
is
 T (5.26)
According to Hooke’s law, the stress ? in the bar is
?  E T (5.27)
where E  modulus of elasticity.
5.2.7 Strain Energy
When a bar is stressed, energy is stored in it. If a bar supporting a load P undergoes
a deformation e the energy stored in it is
1 U  ?2Pe (5.28)
This equation assumes the load was applied gradually and the bar is not stressed
beyond the proportional limit. It represents the area under the load-deformation
curve up to the load P. Applying Eqs. (5.20) and (5.21) to Eq. (5.28) gives another
useful equation for energy:
2 ?
U  AL (5.29)
2E
where ?  unit stress
E  modulus of elasticity of the material
A  cross-sectional area
L  length of the bar
STRUCTURAL THEORY 5.23
Since AL is the volume of the bar, the term ?2/2E indicates the energy stored
per unit of volume. It represents the area under the stress-strain curve up to the
stress ?. Its value when the bar is stressed to the proportional limit is called the
modulus of resilience. This modulus is a measure of the capacity of the material
to absorb energy without danger of being permanently deformed and is of importance
in designing members to resist energy loads.
Equation (5.28) is a general equation that holds true when the principle of superposition
applies (the total deformation produced by a system of forces is equal
to the sum of the elongations produced by each force). In the general sense, P in
Eq. (5.28) represents any group of statically interdependent forces that can be completely
defined by one symbol, and e is the corresponding deformation.
The strain-energy equation can be written as a function of either the load or the
deformation.
For axial tension or compression:
2 2 P L AEe
U  U  (5.30)
2AE 2L
where P  axial load
e  total elongation not shortening
L  length of the member
A  cross-sectional area
E  modulus of elasticity
For pure shear:
2 2 V L AGe
U  U  (5.31)
2AG 2L
where V  shearing load
e  shearing deformation
L  length over which deformation takes place
A  shearing area
G  shearing modulus
For torsion:
2 2 T L JG	
U  U  (5.32)
2JG 2L
where T  torque
	 angle of twist
L  length of shaft
J  polar moment of inertia of the cross section
G  shearing modulus
For pure bending (constant moment):
2 2 M L EI
U  U  (5.33)
2EI 2L
5.24 SECTION FIVE
where M  bending moment
 angle of rotation of one end of the beam with respect to the other
L  length of beam
I  moment of inertia of the cross section
E  modulus of elasticity
For beams carrying transverse loads, the strain energy is the sum of the energy for
bending and that for shear.
See also Art. 5.10.4.
5.3 STRESSES AT A POINT
Tensile and compressive stresses are sometimes referred to also as normal stresses,
because they act normal to the cross section. Under this concept, tensile stresses
are considered as positive normal stresses and compressive stresses as negative.
5.3.1 Stress Notation
Suppose a member of a structure is acted upon by forces in all directions. For
convenience, let us establish a reference set of perpendicular coordinate x, y, and
z axes. Now let us take at some point in the member a small cube with sides parallel
to the coordinate axes. The notations commonly used for the components of stress
acting on the sides of this element and the directions assumed as positive are shown
in Fig. 5.7.
For example, for the sides of the element perpendicular to the z axis, the normal
component of stress is denoted by ?z. The shearing stress v is resolved into two
components and requires two subscript letters for a complete description. The first
letter indicates the direction of the normal to the plane under consideration. The
second letter indicates the direction of the component of the stress. For the sides
perpendicular to the z axis, the shear component in the x direction is labeled vzx
and that in the y direction vzy.
5.3.2 Stress and Strain Components
If, for the small cube in Fig. 5.7, moments of the forces acting on it are taken a
bout the x axis, considering the cube’s dimensions as dx, dy, and dz, the equation
of equilibrium requires that
v dx dy dz  v dx dy dz zy yz
(Forces are taken equal to the product of the area of the face and the stress at the
center.) Two similar equations can be written for moments taken about the y axis
and z axis. These equations show that
STRUCTURAL THEORY 5.25
v v v  v and v  v (5.34) xy yx zx xz zy yx
FIGURE 5.7 Normal and shear stresses in an
orthogonal coordinate system.
In words, the components of shearing
stress on two perpendicular faces and
acting normal to the intersection of the
faces are equal.
Consequently, to describe the
stresses acting on the coordinate planes
through a point, only six quantities need
be known. These stress components are
?x, ?y, ?z vxy  vyx, vyz  vzy, and vzx 
vxz.
If the cube in Fig. 5.7 is acted on
only by normal stresses ?x, ?y , and ?z,
from Hooke’s law and the application of
Poisson’s ratio, the unit strains in the x,
y, and z directions, in accordance with
Arts. 5.2.3 and 5.2.4, are, respectively,
1
  [?  	(?  ? )] x x y z E
1
  [?  	(?  ? )] (5.35) y y x z E
1
  [?  	(?  ? )] z z x y E
where 	  Poisson’s ratio. If only shearing stresses act on the cube in Fig. 5.7,
the distortion of the angle between edges parallel to any two coordinate axes depends
only on shearing-stress components parallel to those axes. Thus, the unit
shearing strains are (see Art. 5.2.4)
1 1 1
  v   v and   v (5.36) xy xy yz yx zx zx G G G
FIGURE 5.8 Normal and shear stresses at a
point on a plane inclined to the axes.
5.3.3 Two-Dimensional Stress
When the six components of stress necessary
to describe the stresses at a point
are known (Art. 5.3.2), the stress on any
inclined plane through the same point
can be determined. For the case of twodimensional
stress, only three stress
components need be known.
Assume, for example, that at a point
O in a stressed plate, the components ?x,
?y , and vxy are known (Fig. 5.8). To find
the stresses for any plane through the z
axis, take a plane parallel to it close to
5.26 SECTION FIVE
O. This plane and the coordinate planes from a triangular prism. Then, if  is the
angle the normal to the plane makes with the x axis, the normal and shearing
stresses on the inclined plane, obtained by application of the equations of equilibrium,
are
2 2 ?  ? cos  ? sin  2v sin  cos  (5.37) x y xy
2 2 v  v (cos  sin )  (?  ? ) sin  cos  (5.38) xy y x
Note. All structural members are three-dimensional. While two-dimensionalstress
calculations may be sufficiently accurate for most practical purposes, this is
not always the case. For example, although loads may create normal stresses on
two perpendicular planes, a third normal stress also exists, as computed with Poisson’s
ratio. [See Eq. (5.35).]
5.3.4 Principal Stresses
A plane through a point on which stresses act may be assigned a direction for
which the normal stress is a maximum or a minimum. There are two such positions,
perpendicular to each other. And on those planes, there are no shearing stresses.
The direction in which the normal stresses become maximum or minimum are
called principal directions and the corresponding normal stresses principal stresses.
To find the principal directions, set the value of v given by Eq. (5.38) equal to
zero. The resulting equation is
2vxy tan 2  (5.39)
?  ? x y
If the x and y axes are taken in the principal directions, vxy is zero. Consequently,
Eqs. (5.37) and (5.38) may be simplified to
2 2 ?  ? cos  ? sin  (5.40) x y
1 v  ?2 sin 2 (?  ? ) (5.41) y x
where ? and v are, respectively, the normal and sharing stress on a plane at an
angle  with the principal planes and ?x and ?y are the principal stresses.
Pure Shear. If on any two perpendicular planes only shearing stresses act, the
state of stress at the point is called pure shear or simple shear. Under such conditions,
the principal directions bisect the angles between the planes on which these
shearing stresses occur. The principal stresses are equal in magnitude to the unit
shearing stresses.
5.3.5 Maximum Shearing Stress
The maximum unit shearing stress occurs on each of two planes that bisect the
angles between the planes on which the principal stresses act. The maximum share
is equal to one-half the algebraic difference of the principal stresses:
STRUCTURAL THEORY 5.27
FIGURE 5.9 Mohr’s circle for stresses at a
point—constructed from known principal
stresses.
FIGURE 5.10 Stress circle constructed from
two known positive stresses ?x and ?y and a
shear stress vxy.
?  ? 1 2 max v  (5.42)
2
where ?1 is the maximum principal stress and ?2 the minimum.
5.3.6 Mohr’s Circle
The relationship between stresses at a point may be represented conveniently on
Mohr’s circle (Fig. 5.9). In this diagram, normal stress ? and shear stress v are
taken as coordinates. Then, for each plane through the point, there will correspond
a point on the circle, whose coordinates are the values of ? and v for the plane.
To construct the circle given the principal stresses, mark off the principal stresses
?1 and ?2 on the ? axis (points A and B in Fig. 5.9). Tensile stresses are measured
to the right of the v axis and compressive stresses to the left. Construct a circle
with its center on the ? axis and passing through the two points representing the
principal stresses. This is the Mohr’s circle for the given stresses at the point under
consideration.
Suppose now, we wish to find the stresses on a plane at an angle  to the plane
of ?1. If a radius is drawn making an angle 2  with the ? axis, the coordinates of
its intersection with the circle represent the normal and sharing stresses acting on
the plane.
Mohr’s circle an also be plotted when the principal stresses are not known but
the stresses ?x, ?y , and vxy , on any two perpendicular planes, are. The procedure is
to plot the two points representing these known stresses with respect to the ? and
v axies (points C and D in Fig. 5.10). The line joining these points is a diameter
5.28 SECTION FIVE
of Mohr’s circle. Constructing the circle on this diameter, we find the principal
stresses at the intersection with the ? axis (points A and B in Fig. 5.10).
For more details on the relationship of stresses and strains at a point, see
Timoshenko and Goodier, ‘‘Theory of Elasticity,’’ McGraw-Hill Publishing Company,
New York.
5.4 TORSION
Forces that cause a member to twist about a longitudinal axis are called torsional
loads. Simple torsion is produced only by a couple, or moment, in a plane perpendicular
to the axis.
If a couple lies in a nonperpendicular plane, it can be resolved into a torsional
moment, in a plane perpendicular to the axis, and bending moments, in planes
through the axis.
5.4.1 Shear Center
The point in each normal section of a member through which the axis passes and
about which the section twists is called the share center. The location of the shear
center depends on the shape and dimensions of the cross section. If the loads on a
beam do not pass through the shear center, they cause the beam to twist. See also
Art. 5.5.19.
If a beam has an axis of symmetry, the shear center lies on it. In doubly symmetrical
beams, the share center lies at the intersection of the two axes of symmetry
and hence coincides with the centroid.
For any section composed of two narrow rectangles, such as a T beam or an
angle, the shear center may be taken as the intersection of the longitudinal center
lines of the rectangles.
For a channel section with one axis of symmetry, the shear center is outside the
section at a distance from the centroid equal to e(1  h2A/4I ), where e is the
distance from the centroid to the center of the web, h is the depth of the channel,
A the cross-sectional area, and I the moment of inertia about the axis of symmetry.
(The web lies between the shear center and the centroid.)
Locations of shear centers for several other sections are given in Friedrich
Bleich, ‘‘Buckling Strength of Metal Structures,’’ Chap. III, McGraw-Hill Publishing
Company, New York.
5.4.2 Stresses Due to Torsion
Simple torsion is resisted by internal shearing stresses. These can be resolved into
radial and tangential shearing stresses, which being normal to each other also are
equal (see Art. 5.3.2). Furthermore, on planes that bisect the angles between the
planes on which the shearing stresses act, there also occur compressive and tensile
stresses. The magnitude of these normal stresses is equal to that of the shear. Therefore,
when torsional loading is combined with other types of loading, the maximum
stresses occur on inclined planes and can be computed by the methods of Arts.
5.3.3 and 5.3.6.
STRUCTURAL THEORY 5.29
Circular Sections. If a circular shaft (hollow or solid) is twisted, a section that is
plane before twisting remains plane after twisting. Within the proportional limit,
the shearing unit stress at any point in a transverse section varies with the distance
from the center of the section. The maximum shear, psi, occurs at the circumference
and is given by
Tr
v  (5.43)
J
where T  torsional moment, in-lb
r  radius of section, in
J  polar moment of inertia, in4
Polar moment of inertia of a cross section is defined by
2 J   dA (5.44)
where  radius from shear center to any point in the section
dA  differential area at the point
In general, J equals the sum of the moments of inertia above any two perpendicular
axes through the shear center. For a solid circular section, J  
r 4 /2. For a hollow
circular section with diameters D and d, J  
(D4  d4) / 32.
Within the proportional limits, the angular twist between two points L inches
apart along the axis of a circular bar is, in radians (1 rad  57.3):
TL
 (5.45)
GJ
where G is the shearing modulus of elasticity (see Art. 5.2.4).
Noncircular Sections. If a shaft is not circular, a plane transverse section before
twisting does not remain plane after twisting. The resulting warping increases the
shearing stresses in some parts of the section and decreases them in others, compared
wit the sharing stresses that would occur if the section remained plane. Consequently,
shearing stresses in a noncircular section are not proportional to distances
from the share center. In elliptical and rectangular sections, for example, maximum
shear occurs on the circumference at a point nearest the shear center.
For a solid rectangular section, this maximum may be expressed in the following
form:
T
v  (5.46) 2 kb d
where b  short side of rectangle, in
d  long side, in
k  constant depending on ratio of these sides;
d/b  1.0 1.5 2.0 3 4 5 10 
k  0.208 0.231 0.246 0.258 0.267 0.282 0.291 0.312 0.333
(S. Timoshenko and J. N. Goodier, ‘‘Theory of Elasticity,’’ McGraw-Hill Publishing
Company, New York.)
5.30 SECTION FIVE
Hollow Tubes. If a thin-shell hollow tube is twisted, the shearing force per unit
of length on a cross section (shear flow) is given approximately by
T
H  (5.47)
2A
where A is the area enclosed by the mean perimeter of the tube, in2, and the unit
shearing stress is given approximately by
H T
v  (5.48)
t 2At
where t is the thickness of the tube, in. For a rectangular tube with sides of unequal
thickness, the total shear flow can be computed from Eq. (5.47) and the shearing
stress along each side from Eq. (5.48), except at the corners, where there may be
appreciable stress concentration.
Channels and I Beams. For a narrow rectangular section, the maximum shear is
very nearly equal to
1 t ?3 v  (5.49) 2 b d
This formula also can be used to find the maximum shearing stress due to torsion
in members, such as I beams and channels, made up of thin rectangular components.
Let J  1?3b3d, where b is the thickness of each rectangular component and d the
corresponding length. Then, the maximum shear is given approximately by
Tb
v  (5.50)
J
where b is the thickness of the web or the flange of the member. Maximum shear
will occur at the center of one of the long sides of the rectangular part that has the
greatest thickness. (A. P. Boresi, O. Sidebottom, F. B. Seely, and J. O. Smith,
‘‘Advanced Mechanics of Materials,’’ 3d ed., John Wiley & Sons, Inc., New York.)
5.5 STRAIGHT BEAMS
Beams are the horizontal members used to support vertically applied loads across
an opening. In a more general sense, they are structural members that external loads
tend to bend, or curve. Usually, the term beam is applied to members with top
continuously connected to bottom throughout their length, and those with top and
bottom connected at intervals are called trusses. See also Structural System, Art.
1.7.
5.5.1 Types of Beams
There are many ways in which beams may be supported. Some of the more common
methods are shown in Figs. 5.11 to 5.16.
STRUCTURAL THEORY 5.31
FIGURE 5.11 Simple beam. FIGURE 5.12 Cantilever beam.
FIGURE 5.13 Beam with one end fixed. FIGURE 5.14 Fixed-end beam.
FIGURE 5.15 Beam with overhangs. FIGURE 5.16 Continuous beam.
The beam in Fig. 5.11 is called a simply supported, or simple beam. It has
supports near its ends, which restrain it only against vertical movement. The ends
of the beam are free to rotate. When the loads have a horizontal component, or
when change in length of the beam due to temperature may be important, the
supports may also have to prevent horizontal motion. In that case, horizontal restraint
at one support is generally sufficient.
The distance between the supports is called the span. The load carried by each
support is called a reaction.
The beam in Fig. 5.12 is a cantilever. It has only one support, which restrains
it from rotating or moving horizontally or vertically at that end. Such a support is
called a fixed end.
If a simple support is placed under the free end of the cantilever, the propped
beam in Fig. 5.13 results. It has one end fixed, one end simply supported.
The beam in Fig. 5.14 has both ends fixed. No rotation or vertical movement
can occur at either end. In actual practice, a fully fixed end can seldom be obtained.
Some rotation of the beam ends generally is permitted. Most support conditions
are intermediate between those for a simple beam and those for a fixed-end beam.
In Fig. 5.15 is shown a beam that overhangs both is simple supports. The overhangs
have a free end, like cantilever, but the supports permit rotation.
When a beam extends over several supports, it is called a continuous beam
(Fig. 5.16).
Reactions for the beams in Figs. 5.11, 5.12, and 5.15 may be found from the
equations of equilibrium. They are classified as statically determinate beams for
that reason.
The equations of equilibrium, however, are not sufficient to determine the reactions
of the beams in Figs. 5.13, 5.14, and 5.16. For those beams, there are more
unknowns than equations. Additional equations must be obtained on the basis of
deformations permitted; on the knowledge, for example, that a fixed end permits
no rotation. Such beams are classified as statically indeterminate. Methods for
finding the stresses in that type of beam are given in Arts. 5.10.4, 5.10.5, 5.11, and
5.13.
5.32 SECTION FIVE
5.5.2 Reactions
As an example of the application of the equations of equilibrium (Art. 5.2.1) to the
determination of the reactions of a statically determinate beam, we shall compute
FIGURE 5.17 Beam with overhangs loaded
with both uniform and concentrated loads.
the reactions of the 60-ft-long beam
with overhangs in Fig. 5.17. This beam
carries a uniform load of 200 lb / lin ft
over its entire length and several concentrated
loads. The supports are 36 ft
apart.
To find reaction R1, we take moments
about R2 and equate the sum of the moments
to zero (clockwise rotation is considered
positive, counterclockwise, negative):
2000 
 48  36R  4000 
 30  6000 
 18  3000 
 12 1
200 
 60 
 18  0
R  14,000 lb 1
In this calculation, the moment of the uniform load was found by taking the moment
of its resultant, which acts at the center of the beam.
To find R2, we can either take moments about R1 or use the equation V  0.
It is generally preferable to apply the moment equation and use the other equation
as a check.
3000 
 48  36R  6000 
 18  4000 
 6  2000 
 12 2
 200 
 60 
 18  0
R  13,000 lb 2
As a check, we note that the sum of the reactions must equal the total applied
load:
14,000  13,000  2000  4000  6000  3000  12,000
27,000  27,000
5.5.3 Internal Forces
Since a beam is in equilibrium under the forces applied to it, it is evident that at
every section internal forces are acting to prevent motion. For example, suppose
we cut the beam in Fig. 5.17 vertically just to the right of its center. If we total
the external forces, including the reaction, to the left of this cut (see Fig. 5.18a),
we find there is an unbalanced downward load of 4000 lb. Evidently, at the cut
section, an upward-acting internal force of 4000 lb must be present to maintain
equilibrium. Again, if we take moments of the external forces about the section,
we find an unbalanced moment of 54,000 ft-lb. So there must be an internal moment
of 54,000 ft-lb acting to maintain equilibrium.
This internal, or resisting, moment is produced by a couple consisting of a force
C acting on the top part of the beam and an equal but opposite force T acting on
STRUCTURAL THEORY 5.33
FIGURE 5.18 Portions of a beam are held in equilibrium by internal
stresses.
the bottom part (Fig. 18b). The top force is the resultant of compressive stresses
acting over the upper portion of the beam, and the bottom force is the resultant of
tensile stresses acting over the bottom part. The surface at which the stresses change
from compression to tension—where the stress is zero—is called the neutral surface.
FIGURE 5.19 .Shear diagram for the beam
with loads shown in Fig. 5.17.
5.5.4 Shear Diagrams
The unbalanced external vertical force
at a section is called the shear. It is equal
to the algebraic sum of the forces that
lie on either side of the section. Upward
acting forces on the left of the section
are considered positive, downward
forces negative; signs are reversed for
forces on the right.
A diagram in which the shear at
every point along the length of a beam
is plotted as an ordinate is called a shear
diagram. The shear diagram for the
beam in Fig. 5.17 is shown in Fig.
5.19b.
The diagram was plotted starting
from the left end. The 2000-lb load was
plotted downward to a convenient scale.
Then, the shear at the next concentrated
load—the left support—was determined.
This equals 2000  200 
 12,
or 4400 lb. In passing from must to
the left of the support to a point just to
the right, however, the shear changes by
the magnitude of the reaction. Hence, on
the right-hand side of the left support the shear is 4400  14,000, or 9600 lb. At
the next concentrated load, the shear is 9600  200 
 6, or 8400 lb. In passing
the 4000-lb load, however, the shear changes to 8400  4000, or 4400 lb. Proceeding
in this manner to the right end of the beam, we terminate with a shear of
3000 lb, equal to the load on the free end there.
It should be noted that the shear diagram for a uniform load is a straight line
sloping downward to the right (see Fig. 5.21). Therefore, the shear diagram was
completed by connecting the plotted points with straight lines.
5.34 SECTION FIVE
FIGURE 5.20 Shear and moment diagrams
for a simply supported beam with concentrated
loads.
FIGURE 5.21 Shear and moment diagrams
for a simply supported, uniformly loaded beam.
Shear diagrams for commonly encountered loading conditions are given in Figs.
5.30 to 5.41.
5.5.5 Bending-Moment Diagrams
The unbalanced moment of the external forces about a vertical section through a
beam is called the bending moment. It is equal to the algebraic sum of the moments
about the section of the external forces that lie on one side of the section. Clockwise
moments are considered positive, counterclockwise moments negative, when the
forces considered lie on the left of the section. Thus, when the bending moment is
positive, the bottom of the beam is in tension.
A diagram in which the bending moment at every point along the length of a
beam is plotted as an ordinate is called a bending-moment diagram.
Figure 5.20c is the bending-moment diagram for the beam loaded with concentrated
loads only in Fig. 5.20a. The bending moment at the supports for this simply
supported beam obviously is zero. Between the supports and the first load, the
bending moment is proportional to the distance from the support, since it is equal
to the reaction times the distance from the support. Hence the bending-moment
diagram for this portion of the beam is a sloping straight line.
STRUCTURAL THEORY 5.35
The bending moment under the 6000-lb load in Fig. 5.20a considering only the
force to the left is 7000 
 10, or 70,000 ft-lb. The bending-moment diagram, then,
between the left support and the first concentrated load is a straight line rising from
zero at the left end of the beam to 70,000 ft-lb, plotted to a convenient scale, under
the 6000-lb load.
The bending moment under the 9000-lb load, considering the forces on the left
of it, is 7000 
 20  6000 
 10, or 80,000 ft-lb. (It could have been more easily
obtained by considering only the force on the right, reversing the sign convention:
8000 
 10  80,000 ft-lb.) Since there are no loads between the two concentrated
loads, the bending-moment diagram between the two sections is a sloping straight
line.
If the bending moment and shear are known at any section of a beam, the
bending moment at any other section may be computed, providing there are no
unknown forces between the two sections. The rule is:
The bending moment at any section of a beam is equal to the bending
moment at any section to the left, plus the shear at that section times the
distance between sections, minus the moments of intervening loads. If the section
with known moment and share is on the right, the sign convention must
be reversed.
For example, the bending moment under the 9000-lb load in Fig. 5.20a could
also have been obtained from the moment under the 6000-lb load and the shear to
the right of the 6000-lb load given in the shear diagram (Fig. 5.20b). Thus,
80,000  70,000  1000 
 10. If there had been any other loads between the two
concentrated loads, the moment of these loads about the section under the 9000-lb
load would have been subtracted.
Bending-moment diagrams for commonly encountered loading conditions are
given in Figs. 5.30 to 5.41. These may be combined to obtain bending moments
for other loads.
5.5.6 Moments in Uniformly Loaded Beams
When a bean carries a uniform load, the bending-moment diagram does not consist
of straight lines. Consider, for example, the beam in Fig. 5.21a, which carries a
uniform load over its entire length. As shown in Fig. 5.21c, the bending-moment
diagram for this beam is a parabola.
The reactions at both ends of a simply supported, uniformly loaded beam are
both equal to wL/2  W/2, where w is the uniform load in pounds per linear foot,
W  wL is the total load on the beam, and L is the span.
The shear at any distance x from the left support is R1 wx  wL/2  wx (see
Fig. 5.21b). Equating this expression to zero, we find that there is no shear at the
center of the beam.
The bending moment at any distance x from the left support is
2 x wLx wx w
M  R x  wx    x(L  x) (5.51) 
  1 2 2 2 2
Hence:
The bending moment at any section of a simply supported, uniformly loaded
beam is equal to one-half the product of the load per linear foot and the
distances to the section from both supports.
The maximum value of the bending moment occurs at the center of the beam.
It is equal to wL2/8  WL/8.
5.36 SECTION FIVE
5.5.7 Shear-Moment Relationship
The slope of the bending-moment curve for any point on a beam is equal to the
shear at that point; i.e.,
dM
V  (5.52)
dx
Since maximum bending moment occurs when the slope changes sign, or passes
through zero, maximum moment (positive or negative) occurs at the point of zero
shear.
After integration, Eq. (5.52) may also be written
x1
M  M   V dx (5.53) 1 2
x2
5.5.8 Moving Loads and Influence Lines
One of the most helpful devices for solving problems involving variable or moving
loads is an influence line. Whereas shear and moment diagrams evaluate the effect
of loads at all sections of a structure, an influence line indicates the effect at a
given section of a unit load placed at any point on the structure.
For example, to plot the influence line for bending moment at some point A on
a beam, a unit load is applied at some point B. The bending moment is A due to
the unit load at B is plotted as an ordinate to a convenient scale at B. The same
procedure is followed at every point along the beam and a curve is drawn through
the points thus obtained.
Actually, the unit load need not be placed at every point. The equation of the
influence line can be determined by placing the load at an arbitrary point and
computing the bending moment in general terms. (See also Art. 5.10.5.)
Suppose we wish to draw the influence line for reaction at A for a simple beam
AB (Fig. 5.22a). We place a unit load at an arbitrary distance of xL from B. The
reaction at A due to this load is 1 xL/L  x. Then, RA  x is the equation of the
influence line. It represents a straight line sloping upward from zero at B to unity
at A (Fig. 5.22a). In other words, as the unit load moves across the beam, the
reaction at A increases from zero to unity in proportion to the distance of the load
from B.
Figure 5.22b shows the influence line for bending moment at the center of a
beam. It resembles in appearance the bending-moment diagram for a load at the
center of the beam, but its significance is entirely different. Each ordinate gives the
moment at midspan for a load at the corresponding location. It indicates that, if a
unit load is placed at a distance xL from one end, it produces a bending moment
of 1?2 xL at the center of the span.
Figure 5.22c shows the influence line for shear at the quarter point of a beam.
When the load is to the right of the quarter point, the shear is positive and equal
to the left reaction. When the load is to the left, the shear is negative and equal to
the right reaction.
The diagram indicates that, to produce maximum shear at the quarter point, loads
should be placed only to the right of the quarter point, with the largest load at the
quarter point, if possible. For a uniform load, maximum shear results when the load
extends from the right end of the beam to the quarter point.
STRUCTURAL THEORY 5.37
FIGURE 5.22 Influence lines for simple beam AB for (a) reaction at A; (b) midspan bending
moment; (c) quarter-point shear; and (d ) bending moments for unit load at several points on
the beam.
Suppose, for example, that the beam is a crane girder with a span of 60 ft. The
wheel loads are 20 and 10 kips, respectively, and are spaced 5 ft apart. For maximum
shear at the quarter point, the wheels should be placed with the 20-kip wheel
at that point and the 10-kip wheel to the right of it. The corresponding ordinates
of the influence line (Fig. 5.22c) are 3?4 and 40?45 
 3?4. Hence, the maximum shear
is 20 
 3?4  10 
 40?45 
 3?4  21.7 kips.
Figure 5.22d shows influence lines for bending moment at several points on a
beam. It is noteworthy that the apexes of the diagrams fall on a parabola, as shown
by the dashed line. This indicates that the maximum moment produced at any given
section by a single concentrated load moving across a beam occurs when the load
is at that section. The magnitude of the maximum moment increases when the
section is moved toward midspan, in accordance with the equation shown in Fig.
5.22d for the parabola.
5.5.9 Maximum Bending Moment
When there is more than one load on the span, the influence line is useful in
developing a criterion for determining the position of the loads for which the bending
moment is a maximum at a given section.
Maximum bending moment will occur at a section C of a simple beam as loads
move across it when one of the loads is at C. The proper load to place at C is the
one for which the expression Wa /a  Wb /b (Fig. 5.23) changes sign as that load
passes from one side of C to the other.
When several loads move across a simple beam, the maximum bending moment
produced in the beam may be near but not necessarily at midspan. To find the
maximum moment, first determine the position of the loads for maximum moment
5.38 SECTION FIVE
FIGURE 5.23 .Moving loads on simple beam
AB ae placed for maximum bending moment at
point C on the beam.
FIGURE 5.24 Moving loads are placed to
subject a simple beam to the largest possible
bending moment.
at midspan. Then shift the loads until the load P2 that was at the center of the beam
is as far from midspan as the resultant of all the loads on the span is on the other
side of midspan (Fig. 5.24). Maximum moment will occur under P2.
When other loads move on or off the span during the shift of P2 away from
midspan, it may be necessary to investigate the moment under one of the other
loads when it and the resultant are equidistant from midspan.
5.5.10 Bending Stresses in a Beam
To derive the commonly used flexure formula for computing the bending stresses
in a beam, we have to make the following assumptions:
1. The unit stress at a point in any plane parallel to the neutral surface of a beam
is proportional to the unit strain in the plane at the point.
2. The modulus of elasticity in tension is the same as that in compression.
3. The total and unit axial strain in any plane parallel to the neutral surface are
both proportional to the distance of that plane from the neutral surface. (Cross
sections that are plane before bending remain plane after bending. This requires
that all planes have the same length before bending; thus, that the beam be
straight.)
4. The loads act in a plane containing the centroidal axis of the beam and are
perpendicular to that axis. Furthermore, the neutral surface is perpendicular to
the plane of the loads. Thus, the plane of the loads must contain an axis of
symmetry of each cross section of the beam. (The flexure formula does not apply
to a beam loaded unsymmetrically. See Arts. 5.5.18 and 5.5.19.)
5. The beam is proportioned to preclude prior failure or serious deformation by
torsion, local buckling, shear, or any cause other than bending.
Equating the bending moment to the resisting moment due to the internal stresses
at any section of a beam yields
STRUCTURAL THEORY 5.39
?I
M  (5.54)
C
FIGURE 5.25 Unit stresses on a beam cross
section caused by bending of the beam.
M is the bending moment at the section,
? is the normal unit stress in a plane at
a distance c from the neutral axis (Fig.
5.25), and I is the moment of inertia of
the cross section with respect to the neutral
axis. If ? is given in pounds per
square inch (psi), I in in4, and c in
inches, then M will be in inch-pounds.
For maximum unit stress, c is the distance
to the outermost fiber. See also
Arts. 5.5.11 and 5.5.12.
5.5.11 Moment of Inertia
The neutral axis in a symmetrical beam is coincidental with the centroidal axis;
i.e., at any section the neutral axis is so located that
 y dA  0 (5.55)
where dA is a differential area parallel to the axis (Fig. 5.25), y is its distance from
the axis, and the summation is taken over the entire cross section.
Moment of inertia with respect to the neutral axis is given by
2 I   y dA (5.56)
Values of I for several common types of cross section are given in Fig. 5.26. Values
for structural-steel sections are presented in manuals of the American Institute of
Steel Construction, Chicago, Ill. When the moments of inertia of other types of
sections are needed, they can be computed directly by application of Eq. (5.56) or
by braking the section up into components for which the moment of inertia is
known.
If I is the moment of inertia about the neutral axis, A the cross-sectional area,
and d the distance between that axis and a parallel axis in the plane of the cross
section, then the moment of inertia about the parallel axis is
2 I   I  Ad (5.57)
With this equation, the known moment of inertia of a component of a section about
the neutral axis of the component can be transferred to the neutral axis of the
complete section. Then, summing up the transferred moments of inertia for all the
components yields the moment of inertia of the complete section.
When the moments of inertia of an area with respect to any two perpendicular
axes are known, the moment of inertia with respect to any other axis passing
through the point of intersection of the two axes may be obtained through the use
5.40 SECTION FIVE
FIGURE 5.26 Geometric properties of various cross sections.
STRUCTURAL THEORY 5.41
of Mohr’s circle, as for stresses (Fig. 5.10). In this analog, Ix corresponds with ?x,
Iy with ?y , and the product of inertia Ixy with vxy (Art. 5.3.6).
I   xy dA (5.58) xy
The two perpendicular axes through a point about which the moments of inertia
are a maximum and a minimum are called the principal axes. The products of
inertia are zero for the principal axes.
5.5.12 Section Modulus
The ratio S  I /c in Eq. (5.54) is called the section modulus. I is the moment of
inertia of the cross section about the neutral axis and c the distance from the neutral
axis to the outermost fiber. Values of S for common types of sections are given in
Fig. 5.26.
FIGURE 5.27 Unit shearing stresses on a
beam cross section.
5.5.13 Shearing Stresses in a
Beam
The vertical shear at any section of a
beam is resisted by nonuniformly distributed,
vertical unit stresses (Fig.
5.27). At every point in the section,
there is also a horizontal unit stress,
which is equal in magnitude to the vertical
unit shearing stress there [see Eq.
(5.34)].
At any distances y from the neutral
axis, both the horizontal and vertical
shearing unit stresses are equal to
V
v  Ay (5.59)
It
where V  vertical shear at the cross section
t  thickness of beam at distance y from neutral axis
I  moment of inertia about neutral axis
A  area between the outermost fiber and the fiber for which the shearing
stress is being computed
 y distance of center of gravity of this area from the neutral axis (Fig.
5.27)
For a rectangular beam with width b and depth d, the maximum shearing stress
occurs at middepth. Its magnitude is
2 12V bd 3 V
v  3 bd b 8 2bd
That is, the maximum shear stress is 50% greater than the average shear stress on
the section. Similarly, for a circular beam, the maximum is one-third greater than
the average. For an I beam, however, the maximum shearing stress in the web is
5.42 SECTION FIVE
not appreciably greater than the average for the web section alone, if it is assumed
that the flanges take no shear.
5.5.14 Combined Shear and Bending Stress
For deep beams on short spans and beams made of low-strength materials, it is
sometimes necessary to determine the maximum stress ? on an inclined plane
caused by a combination of shear and bending stress—v and ?, respectively. This
stress ?, which may be either tension or compression, is greater than the normal
stress. Its value may be obtained by application of Mohr’s circle (Art. 5.3.6), as
indicated in Fig. 5.10, but with ?y  0, and is
2 ? ? 2 ?  v  (5.60) 
   2 2
5.5.15 Beam Deflections
When a beam is loaded, it deflects. The new position of its longitudinal centroidal
axis is called the elastic curve.
At any point of the elastic curve, the radius of curvature is given by
EI
R  (5.61)
M
where M  bending moment at the point
E  modulus of elasticity
I  moment of inertia of the cross section about the neutral axis
Since the slope dy/dx of the curve is small, its square may be neglected, so that,
for all practical purposes, 1/R may be taken equal to d2y/dx2, where y is the
deflection of a point on the curve at a distance x from the origin of coordinates.
Hence, Eq. (5.61) may be rewritten
2 d y
M  EI (5.62) 2 dx
To obtain the slope and deflection of a beam, this equation may be integrated, with
M expressed as a function of x. Constants introduced during the integration must
be evaluated in terms of known points and slopes of the elastic curve.
Equation (5.62), in turn, may be rewritten after one integration as
B M
     dx (5.63) B A
A EI
in which A and B are the slopes of the elastic curve at any two points A and B.
If the slope is zero at one of the points, the integral in Eq. (5.63) gives the slope
of the elastic curve at the other. It should be noted that the integral represents the
area of the bending-moment diagram between A and B with each ordinate divided
by EI.
STRUCTURAL THEORY 5.43
FIGURE 5.28 Load and M/ EI diagrams and
elastic curve for a simple beam with mispan
load.
The tangential deviation t of a point on the elastic curve is the distance of this
point, measured in a direction perpendicular to the original position of the beam,
from a tangent drawn at some other point on the elastic curve.
B Mx
t  t   dx (5.64) B A
A EI
Equation (5.64) indicates that the tangential deviation of any point with respect
to a second point on the elastic curve equals the moment about the first point of
the M/EI diagram between the two points. The moment-area method for determining
the deflection of beams is a technique in which Eqs. (5.63) and (5.64) are
utilized.
Suppose, for example, the deflection at midspan is to be computed for a beam
of uniform cross section with a concentrated load at the center (Fig. 5.28).
Since the deflection at midspan for this loading is the maximum for the span,
the slope of the elastic curve at the center of the beam is zero; i.e., the tangent is
parallel to the undeflected position of the beam. Hence, the deviation of either
support from the midspan tangent is equal to the deflection at the center of the
beam. Then, by the moment-area theorem [Eq. (5.64)], the deflection yc is given
by the moment about either support of the area of the M/EI diagram included
between an ordinate at the center of the beam and that support.
3 1 PL L 2L PL
y  c 2 4EI 2 3 2 48EI
Suppose now, the deflection y at any point D at a distance xL from the left
support (Fig. 5.28) is to be determined. Referring to the sketch, we note that the
distance DE from the undeflected point of D to the tangent to the elastic curve at
support A is given by
5.44 SECTION FIVE
y  t  xt AD AB
where tAD is the tangential deviation of D from the tangent at A and tAB is the
tangential deviation of B from that tangent. This equation, which is perfectly general
for the deflection of any point of a simple beam, no matter how loaded, may be
rewritten to give the deflection directly:
y  xt  t (5.65) AB AD
But tAB is the moment of the area of the M/EI diagram for the whole beam about
support B. And tAD is the moment about D of the area of the M/EI diagram included
between ordinates at A and D. Hence
3 1 PL L 2 1 1PLx xL PL 2 y  x  L  xL  x(3  4x ) 
  2 4EI2 3 3 2 2EI 3 48EI
It is also noteworthy that, since the tangential deviations are very small distances,
the slope of the elastic curve at A is given by
tAB   (5.66) A L
This holds, in general, for all simple beams regardless of the type of loading.
The procedure followed in applying Eq. (5.65) to the deflection of the loaded
beam in Fig. 5.28 is equivalent to finding the bending moment at D with the M/
EI diagram serving as the load diagram. The technique of applying the M/EI diagram
as a load and determining the deflection as a bending moment is known as
the conjugate-beam method.
The conjugate beam must have the same length as the given beam; it must be
in equilibrium with the M/EI load and the reactions produced by the load; and the
bending moment at any section must be equal to the deflection of the given beam
at the corresponding section. The last requirement is equivalent to requiring that
the shear at any section of the conjugate beam with the M/EI load be equal to the
slope of the elastic curve at the corresponding section of the given beam. Figure
5.29 shows the conjugates for various types of beams.
Deflections for several types of loading on simple beams are given in Figs. 5.30
to 5.35 and for overhanging beams and cantilevers in Figs. 5.36 to 5.41.
When a beam carries a number of loads of different types, the most convenient
method of computing its deflection generally is to find the deflections separately
for the uniform and concentrated loads and add them up.
For several concentrated loads, the easiest solution is to apply the reciprocal
theorem (Art. 5.10.5). According to this theorem, if a concentrated load is applied
to a beam at a point A, the deflection it produces at point B is equal to the deflection
at A for the same load applied at B(dAB  dBA).
Suppose, for example, the midspan deflection is to be computed. Then, assume
each load in turn applied at the center of the beam and compute the deflection at
the point where it originally was applied from the equation of the elastic curve
given in Fig. 5.33. The sum of these deflections is the total midspan deflection.
Another method for computing deflections of beams is presented in Art. 5.10.4.
This method may also be applied to determining the deflection of a beam due to
shear.
STRUCTURAL THEORY 5.45
FIGURE 5.29 Various types of beams and corresponding conjugate beams.
5.5.16 Combined Axial and Bending Loads
For stiff beams, subjected to both transverse and axial loading, the stresses are
given by the principle of superposition if the deflection due to bending may be
neglected without serious error. That is, the total stress is given with sufficient
accuracy at any section by the sum of the axial stress and the bending stresses. The
maximum stress equals
P Mc
?  (5.67)
A I
where P  axial load
A  cross-sectional area
M  maximum bending moment
c  distance from neutral axis to outermost surface at the section where
maximum moment occurs
I  moment of inertia of cross section about neutral axis at that section
5.46 SECTION FIVE
FIGURE 5.30 Uniform load over the whole
span of a simple beam.
FIGURE 5.31 Uniform load over only part of
a simple beam.
When the deflection due to bending is large and the axial load produces bending
stresses that cannot be neglected, the maximum stress is given by
P c
? (M  Pd) (5.68)
A I
where d is the deflection of the beam. For axial compression, the moment Pd should
be given the same sign as M, and for tension, the opposite sign, but the minimum
value of M  Pd is zero. The deflection d for axial compression and bending can
be obtained by applying Eq. (5.62). (S. Timoshenko and J. M. Gere, ‘‘Theory of
Elastic Stability,’’ McGraw-Hill Publishing company, New York; Friedrich Bleich,
‘‘Buckling Strength of Metal Structures,’’ McGraw-Hill Publishing Company, New
York.) However, it may be closely approximated by
do d  (5.69)
1  (P/P ) c
where do  deflection for the transverse loading alone
Pc  the critical buckling load 
2EI/L2 (see Art. 5.7.2)
5.5.17 Eccentric Loading
An eccentric longitudinal load in the plane of symmetry produces a bending moment
Pe where e is the distance of the load from the centroidal axis. The total unit
STRUCTURAL THEORY 5.47
FIGURE 5.32 Concentrated load at any point
of a simple beam.
FIGURE 5.33 Concentrated load at midspan
of a simple beam.
stress is the sum of the stress due to this moment and the stress due to P applied
as an axial load:
P Pec P ec
?  
  1 
 (5.70) 
 2 A I A r
where A  cross-sectional area
c  distance from neutral axis to outermost fiber
I  moment of inertia of cross section about neutral axis
r  radius of gyration, which is equal to I /A
Figure 5.26 gives values of the radius of gyration for some commonly used cross
sections.
For an axial compression load, if there is to be no tension on the cross section,
e should not exceed r2 /c. For a rectangular section with width b and depth d, the
eccentricity, therefore, should be less than b/6 and d/ 6; i.e., the load should not
be applied outside the middle third. For a circular cross section with diameter D,
the eccentricity should not exceed D/8.
When the eccentric longitudinal load produces a deflection too large to be neglected
in computing the bending stress, account must be taken of the additional
bending moment Pd, where d is the deflection. This deflection may be computed
by employing Eq. (5.62) or closely approximated by
5.48 SECTION FIVE
FIGURE 5.34 Two equal concentrated
loads on a simple beam.
4eP/Pc d  (5.71)

(1  P/P ) c
Pc is the critical buckling load 
2EI/L2 (see Art. 5.7.2).
If the load P does not lie in a plane containing an axis of symmetry, it produces
bending about the two principal axes through the centroid of the cross section. The
stresses are given by
Pe c P Pec y y x x ?  
 
 (5.72)
A I I y x
where A  cross-sectional area
ex  eccentricity with respect to principal axis YY
ey  eccentricity with respect to principal axis XX
cx  distance from YY to outermost fiber
cy  distance from XX to outermost fiber
Ix  moment of inertia about XX
Iy  moment of inertia about YY
STRUCTURAL THEORY 5.49
FIGURE 5.35 Several equal concentrated loads
on a simple beam.
The principal axes are the two perpendicular axes through the centroid for which
the moments of inertia are a maximum or a minimum and for which the products
of inertia are zero.
5.5.18 Unsymmetrical Bending
Bending caused by loads that do not lie in a plane containing a principal axis of
each cross section of a beam is called unsymmetrical bending. If the bending axis
of the beam lies in the plane of the loads, to preclude torsion (see Art. 5.4.1), and
if the loads are perpendicular to the bending axis, to preclude axial components,
the stress at any point in a cross section is given by
M x M y y x ?  
 (5.73)
I I x y
5.50 SECTION FIVE
FIGURE 5.36 Concentrated load at the end of a
beam overhang.
FIGURE 5.37 Concentrated load at the end
of a cantilever.
STRUCTURAL THEORY 5.51
FIGURE 5.38 Uniform load over the full length of a
beam with overhang.
where Mx  bending moment about principal axis XX
My  bending moment about principal axis YY
x  distance from point for which stress is to be computed to YY axis
y  distance from point to XX axis
Ix  moment of inertia of the cross section about XX
Iy  moment of inertia about YY
If the plane of the loads makes an angle  with a principal plane, the neutral
surface will form an angle  with the other principal plane such that
Ix tan  tan  (5.74)
Iy
5.5.19 Beams with Unsymmetrical Sections
In the derivation of the flexure formula ?  Mc/ I [Eq. (5.54)], the assumption is
made that the beam bends, without twisting, in the plane of the loads and that the
neutral surface is perpendicular to the plane of the loads. These assumptions are
correct for beams with cross sections symmetrical about two axes when the plane
of the loads contains one of these axes. They are not necessarily true for beams
that are not doubly symmetrical. The reason is that in beams that are doubly sym5.52
SECTION FIVE
FIGURE 5.39 Uniform load over the whole
length of a cantilever.
FIGURE 5.40 Uniform load on a beam overhang.
metrical the bending axis coincides with the centroidal axis, whereas in unsymmetrical
sections the two axes may be separate. In the latter case, if the plane of
the loads contains the centroidal axis but not the bending axis, the beam will be
subjected to both bending and torsion.
The bending axis may be defined as the longitudinal line in a beam through
which transverse loads must pass to preclude the beam’s twisting as it bends. The
point in each section through which the bending axis passes is called the shear
center, or center of twist. The shear center is also the center of rotation of the
section in pure torsion (Art. 5.4.1).
Computation of stresses and strains in members subjected to both bending and
torsion is complicated, because warping of the cross section and buckling effects
should be taken into account. Preferably, twisting should be prevented by use of
bracing or avoided by selecting appropriate shapes for the members and by locating
and directing loads to pass through the bending axis.
(F. Bleich, ‘‘Blucking Strength of Metal Structures,’’ McGraw-Hill Publishing
Company, New York.)
5.6 CURVED BEAMS
Structural members, such as arches, crane hooks, chain links, and frames of some
machines, that have considerable initial curvature in the plane of loading are called
STRUCTURAL THEORY 5.53
FIGURE 5.41 Triangular loading on a cantilever.
curved beams. The flexure formula of Art. 5.5.10, ?  Mc/ I, cannot be applied to
them with any reasonable degree of accuracy unless the depth of the beam is small
compared with the radius of curvature.
Unlike the condition in straight beams, unit strains in curved beams are not
proportional to the distance from the neutral surface, and the centroidal axis does
not coincide with the neutral axis. Hence the stress distribution on a section is not
linear but more like the distribution shown in Fig. 5.42c.
5.6.1 Stresses in Curved Beams
Just as for straight beams, the assumption that plane sections before bending remain
plane after bending generally holds for curved beams. So the total strains are proportional
to the distance from the neutral axis. But since the fibers are initially of
unequal length, the unit strains are a more complex function of this distance. In
Fig. 5.42a, for example, the bending couples have rotated section AB of the curved
beam into section AB through an angle d . If o is the unit strain at the centroidal
axis and  is the angular unit strain d /d , then the unit strain at a distance y
from the centroidal axis (measured positive in the direction of the center of curvature)
is
5.54 SECTION FIVE
FIGURE 5.42 Bending stresses in a curved beam.
DD R d yd  y o     (  ) (5.75) o o DD (R  y) d  R  y o
where R  radius of curvature of centroidal axis.
Equation (5.75) can be expressed in terms of the bending moment if we take
advantage of the fact that the sum of the tensile and compressive forces on the
section must be zero and the moment of these forces must be equal to the bending
moment M. These two equations yield
2 M M AR
  and  1  (5.76) 
  o ARE ARE I 
where A is the cross-sectional area, E the modulus of elasticity, and
2 2 y dA y y 2 I      y 1     dA (5.77) 
  2 1  y/R R R
It should be noted that I  is very nearly equal to the moment of inertia I about the
centroidal axis when the depth of the section is small compared with R, so that the
maximum ratio of y to R is small compared with unity. M is positive when it
decreases the radius of curvature.
Since the stress ?  E , we obtain the stresses in the curved beam from Eq.
(5.75) by multiplying it by E and substituting o and  from Eq. (5.76):
M My 1
?  (5.78)
AR I  1  y/R
The distance yo of the neutral axis from the centroidal axis (Fig. 5.42) may be
obtained from Eq. (5.78) by setting ?  0:
STRUCTURAL THEORY 5.55
I R
y  (5.79) o 2 I   AR
Since yo is positive, the neutral axis shifts toward the center of curvature.
5.6.2 Curved Beams with Various Cross Sections
Equation (5.78) for bending stresses in curved beams subjected to end moments in
the plane of curvature can be expressed for the inside and outside beam faces in
the form:
Mc
?  K (5.80)
I
where c  distance from the centroidal axis to the inner or outer surface. Table 5.4
gives values of K calculated from Eq. (5.78) for circular, elliptical, and rectangular
cross sections.
If Eq. (5.78) is applied to 1 or T beams or tubular members, it may indicate
circumferential flange stresses that are much lower than will actually occur. The
error is due to the fact that the outer edges of the flanges deflect radially. The effect
is equivalent to having only part of the flanges active in resisting bending stresses.
Also, accompanying the flange deflections, there are transverse bending stresses in
the flanges. At the junction with the web, these reach a maximum, which may be
greater than the maximum circumferential stress. Furthermore, there are radial
stresses (normal stresses acting in the direction of the radius of curvature) in the
web that also may have maximum values greater than the maximum circumferential
stress.
A good approximation to the stresses in I or T beams is as follows: for circumferential
stresses, Eq. (5.78) may be used with a modified cross section, which is
obtained by using a reduced flange width. The reduction is calculated from b 
b, where b is the length of the portion of the flange projecting on either side from
the web, b is the corrected length, and  is a correction factor determined from
equations developed by H. Bleich,  is a function of b2 / rt, where t is the flange
thickness and r the radius of the center of the flange:
b2 / rt  0.5 0.7 1.0 1.5 2 3 4 5
 0.9 0.6 0.7 0.6 0.5 0.4 0.37 0.33
When the parameter b2 / rt is greater than 1.0, the maximum transverse bending
stress is approximately equal to 1.7 times the stress obtained at the center of the
flange from Eq. (5.78) applied to the modified section. When the parameter equals
0.7, that stress should be multiplied by 1.5, and when it equals 0.4, the factor is
1.0 in Eq. (5.78), I  for I beams may be taken for this calculation approximately
equal to
2 c
I   I 1  (5.81) 
 2 R
5.56 SECTION FIVE
TABLE 5.4 Values of K for Curved Beams
Section
R
c
K
Inside face Outside face yo
1.2
1.4
1.6
1.8
2.0
3.0
4.0
6.0
8.0
10.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
6.0
8.0
10.0
1.2
1.4
1.6
1.8
2.0
3.0
4.0
6.0
8.0
10.0
3.41
2.40
1.96
1.75
1.62
1.33
1.23
1.14
1.10
1.08
3.28
2.31
1.89
1.70
1.57
1.31
1.21
1.13
1.10
1.07
2.89
2.13
1.79
1.63
1.52
1.30
1.20
1.12
1.09
1.07
0.54
0.60
0.65
0.68
0.71
0.79
0.84
0.89
0.91
0.93
0.58
0.64
0.68
0.71
0.73
0.81
0.85
0.90
0.92
0.93
0.57
0.63
0.67
0.70
0.73
0.81
0.85
0.90
0.92
0.94
0.224R
0.141R
0.108R
0.0847R
0.069R
0.030R
0.016R
0.0070R
0.0039R
0.0025R
0.269R
0.182R
0.134R
0.104R
0.083R
0.038R
0.020R
0.0087R
0.0049R
0.0031R
0.305R
0.204R
0.149R
0.112R
0.090R
0.041R
0.0217R
0.0093R
0.0052R
0.0033R
where I  moment of inertia of modified section about its centroidal axis
R  radius of curvature of centroidal axis
c  distance from centroidal axis to center of the more sharply curved flange
Because of the high stress factor, it is advisable to stiffen or brace curved I-beam
flanges.
The maximum radial stress will occur at the junction of web and flange of I
beams. If the moment is negative, that is, if the loads tend to flatten out the beam,
the radial stress is tensile, and there is a tendency for the more sharply curved
flange to pull away from the web. An approximate value of this maximum stress
is
A M ? ?   (5.82) r A t c r w g
STRUCTURAL THEORY 5.57
where ?r  radial stress at junction of flange and web of a symmetrical I beam
A?  area of one flange
A  total cross-sectional area
M  bending moment
tw  thickness of web
cg  distance from centroidal axis to center of flange
r  radius of curvature of inner face of more sharply curved flange
(A. P. Boresi, O. Sidebottom, F. B. Seely, and J. O. Smith, ‘‘Advanced Mechanics
of Materials,’’ John Wiley & Sons, Inc., New York.)
5.6.3 Axial and Bending Loads on Curved Beams
If a curved beam carries an axial load P as well as bending loads, the maximum
unit stress is
P Mc
?  
 K (5.83)
A I
where K is a correction factor for the curvature [see Eq. (5.80)]. The sign of M is
taken positive in this equation when it increases the curvature, and P is positive
when it is a tensile force, negative when compressive.
5.6.4 Slope and Deflection of Curved Beams
If we consider two sections of a curved beam separated by a differential distance
ds (Fig. 5.42), the change in angle d  between the sections caused by a bending
moment M and an axial load P may be obtained from Eq. (5.76), noting that d 
ds/R.
M ds I P ds
d  1  (5.84) 
 2 EI AR ARE
where E is the modulus of elasticity, A the cross-sectional area, R the radius of
curvature of the centroidal axis, and I  is defined by Eq. (5.77).
If P is a tensile force, the length of the centroidal axis increases by
P ds M ds
ds  (5.85)
AE ARE
The effect of curvature on shearing deformations for most practical applications is
negligible.
For shallow sections (depth of section less than about one-tenth the span), the
effect of axial forces on deformations may be neglected. Also, unless the radius of
curvature is very small compared with the depth, the effect of curvature may be
ignored. Hence, for most practical applications, Eq. (5.84) may be used in the
simplified form:
M ds
d  (5.86)
EI
For deeper beams, the action of axial forces, as well as bending moments, should
5.58 SECTION FIVE
be taken into account; but unless the curvature is sharp, its effect on deformations
may be neglected. So only Eq. (5.86) and the first term in Eq. (5.85) need be used.
(S. Timoshenko and D. H. Young, ‘‘Theory of Structures,’’ McGraw-Hill Publishing
Company, New York.) See also Arts. 5.14.1 to 5.14.3.
5.7 BUCKLING OF COLUMNS
Columns are compression members whose cross-sectional dimensions are relatively
small compared with their length in the direction of the compressive force. Failure
of such members occurs because of instability when a certain axial load Pc (called
critical or Euler load) is equated or exceeded. The member may bend, or buckle,
suddenly and collapse.
Hence the strength P of a column is not determined by the unit stress in Eq.
(5.21) (P  A?) but by the maximum load it can carry without becoming unstable.
The condition of instability is characterized by disproportionately large increases
in lateral deformation with slight increase in axial load. Instability may occur in
slender columns before the unit stress reaches the elastic limit.
FIGURE 5.43 Buckling of a pin-ended long
column.
5.7.1 Stable Equilibrium
Consider, for example, an axially loaded
column with ends unrestrained against
rotation, shown in Fig. 5.43. If the member
is initially perfectly straight, it will
remain straight as long as the load P is
less than the critical load Pc. If a small
transverse force is applied, the column
will deflect, but it will return to the
straight position when this force is removed.
Thus, when P is less than Pc,
internal and external forces are in stable
equilibrium.
5.7.2 Unstable Equilibrium
If P  Pc and a small transverse force
is applied, the column again will deflect,
but this time, when the force is removed,
the column will remain in the
bent position (dashed line in Fig. 5.43).
The equation of this elastic curve can be obtained from Eq. (5.62):
2 d y
EI  P y (5.87) c 2 dx
in which E  modulus of elasticity
I  least moment of inertia
y  deflection of the bent member from the straight position at a distance
x from one end
STRUCTURAL THEORY 5.59
This assumes, of course, that the stresses are within the elastic limit. Solution of
Eq. (5.87) gives the smallest value of the Euler load as
2 
 EI
P  (5.88) c 2 L
Equation (5.88) indicates that there is a definite finite magnitude of an axial load
that will hold a column in equilibrium in the bent position when the stresses are
below the elastic limit. Repeated application and removal of small transverse forces
or small increases in axial load above this critical load will cause the member to
fail by buckling. Internal and external forces are in a state of unstable equilibrium.
It is noteworthy that the Euler load, which determines the load-carrying capacity
of a column, depends on the stiffness of the member, as expressed by the modulus
of elasticity, rather than on the strength of the material of which it is made.
By dividing both sides of Eq. (5.88) by the cross-sectional area A and substituting
r 2 for I /A (r is the radius of gyration of the section), we can write the solution
of Eq. (5.87) in terms of the average unit stress on the cross section:
2 P 
 E c  (5.89) 2 A (L/ r)
This holds only for the elastic range of buckling; i.e. for values of the slenderness
ratio L/ r above a certain limiting value that depends on the properties of the material.
For inelastic buckling, see Art. 5.7.4.
5.7.3 Effect of End Conditions
Equation (5.89) was derived on the assumption that the ends of the column are free
to rotate. It can be generalized, however, to take into account the effect of end
conditions:
2 P 
 E c  (5.90) 2 A (kL/ r)
where k is the factor that depends on the end conditions. For a pin-ended column,
k  1; for a column with both ends fixed, k  1?2; for a column with one end fixed
and one end pinned, k is about 0.7; and for a column with one end fixed and one
end free from all restraint, k  2.
5.7.4 Inelastic Buckling
Equations (5.88) and (5.90) are derived from Eq. (5.87), the differential equation
for the elastic curve. They are based on the assumption that the critical average
stress is below the elastic limit when the state of unstable equilibrium is reached.
In members with slenderness ratio L/ r below a certain limiting value, however, the
elastic limit is exceeded before the column buckles. As the axial load approaches
the critical load, the modulus of elasticity varies with the stress. Hence Eqs. (5.88)
and (5.90), based on the assumption that E is a constant, do not hold for these short
columns.
5.60 SECTION FIVE
FIGURE 5.44 Column curves: (a) stress-strain curve for a material that does not have a sharply
defined yield pont: (b) column curve for this material; (c) stress-strain curve for a material with a
sharply defined yield point; (d ) column curve for that material.
After extensive testing and analysis, prevalent engineering opinion favors the
Engesser equation for metals in the inelastic range:
2 P 
 E t t  (5.91) 2 A (kL/ r)
This differs from Eqs. (5.88) to (5.90) only in that the tangent modulus Et (the
actual slope of the stress-strain curve for the stress Pt /A) replaced the modulus of
elasticity E in the elastic range. Pt is the smallest axial load for which two equilibrium
positions are possible, the straight position and a deflected position.
5.7.5 Column Curves
Curves obtained by plotting the critical stress for various values of the slenderness
ratio are called column curves. For axially loaded, initially straight columns, the
column curve consists of two parts: (1) the Euler critical values, and (2) the Engesser,
or tangent-modulus critical values.
The latter are greatly affected by the shape of the stress-strain curve for the
material of which the column is made, as shown in Fig. 5.44. The stress-strain
curve for a material, such as an aluminum alloy or high-strength steel, which does
not have a sharply defined yield point, is shown in Fig. 5.44a. The corresponding
STRUCTURAL THEORY 5.61
column curve is drawn in Fig. 5.44b. In contrast, Fig. 5.44c presents the stressstrain
curve for structural steel, with a sharply defined point, and Fig. 5.44d the
related column curve. This curve becomes horizontal as the critical stress approaches
the yield strength of the material and the tangent modulus becomes zero,
whereas the column curve in Fig. 5.44b continues to rise with decreasing values of
the slenderness ratio.
Examination of Fig. 44d also indicates that slender columns, which fall in the
elastic range, where the column curve has a large slope, are very sensitive to variations
in the factor k, which represents the effect of end conditions. On the other
hand, in the inelastic range, where the column curve is relatively flat, the critical
stress is relatively insensitive to changes in k. Hence the effect of end conditions
on the stability of a column is of much greater significance for long columns than
for short columns.
5.7.6 Local Buckling
A column may not only fail by buckling of the member as a whole but as an
alternative, by buckling of one of its components. Hence, when members like I
beams, channels, and angles are used as columns or when sections are built up of
plates, the possibility of the critical load on a component (leg, half flange, web,
lattice bar) being less than the critical load on the column as a whole should be
investigated.
Similarly, the possibility of buckling of the compression flange or the web of a
beam should be looked into.
Local buckling, however, does not always result in a reduction in the loadcarrying
capacity of a column. Sometimes, it results in a redistribution of the
stresses enabling the member to carry additional load.
5.7.7 Behavior of Actual Columns
For many reasons, columns in structures behave differently from the ideal column
assumed in deriving Eqs. (5.88) and (5.91). A major consideration is the effect of
accidental imperfections, such as nonhomogeneity of materials, initial crookedness,
and unintentional eccentricities of the axial load, since neither field nor shopwork
can be perfect. These and the effects of residual stresses usually are taken into
account by a proper choice of safety factor.
There are other significant conditions, however, that must be considered in any
design rule: continuity in frame structures and eccentricity of the axial load. Continuity
affects column action in two ways. The restraint at column ends determines
the value of k, and bending moments are transmitted to the column by adjoining
structural members.
Because of the deviation of the behavior of actual columns from the ideal,
columns generally are designed by empirical formulas. Separate equations usually
are given for short columns, intermediate columns, and long columns. For specific
materials—steel, concrete, timber—these formulas are given in Secs. 7 to 10.
For more details on column action, see F. Bleich, ‘‘Buckling Strength of Metal
Structures,’’ McGraw-Hill Publishing Company, New York, 1952: S. Timoshenko
and J. M. Gere, ‘‘Theory of Elastic Stability,’’ McGraw-Hill Publishing Company,
New York, 1961; and T. V. Galambos, ‘‘Guide to Stability Design Criteria for Metal
Structures,’’ 4th ed., John Wiley & Sons, Inc., Somerset, N.J., 1988.
5.62 SECTION FIVE
FIGURE 5.45 Addition of forces by (a) parallelogram law; (b) triangle
construction; (c) polygon construction.
5.8 GRAPHIC-STATICS FUNDAMENTALS
A force may be represented by a straight line of fixed length. The length of line to
a given scale represents the magnitude of the force. The position of the line parallels
the line of action of the force. And an arrowhead on the line indicates the direction
in which the force acts.
Forces are concurrent when their lines of action meet. If they lie in the same
plane, they are coplanar.
5.8.1 Parallelogram of Forces
The resultant of several forces is a single forces that would produce the same effect
on a rigid body. The resultant of two concurrent forces is determined by the parallelogram
law:
If a parallelogram is constructed with two forces as sides, the diagonal represents
the resultant of the forces (Fig. 5.45a).
The resultant is said to be equal to the sum of the forces, sum here meaning,
of course, addition by the parallelogram law. Subtraction is carried out in the same
manner as addition, but the direction of the force to be subtracted is reversed.
If the direction of the resultant is reversed, it becomes the equilibrant, a single
force that will hold the two given forces in equilibrium.
5.8.2 Resolution of Forces
To resolve a force into two components, a parallelogram is drawn with the force
as a diagonal. The sides of the parallelogram represent the components. The procedure
is: (1) Draw the given force. (2) From both ends of the force draw lines
parallel to the directions in which the components act. (3) Draw the components
along the parallels through the origin of the given force to the intersections with
the parallels through the other end. Thus, in Fig. 5.45a, P1 and P2 are the components
in directions OA and OB of the force represented by OC.
5.8.3 Force Polygons
Examination of Fig. 5.45a indicates that a step can be saved in adding the two
forces. The same resultant could be obtained by drawing only the upper half of the
parallelogram. Hence, to add two forces, draw the first force; then draw the second
STRUCTURAL THEORY 5.63
force beginning at the end of the first one. The resultant is the force drawn from
the origin of the first force to the end of the second force, as shown in Fig. 5.45b.
Again, the equilibrant is the resultant with direction reversed.
From this diagram, an important conclusion can be drawn: If three forces meeting
at a point are in equilibrium, they will form a closed force triangle.
The conclusions reached for addition of two forces can be generalized for several
concurrent forces: To add several forces, P1, P2, P3, . . . , Pn, draw P2 from the end
of P1, P3 from the end of P2, etc. The force required to close the force polygon is
the resultant (Fig. 5.45c).
If a group of concurrent forces are in equilibrium, they will form a closed
force polygon.
5.9 ROOF TRUSSES
A truss is a coplanar system of structural members joined together at their ends to
form a stable framework. If small changes in the lengths of the members due to
loads are neglected, the relative positions of the joints cannot change.
5.9.1 Characteristics of Trusses
Three bars pinned together to form a triangle represents the simplest type of truss.
Some of the more common types of roof trusses are shown in Fig. 6.46.
The top members are called the upper chord; the bottom members, the lower
chord; and the verticals and diagonals web members.
The purpose of roof trusses is to act like big beams, to support the roof covering
over long spans. They not only have to carry their own weight and the weight of
the roofing and roof beams, or purlins, but cranes, wind loads, snow loads, suspended
ceilings, and equipment, and a live load to take care of construction, maintenance,
and repair loading. These loads are applied at the intersection of the members,
or panel points, so that the members will be subjected principally to axial
stresses—tension or compression.
Methods of computing stresses in trusses are presented in Arts. 5.9.3 and 5.9.4.
A method of computing truss deflections is described in Art. 5.10.4.
5.9.2 Bow’s Notation
For simple designation of loads and stresses, capital letters are placed in the spaces
between truss members and between forces. Each member and load is then designated
by the letters on opposite sides of it. For example, in Fig. 5.47a, the upper
chord members are AF, BH, CJ, and DL. The loads are AB, BC, and CD, and the
reactions are EA and DE. Stresses in the members generally are designated by the
same letters but in lowercase.
5.9.3 Method of Joints
A useful method for determining the stresses in truss members is to select sections
that isolate the joints one at a time and then apply the laws of equilibrium to each.
5.64 SECTION FIVE
FIGURE 5.46 Common types of roof trusses.
Considering the stresses in the cut members as external forces, the sum of the
horizontal components of the forces acting at a joint must be zero, and so must be
the sum of the vertical components. Since the lines of action of all the forces are
known, we can therefore compute two unknown magnitudes at each joint by this
method. The procedure is to start at a joint that has only two unknowns (generally
at the support) and then, as stresses in members are determined, analyze successive
joints.
Let us, for illustration, apply the method to joint 1 of the truss in Fig. 5.47a.
Equating the sum of the vertical components to zero, we find that the vertical
component of the top-chord must be equal and opposite to the reaction, 12 kips
(12,000 lb). The stress in the top chord at this joint, then, must be a compression
equal to 12 
 30?18  20 kips. From the fact that the sum of the horizontal components
must be zero, we find that the stress in the bottom chord at the joint must
be equal and opposite to the horizontal component of the top chord. Hence the
stress in the bottom chord must be a tension equal to 20 
 24?30  16 kips.
Moving to joint 2, we note that, with no vertical loads at the joint, the stress in
the vertical is zero. Also, the stress is the same in both bottom chord members at
the joint, since the sum of the horizontal components must be zero.
Joint 3 now contains only two unknown stresses. Denoting the truss members
and the loads by the letters placed on opposite sides of them, as indicated in Fig.
5.47a, the unknown stresses are SBH and SHG. The laws of equilibrium enable us to
STRUCTURAL THEORY 5.65
FIGURE 5.47 Method of joints applied to the roof truss shown in (a).
Stresses in members at each joint are determined graphically in sucession (b)
to (e).
write the following two equations, one for the vertical components and the second
for the horizontal components:
V  0.6S  8  0.6S  0.6S  0 FA BH HG
H  0.8S  0.8S  0.8S  0 FA BH HG
Both unknown stresses are assumed to be compressive; i.e., acting toward the joint.
The stress in the vertical does not appear in these equations, because it was already
determined to be zero. The stress in FA, SFA, was found from analysis of joint 1 to
be 20 kips. Simultaneous solution of the two equations yields SHG  6.7 kips and
SBH  13.3 kips. (If these stresses had come out with a negative sign, it would
have indicated that the original assumption of their directions was incorrect; they
would, in that case, be tensile forces instead of compressive forces.) See also Art.
5.9.4.
All the force polygons in Fig. 5.47 can be conveniently combined into a single
stress diagram. The combination (Fig. 5.47?) is called a Maxwell diagram.
5.66 SECTION FIVE
FIGURE 5.48 Stresses in truss members cut by section XX, shown in (a),
are determined by method of sections (b).
5.9.4 Method of Sections
An alternative method to that described in Art. 5.9.3 for determining the stresses
in truss members is to isolate a portion of the truss by a section so chosen as to
cut only as many members with unknown stresses as can be evaluated by the laws
of equilibrium applied to that portion of the truss. The stresses in the cut members
are treated as external forces. Compressive forces act toward the panel point and
tensile forces away from the joint.
Suppose, for example, we wish to find the stress in chord AB of the truss in
Fig. 5.48a. We can take a vertical section XX close to panel point A. This cuts not
only AB but AD and ED as well. The external 10-kip (10,000-lb) loading and 25-
kip reaction at the left are held in equilibrium by the compressive force C in AB,
tensile force T in ED, and tensile force S in AD (Fig. 5.48b). The simplest way to
find C is to take moments about D, the point of intersection of S and T, eliminating
these unknowns from the calculation.
9C  36 
 25  24 
 10  12 
 10  0
from which C is found to be 60 kips.
Similarly, to find the stress in ED, the simplest way is to take moments about
A, the point of intersection of S and C:
9T  24 
 25  12 
 10  0
from which T is found to be 53.3 kips.
STRUCTURAL THEORY 5.67
On the other hand, the stress in AD can be easily determined by two methods.
One takes advantage of the fact that AB and ED are horizontal members, requiring
AD to carry the full vertical shear at section XX. Hence we know that the vertical
component V of S  25  10  10  5 kips. Multiplying V by sec  (Fig. 5.48b),
which is equal to the ratio of the length of AD to the rise of the truss (15?9), S is
found to be 8.3 kips. The second method—presented because it is useful when the
chords are not horizontal—is to resolve S into horizontal and vertical components
at D and take moments about E. Since both T and the horizontal component of S
pass through E, they do not appear in the computations, and C already has been
computed. Equating the sum of the moments to zero gives V  5, as before.
Some trusses are complex and require special methods of analysis. (Norris et
al., ‘‘Elementary Structural Analysis,’’ 4th ed., McGraw-Hill Book Company, New
York).
5.10 GENERAL TOOLS FOR
STRUCTURAL ANALYSIS
For some types of structures, the equilibrium equations are not sufficient to determine
the reactions or the internal stresses. These structures are called statically
indeterminate.
For the analysis of such structures, additional equations must be written on the
basis of a knowledge of the elastic deformations. Hence methods of analysis that
enable deformations to be evaluated in terms of unknown forces or stresses are
important for the solution of problems involving statically indeterminate structures.
Some of these methods, like the method of virtual work, are also useful in solving
complicated problems involving statically determinate systems.
5.10.1 Virtual Work
A virtual displacement is an imaginary small displacement of a particle consistent
with the constraints upon it. Thus, at one support of a simply supported beam, the
virtual displacement could be an infinitesimal rotation d  of that end but not a
vertical movement. However, if the support is replaced by a force, then a vertical
virtual displacement may be applied to the beam at that end.
Virtual work is the product of the distance a particle moves during a virtual
displacement by the component in the direction of the displacement of a force
acting on the particle. If the displacement and the force are in opposite directions,
the virtual work is negative. When the displacement is normal to the force, no work
is done.
Suppose a rigid body is acted upon by a system of forces with a resultant R.
Given a virtual displacement ds at an angle  with R, the body will have virtual
work done on it equal to R cos  ds. (No work is done by internal forces. They
act in pairs of equal magnitude but opposite direction, and the virtual work done
by one force of a pair is equal but opposite in sign to the work done by the other
force.) If the body is in equilibrium under the action of the forces, then R  0 and
the virtual work also is zero.
Thus, the principle of virtual work may be stated: If a rigid body in equilibrium
is given a virtual displacement, the sum of the virtual work of the forces acting
on it must be zero.
5.68 SECTION FIVE
FIGURE 5.49 Principle of virtual work applied
to determination of a simple-beam reaction
(a) and (b) and to the reaction of a beam with
a suspended span (c) and (d ).
As an example of how the principle
may be used to find a reaction of a statically
determinate beam, consider the
simple beam in Fig. 5.49a, for which the
reaction R is to be determined. First, replace
the support by an unknown force
R. Next, move that end of the beam upward
a small amount dy as in Fig. 5.49b.
The displacement under the load P will
be x dy/L, upward. Then, by the principle
of virtual work, R dy  Px dy/L 
0, from which R  Px/L.
The principle may also be used to
find the reaction R of the more complex
beam in Fig. 5.49c. The first step again
is to replace the support by an unknown
force R. Next, apply a virtual downward
displacement dy at hinge A (Fig. 5.49d
). Displacement under load P is x dy/c,
and at the reaction R, a dy/ (a  b). According
to the principle of virtual work,
Ra dy/ (a  b)  Px dy/c  0, from
which reaction R  Px(a  b) /ac. In
this type of problem, the method has the
advantage that only one reaction need
be considered at a time and internal
forces are not involved.
5.10.2 Strain Energy
When an elastic body is deformed, the
virtual work done by the internal forces
is equal to the corresponding increment
of the strain energy dU, in accordance with the principle of virtual work.
Assume a constrained elastic body acted upon by forces P1, P2, . . . , for which
the corresponding deformations are e1, e2 . . . . Then, Pn den  dU. The increment
of the strain energy due to the increments of the deformations is given by
U U
dU  de  de     1 2 e e 1 2
In solving a specific problem, a virtual displacement that is not convenient in simplifying
the solution should be chosen. Suppose, for example, a virtual displacement
is selected that affects only the deformation en corresponding to the load Pn, other
deformations being unchanged. Then, the principle of virtual work requires that
U
P de  de n n n en
This is equivalent to
STRUCTURAL THEORY 5.69
U
 P (5.92) n en
FIGURE 5.50 Statically indeterminate truss.
which states that the partial derivative of
the strain energy with respect to any
specific deformation gives the corresponding
force.
Suppose, for example, the stress in
the vertical bar in Fig. 5.50 is to be determined.
All bars are made of the same
material and have the same cross section.
If the vertical bar stretches an
amount e under the load P, the inclined
bars will each stretch an amount e cos
. The strain energy in the system is
[from Eq. (5.30)]
AE 2 2 3 U  (e  2e cos )
2L
and the partial derivative of this with respect to e must be equal to P; that is
AE 3 P  (2e  4e cos )
2L
AEe 3  (1  2 cos )
L
Noting that the force in the vertical bar equals AEe/L, we find from the above
equation that the required stress equals P/ (1  2 cos3 ).
Castigliano’s Theorems. It can also be shown that, if the strain energy is expressed
as a function of statically independent forces, the partial derivative of the
strain energy with respect to one of the forces gives the deformation corresponding
to that force. (See Timoshenko and Young, ‘‘Theory of Structures,’’ McGraw-Hill
Publishing Company, New York.)
U
 e (5.93) n Pn
This is known as Castigliano’s first theorem. (His second theorem is the principle
of least work.)
5.10.3 Method of Least Work
If displacement of a structure is prevented, as at a support, the partial derivative of
the strain energy with respect to that supporting force must be zero, according to
Castigliano’s first theorem. This establishes his second theorem:
The strain energy in a statically indeterminate structure is the minimum
consistent with equilibrium.
5.70 SECTION FIVE
As an example of the use of the method of least work, we shall solve again for
the stress in the vertical bar in Fig. 5.50. Calling this stress X, we note that the
stress in each of the inclined bars must be (P  X)/2 cos . With the aid of Eq.
(5.30), we can express the strain energy in the system in terms of X as
2 2 X L (P  X) L
U  3 2AE 4AE cos 
Hence, the internal work in the system will be a minimum when
U XL (P  X)L
  0 3 X AE 2AE cos 
Solving for X gives the stress in the vertical bar as P/ (1  2 cos3 ), as before
(Art. 5.10.1).
5.10.4 Dummy Unit-Load Method
In Art. 5.2.7, the strain energy for pure bending was given as U  M2L/2EI in Eq.
(5.33). To find the strain energy due to bending stress in a beam, we can apply this
equation to a differential length dx of the beam and integrate over the entire span.
Thus,
L 2 M dx
U   (5.94)
0 2EI
If M represents the bending moment due to a generalized force P, the partial derivative
of the strain energy with respect to P is the deformation d corresponding
to P. Differentiating Eq. (5.94) under the integral sign gives
L M M
d   dx (5.95)
0 EI P
The partial derivative in this equation is the rate of change of bending moment with
the load P. It is equal to the bending moment m produced by a unit generalized
load applied at the point where the deformation is to be measured and in the
direction of the deformation. Hence, Eq. (5.95) can also be written
L Mm
d   dx (5.96)
0 EI
To find the vertical deflection of a beam, we apply a vertical dummy unit load at
the point where the deflection is to be measured and substitute the bending moments
due to this load and the actual loading in Eq. (5.96). Similarly, to compute a rotation,
we apply a dummy unit moment.
Beam Deflections. As a simple example, let us apply the dummy unit-load
method to the determination of the deflection at the center of a simply supported,
uniformly loaded beam of constant moment of inertia (Fig. 5.51a). As indicated in
Fig. 5.51b, the bending moment at a distance x from one end is (wL/2)x  (w/
2)x2. If we apply a dummy unit load vertically at the center of the beam (Fig.
STRUCTURAL THEORY 5.71
FIGURE 5.51 Dummy unit-load method applied
to a uniformly loaded, simple beam (a) to
find mid-span deflection; (b) moment diagram
for the uniform load; (c) unit load at midspan:
(d ) moment diagram for the unit load.
FIGURE 5.52 End rotation of a simple beam
due to an end moment: (a) by dummy unit-load
method; (b) moment diagram for the end moment;
(c) unit moment applied at beam end;
(d ) moment diagram for the unit moment.
5.51c), where the vertical deflection is to be determined, the moment at x is x/2,
as indicated in Fig. 5.51d. Substituting in Eq. (5.96) and taking advantage of the
symmetry of the loading gives
L / 2 4 wL w x dx 5wL 2 d  2  x  x  
  0 2 2 2EI 384EI
Beam End Rotations. As another example, let us apply the method to finding the
end rotation at one end of a simply supported, prismatic beam produced by a
moment applied at the other end. In other words, the problem is to find the end
rotation at B, B, in Fig. 5.52a, due to MA. As indicated in Fig. 5.52b, the bending
moment at a distance x from B caused by MA is MAx/L. If we applied a dummy
unit moment at B (Fig. 5.52c), it would produce a moment at x of (L  x) /L (Fig.
5.52d). Substituting in Eq. (5.96) gives
L x L  x dx M L A    M  B A
0 L L EI 6EI
Shear Deflections. To determine the deflection of a beam caused by shear, Castigliano’s
theorems can be applied to the strain energy in shear
2 v
V    dA dx
2G
5.72 SECTION FIVE
where v  shearing unit stress
G  modulus of rigidity
A  cross-sectional area
Truss Deflections. The dummy unit-load method may also be adapted for the
determination of the deformation of trusses. As indicated by Eq. (5.30), the strain
energy in a truss is given by
2 S L
U  (5.97) 	 2AE
which represents the sum of the strain energy for all the members of the truss. S
is the stress in each member caused by the loads. Applying Castigliano’s first
theorem and differentiating inside the summation sign yield the deformation:
SL S
d  (5.98) 	 AE P
The partial derivative in this equation is the rate of change of axial stress with the
load P. It is equal to the axial stress u in each bar of the truss produced by a unit
load applied at the point where the deformation is to be measured and in the
direction of the deformation. Consequently, Eq. (5.98) can also be written
Sul
d  (5.99) 	 AE
To find the deflection of a truss, apply a vertical dummy unit load at the panel
point where the deflection is to be measured and substitute in Eq. (5.99) the stresses
in each member of the truss due to this load and the actual loading. Similarly, to
find the rotation of any joint, apply a dummy unit moment at the joint, compute
the stresses in each member of the truss, and substitute in Eq. (5.99). When it is
necessary to determine the relative movement of two panel points, apply dummy
unit loads in opposite directions at those points.
It is worth noting that members that are not stressed by the actual loads or the
dummy loads do not enter into the calculation of a deformation.
As an example of the application of Eq. (5.99), let us compute the deflection of
the truss in Fig. 5.53. The stresses due to the 20-kip load at each panel point are
shown in Fig. 5.53a, and the ratio of length of members in inches to their crosssectional
area in square inches is given in Table 5.5. We apply a vertical dummy
unit load at L2, where the deflection is required. Stresses u due to this load are
shown in Fig. 5.53b and Table 5.5.
The computations for the deflection are given in Table 5.5. Members not stressed
by the 20-kip loads or the dummy unit load are not included. Taking advantage of
the symmetry of the truss, we tabulate the values for only half the truss and double
the sum.
SuL 2 
 13.742,000
d  0.916 in
AE 30,000,000
Also, to reduce the amount of calculation, we do not include the modulus of
elasticity E, which is equal to 30,000,000, until the very last step, since it is the
same for all members.
STRUCTURAL THEORY 5.73
FIGURE 5.53 Dummy unit-load method applied to the loaded truss shown in (a) to find midspan
deflection; (b) unit load applied at midspan.
TABLE 5.5 Deflection of a Truss
Member L/A S u SuL/A
L0L2
L0U1
U1U2
U1L2
160
75
60
150
40
50
53.3
16.7
2?3
5?6
4?3
5?6
4,267
3,125
4,267
2,083
13,742
5.10.5 Reciprocal Theorem and Influence Lines
Consider a structure loaded by a group of independent forces A, and suppose that
a second group of forces B are added. The work done by the forces A acting over
the displacements due to B will be WAB.
Now, suppose the forces B had been on the structure first, and then load A had
been applied. The work done by the forces B acting over the displacements due to
A will be WBA.
The reciprocal theorem states that WAB  WBA.
Some very useful conclusions can be drawn from this equation. For example,
there is the reciprocal deflection relationship: The deflection at a point A due to
a load at B is equal to the deflection at B due to the same load applied at A.
Also, the rotation at A due to a load (or moment) at B is equal to the rotation
at B due to the same load (or moment) applied at A.
Another consequence is that deflection curves may also be influence lines to
some scale for reactions, shears, moments, or deflections (Muller-Breslau principles).
(Influence lines are defined in Art. 5.5.8.) For example, suppose the influence
5.74 SECTION FIVE
FIGURE 5.56 Moment-influence line for a
continuous beam.
FIGURE 5.57 Deflection-influence line for a
continuous beam.
FIGURE 5.54 Reaction-influence line for a
continuous beam.
FIGURE 5.55 Shear-influence line for a continuous
beam.
line for a reaction is to be found; that is, we wish to plot the reaction R as a unit
load moves over the structure, which may be statically indeterminate. For the loading
condition A, we analyze the structure with a unit load on it at a distance x from
some reference point. For loading condition B, we apply a dummy unit vertical
load upward at the place where the reaction is to be determined, deflecting the
structure off the support. At a distance x from the reference point, the displacement
in dxR and over the support the displacement is dRR. Hence WAB   1 (DxR) 
RdRR. On the other hand, WBA is zero, since loading condition A provides no displacement
for the dummy unit load at the support in condition B. Consequently,
from the reciprocal theorem,
dxR R 
dRR
Since dRR is a constant, R is proportional to dxR. Hence the influence line for a
reaction can be obtained from the deflection curve resulting from a displacement
of the support (Fig. 5.54). The magnitude of the reaction is obtained by dividing
each ordinate of the deflection curve by the displacement of the support.
Similarly, the influence line for shear can be obtained from the deflection curve
produced by cutting the structure and shifting the cut ends vertically at the point
for which the influence line is desired (Fig. 5.55).
The influence line for bending moment can be obtained from the deflection curve
produced by cutting the structure and rotating the cut ends at the point for which
the influence line is desired (Fig. 5.56).
And finally, it may be noted that the deflection curve for a load of unity at some
point of a structure is also the influence line for deflection at that point (Fig. 5.57).
5.10.6 Superposition Methods
The principle of superposition applies when the displacement (deflection or rotation)
of every point of a structure is directly proportional to the applied loads. The
STRUCTURAL THEORY 5.75
principle states that the displacement at each point caused by several loads equals
the sum of the displacements at the point when the loads are applied to the structure
individually in any sequence. Also, the bending moment (or shear) at every point
induced by applied loads equals the sum of the bending moments (or shears) induced
at the point by the loads applied individually in any sequence.
The principle holds for linearly elastic structures, for which unit stresses are
proportional to unit strains, when displacements are very small and calculations can
be based on the underformed configuration of the structure without significant error.
As a simple example, consider a bar with length L and cross-sectional area A
loaded with n axial loads P1, P2 . . . Pn. Let F equal the sum of the loads. From
Eq. (5.23), F causes an elongation  FL/AE, where E is the modulus of elasticity
of the bar. According to the principle of superposition, if e1 is the elongation caused
by P1 alone, e2 by P2 alone, . . and en by Pn alone, then regardless of the sequence
in which the loads are applied, when all the loads are on the bar,
 e  e      e 1 2 n
This simple case can be easily verified by substituting e1  P1L/AE, e2  P2L/AE,
. . . , and en  PnL/AE in this equation and noting that F  P1  P2      Pn:
P L P L P L L FL 1 2 n      (P  P      P )  1 2 n AE AE AE AE AE
In the preceding equations, L/AE represents the elongation induced by a unit
load and is called the flexibility of the bar.
The reciprocal, AE/L, represents the force that causes a unit elongation and is
called the stiffness of the bar.
Analogous properties of beams, columns, and other structural members and the
principle of superposition are useful in analysis of many types of structures. Calculation
of stresses and displacements of statically indeterminate structures, for
example, often can be simplified by resolution of bending moments, shears, and
displacements into components chosen to supply sufficient equations for the solution
from requirements for equilibrium of forces and compatibility of displacements.
Consider the continuous beam ALRBC shown in Fig. 5.58a. Under the loads
shown, member LR is subjected to end moments ML and MR (Fig. 5.58b) that are
initially unknown. The bending-moment diagram for LR for these end moments is
shown at the left in Fig. 5.58c. If these end moments were known, LR would be
statically determinate; that is LR could be treated as a simply supported beam
subjected to known end moments ML and MR. The analysis can be further simplified
by resolution of the bending-moment diagram into the three components shown to
the right of the equal sign in Fig. 5.58c. This example leads to the following
conclusion:
The bending moment at any section of a span LR of a continuous beam or
frame equals the simple-beam moment due to the applied loads, plus the simple-
beam moment due to the end moment at L, plus the simple-beam moment
due to the end moment at R.
When the moment diagrams for all the spans of ALRBC in Fig. 5.58 have been
resolved into components so that the spans may be treated as simple beams, all the
end moments (moments at supports) can be determined from two basic requirements:
5.76 SECTION FIVE
FIGURE 5.58 Any span of a continuous beam (a) can be treated as a
simple beam, as shown in (b) and (c), the moment diagram is resolved into
basic components.
1. The sum of the moments at every support equals zero.
2. The end rotation (angular change at the support) of each member rigidly connected
at the support is the same.
5.10.7 Influence-Coefficient Matrices
A matrix is a rectangular array of numbers in rows and columns that obeys certain
mathematical rules known generally as matrix algebra and matrix calculus. A matrix
consisting of only a single column is called a vector. In this book, matrices and
vectors are represented by boldfaced letters and their elements by lightface symbols,
with appropriate subscripts. It often is convenient to use numbers for the subscripts
to indicate the position of an element in the matrix. Generally, the first digit indicates
the row and the second digit the column. Thus, in matrix A, A23 represents
the element in the second row and third column:
A A A 11 12 13
A  A A A (5.100) 21 22 23  	 A A A 31 32 33
Methods based on matrix representations often are advantageous for structural
analysis and design of complex structures. One reason is that matrices provide a
compact means of representing and manipulating large quantities of numbers. Another
reason is that computers can perform matrix operations automatically and
speedily. Computer programs are widely available for this purpose.
Matrix Equations. Matrix notation is especially convenient in representing the
solution of simultaneous liner equations, which arise frequently in structural analysis.
For example, suppose a set of equations is represented in matrix notation by
STRUCTURAL THEORY 5.77
AX  B, where X is the vector of variables X1, X2, . . . , Xn, B is the vector of the
constants on the right-hand side of the equations, and A is a matrix of the coeffi-
cients of the variables. Multiplication of both sides of the equation by A , the 1
inverse of A, yieldsA AXA B. SinceA A I, the identity matrix, and IX 1 1 1
 X, the solution of the equations is represented by X A B. The matrix inver- 1
sion A can be readily performed by computers. For large matrices, however, it 1
often is more practical to solve the equations, for example, by the Gaussian procedure
of eliminating one unknown at a time.
In the application of matrices to structural analysis, loads and displacements are
considered applied at the intersection of members (joints, or nodes). The loads may
be resolved into moments, torques, and horizontal and vertical components. These
may be assembled for each node into a vector and then all the node vectors may
be combined into a force vector P for the whole structure.
P1
P2 P  (5.101)

  	 Pn
Similarly, displacement corresponding to those forces may be resolved into rotations,
twists, and horizontal and vertical components and assembled for the whole
structure into a vector 
.
1
2 
  (5.102)

  	 n
If the structure meets requirements for application of the principle of superposition
(Art. 5.10.6) and forces and displacements are arranged in the proper sequence, the
vectors of forces and displacements are related by
P  K
 (5.103a)

  FP (5.103b)
where K  stiffness matrix of the whole structure
F  flexibility matrix of the whole structure  K1
The stiffness matrix K transform displacements into loads. The flexibility matrix
F transforms loads into displacements. The elements of K and F are functions of
material properties, such as the modules of elasticity; geometry of the structure;
and sectional properties of members of the structure, such as area and moment of
inertia. K and F are square matrices; that is, the number of rows in each equals
the number of columns. In addition, both matrices are symmetrical; that is, in each
matrix, the columns and rows may be interchanged without changing the matrix.
Thus, Kij  Kji, and Fij  Fji, where i indicates the row in which an element is
located and j the column.
Influence Coefficients. Elements of the stiffness and flexibility matrices are in-
fluence are coefficients. Each element is derived by computing the displacements
(or forces) occurring at nodes when a unit displacement (or force) is imposed at
one node, while all other displacements (or forces) are taken as zero.
5.78 SECTION FIVE
Let i be the ith element of matrix 
. Then a typical element Fij of F gives the
displacement of anode i in the direction of i when a unit force acts at a node j in
the direction of force Pj and no other forces are acting on the structure. The jth
column of F, therefore, contains all the nodal displacements induced by a unit force
acting at node j in the direction of Pj.
Similarly, Let Pi be the ith element of matrix P. Then, a typical element Kij of
K gives the force at a node i in the direction of Pi when a node j is given a unit
displacement in the direction of displacement j and no other displacements are
permitted. The jth column of K, therefore, contains all the nodal forces caused by
a unit displacement of node j in the direction of j.
Application to a Beam. A general method for determining the forces and moments
in a continuous beam is as follows: Remove as many redundant supports or
members as necessary to make the structure statically determinant. Compute for
the actual loads the deflections or rotations of the statically determinate structure
in the direction of the unknown forces and couples exerted by the removed supports
and members. Then, in terms of these forces and couples, treated as variables,
compute the corresponding deflections or rotations the forces and couples produce
in the statically determinate structure (see Arts. 5.5.16 and 5.10.4). Finally, for each
redundant support or member write equations that give the known rotations or
deflections of the original structure in terms of the deformations of the statically
determinate structure.
For example, one method of finding the reactions of the continuous beam AC
in Fig. 5.59a is to remove supports 1, 2, and 3 temporarily. The beam is now
simply supported between A and C, and the reactions and moments can be computed
from the laws of equilibrium. Beam AC deflects at points 1, 2, and 3, whereas
we know that the continuous beam is prevented from deflecting at these points by
the supports there. This information enables us to write three equations in terms of
the three unknown reactions that were eliminated to make the beam statically determinate.
To determine the equations, assume that nodes exist at the location of the supports
1, 2, and 3. Then, for the actual loads, compute the vertical deflections d1,
d2, and d3 of simple beam AC at nodes 1, 2, and 3, respectively (Fig. 5.59b). Next,
form two vectors, d with element d1, d2 and R with the unknown reactions R1 at
node 1, R2 at node 2, and R3 at node 3 as elements. Since the beam may be assumed
to be linearly elastic, set d  FR, where F is the flexibility matrix for simple beam
AC. The elements yij of F are influence coefficients. To determine them, calculate
column 1 of F as the deflections y11, y21, and y31 at nodes 1, 2, and 3, respectively,
when a unit force is applied at node 1 (Fig. 5.59c). Similarly, compute column 2
of F for a unit force at node 2 (Fig. 5.59d) and column 3 for a unit force at node
3 (Fig. 5.59e). The three equations then are given by
y y y R d 11 12 13 1 1
y y y R  d (5.104) 21 22 23 2 2  		 	 y y y R d 31 32 33 3 3
The solution may be represented by R F dand obtained by matrix or algebraic 1
methods. See also Art. 5.13.
5.11 CONTINUOUS BEAMS AND FRAMES
Fixed-end beams, continuous beams, continuous trusses, and rigid frames are statically
indeterminate. The equations of equilibrium are not sufficient for the deterSTRUCTURAL
THEORY 5.79
FIGURE 5.59 Determination of reactions of
continuous beam AC: (a) Loaded beam with supports
at points 1, 2, and 3. (b) Deflection of beam
when supports are removed. (c) to (e) Deflections
when a unit load is applied successively at points
1, 2, and 3.
mination of all the unknown forces and moments. Additional equations based on a
knowledge of the deformation of the member are required.
Hence, while the bending moments in a simply supported beam are determined
only by the loads and the span, bending moments in a statically indeterminate
member are also a function of the geometry, cross-sectional dimensions, and modulus
of elasticity.
5.11.1 Sign Convention
For computation of end moments in continuous beams and frames, the following
sign convention is most convenient: A moment acting at an end of a member or at
a joint is positive if it tends to rotate the joint clockwise, negative if it tends to
rotate the joint counterclockwise.
Similarly, the angular rotation at the end of a member is positive if in a clockwise
direction, negative if counterclockwise. Thus, a positive end moment produces a
positive end rotation in a simple beam.
For ease in visualizing the shape of the elastic curve under the action of loads
and end moments, bending-moment diagrams should be plotted on the tension side
5.80 SECTION FIVE
FIGURE 5.60 End rotations of a simple beam LR when a unit moment
is applied (a) at end L and (b) at end R.
of each member. Hence, if an end moment is represented by a curved arrow, the
arrow will point in the direction in which the moment is to be plotted.
5.11.2 Carry-Over Moments
When a member of a continuous beam or frame is loaded, bending moments are
induced at the ends of the member as well as between the ends. The magnitude of
the end moments depends on the magnitude and location of the loads, the geometry
of the member, and the amount of restraint offered to end rotation of the member
by other members connected to it. Because of the restraint, end moments are induced
in the connecting members, in addition to end moments that may be induced
by loads on those spans.
If the far end of a connecting member is restrained by support conditions against
rotation, a resisting moment is induced at that end. That moment is called a carryover
moment. The ratio of the carry-over moment to the other end moment is called
carry-over factor. It is constant for the member, independent of the magnitude and
direction of the moments to be carried over. Every beam has two carry-over factors,
one directed toward each end.
As pointed out in Art. 5.10.6, analysis of a continuous span can be simplified
by treating it as a simple beam subjected to applied end moments. Thus, it is
convenient to express the equations for carry-over factors in terms of the end rotations
of simple beams: Convert a continuous member LR to a simple beam with
the same span L. Apply a unit moment to one end (Fig. 5.60). The end rotation at
the support where the moment is applied is , and at the far end, the rotation is .
By the dummy-load method (Art. 5.10.4), if x is measured from the  end,
L 2 1 x
  dx (5.105) 2 0 L EIx
L 1 x(L  x)
  dx (5.106) 2 0 L EIx
in which Ix  moment of inertia at a section a distance of x from the  end
E  modulus of elasticity
In accordance with the reciprocal theorem (Art. 5.10.5)  has the same value regardless
of the beam end to which the unit moment is applied (Fig. 5.60). For
prismatic beams (Ix  constant),
STRUCTURAL THEORY 5.81
FIGURE 5.61 Effect of applying an end moment M to any span of a continuous
beam: (a) An end moment CRM is induced at the opposite end. (b) and (c) The
moment diagram in (a) is resolved into moment diagrams for a simple beam. (d )
and (e) Addition of the end rotations corresponding to conditions (b) and (c) yields
( ? ), the end rotations induced by M in the beam shown in (a)
L
    (5.107) L R 3EI
L
 (5.108)
6EI
Carry-Over Factors. The preceding equations can be used to determine carryover
factors for any magnitude of end restraint. The carry-over factors toward fixed
ends, however, are of special importance.
The bending-moment diagram for a continuous span LR that is not loaded except
for a moment M applied at end L is shown in Fig. 5.61a. For determination of the
carry-over factor CR toward R, that end is assumed fixed (no rotation can occur
there). The carry-over moment to R then is CRM. The moment diagram in Fig.
5.61a can be resolved into two components: a simple beam with M applied at L
(Fig. 5.61b) and a simple beam with CRM applied at R (Fig. 5.61c). As indicated
in Fig. 5.61d, M causes an angle change at R of . As shown in Fig. 5.61e, CR
M induces an angle change at R of CRMR. Since the net angle change at R is zero
(Fig. 5.61?), CRMR  M 0, from which

C  (5.109) R R
Similarly, the carry-over factor toward support L is given by

C  (5.110) L L
Since the carry-over factors are positive, the moment carried over has the same
sign as the applied moment. For prismatic beams,   L/6EI and   L/3EI.
Hence,
5.82 SECTION FIVE
L 3EI 1
C  C   (5.111) L R 6EI L 2
For beams with variable moment of inertia,  and  can be determined from Eqs.
(5.105) and (5.106) and the carry-over factors from Eqs. (5.109) and (5.110).
If an end of a beam is free to rotate, the carry-over factor toward that end is
zero.
FIGURE 5.62 Determination of fixed-end
stiffness: (a) elastic curve for moment KR causing
a unit end rotation; (b) the moment diagram
for condition (a).
5.11.3 Fixed-End Stiffness
The fixed-end stiffness of a beam is de-
fined as the moment that is required to
induce a unit rotation at the support
where it is applied while the other end
of the beam is fixed against rotation.
Stiffness is important because, in the
moment-distribution method, it determines
the proportion of the total moment
applied at a joint, or intersection
of members, that is distributed to each
member of the joint.
In Fig. 5.62a, the fixed-end stiffness
of beam LR at end R is represented by
KR. When KR is applied to beam LR at
R, a moment ML  CLKR is carried over
to end L, where CL is the carry-over factor
toward L (see Art. 5.11.2). KR induces
an angle change R at R, where R is given by Eq. (5.105). The carry-over
moment induces at R an angle change CLkR , where  is given by Eq. (5.106).
Since, by the definition of stiffness, the total angle change at R is unit, KR R 
CLKR  1, from which
1/ R K  (5.112) R 1  C C R L
when CR is substituted for / R [see Eq. (5.109)].
In a similar manner, the stiffness at L is found to be
1/ L K  (5.113) L 1  C C R L
With the use of Eqs. (5.107) and (5.111), the stiffness of a beam with constant
moment of inertia is given by
3EI/L 4EI
K  K  (5.114) L R 1  1/2 
 1/2 L
where L  span of the beam
E  modulus of elasticity
I  moment of inertia of beam cross section
Beam with Hinge. The stiffness of one end of a beam when the other end is free
to rotate can be obtained from Eqs. (5.112) or (5.113) by setting the carry-over
factor toward the hinged end equal to zero. Thus, for a prismatic beam with one
end hinged, the stiffness of the beam at the other end is given by
STRUCTURAL THEORY 5.83
FIGURE 5.63 Determination of fixed-end moments in beam LR: (a) Loads on the fixed-end
beam are resolved (b) to (d ) into the sum of loads on a simple beam. (e) to (h) Bending-moment
diagrams for conditions (a) to (d ), respectively.
3EI
K  (5.115)
L
This equation indicates that a prismatic beam hinged at only one end has threefourths
the stiffness, or resistance to end rotation, of a beam fixed at both ends.
5.11.4 Fixed-End Moments
A beam so restrained at its ends that no rotation is produced there by the loads is
called a fixed-end beam, and the end moments are called fixed-end moments. Fixedend
moments may be expressed as the product of a coefficient and WL, where W
is the total load on the span L. The coefficient is independent of the properties of
other members of the structure. Thus, any member can be isolated from the rest of
the structure and its fixed-end moments computed.
Assume, for example, that the fixed-end moments for the loaded beam in Fig.
5.63a are to be determined. Let M be the moment at the left end L and M the F F
L R
moment at the right end R of the beam. Based on the condition that no rotation is
permitted at either end and that the reactions at the supports are in equilibrium with
the applied loads, two equations can be written for the end moments in terms of
the simple-beam end rotations, L at L and R, at R for the specific loading.
Let KL be the fixed-end stiffness at L and KR the fixed-end stiffness at R, as
given by Eqs. (5.112) and (5.113). Then, by resolution of the moment diagram into
simple-beam components, as indicated in Fig. 5.63? to h, and application of the
superposition principle (Art. 5.10.6), the fixed-end moments are found to be
F M  K (   C  ) (5.116) L L L R R
F M  K (   C  ) (5.117) R R R L L
where CL and CR are the carry-over factors to L and R, respectively [Eqs. (5.109)
and (5.110)]. The end rotations L and R can be computed by a method described
in Art. 5.5.15 or 5.10.4.
Prismatic Beams. The fixed-end moments for beams with constant moment of
inertia can be derived from the equations given above with the use of Eqs. (5.111)
and (5.114):
5.84 SECTION FIVE
FIGURE 5.64 End moments caused by displacement
d of one end of a fixed-end beam.
FIGURE 5.65 End moment caused by displacement
d of one end of a propped beam.
4EI 1 F M      (5.118) 
  L L R L 2
4EI 1 F M      (5.119) 
  R R L L 2
where L  span of the beam
E  modulus of elasticity
I  moment of inertia
For horizontal beams with gravity loads only, R is negative. As a result, M is FL
negative and M positive. FR
For propped beams (one end fixed, one end hinged) with variable moment of
inertia, the fixed-end moments are given by
  L R F F M  or M  (5.120) L R   L R
where L and R are given by Eq. (5.105). For prismatic propped beams, the fixedend
moments are
3EI  3EI  L R F F M  or M  (5.121) L R L L
Deflection of Supports. Fixed-end moments for loaded beams when one support
is displaced vertically with respect to the other support may be computed with the
use of Eqs. (5.116) to (5.121) and the principle of superposition: Compute the fixedend
moments induced by the deflection of the beam when not loaded and add them
to the fixed-end moments for the loaded condition with immovable supports.
The fixed-end moments for the unloaded condition can be determined directly
from Eqs. (5.116) and (5.117). Consider beam LR in Fig. 5.64, with span L and
support R deflected a distance d vertically below its original position. If the beam
were simply supported, the angle change caused by the displacement of R would
be very nearly d/L. Hence, to obtain the fixed-end moments for the deflected conditions,
set L  R  d/L and substitute these simple-beam end rotations in Eqs.
(5.116) and (5.117):
F M  K (1  C )d/L (5.122) L L R
F M  K (1  C )d/L (5.123) R R L
If end L is displaced downward with respect to R, d/L would be negative and the
fixed-end moments positive.
STRUCTURAL THEORY 5.85
FIGURE 5.68 Moments for two equal loads
on a prismatic fixed-end beam.
FIGURE 5.69 Moments for several equal
loads on a prismatic fixed-end beam.
FIGURE 5.66 Moments for concentrated load
on a prismatic fixed-end beam.
FIGURE 5.67 Moments for a uniform load on
a prismatic fixed-end beam.
For beams with constant moment of inertia, the fixed-end moments are given
by
6EI d F F M  M   (5.124) L R L L
The fixed-end moments for a propped beam, such as beam LR shown in Fig.
5.65, can be obtained similarly from Eq. (5.120). For variable moment of inertia,
d 1 F M  (5.125)
L L
For a prismatic propped beam,
3EI d F M   (5.126)
L L
Reverse signs for downward displacement of end L.
Computation Aids for Prismatic Beams. Fixed-end moments for several common
types of loading on beams of constant moment of inertia (prismatic beams) are
given in Figs. 5.66 to 5.69. Also, the curves in Fig. 5.71 enable fixed-end moments
to be computed easily for any type of loading on a prismatic beam. Before the
5.86 SECTION FIVE
FIGURE 5.70 Characteristics of loadings.
curves can be entered, however, certain characteristics of the loading must be calculated.
These include L, the location of the center of gravity of the loading with x
respect to one of the loads: G2  b Pn /W, where bnL is the distance from each 2n
load Pn to the center of gravity of the loading (taken positive to the right); and
S3  b Pn /W. (See Case 9, Fig. 5.70.) These values are given in Fig. 5.70 for 3n
some common types of loading.
The curves in Fig. 5.71 are entered with the location a of the center of gravity
with respect to the left end of the span. At the intersection with the proper G curve,
proceed horizontally to the left to the intersection within the proper S line, then
vertically to the horizontal scale indicating the coefficient m by which to multiply
WL to obtain the fixed-end moment. The curves solve the equations:
F ML 2 2 3 m G [1  3(1  a)]  a(1  a)  S (5.127) L WL
F MR 2 2 3 m  G (1  3a)  a (1  a)  S (5.128) R WL
where M is the fixed-end moment at the left support and M at the right support. F F
L R
As an example of the use of the curves, find the fixed-end moments in a prismatic
beam of 20-ft span carrying a triangular loading of 100 kips, similar to the
loading shown in Case 4, Fig. 5.70, distributed over the entire span, with the maximum
intensity at the right support.
STRUCTURAL THEORY 5.87
FIGURE 5.71 Chart for fixed-end moments due to any type of loading.
FIGURE 5.72 Elastic curve for a span LR of a continuous
beam subjected to end moments and displacement of one end.
Case 4 gives the characteristics of the loading: y  1; the center of gravity is
0.33L from the right support, so a  0.667; G2  1?18  0.056; and S3  1?135 
0.007. To find M , enter Fig. 5.71 with a  0.67 on the upper scale at the bottom FR
of the diagram, and proceed vertically to the estimated location of the intersection
of the coordinate with the G2  0.06 curve. Then, move horizontally to the intersection
with the line for S3  0.007, as indicated by the dash line in Fig. 5.71.
Referring to the scale at the top of the diagram, find the coefficient mR to be 0.10.
Similarly, with a  0.67 on the lowest scale, find the coefficient mL to be 0.07.
Hence, the fixed-end moment at the right support is 0.10 
 100 
 20  200 ftkips,
and at the left support 0.07 
 100 
 20  140 ft-kips.
5.11.5 Slope-Deflection Equations
In Arts. 5.11.2 and 5.11.4, moments and displacements in a member of a continuous
beam or frame are obtained by addition of their simple-beam components. Similarly,
moments and displacements can be determined by superposition of fixed-end-beam
components. This method, for example, can be used to derive relationships between
end moments and end rotations of a beam known as slope-deflection equations.
These equations can be used to compute end moments in continuous beams.
Consider a member LR of a continuous beam or frame (Fig. 5.72). LR may have
a moment of inertia that varies along its length. The support R is displaced vertically
5.88 SECTION FIVE
FIGURE 5.73 Elastic curve for a simple beam LR
subjected to end moments.
downward a distance d from its original position. Because of this and the loads on
the member and adjacent members, LR is subjected to end moments ML are so
small that the member can be considered to rotate clockwise through an angle
nearly equal to d/L, where L is the span of the beam.
Assume that rotation is prevented at ends L and R by end moments mL at L and
mR at R. Then, by application of the principle of superposition (Art. 5.10.6) and
Eqs. (5.122) and (5.123),
d F m  M  K (1  C ) (5.129) L L L R L
d F m  M  K (1  C ) (5.130) R R R L L
where M  FL
fixed-end moment at L due to the load on LR
M  FR
fixed-end moment at R due to the load on LR
KL  fixed-end stiffness at end L
KR  fixed-end stiffness at end R
CL  carry-over factor toward end L
CR  carry-over factor toward end R
Since ends L and R are not fixed but actually undergo angle changes L and R
at L and R, respectively, the joints must now be permitted to rotate while an end
moment M is applied at L and an end moment M at R to produce those angle   L R
changes (Fig. 5.73). With the use of the definitions of carry-over factor (Art. 5.11.2)
and fixed-end stiffness (Art. 5.11.3), these moments are found to be
M  K (   C  ) (5.131) L L L RR
M  K (   C  ) (5.132) R R R LL
The slope-deflection equations for LR then result from addition of M to mL, which L
yields ML, and of M to mR, which yields MR: R
d F M  K (   C  )  M  K (1  C ) (5.133) L L L RR L L R L
d F M  K (   C  )  M  K (1  C ) (5.134) R R R LL R R L L
For beams with constant moment of inertia, the slope-deflection equations become
STRUCTURAL THEORY 5.89
4EI 1 6EI d F M      M  (5.135) 
  L L R L L 2 L L
4EI 1 6EI d F M      M  (5.136) 
  R R L R L 2 L L
where E  modulus of elasticity
I  moment of inertia of the cross section
Note that if end L moves downward with respect to R, the sign for d in the
preceding equations is changed.
If the end moments ML and MR are known and the end rotations are to be
determined, Eqs. (5.131) to (5.134) can be solved for L and R or derived by
superposition of simple-beam components, as is done in Art. 5.11.4. For beams
with moment of inertia varying along the span:
d F F   (M  M )   (M  M )  (5.137) L L L L R R L
d F F   (M  M )   (M  M )  (5.138) R R R R L L L
where  is given by Eq. (5.105) and  by Eq. (5.106). For beams with constant
moment of inertia:
L L d F F   (M  M )  (M  M )  (5.139) L L L R R 3EI 6EI L
L L d F F   (M  M )  (M  M )  (5.140) R R R L L 3EI 6EI L
The slope-deflection equations can be used to determine end moments and rotations
of the spans of continuous beams by writing compatibility and equilibrium
equations for the conditions at each support. For example, the sum of the moments
at each support must be zero. Also, because of continuity, the member must rotate
through the same angle on both sides of every support. Hence, ML for one span,
given by Eq. (5.133) or (5.135), must be equal to MR for the adjoining span,
given by Eq. (5.134) or (5.136), and the end rotation  at that support must be the
same on both sides of the equation. One such equation with the end rotations at
the supports as the unknowns can be written for each support. With the end rotations
determined by simultaneous solution of the equations, the end moments can be
computed from the slope-deflection equations and the continuous beam can now
be treated as statically determinate.
See also Arts. 5.11.9 and 5.13.2.
(C. H. Norris et al., ‘‘Elementary Structural Analysis,’’ 4th ed., McGraw-Hill
Book Company, New York.)
5.11.6 Moment Distribution
The frame in Fig. 5.74 consists of four prismatic members rigidly connected together
at O at fixed at ends A, B, C, and D. If an external moment U is applied at
5.90 SECTION FIVE
O, the sum of the end moments in each member at O must be equal to U. Furthermore,
all members must rotate at O through the same angle , since they are
assumed to be rigidly connected there. Hence, by the definition of fixed-end stiffness,
the proportion of U induced in the end of each member at O is equal to the
ratio of the stiffness of that member to the sum of the stiffnesses of all the members
at the joint (Art. 5.11.3).
FIGURE 5.74 Effect of an unbalanced moment
at a joint in a frame.
Suppose a moment of 100 ft-kips is
applied at O, as indicated in Fig. 5.74b.
The relative stiffness (or I /L) is assumed
as shown in the circle on each member.
The distribution factors for the moment
at O are computed from the stiffnesses
and shown in the boxes. For example,
the distribution factor for OA equals its
stiffness divided by the sum of the stiffnesses
of all the members at the joint:
3/(3  2  4  1)  0.3. Hence, the
moment induced in OA at O is 0.3 

100  30 ft-kips. Similarly, OB gets 10
ft-kips, OC 40 ft-kips and OD 20 ftkips.
Because the far ends of these members
are fixed, one-half of these moments
are carried over to them (Art.
5.11.2). Thus MAO  0.5 
 30  15;
MBO  0.5 
 10  5; MCO  0.5 

40  20; and MDO  0.5 
 20  10.
Most structures consist of frames
similar to the one in Fig. 5.74, or even
simpler, joined together. Though the
ends of the members are not fixed, the
technique employed for the frame in
Fig. 5.74b can be applied to find end
moments in such continuous structures.
Before the general method is presented, one short cut is worth noting. Advantage
can be taken when a member has a hinged end to reduce the work of distributing
moments. This is done by using the true stiffness of a member instead of the fixedend
stiffness. (For a prismatic beam with one end hinged, the stiffness is threefourth
the fixed-end stiffness; for a beam with variable I, it is equal to the fixedend
stiffness times 1  CLCR, where CL and CR are the carry-over factors for the
beam.) Naturally, the carry-over factor toward the hinge is zero.
When a joint is neither fixed nor pinned but is restrained by elastic members
connected there, moments can be distributed by a series of converging approximations.
All joints are locked against rotation. As a result, the loads will create
fixed-end moments at the ends of every member. At each joint, a moment equal to
the algebraic sum of the fixed-end moments there is required to hold it fixed. Then,
one joint is unlocked at a time by applying a moment equal but opposite in sign
to the moment that was needed to prevent rotation. The unlocking moment must
be distributed to the members at the joint in proportion to their fixed-end stiffnesses
and the distributed moments carried over to the far ends.
After all joints have been released at least once, it generally will be necessary
to repeat the process—sometimes several times—before the corrections to the fixedSTRUCTURAL
THEORY 5.91
FIGURE 5.75 Moment distribution by converging approximations for a
continuous beam.
end moments become negligible. To reduce the number of cycles, the unlocking of
joints should start with those having the greatest unbalanced moments.
Suppose the end moments are to be found for the prismatic continuous beam
ABCD in Fig. 5.75. The I /L values for all spans are equal; therefore, the relative
fixed-end stiffness for all members is unity. However, since A is a hinged end, the
computation can be shortened by using the actual relative stiffness, which is 3?4.
Relative stiffnesses for all members are shown in the circle on each member. The
distribution factors are shown in boxes at each joint.
The computation starts with determination of fixed-end moments for each member
(Art. 5.11.4). These are assumed to have been found and are given on the first
line in Fig. 5.75. The greatest unbalanced moment is found from inspection to be
at hinged end A; so this joint is unlocked first. Since there are no other members
at the joint, the full unlocking moment of 400 is distributed to AB at A and onehalf
of this is carried over to B. The unbalance at B now is 400  480 plus the
carry-over of 200 from A, or a total of 120. Hence, a moment of 120 must
be applied and distributed to the members at B by multiplying by the distribution
factors in the corresponding boxes.
The net moment at B could be found now by adding the entries for each member
at the joint. However, it generally is more convenient to delay the summation until
the last cycle of distribution has been completed.
The moment distributed to BA need not be carried over to A, because the carryover
factor toward the hinged end is zero. However, half the moment distributed to
BC is carried over to C.
Similarly, joint C is unlocked and half the distributed moments carried over to
B and D, respectively. Joint D should not be unlocked, since it actually is a fixed
end. Thus, the first cycle of moment distribution has been completed.
The second cycle is carried out in the same manner. Joint B is released, and the
distributed moment in BC is carried over to C. Finally, C is unlocked, to complete
the cycle. Adding the entries for the end of each member yields the final moments.
5.11.7 Maximum Moments in Continuous Frames
In design of continuous frames, one objective is to find the maximum end moments
and interior moments produced by the worst combination of loading. For maximum
moment at the end of a beam, live load should be placed on that beam and on the
5.92 SECTION FIVE
FIGURE 5.76 Bending moments in a continuous frame obtained by moment distribution.
beam adjoining the end for which the moment is to be computed. Spans adjoining
these two should be assumed to be carrying only dead load.
For maximum midspan moments, the beam under consideration should be fully
loaded, but adjoining spans should be assumed to be carrying only dead load.
The work involved in distributing moments due to dead and live loads in continuous
frames in buildings can be greatly simplified by isolating each floor. The
tops of the upper columns and the bottoms of the lower columns can be assumed
fixed. Furthermore, the computations can be condensed considerably by following
the procedure recommended in ‘‘Continuity in Concrete Building Frames.’’
EB033D, Portland Cement Association, Skokie, IL 60077, and indicated in Fig.
5.74.
Figure 5.74 presents the complete calculation for maximum end and midspan
moments in four floor beams AB, BC, CD, and DE. Building columns are assumed
to be fixed at the story above and below. None of the beam or column sections is
known to begin with; so as a start, all members will be assumed to have a fixedend
stiffness of unity, as indicated on the first line of the calculation.
On the second line, the distribution factors for each end of the beams are shown,
calculated from the stiffnesses (Arts. 5.11.3 and 5.11.4). Column stiffnesses are not
shown, because column moments will not be computed until moment distribution
to the beams has been completed. Then the sum of the column moments at each
joint may be easily computed, since they are the moments needed to make the sum
of the end moments at the joint equal to zero. The sum of the column moments at
each joint can then be distributed to each column there in proportion to its stiffness.
In this example, each column will get one-half the sum of the column moments.
Fixed-end moments at each beam end for dead load are shown on the third line,
just above the heavy line, and fixed-end moments for live plus dead load on the
fourth line. Corresponding midspan moments for the fixed-end condition also are
shown on the fourth line and, like the end moments, will be corrected to yield
actual midspan moments.
For maximum end moment at A, beam AB must be fully loaded, but BC should
carry dead load only. Holding A fixed, we first unlock joint B, which has a totalload
fixed-end moment of 172 in BA and a dead-load fixed-end moment of 37
in BC. The releasing moment required, therefore, is (172  37), or  135. When
B is released, a moment of 135 
 1?4 is distributed to BA One-half of this is
carried over to A, or 135 
 1?4 
 1?2  17. This value is entered as the carryover
at A on the fifth line in Fig. 5.76. Joint B is then relocked.
STRUCTURAL THEORY 5.93
At A, for which we are computing the maximum moment, we have a total-load
fixed-end moment of 172 and a carry-over of 17, making the total 189, shown
on the sixth line. To release A, a moment of 189 must be applied to the joint. Of
this, 189 
 1?3, or 63, is distributed to AB, as indicated on the seventh line of the
calculation. Finally, the maximum moment at A is found by adding lines 6 and 7:
189  63  126.
For maximum moment at B, both AB and BC must be fully loaded but CD
should carry only dead load. We begin the determination of the moment at B by
first releasing joints A and C, for which the corresponding carry-over moments at
BA and BC are 29 and (78  70) 
 1?4 
 1?2  1, shown on the fifth line
in Fig. 5.76. These bring the total fixed-end moments in BA and BC to 201 and
79, respectively. The releasing moment required is (201  79)  122. Multiplying
this by the distribution factors for BA and BC when joint B is released, we
find the distributed moments, 30, entered on line 7. The maximum end moments
finally are obtained by adding lines 6 and 7: 171 at BA and 109 at BC. Maximum
moments at C, D, and E are computed and entered in Fig. 5.76 in a similar
manner. This procedure is equivalent to two cycles of moment distribution.
The computation of maximum midspan moments in Fig. 5.76 is based on the
assumption that in each beam the midspan moment is the sum of the simple-beam
midspan moment and one-half the algebraic difference of the final end moments
(the span carries full load but adjacent spans only dead load). Instead of starting
with the simple-beam moment, however, we begin with the midspan moment for
the fixed-end condition and apply two corrections. In each span, these corrections
are equal to the carry-over moments entered on line 5 for the two ends of the beam
multiplied by a factor.
For beams with variable moment of inertia, the factor is 1?2[(1 /C )  D  1] F
where C is the fixed-end-carry-over factor toward the end for which the correction F
factor is being computed and D is the distribution factor for that end. The plus sign
is used for correcting the carry-over at the right end of a beam, and the minus sign
for the carry-over at the left end. For prismatic beams, the correction factor becomes

1?2(1  D).
For example, to find the corrections to the midspan moment in AB, we first
multiply the carry-over at A on line 5, 17, by 1?2(1  1?3). The correction, 11,
is also entered on the fifth line. Then, we multiply the carry-over at B,  29, by
1?2(1  1?4) and enter the correction, 18, on line 6. The final midspan moment
is the sum of lines 4, 5, and 6: 99  11  18  128. Other midspan moments
in Fig. 5.74 are obtained in a similar manner.
See also Arts. 5.11.9 and 5.11.10.
5.11.8 Moment-Influence Factors
In certain types of framing, particularly those in which different types of loading
conditions must be investigated, it may be convenient to find maximum end moments
from a table of moment-influence factors. This table is made up by listing
for the end of each member in the structure the moment induced in that end when
a moment (for convenience, 1000) is applied to every joint successively. Once
this table has been prepared, no additional moment distribution is necessary for
computing the end moments due to any loading condition.
For a specific loading pattern, the moment at any beam end MAB may be obtained
from the moment-influence table by multiplying the entries under AB for the various
5.94 SECTION FIVE
TABLE 5.6 Moment-Influence Factors
for Fig. 5.77
Member 1000 at B 1000 at C
AB
BA
BC
CB
CD
DC
351
702
298
70
70
35
105
210
210
579
421
210
joints by the actual unbalanced moments at those joints divided by 1000, and summing
(see also Art. 5.11.9 and Table 5.6).
5.11.9 Procedure for Sidesway
Computations of moments due to sidesway, or drift, in rigid frames is conveniently
executed by the following method:
1. Apply forces to the structure to prevent sidesway while the fixed-end moments
due to loads are distributed.
2. Compute the moments due to these forces.
3. Combine the moments obtained in Steps 1 and 2 to eliminate the effect of the
forces that prevented sidesway.
FIGURE 5.77 Rigid frame.
Suppose the rigid frame in Fig. 5.77
is subjected to a 2000-lb horizontal load
acting to the right at the level of beam
BC. The first step is to compute the moment-
influence factors (Table 5.6) by
applying moments of 1000 at joints B
and C, assuming sidesway prevented.
Since there are no intermediate loads
on the beams and columns, the only
fixed-end moments that need be considered
are those in the columns resulting
from lateral deflection of the frame
caused by the horizontal load. This de-
flection, however is not known initially.
So assume an arbitrary deflection, which
produces a fixed-end moment of
1000M at the top of column CD. M is an unknown constant to be determined
from the fact that the sum of the shears in the deflected columns must be equal to
the 2000-lb load. The same deflection also produces a moment of 1000M at the
bottom of CD [see Eq. (5.126)].
From the geometry of the structure, furthermore, note that the deflection of B
relative to A is equal to the deflection of C relative to D. Then, according to Eq.
(5.126) the fixed-end moments in the columns are proportional to the stiffnesses of
STRUCTURAL THEORY 5.95
the columns and hence are equal in AB to 1000M 
 6?2  3000M. The column
fixed-end moments are entered in the first line of Table 5.7, which is called a
moment-collection table.
In the deflected position of the frame, joints B and C are unlocked. First, apply
a releasing moment of 3000M at B and distribute it by multiplying by 3 the
entries in the column marked ‘‘1000 at B’’ in Table 5.6. Similarly, a releasing
moment of 1000M is applied at C and distributed with the aid of Table 5.6. The
distributed moments are entered in the second and third lines of Table 5.7. The
final moments are the sum of the fixed-end moments and the distributed moments
and are given in the fifth line.
Isolating each column and taking moments about one end, we find that the
overturning moment due to the shear is equal to the sum of the end moments. There
is one such equation for each column. Addition of these equations, noting that the
sum of the shears equals 2000 lb, yields
M(2052  1104  789  895)  2000 
 20
from which M  8.26. This value is substituted in the sidesway totals in Table 5.7
to yield the end moments for the 2000-lb horizontal load.
Suppose now a vertical load of 4000 lb is applied to BC of the rigid frame in
Fig. 5.77, 5 ft from B. Tables 5.6 and 5.7 can again be used to determine the end
moments with a minimum of labor:
The fixed-end moment at B, with sidesway prevented, is 12,800, and at C 
3200. With the joints locked, the frame is permitted to move laterally an arbitrary
amount, so that in addition to the fixed-end moments due to the 4000-lb load,
column fixed-end moments of 3000M at B and  1000M at C are induced. Table
5.7 already indicates the effect of relieving these column moments by unlocking
joints B and C. We now have to superimpose the effect of releasing joints B and
C to relieve the fixed-end moments for the vertical load. This we can do with the
aid of Table 5.6. The distribution is shown in the lower part of Table 5.7. The sums
of the fixed-end moments and distributed moments for the 4000-lb load are shown
on the line ‘‘No-sidesway sum.’’
The unknown M can be evaluated from the fact that the sum of the horizontal
forces acting on the columns must be zero. This is equivalent to requiring that the
sum of the column end moments equals zero:
M(2052  1104  789  895)  4826  9652  2244  1120  0
from which M  2.30. This value is substituted in the sidesway total in Table 5.7
to yield the sidesway moments for the 4000-lb load. The addition of these moments
to the totals for no sidesway yields the final moments.
This procedure enables one-story bents with straight beams to be analyzed with
the necessity of solving only one equation with one unknown regardless of the
number of bays. If the frame is several stories high, the procedure can be applied
to each story. Since an arbitrary horizontal deflection is introduced at each floor or
roof level, there are as many unknowns and equations as there are stories.
The procedure is more difficult to apply to bents with curved or polygonal
members between the columns. The effect of the change in the horizontal projection
of the curved or polygonal portion of the bent must be included in the calculations.
In many cases, it may be easier to analyze the bent as a curved beam (arch).
(A. Kleinlogel, ‘‘Rigid Frame Formulas,’’ Frederick Ungar Publishing Co., New
York.)
5.96
TABLE 5.7 Moment-Collection Table for Fig. 5.77
Remarks
AB
 
BA
 
BC
 
CB
 
CD
 
DC
 
Sidesway, FEM 3,000M 3,000M 1,000M 1,000M
B moments 1,053M 2,106M 894M 210M 210M 105M
C moments 105M 210M 210M 579M 421M 210M
Partial sum 1,053M 3,105M 2,106M 3,210M 1,104M 789M 421M 1,210M 210M 1,105M
Totals 2,052M 1,104M 1,104M 789M 789M 895M
For 2000-lb load 17,000 9,100 9,100 6,500 6,500 7,400
4000-lb load, FEM 12,800 3,200
B moments 4,490 8,980 3,820 897 897 448
C moments 336 672 672 1,853 1,347 672
Partial sum 4,826 9,652 3,820 13,472 4,097 1,853 2,244 1,120
No-sidesway sum 4,826 9,652 9,652 2,244 2,244 1,120
Sidesway M 4,710 2,540 2,540 1,810 1,810 2,060
Totals 120 7,110 7,110 4,050 4,050 3,180
STRUCTURAL THEORY 5.97
5.11.10 Rapid Approximate Analysis of Multistory Frames
Exact analysis of multistory rigid frames subjected to lateral forces, such as those
from wind or earthquakes, involves lengthy calculations, and they are timeconsuming
and expensive, even when performed with computers. Hence, approximate
methods of analysis are an alternative, at least for preliminary designs and,
for some structures, for final designs.
It is noteworthy that for some buildings even the ‘‘exact’’ methods, such as those
described in Arts. 5.11.8 and 5.11.9, are not exact. Usually, static horizontal loads
are assumed for design purposes, but actually the forces exerted by wind and earthquakes
are dynamic. In addition, these forces generally are uncertain in intensity,
direction, and duration. Earthquake forces, usually assumed as a percentage of the
mass of the building above each level, act at the base of the structure, not at each
floor level as is assumed in design, and accelerations at each level vary nearly
linearly with distance above the base. Also, at the beginning of a design, the sizes
of the members are not known. Consequently, the exact resistance to lateral deformation
cannot be calculated. Furthermore, floors, walls, and partitions help resist
the lateral forces in a very uncertain way. See Art. 5.12 for a method of calculating
the distribution of loads to rigid-frame bents.
Portal Method. Since an exact analysis is impossible, most designers prefer a
wind-analysis method based on reasonable assumptions and requiring a minimum
of calculations. One such method is the so-called ‘‘portal method.’’
It is based on the assumptions that points of inflection (zero bending moment)
occur at the midpoints of all members and that exterior columns take half as much
shear as do interior columns. These assumptions enable all moments and shears
throughout the building frame to be computed by the laws of equilibrium.
Consider, for example, the roof level (Fig. 5.78a) of a tall building. A wind load
of 600 lb is assumed to act along the top line of girders. To apply the portal method,
we cut the building along a section through the inflection points of the top-story
columns, which are assumed to be at the column midpoints, 6 ft down from the
top of the building. We need now consider only the portion of the structure above
this section.
Since the exterior columns take only half as much shear as do the interior columns,
they each receive 100 lb, and the two interior columns, 200 lb. The moments
at the tops of the columns equal these shears times the distance to the inflection
point. The wall end of the end girder carries a moment equal to the moment in the
column. (At the floor level below, as indicated in Fig. 5.78b, that end of the end
girder carries a moment equal to the sum of the column moments.) Since the
inflection point is at the midpoint of the girder, the moment at the inner end of the
girder must the same as at the outer end. The moment in the adjoining girder can
be found by subtracting this moment from the column moment, because the sum
of the moments at the joint must be zero. (At the floor level below, as shown in
Fig. 5.78b, the moment in the interior girder is found by subtracting the moment
in the exterior girder from the sum of the column moments.)
Girder shears then can be computed by dividing girder moments by the half
span. When these shears have been found, column loads can be easily computed
from the fact that the sum of the vertical loads must be zero, by taking a section
around each joint through column and girder inflection points. As a check, it should
be noted that the column loads produce a moment that must be equal to the moments
of the wind loads above the section for which the column loads were computed.
For the roof level (Fig. 5.78a), for example, 50 
 24  100 
 48 
600 
 6.
5.98 SECTION FIVE
FIGURE 5.78 Portal method for computing wind stresses in a tall building.
Cantilever Method. Another wind-analysis procedure that is sometimes employed
is the cantilever method. Basic assumptions here are that inflection points are at
the midpoints of all members and that direct stresses in the columns vary as the
distances of the columns from the center of gravity of the bent. The assumptions
are sufficient to enable shears and moments in the frame to be determined from the
laws of equilibrium.
For multistory buildings with height-to-width ratio of 4 or more, the Spurr modification
is recommended (‘‘Welded Tier Buildings,’’ U.S. Steel Corp.). In this
method, the moments of inertia of the girders at each level are made proportional
to the girder shears.
The results obtained from the cantilever method generally will be different from
those obtained by the portal method. In general, neither solution is correct, but the
answers provide a reasonable estimate of the resistance to be provided against
lateral deformation. (See also Transactions of the ASCE, Vol. 105, pp. 1713–1739,
1940.)
5.11.11 Beams Stressed into the Plastic Range
When an elastic material, such as structural steel, is loaded in tension with a gradually
increasing load, stresses are proportional to strains up to the proportional limit
(near the yield point). If the material, like steel, also is ductile, then it continues to
carry load beyond the yield point, though strains increase rapidly with little increase
in load (Fig. 5.79a).
STRUCTURAL THEORY 5.99
Similarly, a beam made of a ductile material continues to carry more load after
the stresses in the outer surfaces reach the yield point. However, the stresses will
no longer vary with distance from the neutral axis, so the flexure formula [Eq.
(5.54)] no longer holds. However, if simplifying assumptions are made, approximating
the stress-strain relationship beyond the elastic limit, the load-carrying capacity
of the beam can be computed with satisfactory accuracy.
FIGURE 5.79 Stress-strain relationship for a
ductile material generally is similar to the curve
shown in (a). To simplify plastic analysis, the
portion of (a) enclosed by the dash lines is approximated
by the curve in (b), which extends
to the range where strain hardening begins.
Modulus of rupture is defined as
the stress computed from the flexure
formula for the maximum bending moment
a beam sustains at failure. This is
not a true stress but it is sometimes used
to compare the strength of beams.
For a ductile material, the idealized
stress-strain relationship in Fig. 5.79b
may be assumed. Stress is proportional
to strain until the yield-point stress ?y is
reached, after which strain increases at
a constant stress.
For a beam of this material, the following
assumptions will also be made:
1. Plane sections remain plane, strains
thus being proportional to distance
from the neutral axis.
2. Properties of the material in tension
are the same as those in compression.
3. Its fibers behave the same in flexure
as in tension.
4. Deformations remain small.
Strain distribution across the cross
section of a rectangular beam, based on
these assumptions, is shown in Fig. 5.80a. At the yield point, the unit strain is y
and the curvature 	y, as indicated in (1). In (2), the strain has increased several
times, but the section still remains plane. Finally, at failure, (3), the strains are very
large and nearly constant across upper and lower halves of the section.
Corresponding stress distributions are shown in Fig. 5.80b. At the yield point,
(1), stresses vary linearly and the maximum if ?y . With increase in load, more and
more fibers reach the yield point, and the stress distribution becomes nearly constant,
as indicated in (2). Finally, at failure, (3), the stresses are constant across the
top and bottom parts of the section and equal to the yield-point stress.
The resisting moment at failure for a rectangular beam can be computed from
the stress diagram for stage 3. If b is the width of the member and d its depth, then
the ultimate moment for a rectangular beam is
2 bd
M  ? (5.141) p y 4
Since the resisting moment at stage 1 is My  ?ybd2 / 6, the beam carries 50% more
moment before failure than when the yield-point stress is first reached at the outer
surfaces.
5.100 SECTION FIVE
FIGURE 5.80 Strain distribution is shown in (a) and stress distribution in
(b) for a cross section of a beam as it is loaded beyond the yield point, for
the idealized stress-strain relationship in Fig. 5.79b: stage (1) shows the condition
at the yield point of the outer surface; (2) after yielding starts; (3) at
ultimate load.
A circular section has an Mp /My ratio of about 1.7, while a diamond section has
a ratio of 2. The average wide-flange rolled-steel beam has a ratio of about 1.14.
Plastic Hinges. The relationship between moment and curvature in a beam can
be assumed to be similar to the stress-strain relationship in Fig. 5.80b. Curvature
	 varies linearly with moment until My  Mp is reached, after which 	 increases
indefinitely at constant moment. That is, a plastic hinge forms.
Moment Redistribution. This ability of a ductile beam to form plastic hinges
enables a fixed-end or continuous beam to carry more load after MP occurs at a
section, because a redistribution of moments takes place. Consider, for example, a
uniformly loaded, fixed-end, prismatic beam. In the elastic range, the end moments
of ML  MR  WL/12, while the midspan moment MC is WL/24. The load when
the yield point is reached at the outer surfaces at the beam ends is Wy  12My /L.
Under this load the moment capacity of the ends of the beam is nearly exhausted;
plastic hinges form there when the moment equals MP. As load is increased, the
ends then rotate under constant moment and the beam deflects like a simply supSTRUCTURAL
THEORY 5.101
ported beam. The moment at midspan increases until the moment capacity at that
section is exhausted and a plastic hinge forms. The load causing that condition is
the ultimate load Wu since, with three hinges in the span, a link mechanism is
formed and the member continues to deform at constant load. At the time the third
hinge is formed, the moments at ends and center are all equal to MP. Therefore,
for equilibrium, 2MP  WuL/8, from which Wu  16MP /L. Since for the idealized
moment-curvature relationship, MP was assumed equal to My , the carrying capacity
due to redistribution of moments is 33% greater than Wy .
5.12 LOAD DISTRIBUTION TO BENTS AND
SHEAR WALLS
Buildings must be designed to resist horizontal forces as well as vertical loads. In
tall buildings, the lateral forces must be given particular attention, because if they
are not properly provided for, they can collapse the structure (Art. 3.2.3). The usual
procedure for preventing such disasters is to provide structural framing capable of
transmitting the horizontal forces from points of application to the building foundations.
Because the horizontal loads may come from any direction, they generally are
resolved into perpendicular components, and correspondingly the lateral-forceresisting
framing is also placed in perpendicular directions. The maximum magnitude
of load is assumed to act in each of those directions. Bents or shear walls,
which act as vertical cantilevers and generally are often also used to support some
of the building’s gravity loads, usually are spaced at appropriate intervals for transmitting
the loads to the foundations.
A bent consists of vertical trusses or continuous rigid frames located in a plane.
The trusses usually are an assemblage of columns, horizontal girders, and diagonal
bracing (Art. 3.2.4). The rigid frames are composed of girders and columns, with
so-called wind connections between them to establish continuity. Shear walls are
thin cantilevers braced by floors and roofs (Art. 3.2.4).
5.12.1 Diaphragms
Horizontal distribution of lateral forces to bents and shear walls is achieved by the
floor and roof systems acting as diaphragms (Fig. 5.81).
To qualify as a diaphragm, a floor or roof system must be able to transmit the
lateral forces to bents and shear walls without exceeding a horizontal deflection
that would cause distress to any vertical element. The successful action of a diaphragm
also requires that it be properly tied into the supporting framing. Designers
should ensure this action by appropriate detailing at the juncture between horizontal
and vertical structural elements of the building.
Diaphragms may be considered analogous to horizontal (or inclined, in the case
of some roofs) plate girders. The roof or floor slab constitutes the web; the joists,
beams, and girders function as stiffeners; and the bents and shear walls act as
flanges.
Diaphragms may be constructed of structural materials, such as concrete, wood,
or metal in various forms. Combinations of such materials are also possible. Where
a diaphragm is made up of units, such as plywood, precast-concrete planks, or steel
5.102 SECTION FIVE
FIGURE 5.81 Floors of building distribute horizontal
loads to shear walls (diaphragm action).
FIGURE 5.82 Horizontal section through shear walls connected
by a rigid diaphragm. R  relative rigidity and  shear-wall v
deflection.
decking, its characteristics are, to a large degree, dependent on the attachments of
one unit to another and to the supporting members. Such attachments must resist
shearing stresses due to internal translational and rotational actions.
The stiffness of a horizontal diaphragm affects the distribution of the lateral
forces to the bents and shear walls. For the purpose of analysis, diaphragms may
be classified into three groups—rigid, semirigid or semiflexible, and flexible—
although no diaphragm is actually infinitely rigid or infinitely flexible.
A rigid diaphragm is assumed to distribute horizontal forces to the vertical
resisting elements in proportion to the relative rigidities of these elements (Fig.
5.82).
Semirigid or semiflexible diaphragms are diaphragms that deflect significantly
under load, but have sufficient stiffness to distribute a portion of the load to the
vertical elements in proportion to the rigidities of these elements. The action is
analogous to a continuous beam of appreciable stiffness on yielding supports (Fig.
5.83). Diaphragm reactions are dependent on the relative stiffnesses of diaphragm
and vertical resisting elements.
A flexible diaphragm is analogous to a continuous beam or series of simple
beams spanning between nondeflecting supports. Thus, a flexible diaphragm is conSTRUCTURAL
THEORY 5.103
FIGURE 5.83 Horizontal sections through shear walls connected
by a semirigid diaphragm. D  diaphragm horizontal deflection.
FIGURE 5.84 Horizontal section through shear walls connected by
a flexible diaphragm.
sidered to distribute the lateral forces to the vertical resisting elements in proportion
to the exterior-wall tributary areas (Fig. 5.84).
A rigorous analysis of lateral-load distribution to shear walls or bents is sometimes
very time-consuming, and frequently unjustified by the results. Therefore, in
many cases, a design based on reasonable limits may be used. For example, the
load may be distributed by first considering the diaphragm rigid, and then by considering
it flexible. If the difference in results is not great, the shear walls can then
be safely designed for the maximum applied load. (See also Art. 5.12.2.)
5.12.2 Torque Distribution to Shear Walls
When the line of action of the resultant of lateral forces acting on a building does
not pass through the center of rigidity of a vertical, lateral-force-resisting system,
distribution of the rotational forces must be considered as well as distribution of
the transnational forces. If rigid or semirigid diaphragms are used, the designer may
assume that torsional forces are distributed to the shear walls in proportion to their
relative rigidities and their distances from the center of rigidity. A flexible diaphragm
should not be considered capable of distributing torsional forces.
5.104 SECTION FIVE
See also Art. 5.12.5.
Example of Torque Distribution to Shear Walls. To illustrate load-distribution
calculations for shear walls with rigid or semirigid diaphragms, Fig. 5.85 shows a
horizontal section through three shear walls A, B, and C taken above a rigid floor.
Wall B is 16 ft from wall A, and 24 ft from wall C. Rigidity of A 0.33, of B 0.22,
and of C 0.45 (Art. 5.12.5). A 20-kip horizontal force acts at floor level parallel to
the shear walls and midway between A and C.
FIGURE 5.85 Rigid diaphragm distributes
20-kip horizontal force to shear walls A, B, and
C.
The center of rigidity of the shear
walls is located, relative to wall A, by
taking moments about A of the wall rigidities
and dividing the sum of these
moments by the sum of the wall rigidities,
in this case 1.00.
x  0.22 
 16  0.45 
 40
 21.52 ft
Thus, the 20-kip lateral force has an eccentricity
of 21.52  20  1.52 ft. The
eccentric force may be resolved into a
20-kip force acting through the center of
rigidity and not producing torque, and a
couple producing a torque of 20 

1.52  30.4 ft-kips.
The nonrotational force is distributed to the shear walls in proportion to their
rigidities:
Wall A: 0.33 
 20  6.6 kips
Wall B: 0.22 
 20  4.4 kips
Wall C: 0.45 
 20  9.0 kips
For distribution of the torque to the shear walls, the equivalent of moment of inertia
must first be computed:
2 2 2 I  0.33(21.52)  0.22(5.52)  0.45(18.48)  313
Then, the torque is distributed in direct proportion to shear-wall rigidity and distance
from center of rigidity and in inverse proportion to I.
Wall A: 30.4 
 0.33 
 21.52/313  0.690 kips
Wall B: 30.4 
 0.22 
 5.52/313  0.118 kips
Wall C: 30.4 
 0.45 
 18.48/313  0.808 kips
The torsional forces should be added to the nonrotational forces acting on walls
A and B, whereas the torsional force on wall C acts in the opposite direction to the
nonrotational force. For a conservative design, the torsional force on wall C should
not be subtracted. Hence, the walls should be designed for the following forces:
STRUCTURAL THEORY 5.105
Wall A: 6.6  0.7  7.3 kips
Wall B: 4.4  0.1  4.5 kips
Wall C: kips
5.12.3 Deflections of Bents or Shear Walls
When parallel bents or shear walls are connected by rigid diaphragms (Art. 5.12.1)
and horizontal loads are distributed to the vertical resisting elements in proportion
to their relative rigidities, the relative rigidity of the framing depends on the combined
horizontal deflections due to shear and flexure. For the dimensions of lateralforce-
resisting framing used in many high-rise buildings, however, deflections due
to flexure greatly exceed those due to shear. In such cases, only flexural rigidity
need be considered in determination of relative rigidity of the bents and shear walls
(Art. 5.12.5).
Horizontal deflections can be determined by treating the bents and shear walls
as cantilevers. Deflections of braced bents can be calculated by the dummy-unitload
method (Art. 5.10.4) or a matrix method (Art. 5.13.3). Deflections of rigid
frames can be obtained by summing the drifts of the stories, as determined by
moment distribution (Art. 5.11.9) or a matrix method. And deflections of shear
walls can be computed from formulas given in Art. 5.5.15, the dummy-unit-load
method, or a matrix method.
For a shear wall with a solid, rectangular cross section, the flexural deflection
at the top under uniform loading is given by the formula for a cantilever in Fig.
5.39:
4 wH
  (5.142) c 8EI
where w  uniform lateral load
H  height of the wall
E  modulus of elasticity of the wall material
I  moment of inertia of wall cross section  tL3/12
t  wall thickness
L  length of wall
The cantilever shear deflection under uniform loading may be computed from
2 0.6wH
  (5.143) v E A v
where E  v modulus of rigidity of wall cross section
 E/2(1  	)
	 Poisson’s ratio for the wall material (0.25 for concrete and masonry)
A  cross-sectional area of the wall  tL
The total deflection then is
3 1.5wH H H
    (5.144) 
  
 c v Et L L
For a cantilever wall subjected to a concentrated load P at the top, the flexural
deflection at the top is
5.106 SECTION FIVE
3 PH
  (5.145) c 3EI
The shear deflection at the top of the wall is
1.2PH
  (5.146) v E A v
Hence, the total deflection of the cantilever is
3 4P H H
 0.75 (5.147) 
  
 Et L L
For a wall fixed against rotation a the top and subjected to a concentrated load
P at the top, the flexural deflection at the top is
3 PH
  (5.148) c 12EI
The shear deflection for the fixed-end wall is given by Eq. (5.145). Hence, the total
deflection for the wall is
3 P H H
 3 (5.149) 
  
 Et L L
5.12.4 Diaphragm-Deflection Limitations
As indicated in Art. 5.12.1, horizontal deflection of diaphragms plays an important
role in determining lateral-load distribution to bents and shear walls. Another design
consideration is the necessity of limiting diaphragm deflection to prevent excessive
stresses in walls perpendicular to shear walls. Equation (5.150) was suggested by
the Structural Engineers Association of Southern California for allowable story
deflection , in, of masonry or concrete building walls.
2 h ?
  (5.150)
0.01Et
where h  height of wall between adjacent horizontal supports, ft
t  thickness of wall, in
?  allowable flexural compressive stress of wall material, psi
E  modulus of elasticity of wall material, psi
This limit on deflection must be applied with engineering judgment. For example,
continuity of wall at floor level is assumed, and in many cases is not present
because of through-wall flashing. In this situation, the deflection may be based on
the allowable compressive stress in the masonry, if a reduced cross section of wall
is assumed. The effect of reinforcement, which may be present in a reinforced brick
masonry wall or as a tie to the floor system in a nonreinforced or partly reinforced
masonry wall, was not considered in development of Eq. (5.150). Note also that
the limit on wall deflection is actually a limit on differential deflection between
two successive floor, or diaphragm, levels.
Maximum span-width or span-depth ratios for diaphragms are usually used to
control horizontal diaphragm deflection indirectly. Normally, if the diaphragm is
STRUCTURAL THEORY 5.107
designed with the proper ratio, the diaphragm deflection will not be critical. Table
5.8 may be used as a guide for proportioning diaphragms.
5.12.5 Shear-Wall Rigidity
Where shear walls are connected by rigid diaphragms so that they must deflect
equally under horizontal loads, the proportion of total horizontal load at any level
carried by a shear wall parallel to the load depends on the relative rigidity, or
stiffness, of the wall in the direction of the load (Art. 5.12.1). Rigidity of a shear
wall is inversely proportional to its deflection under unit horizontal load. This de-
flection equals the sum of the shear and flexural deflections under the load (Art.
5.12.3).
Where a shear wall contains no openings, computations for deflection and rigidity
are simple. In Fig. 5.86a, each of the shear walls has the same length and
rigidity. So each takes half the total load. In Fig. 5.86b, length of wall C is half
that of wall D. By Eq. (5.142), C therefore receives less than one-eighth the total
load.
Walls with Openings. Where shear walls contain openings, such as doors and
windows, computations for deflection and rigidity are more complex. But approximate
methods may be used.
FIGURE 5.87 Shear wall, 8 in thick, with
openings.
For example, the wall in Fig. 5.87,
subjected to a 1000-kip load at the top,
may be treated in parts. The wall is 8 in
thick, and its modulus of elasticity E 
2400 ksi. Its height-length ratio H/L is
12?20  0.6. The wall is perforated by
two, symmetrically located, 4-ft-square
openings.
Deflection of this wall can be estimated
by subtracting from the deflection
it would have if it were solid the deflection
of a solid, 4-ft-deep, horizontal
midstrip, and then adding the deflection
of the three coupled piers B, C, and D.
Deflection of the 12-ft-high solid
wall can be obtained from Eq. (5.147):
3 4 
 10 3  [(0.6)  0.75 
 0.6]  0.138 in 3 2.4 
 10 
 8
Rigidity of the solid wall then is
1
R 7.22
0.138
Similarly, the deflection of the 4-ft-deep solid midstrip can be computed from
Eq. (5.147), with H/L  4?20  0.20.
3 4 
 10 3  [(0.20)  0.75 
 0.20]  0.033 in 3 2.4 
 10 
 8
Deflection of the piers, which may be considered fixed top and bottom, can be
5.108 SECTION FIVE
TABLE 5.8 Maximum Span-Width or Span-Depth Ratios for diaphragms—Roofs or
Floors*
Diaphragm construction
Masonry and
concrete
walls
Wood
and light
steel
walls
Concrete Limited by deflection
Steel deck (continuous sheet in a single
plane)
4:1 5:1
Steel deck (without continuous sheet) 2:1 21?2:1
Cast-in-place reinforced gypsum roofs 3:1 4:1
Plywood (nailed all edges) 3:1 4:1
Plywood (nailed to supports only—blocking
may be omitted between joists)
21?2:1 31?2:1
Diagonal sheating (special) 3:1† 31?2:1
Diagonal sheating (conventional
construction)
2:1† 21?2:1
*From California Administrative code, Title 21, Public Works.
† Use of diagonal sheathed or unblocked plywood diaphragms for buildings having masonry or reinforced
concrete walls shall be limited to one-story buildings or to the roof of a top story.
FIGURE 5.86 Distribution of horizontal load to parallel
shear walls: (a) walls with the same length and rigidity share
the load equally; (b) wall half the length of another carries
less than one-eighth of the load.
obtained from Eq. (5.149), with H/L  4?4  1. For any one of the piers, the
deflection is
3 10
v  (1  3)  0.208 in 3 2.4 
 10 
 8
The rigidity of a single pier is 1/0.208  4.81, and of the three piers, 3 
 4.81 
14.43. Therefore, the deflection of the three piers when coupled is
STRUCTURAL THEORY 5.109
1
 0.069 in
14.43
The deflection of the whole wall, with openings, then is approximately
 0.138  0.033  0.069  0.174 in
And its rigidity is
1
R 5.74
0.174
5.12.6 Effects of Shear-Wall Arrangements
To increase the stiffness of shear walls and thus their resistance to bending, intersecting
walls or flanges may be used. Often in the design of buildings, A-, T-,
FIGURE 5.88 Effective flange width of shear
walls may be less than the actual width: (a) limits
for flanges of I and T shapes; (b) limits for
C and L shapes.
U-, L-, and I-shaped walls in plan develop
as natural parts of the design.
Shear walls with these shapes have better
flexural resistance than a single,
straight wall.
In calculation of flexural stresses in
masonry shear walls for symmetrical T
or I sections, the effective flange width
may not exceed one-sixth the total wall
height above the level being analyzed.
For unsymmetrical L or C sections, the
width considered effective may not exceed
one-sixteenth the total wall height
above the level being analyzed. In either
case, the overhang for any section may
not exceed six times the flange thickness
(Fig. 5.88).
The shear stress at the intersection of the walls should not exceed the permissible
shear stress.
5.12.7 Coupled Shear Walls
Another method than that described in Art. 5.12.6 for increasing the stiffness of a
bearing-wall structure and reducing the possibility of tension developing in masonry
shear walls under lateral loads is coupling of coplanar shear walls.
Figure 5.89 and 5.90 indicate the effect of coupling on stress distribution in a
pair of walls under horizontal forces parallel to the walls. A flexible connection
between the walls is assumed in Figs. 5.89a and 5.90a, so that the walls act as
independent vertical cantilevers in resisting lateral loads. In Figs. 5.89b and 5.90b,
the walls are assumed to be connected with a more rigid member, which is capable
of shear and moment transfer. A rigid-frame type action results. This can be accomplished
with a steel-reinforced concrete, or reinforced brick masonry coupling.
5.110 SECTION FIVE
FIGURE 5.89 Stress distribution in end shear walls: (a) with flexible
coupling; (b) with rigid-frame-type action; (c) with plate-type action.
FIGURE 5.90 Stress distribution in interior shear walls: (a) with flexible
coupling; (b) with rigid-frame-type action; (c) with plate-type action.
A plate-type action is indicated in Figs. 5.89c and 5.90c. This assumes an extremely
rigid connection between walls, such as fully story-height walls or deep rigid spandrels.
5.13 FINITE-ELEMENT METHODS
From the basic principles given in preceding articles, systematic procedures have
been developed for determining the behavior of a structure from a knowledge of
the behavior under load of its components. In these methods, called finite-element
methods, a structural system is considered an assembly of a finite number of finitesize
components, or elements. These are assumed to be connected to each other
only at discrete points, called nodes. From the characteristics of the elements, such
as their stiffness or flexibility, the characteristics of the whole system can be derived.
With these known, internal stresses and strains throughout can be computed.
Choice of elements to be used depends on the type of structure. For example,
for a truss with joints considered hinged, a natural choice of element would be a
bar, subjected only to axial forces. For a rigid frame, the elements might be beams
subjected to bending and axial forces, or to bending, axial forces, and torsion. For
STRUCTURAL THEORY 5.111
a thin plate or shell, elements might be triangles or rectangles, connected at vertices.
For three-dimensional structures, elements might be beams, bars, tetrahedrons,
cubes, or rings.
For many structures, because of the number of finite elements and nodes, analysis
by a finite-element method requires mathematical treatment of large amounts
of data and solution of numerous simultaneous equations. For this purpose, the use
of computers is advisable. The mathematics of such analyses is usually simpler and
more compact when the data are handled in matrix for. (See also Art. 5.10.7.)
5.13.1 Force and Displacement Methods
The methods used for analyzing structures generally may be classified as force
(flexibility) or displacement (stiffness) methods.
In analysis of statically indeterminate structures by force methods, forces are
chosen as redundants, or unknowns. The choice is made in such a way that equilibrium
is satisfied. These forces are then determined from the solution of equations
that ensure compatibility of all displacements of elements at each node. After the
redundants have been computed, stresses and strains throughout the structure can
be found from equilibrium equations and stress-strain relations.
In displacement methods, displacements are chosen as unknowns. The choice is
made in such a way that geometric compatibility is satisfied. These displacements
are then determined from the solution of equations that ensure that forces acting at
each node are in equilibrium. After the unknowns have been computed, stresses
and stains throughout the structure can be found from equilibrium equations and
stress-strain relations.
In choosing a method, the following should be kept in mind: In force methods,
the number of unknowns equals the degree of indeterminacy. In displacement methods,
the number of unknowns equals the degrees of freedom of displacement at
nodes. The fewer the unknowns, the fewer the calculations required.
Both methods are based on the force-displacement relations and utilize the stiffness
and flexibility matrices described in Art. 5.10.7. In these methods, displacements
and external forces are resolved into components—usually horizontal, vertical,
and rotational—at nodes, or points of connection of the finite elements. In
accordance with Eq. (5.103a), the stiffness matrix transforms displacements into
forces. Similarly, in accordance with Eq. (5.103b), the flexibility matrix transforms
forces into displacements. To accomplish the transformation, the nodal forces and
displacements must be assembled into correspondingly positioned elements of force
and displacement vectors. Depending on whether the displacement or the force
method is chosen, stiffness or flexibility matrices are then established for each of
the finite elements and these matrices are assembled to form a square matrix, from
which the stiffness or flexibility matrix for the structure as a whole is derived. With
that matrix known and substituted into equilibrium and compatibility equations for
the structure, all nodal forces and displacements of the finite elements can be determined
from the solution of the equations. Internal stresses and strains in the
elements can be computed from the now known nodal forces and displacements.
5.13.2 Element Flexibility and Stiffness Matrices
The relationship between independent forces and displacements at nodes of finite
elements comprising a structure is determined by flexibility matrices f or stiffness
5.112 SECTION FIVE
FIGURE 5.92 Beam subjected to end moments and shears.
matrices k of the elements. In some cases, the components of these matrices can
be developed from the defining equations:
The jth column of a flexibility matrix of a finite element contains all the nodal
displacements of the element when one force Sj is set equal to unity and all other
independent forces are set equal to zero.
The jth column of a stiffness matrix of a finite element consists of the forces
acting at the nodes of the element to produce a unit displacement of the node at
which displacement j occurs and in the direction of j but no other nodal displacements
of the element.
Bars with Axial Stress Only. As an example of the use of the definitions of
flexibility and stiffness, consider the simple case of an elastic bar under tension
FIGURE 5.91 Elastic bar in tension.
applied by axial forces Pi and Pj at
nodes i and j, respectively (Fig. 5.91).
The bar might be the finite element of a
truss, such as a diagonal or a hanger.
Connections to other members are made
at nodes i and j, which an transmit only
forces in the directions i to j or j to i.
For equilibrium, Pi  Pj  P. Displacement of node j relative to node i is e.
From Eq. (5.23), e  PL/AE, where L is the initial length of the bar, A the bar
cross-sectional area, and E the modulus of elasticity. Setting P eq 1 yields the
flexibility of the bar,
L
?  (5.151)
AE
Setting e  1 gives the stiffness of the bar,
AE
k  (5.152)
L
Beams with Bending Only. As another example of the use of the definition to
determine element flexibility and stiffness matrices, consider the simple case of an
elastic prismatic beam in bending applied by moments Mi and Mj at nodes i and j,
respectively (Fig. 5.92a). The beam might be a finite element of a rigid frame.
Connections to other members are made at nodes i and j, which can transmit moments
and forces normal to the beam.
Nodal displacements of the element can be sufficiently described by rotations i
and j relative to the straight line between nodes i and j. For equilibrium, forces
Vj  Vi normal to the beam are required at nodes j and i, respectively, and Vj 
(Mi  Mj) /L, where L is the span of the beam. Thus, Mi and Mj are the only
STRUCTURAL THEORY 5.113
independent forces acting. Hence, the force-displacement relationship can be written
for this element as
 M i i  f  fM (5.153) 
 
  M j j
M  i i M k  k  (5.154) 
 
 M  j j
The flexibility matrix f then will be a 2 
 2 matrix. The first column can be
obtained by setting Mi  1 and Mj  0 (Fig. 5.92b). The resulting angular rotations
are given by Eqs. (5.107) and (5.108): For a beam with constant moment of inertia
I and modulus of elasticity E, the rotations are   L/3EI and   L/6EI.
Similarly, the second column can be developed by setting Mi  0 and Mj  1.
The flexibility matrix for a beam in bending then is
L L
 L 3EI 6EI 2 1 f  (5.155) 
 1 2 L L 6EI  	 
6EI 3EI
The stiffness matrix, obtained in a similar manner or by inversion of f, is
4EI 2EI
2EI 2 1 L L k  (5.156) 
 2EI 4EI 1 2 L  	 L L
Beams Subjected to Bending and Axial Forces. For a beam subjected to nodal
moments Mi and Mj and axial forces P, flexibility and stiffness are represented by
3 
 3 matrices. The load-displacement relations for a beam of span L, constant
moment of inertia I, modulus of elasticity E, and cross-sectional area A are given
by
 M M  i i i
  f M M  k  (5.157) j j j j  	  	  	  	 e P P e
In this case, the flexibility matrix is
2 1 0 L
f 1 2 0 (5.158)
6EI 	 0 0 
where  6I /A, and the stiffness matrix is
4 2 0 EI
k  2 4 0 (5.159)
L 	 0 0 
where  A/ I.
5.114 SECTION FIVE
5.13.3 Displacement (Stiffness) Method
With the stiffness or flexibility matrix of each finite element of a structure known,
the stiffness or flexibility matrix for the whole structure can be determined, and
with that matrix, forces and displacements throughout the structure can be computed
(Art. 5.13.2). To illustrate the procedure, the steps in the displacement, or stiffness,
method are described in the following. The steps in the flexibility method are similar.
For the stiffness method:
Step 1. Divide the structure into interconnected elements and assign a number,
for identification purposes, to every node (intersection and terminal of elements).
It may also be useful to assign an identifying number to each element.
Step 2. Assume a right-handed cartesian coordinate system, with axes x, y, z.
Assume also at each node of a structure to be analyzed a system of base unit
vectors, e1 in the direction of the x axis, e2 in the direction of the y axis, and e3 in
the direction of the z axis. Forces and moments acting at a node are resolved into
components in the directions of the base vectors. Then, the forces and moments at
the node may be represented by the vector Piei, where Pi is the magnitude of the
force or moment acting in the direction of ei. This vector, in turn, may be conveniently
represented by a column matrix P. Similarly, the displacements—translations
and rotation—of the node may be represented by the vector iei, where i is the
magnitude of the displacement acting in the direction of ei. This vector, in turn,
may be represented by a column matrix .
For compactness, and because, in structural analysis, similar operations are performed
on all nodal forces, all the loads, including moments, acting on all the
nodes may be combined into a single column matrix P. Similarly, all the nodal
displacements may be represented by a single column matrix .
When loads act along a beam, they should be replaced by equivalent forces at
the nodes—simple-beam reactions and fixed-end moments, both with signs reversed
from those induced by the loads. The final element forces are then determined by
adding these moments and reactions to those obtained from the solution with only
the nodal forces.
Step 3. Develop a stiffness matrix ki for each element i of the structure (see Art.
5.13.2). By definition of stiffness matrix, nodal displacements and forces for the i
the element are related by
S  k  i  1, 2, . . . , n (5.160) i ii
where Si  matrix of forces, including moments and torques acting at the nodes
of the ith element
i  matrix of displacements of the nodes of the i th element
Step 4. For compactness, combine this relationship between nodal displacements
and forces for each element into a single matrix equation applicable to all the
elements:
S  k (5.161)
where S  matrix of all forces acting at the nodes of all elements
  matrix of all nodal displacements for all elements
STRUCTURAL THEORY 5.115
k 0 . . . 0 1
0 k . . . 0 2 k  (5.162)
. . . . . . . . .  	 0 0 . . . kn
Step 5. Develop a matrix b0 that will transform the displacements of the nodes
of the structure into the displacement vector  while maintaining geometric compatibility:
  b 
 (5.163) 0
b0 is a matrix of influence coefficients. The jth column of b0 contains the element
nodal displacements when the node where j occurs is given a unit displacement
in the direction of j, and no other nodes are displaced.
Step 6. Compute the stiffness matrix K for the whole structure from
T K  b kb (5.164) 0 0
where b  transpose of b0  matrix b0 with rows and columns interchanged T0
This equation may be derived as follows: From energy relationship, P  b S. T0
Substitution of k for S [Eq. (5.161)] and then substitution of b0
 for  [Eq.
(5.163)] yields P  b kb0 
. Comparison of this with Eq. (5.103a), P  k
 leads T0
to Eq. (5.164).
Step 7. With the stiffness matrix K now known, solve the simultaneous equations
1 
 K P (5.165)
for the nodal displacements 
. With these determined, calculate the member forces
from
S  kb 
 (5.166) 0
(N. M. Baran, ‘‘Finite Element Analysis on Microcomputers,’’ and H. Kardesluncer
and D. H. Norris, ‘‘Finite Element Handbook,’’ McGraw-Hill Publishing
Company, New York; K. Bathe, ‘‘Finite Element Procedures in Engineering Analysis,’’
T. R. Hughes, ‘‘The Finite Element Method,’’ W. Weaver, Jr., and P. R.
Johnston, ‘‘Structural Dynamics by Finite Elements,’’ and H. T. Y. Yang, ‘‘Finite
Element Structural Analysis,’’ Prentice-Hall, Englewood Cliffs, N.J.)
5.14 STRESSES IN ARCHES
An arch is a curved beam, the radius of curvature of which is very large relative
to the depth of the section. It differs from a straight beam in that: (1) loads induce
both bending and direct compressive stresses in an arch; (2) arch reactions have
horizontal components even though loads are all vertical; and (3) deflections have
horizontal as well as vertical components (see also Arts. 5.6.1 to 5.6.4). Names of
arch parts are given in Fig. 5.93.
5.116 SECTION FIVE
FIGURE 5.93 Components of an arch.
The necessity of resisting the horizontal components of the reactions is an important
consideration in arch design. Sometimes these forces are taken by the tie
rods between the supports, sometimes by heavy abutments or buttresses.
Arches may be built with fixed ends, as can straight beams, or with hinges at
the supports. They may also be built with a hinge at the crown.
5.14.1 Three-Hinged Arches
An arch with a hinge at the crown as well as at both supports (Fig. 5.94) is statically
determinate. There are four unknowns—two horizontal and two vertical components
of the reactions—but four equations based on the laws of equilibrium are
available: (1) The sum of the horizontal forces must be zero. (2) The sum of the
moments about the left support must be zero. (3) The sum of the moments about
the right support must be zero. (4) The bending moment at the crown hinge must
be zero (not to be confused with the sum of the moments about the crown, which
also must be equal to zero but which would not lead to an independent equation
for the solution of the reactions).
FIGURE 5.94 Three-hinged arch.
Stresses and reactions in threehinged
arches can be determined graphically
by taking advantage of the fact
that the bending moment at the crown
hinge is zero. For example, in Fig.
5.94a, a concentrated load P is applied
to segment AB of the arch. Then, since
the bending moment at B must be zero,
the line of action of the reaction at C
must pass through the crown hinge. It
intersects the line of action of P at X.
The line of action of the reaction at A
must also pass through X. Since P is
equal to the sum of the reactions, and
since the directions of the reactions have
thus been determined, the magnitude of
the reactions can be measured from a parallelogram of forces (Fig. 5.94b). When
the reactions have been found, the stresses can be computed from the laws of statics
(see Art. 5.14.3) or, in the case of a trussed arch, determined graphically.
STRUCTURAL THEORY 5.117
FIGURE 5.95 Two-hinged arch.
5.14.2 Two-Hinged Arches
When an arch has hinges at the supports only (Fig. 5.95), it is statically indeterminate,
and some knowledge of its deformations is required to determine the reactions.
One procedure is to assume that one of the supports is on rollers. This
makes the arch statically determinate. The reactions and the horizontal movement
of the support are computed for this condition (Fig. 5.95b). Then, the magnitude
of the horizontal force required to return the movable support to its original position
is calculated (Fig. 5.95c). The reactions for the two-hinged arch are finally found
by superimposing the first set of reactions on the second (Fig. 5.95d).
For example, if x is the horizontal movement of the support due to the loads,
and if x is the horizontal movement of the support due to a unit horizontal force
applied to the support, then
x  Hx  0 (5.167)
x
H   (5.168)
x
where H is the unknown horizontal reaction. (When a tie rod is used to take the
thrust, the right-hand side of Eq. (5.167) is not zero, but the elongation of the rod,
HL/AE.) The dummy unit-load method [Eq. (5.96)] can be used to compute x and
x:
B B My N dx
x   ds   (5.169)
A A EI AE
5.118 SECTION FIVE
FIGURE 5.96 Interior stresses at X hold portion LX of an
arch rib in equilibrium.
where M  moment at any section resulting from loads
N  normal thrust on cross section
A  cross-sectional area of arch
y  ordinate of section measured from A as origin, when B is on rollers
I  moment of inertia of section
E  modulus of elasticity
ds  differential length along axis of arch
dx  differential length along horizontal
B B 2 2 y cos  dx
x    ds   (5.170)
A A EI AE
where  the angle the tangent to the axis at the section makes with the horizontal.
Unless the thrust is very large and would be responsible for large strains in the
direction of the arch axis, the second term on the right-hand side of Eq. (5.169)
can usually be ignored.
In most cases, integration is impracticable. The integrals generally must be evaluated
by approximate methods. The arch axis is divided into a convenient number
of sections and the functions under the integral sign evaluated for each section. The
sum is approximately equal to the integral. Thus, for the usual two-hinged arch,
B
(My s /EI) 	A H  (5.171) B B
2 2 (y s /EI)  (cos  x/AE) 	 	 A A
(S. Timoshenko and D. H. Young, ‘‘Theory of Structures,’’ McGraw-Hill Book
Company, New York; S. F. Borg and J. J. Gennaro, ‘‘Modern Structural Analysis,’’
Van Nostrand Reinhold Company, Inc., New York.)
5.14.3 Stresses in Arch Ribs
When the reactions have been found for an arch (Arts. 5.14.1 to 5.14.2), the principal
forces acting on any cross section can be found by applying the equations of
equilibrium. For example, consider the portion of an arch in Fig. 5.96, where the
STRUCTURAL THEORY 5.119
forces acting at an interior section X are to be found. The load P, HL (or HR), and
VL (or VR) may be resolved into components parallel to the axial thrust N and the
shear S at X, as indicated in Fig. 5.96. Then, by equating the sum of the forces in
each direction to zero, we get
N  V sin   H cos   P sin (   ) (5.172) L x L x x
S  V cos   H sin   P cos (   ) (5.173) L x L x x
And the bending moment at X is
M  V x  H y  Pa cos  Pb sin  (5.174) L 1
The shearing unit stress on the arch cross section at X can be determined from
S wit the aid of Eq. (5.59). The normal unit stresses can be calculated from N and
M with the aid of Eq. (5.67).
In designing an arch, it may be necessary to compute certain secondary stresses,
in addition to those caused by live, dead, wind, and snow loads. Among the secondary
stresses to be considered are those due to temperature changes, rib shortening
due to thrust or shrinkage, deformation of tie rods, and unequal settlement
of footings. The procedure is the same as for loads on the arch, with the deformations
producing the secondary stresses substituted for or treated the same as the
deformations due to loads.
5.15 THIN-SHELL STRUCTURES
A structural membrane or shell is a curved surface structure. Usually, it is capable
of transmitting loads in more than two directions to supports. It is highly efficient
structurally when it is so shaped, proportioned, and supported that it transmits the
loads without bending or twisting.
A membrane or a shell is defined by its middle surface, halfway between its
extrados, or outer surface and intrados, or inner surface. Thus, depending on the
geometry of the middle surface, it might be a type of dome, barrel arch, cone, or
hyperbolic paraboloid. Its thickness is the distance, normal to the middle surface,
between extrados and intrados.
5.15.1 Thin-Shell Analysis
A thin shell is a shell with a thickness relatively small compared with its other
dimensions. But it should not be so thin that deformations would be large compared
with the thickness.
The shell should also satisfy the following conditions: Shearing stresses normal
to the middle surface are negligible. Points on a normal to the middle surface before
it is deformed lie on a straight line after deformation. And this line is normal to
the deformed middle surface.
Calculation of the stresses in a thin shell generally is carried out in two major
steps, both usually involving the solution of differential equations. In the first, bending
and torsion are neglected (membrane theory, Art. 5.15.2). In the second step,
corrections are made to the previous solution by superimposing the bending and
5.120 SECTION FIVE
shear stresses that are necessary to satisfy boundary conditions (bending theory,
Art. 5.15.3).
Ribbed Shells. For long-span construction, thin shells often are stiffened at intervals
by ribs. Usually, the construction is such that the shells transmit some of the
load imposed on them to the ribs, which then perform structurally as more than
just stiffeners. Stress and strain distributions in shells and ribs consequently are
complicated by the interaction between shells and ribs. The shells restrain the ribs,
and the ribs restrain the shells. Hence, ribbed shells usually are analyzed by approximate
methods based on reasonable assumptions.
For example, for a cylindrical shell with circumferential ribs, the ribs act like
arches. For an approximate analysis, the ribbed shell therefore may be assumed to
be composed of a set of arched ribs with the thin shell between the ribs acting in
the circumferential direction as flanges of the arches. In the longitudinal direction,
it may be assumed that the shell transfers load to the ribs in flexure. Designers may
adjust the results of a computation based on such assumptions to correct for a
variety of conditions, such as the effects of free edges of the shell, long distances
between ribs, relative flexibility of ribs and shell, and characteristics of the structural
materials.
5.15.2 Membrane Theory for Thin Shells
Thin shells usually are designed so that normal shears, bending moments, and
torsion are very small, except in relatively small portions of the shells. In the
membrane theory, these stresses are ignored.
Despite the neglected stresses, the remaining stresses ae in equilibrium, except
possibly at boundaries, supports, and discontinuities. At any interior point, the number
of equilibrium conditions equals the number of unknowns. Thus, in the
membrane theory, a thin shell is statically determinate.
The membrane theory does not hold for concentrated loads normal to the middle
surface, except possibly at a peak or valley. The theory does not apply where
boundary conditions are incompatible with equilibrium. And it is in exact where
there is geometric incompatibility at the boundaries. The last is a common condition,
but the error is very small if the shell is not very flat. Usually, disturbances
of membrane equilibrium due to incompatibility with deformations at boundaries,
supports, or discontinuities are appreciable only in a narrow region about each
source of disturbance. Much larger disturbances result from incompatibility with
equilibrium conditions.
To secure the high structural efficiency of a thin shell, select a shape, proportions,
and supports for the specific design conditions that come as close as possible to
satisfying the membrane theory. Keep the thickness constant; if it must change, use
a gradual taper. Avoid concentrated and abruptly changing loads. Change curvature
gradually. Keep discontinuities to a minimum. Provide reactions that are tangent to
the middle surface. At boundaries, ensure, to the extent possible, compatibility of
shell deformations with deformations of adjoining members, or at least keep restraints
to a minimum. Make certain that reactions along boundaries are equal in
magnitude and direction to the shell forces there.
Means usually adopted to satisfy these requirements at boundaries and supports
are illustrated in Fig. 5.97. In Fig. 5.97a, the slope of the support and provision for
movement normal to the middle surface ensure a reaction tangent to the middle
surface. In Fig. 5.97b, a stiff rib, or ring girder, resists unbalanced shears and
STRUCTURAL THEORY 5.121
FIGURE 5.97 Special provisions made at supports and boundaries of thin shells to
meet requirements of the membrane theory include: (a) a device to ensure a reaction
tangent to the middle surface; (b) stiffened edges, such as the ring girder at the base of
a dome; (c) gradually increased shell thicknesses at a stiffening member; (d ) a transition
curve at changes in section; (e) a stiffening edge obtained by thickening the shell; ( ? )
scalloped edges; (g) a flared support.
transmits normal forces to columns below. The enlarged view of the ring girder in
Fig. 5.97c shows gradual thickening of the shell to reduce the abruptness of the
change in section. The stiffening ring at the lantern in Fig. 5.97d, extending around
the opening at the crown, projects above the middle surface, for compatibility of
strains, and connects through a transition curve with the shell; often, the rim need
merely be thickened when the edge is upturned, and the ring can be omitted. In
Fig. 5.97e, the boundary of the shell is a stiffened edge. In Fig. 5.97f, a scalloped
shell provides gradual tapering for transmitting the loads to the supports, at the
same time providing access to the shell enclosure. And in Fig. 5.97g, a column is
flared widely at the top to support a thin shell at an interior point.
Even when the conditions for geometric compatibility are not satisfactory, the
membrane theory is a useful approximation. Furthermore, it yields a particular
solution to the differential equations of the bending theory.
(D. P. Billington, ‘‘Thin Shell Concrete Structures,’’ 2d ed., and S. Timoshenko
and S. Woinowsky-Krieger, ‘‘Theory of Plates and Shells,’’ McGraw-Hill Book
Company, New York: V. S. Kelkar and R. T. Sewell, ‘‘Fundamentals of the Analysis
and Design of Shell Structures,’’ Prentice-Hall, Englewood Cliffs, N.J.)
5.15.3 Bending Theory for Thin Shells
When equilibrium conditions are not satisfied or incompatible deformations exist
at boundaries, bending and torsion stresses arise in the shell. Sometimes, the design
of the shell and its supports can be modified to reduce or eliminate these stresses
(Art. 5.15.2). When the design cannot eliminate them, provisions must be made for
the shell to resist them.
5.122 SECTION FIVE
But even for the simplest types of shells and loading, the stresses are difficult
to compute. In bending theory, a thin shell is statically indeterminate; deformation
conditions must supplement equilibrium conditions in setting up differential equations
for determining the unknown forces and moments. Solution of the resulting
equations may be tedious and time-consuming, if indeed solution if possible.
In practice, therefore, shell design relies heavily on the designer’s experience
and judgment. The designer should consider the type of shell, material of which it
is made, and support and boundary conditions, and then decide whether to apply a
bending theory in full, use an approximate bending theory, or make a rough estimate
of the effects of bending and torsion. (Note that where the effects of a disturbance
are large, these change the normal forces and shears computed by the membrane
theory.) For concrete domes, for example, the usual procedure is to use as support
a deep, thick girder or a heavily reinforced or prestressed tension ring, and the shell
is gradually thickened in the vicinity of this support (Fig. 5.97c).
Circular barrel arches, with ratio of radius to distance between supporting arch
ribs less than 0.25 may be designed as beams with curved cross section. Secondary
stresses, however, must be taken into account. These include stresses due to volume
change of rib and shell, rib shortening, unequal settlement of footings, and temperature
differentials between surfaces.
Bending theory for cylinders and domes is given in W. Flu?gge, ‘‘Stresses in
Shells,’’ Springer-Verlag, New York; D. P. Billington, ‘‘Thin Shell Concrete Structures,’’
2d ed., and S. Timoshenko and S. Woinowsky-Krieger, ‘‘Theory of Plates
and Shells,’’ McGraw-Hill Book Company, New York; ‘‘Design of Cylindrical Concrete
Shell Roofs,’’ Manual of Practice No. 31, American Society of Civil Engineers.
5.15.4 Stresses in Thin Shells
The results of the membrane and bending theories are expressed in terms of unit
forces and unit moments, acting per unit of length over the thickness of the shell.
To compute the unit stresses from these forces and moments, usual practice is to
assume normal forces and shears to be uniformly distributed over the shell thickness
and bending stresses to be linearly distributed.
Then, normal stresses can be computed from equations of the form
N M x x ?   z (5.175) x 3 t t /12
where z  distance from middle surface
t  shell thickness
Mx  unit bending moment about axis parallel to direction of unit normal
force Nx
Similarly, shearing stresses produced by central shears and twisting moments may
be calculated from equations of the form
T D
v  
 z (5.176) xy 3 t t /12
where D  twisting moment and T  unit shear force along the middle surface.
Normal shearing stresses may be computed on the assumption of a parabolic stress
distribution over the shell thickness:
STRUCTURAL THEORY 5.123
FIGURE 5.98 Folded-plate structure.
2 V t 2 v  z (5.177) 
  xz 3 t / t 4
where V  unit shear force normal to middle surface.
5.15.5 Folded Plates
A folded-plate structure consists of a series of thin planar elements, or flat plates,
connected to one another along their edges. Usually used on long spans, especially
for roofs, folded plates derive their economy from the girder action of the plates
and the mutual support they give one another.
Longitudinally, the plates may be continuous over their supports. Transversely,
there may be several plates in each bay (Fig. 5.98). At the edges, or folds, they
may be capable of transmitting both moment and shear or only shear.
A folded-plate structure has a two-way action in transmitting loads to its supports.
Transversely, the elements act as slabs spanning between plates on either
side. The plates then act as girders in carrying the load from the slabs longitudinally
to supports, which must be capable of resisting both horizontal and vertical forces.
If the plates are hinged along their edges, the design of the structure is relatively
simple. Some simplification also is possible if the plates, though having integral
edges, are steeply sloped or if the span is sufficiently long with respect to other
dimensions that beam theory applies. But there are no criteria for determining when
such simplification is possible with acceptable accuracy. In general, a reasonably
accurate analysis of folded-plate stresses is advisable.
Several good methods are available (D. Yitzhaki, ‘‘The Design of Prismatic and
Cylindrical Shell Roofs,’’ North Holland Publishing Company, Amsterdam; ‘‘Phase
I Report on Folded-plate Construction,’’ Proceedings Paper 3741, Journal of the
Structural Division, American Society of Civil Engineers, December 1963; and A.
L. Parme and J. A. Sbarounis, ‘‘Direct Solution of Folded Plate Concrete Roofs,’’
EB021D, Portland Cement Association, Skokie, Ill.). They all take into account the
effects of plate deflections on the slabs and usually make the following assumptions:
The material is elastic, isotropic, and homogeneous. The longitudinal distribution
of all loads on all plates is the same. The plates carry loads transversely only by
5.124 SECTION FIVE
bending normal to their planes and longitudinally only by bending within their
planes. Longitudinal stresses vary linearly over the depth of each plate. Supporting
members, such as diaphragms, frames, and beams, are infinitely stiff in their own
planes and completely flexible normal to their own planes. Plates have no torsional
stiffness normal to their own planes. Displacements due to forces other than bending
moments are negligible.
Regardless of the method selected, the computations are rather involved; so it
is wise to carry out the work by computer or, when done manually, in a wellorganized
table. The Yitzhaki method offers some advantages over others in that
the calculations can be tabulated, it is relatively simple, it requires the solution of
no more simultaneous equations than one for each edge for simply supported plates,
it is flexible, and it can easily be generalized to cover a variety of conditions.
Yitzhaki Method. Based on the assumptions and general procedure given above,
the Yitzhaki method deals with the slab and plate systems that comprise a foldedplate
structure in two ways. In the first, a unit width of slab is considered continuous
over supports immovable in the direction of the load (Fig. 5.99b). The strip usually
is taken where the longitudinal plate stresses are a maximum. Second, the slab
reactions are taken as loads on the plates, which now are assumed to be hinged
along the edged (Fig. 5.99c). Thus, the slab reactions cause angle changes in the
plates at each fold. Continuity is restored by applying to the plates an unknown
moment at each edge. The moments can be determined from the fact that at each
edge the sum of the angle changes due to the loads and to the unknown moments
must equal zero.
The angle changes due to the unknown moments have two components. One is
the angle change at each slab end, now hinged to an adjoining slab, in the transverse
strip of unit width. The second is the angle change due to deflection of the plates.
The method assumes that the angle change at each fold varies in the same way
longitudinally as the angle changes along the other folds.
For example, for the folded-plate structure in Fig. 5.99a, the steps in analysis
are as follows:
Step 1. Compute the loads on a 12-in-wide transverse strip at midspan.
Step 2. Consider the strip as a continuous slab supported at the folds (Fig. 5.99b),
and compute the bending moments by moment distribution.
Step 3. From the end moments M found in Step 2, compute slab reactions and
plate loads. Reactions (positive upward) at the nth edge are
M M M  M n1 n n n1 R  V  V   (5.178) n n n1 a a n n1
where Vn, V  n1 shears at both sides of edge n
Mn  moment at edge n
M  n1 moment at edge (n  1)
M  n1 moment at edge (n  1)
a  horizontal projection of depth h
Let k  tan 	n  tan 	 , where 	 is positive as shown in Fig. 99a. Then, the n1
load (positive downward) on the nth plate is
STRUCTURAL THEORY 5.125
FIGURE 5.99 Folded plate is analyzed by first considering a transverse strip (a) as a continuous
slab on supports that do not settle (b). then, (c) the slabs are assumed hinged and acted upon by
the reactions computed in the first step and by unknown moments to correct for this assumption.
(d ) Slab reactions are resolved into plate forces, parallel to the planes of the plates. (e) In the
longitudinal direction, the plates act as deep girders with shears along the edges. ( ? ) Arrows
indicate the positive directions for the girder shears.
R R n n1 P  (5.179) n k cos 	 k cos 	 n n n1 n
(Figure 5.99d shows the resolution of forces at edge n; n  1 is similar.) Equation
(5.179) does not apply for the case of a vertical reaction on a vertical plate, for
R/k is the horizontal component of the reaction.
Step 4. Calculate the midspan (maximum) bending moment in each plate. In this
example, each plate is a simple beam and M  PL2 / 8, where L is the span in feet.
Step 5. Determine the free-edge longitudinal stresses at midspan. In each plate,
these can be computed from
5.126 SECTION FIVE
72M 72M
?  ?   (5.180) n1 n Ah Ah
where ? is the stress in psi, M the moment in ft-lb from Step 4, A  plate crosssectional
area and tension is taken as positive, compression as negative.
Step 6. Apply a shear to adjoining edges to equalize the stresses there. Compute
the adjusted stresses by converging approximations, similar to moment distribution.
To do this, distribute the unbalanced stress at each edge in proportion to the reciprocals
of the areas of the plates, and use a carry-over factor of 1?2 to distribute
the tress to a far edge. Edge 0, being a free edge, requires no distribution of the
stress there. Edge 3, because of symmetry, may be treated the same, and distribution
need be carried out only in the left half of the structure.
Step 7. Compute the midspan edge deflections. In general, the vertical component
 can be computed from
E 15 ? ? ?  ? n1 n n n1   (5.181) 
  n 2L k a a n n n1
where E  modulus of elasticity, psi
k  tan 	n  tan 	 , as in Step 3 n1
The factor E/L2 is retained for convenience; it is eliminated by dividing the simultaneous
angle equations by it. For a vertical plate, the vertical deflection is
given by
E 15(?  ? ) n1 n   (5.182) n 2L hn
Step 8. Compute the midspan angle change P at each edge. This can be determined
from
E     n1 n n n1     (5.183) P 2L a a n n1
Step 9. To correct the edge rotations with a symmetrical loading, apply an unknown
moment of 100mn sin (
x/L), in-lb (positive when clockwise) to plate n
at edge n and 1000mn sin (
x/L) to its counterpart, plate n at edge n. Also,
apply 1000mn sin (
x/L) to plate (n  1) at edge n and 1000mn sin (
x/L)
sine function is assumed to make the loading vary longitudinally in approximately
the same manner as the deflections.) At midspan, the absolute value of these moments
is 1000mn.
The 12-in-wide transverse strip at midspan, hinged at the supports, will then be
subjected at the supports to moments of 1000mn. Compute the rotations thus caused
in the slabs from
STRUCTURAL THEORY 5.127
E 166.7h m n n   n1 2 23 L Lt n
E 333.3m h h n n n1   (5.184) 
  n 2 2 3 3 L L t t n n1
E 166.7h m n1 n   n1 2 23 L Lt n1
Step 10. Compute the slab reactions and plate loads due to the unknown moments.
The reactions are
1000m 1 1 1000m n n R  R  1000m  R   (5.185) 
  n1 n n n1 a a a a n n n1 n1
The plate loads are
1 R R n n1 P  (5.186) 
  n cos 	 k k n n n1
Step 11. Assume that the loading on each plate is Pn sin (
x/L) (Fig. 5.99e), and
calculate the midspan (maximum) bending moment. For a simple beam,
2 PL
M  2 

Step 12. Using Eq. (5.180), compute the free-edge longitudinal stresses at midspan.
Then, as in Step 6, apply a shear at each edge to equalize the stresses.
Determine the adjusted stresses by converging approximations.
Step 13. Compute the vertical component of the edge deflections at midspan from
n1 E 144 ? ? ?  ? n n n1   (5.187) 
  n 2 2 L 
k a a n n n1
or for a vertical plate from
E 144(?  ? ) n1 n   (5.188) n 2 2 L 
 hn
Step 14. Using Eq. (5.183), determine the midspan angle change  at each edge.
Step 15. At each edge, set up an equation by putting the sum of the angle changes
equal to zero. Thus, after division by E/L2: P      0. Solve these
simultaneous equations for the unknown moments.
Step 16. Determine the actual reactions, loads, stresses, and deflections by substituting
for the moments the values just found.
Step 17. Compute the shear stresses. The shear stresses at edge n (Fig. 5.99?) is
5.128 SECTION FIVE
?  ? n1 n T T A (5.189) n n1 n 2
In the example, To  0, so the shears at the edges can be obtained successively,
since the stresses ? are known.
For a uniformly loaded folded plate, the shear stress S, psi, at any point on an
edge n is approximately
2T 1 x max S  (5.190) 
  3Lt 2 L
With a maximum at plate ends of
Tmax S  (5.191) max 3Lt
The shear stress, psi, at middepth (not always a maximum) is
3P L S  S 1 x n n1 n 
 v    (5.192) 
   n 2A 2 2 L n
and has its largest value at x  0:
0.75P L S  S n n1 n v   (5.193) max A 4 n
For more details, see D. Yitzhaki and Max Reiss, ‘‘Analysis of Folded Plates,’’
Proceedings Paper 3303, Journal of the Structural Division, American Society of
Civil Engineers, October 1962.
5.16 CABLE-SUPPORTED STRUCTURES*
A cable is a linear structural member, like a bar of a truss. The cross-sectional
dimensions of a cable relative to its length, however, are so small that it cannot
withstand bending or compression. Consequently, under loads at an angle to its
longitudinal axis, a cable sags and assumes a shape that enables it to develop tensile
stresses that resist the loads.
Structural efficiency results from two cable characteristics: (1) uniformity of
tensile stresses over the cable cross section, and (2) usually, small variation of
tension along the longitudinal axis. Hence, it is economical to use materials with
very high tensile strength for cables.
Cables sometimes are used in building construction as an alternative to such
tension members as hangers, ties, or tension chords of trusses. For example, cables
are used in a form of long-span cantilever-truss construction in which a horizontal
* Reprinted with permission from F. S. Merritt, ‘‘Structural Steel Designers’ Handboo,’’ McGraw-Hill
Book Company, New York.
STRUCTURAL THEORY 5.129
FIGURE 5.101 Simple cable: (a) cable with a uniformly distributed load; (b) cable with
supports at different levels.
FIGURE 5.100 Two types of cable-stayed girder construction for roofs.
roof girder is supported at one end by a column and near the other end by a cable
that extends diagonally upward to the top of a vertical mast above the column
support (cable-stayed-girder construction, Fig. 5.100). Cable stress an be computed
for this case from the laws of equilibrium.
Cables also may be used in building construction instead of girders, trusses, or
membranes to support roofs, For the purpose, cables may be arranged in numerous
ways. It is consequently impractical to treat in detail in this book any but the
simplest types of such applications of cables. Instead, general procedures for analyzing
cable-supported structures are presented in the following.
5.16.1 Simple Cables
An ideal cable has o resistance to bending. Thus, in analysis of a cable in equilibrium,
not only is the sum of the moments about any point equal to zero but so is
the bending moment at any point. Consequently, the equilibrium shape of the cable
corresponds to the funicular, or bending-moment, diagram for the loading (Fig.
5.101a). As a result, the tensile force at any point of the cable is tangent there to
the cable curve.
The point of maximum sag of a cable coincides with the point of zero shear.
(Sag in this case should be measured parallel to the direction of the shear forces.)
Stresses in a cable are a function of the deformed shape. Equations needed for
analysis, therefore, usually are nonlinear. Also, in general, stresses and deformations
cannot be obtained accurately by superimposition of loads. A common procedure
5.130 SECTION FIVE
in analysis is to obtain a solution in steps by using linear equations to approximate
the nonlinear ones and by starting with the initial geometry to obtain better estimates
of the final geometry.
For convenience in analysis, the cable tension, directed along the cable curve,
usually is resolved into two components. Often, it is advantageous to resolve the
tension T into a horizontal component H and a vertical component V (Fig. 5.100b).
Under vertical loading then, the horizontal component is constant along the cable.
Maximum tension occurs at the support. V is zero at the point of maximum sag.
For a general, distributed vertical load q, the cable must satisfy the second-order
linear differential equation
n Hy  q (5.194)
where y  rise of cable at distance x from low point (Fig. 5.100b)
y  n d2y/dx2
Catenary. Weight of a cable of constant cross-section represents a vertical loading
that is uniformly distributed along the length of cable. Under such a loading, a
cable takes the shape of a catenary.
Take the origin of coordinates at the low point C and measure distance s along
the cable from C (Fig. 5.100b). If qo is the load per unit length of cable, Eq. (5.194)
becomes
q ds o n 2 Hy q 1  y (5.195) o dx
where y  dy/dx. Solving for y gives the slope at any point of the cable
3 q x q x 1 q x o o o y  sinh      (5.196) 
  H H 3! H
A second integration then yields the equation for the cable shape, which is called
a catenary.
3 2 4 H qx qx q x o o o y  cosh  1      (5.197) 
  
 q H H 2! H 4! o
If only the first term of the series expansion is used, the cable equation represents
a parabola. Because the parabolic equation usually is easier to handle, a catenary
often is approximated by a parabola.
For a catenary, length of arc measured from the low point is
2 H qx 1 q o o 3 s  sinh  x  x     (5.198) 
  q H 3! H o
Tension at any point is
2 22 T  H  q s  H  q y (5.199) o o
The distance from the low point C to the left support L is
STRUCTURAL THEORY 5.131
H qo 1 a  cosh ?  1 (5.200) 
  L q H o
where ?L  vertical distance from C to L. The distance from C to the right support
R is
H qo 1 b  cosh ?  1 (5.201) 
  R q H o
where ?R  vertical distance from C to R.
Given the sags of a catenary ?L and ?R under a distributed vertical load qo, the
horizontal component of cable tension H may be computed from
q l q ? q ? o oL o R 1 1  cosh  1  cosh  1 (5.202) 
  
  H H H
where l  span, or horizontal distance between supports L and R  a  b. This
equation usually is solved by trial. A first estimate of H for substitution in the righthand
side of the equation may be obtained by approximating the catenary by a
parabola. Vertical components of the reactions at the supports can be computed
from
q a q b o o R  H sinh R  H sinh (5.203) L R H H
Parabola. Uniform vertical live loads and uniform vertical dead loads other than
cable weight generally may be treated as distributed uniformly over the horizontal
projection of the cable. Under such loadings, a cable takes the shape of a parabola.
Take the origin of coordinates at the low point C (Fig. 5.100b). If wo is the load
per foot horizontally, Eq. (5.194) becomes
n Hy  w (5.204) o
Integration gives the slope at any point of the cable
w x o y  (5.205)
H
A second integration yields the parabolic equation for the cable shape
2 w x o y  (5.206)
2H
The distance from the low point C to the left support L is
l Hh
a  (5.207)
2 w l o
where l  span, or horizontal distance between supports L and R  a  b
h  vertical distance between supports
The distance from the low point C to the right support R is
5.132 SECTION FIVE
l Hh
b  (5.208)
2 w l o
When supports are not at the same level, the horizontal component of cable
tension H may be computed from
2 2 w l h w l o o H  ?  
 ? ?  (5.209) 
  R LR 2 h 2 8?
where ?L  vertical distance from C to L
?R  vertical distance from C to R
?  sag of cable measured vertically from chord LR midway between supports
(at x  Hh/wo l )
As indicated in Fig. 5.100b,
h
?  ?  y (5.210) L M 2
where yM  Hh2/2wo l 2. The minus sign should be used in Eq. (5.209) when low
point C is between supports. If the vertex of the parabola is not between L and R,
the plus sign should be used.
The vertical components of the reactions at the supports can be computed from
w l Hh w l Hh o o V  w a  V  w b  (5.211) L o R o 2 l 2 l
Tension at any point is
2 2 2 T  H  w x (5.212) o
Length of parabolic arc RC is
2 2 b wb H w b 1 w o o o 3 L  1  sinh  b  b     (5.213) 
  
  RC  2 KH 2w H 6 H o
Length of parabolic are LC is
2 2 a wa H w a 1 w o o o 3 L  1  sinh  a  a     (5.214) 
  
  LC  2 H 2w H 6 H o
When supports are at the same level, ?L  ?R  ?, h  0, and a  b  l/2.
The horizontal component of cable tension H may be computed from
2 w l o H  (5.215)
8?
The vertical components of the reactions at the supports are
w l o V  V  (5.216) L R 2
Maximum tension occurs at the supports and equals
STRUCTURAL THEORY 5.133
2 w l l o T  T  1  (5.217) L R 2  2 16?
Length of cable between supports is
2 1 w l H w l o o L  1  sinh 
   2 2H w 2H o (5.218)
2 4 6 8 ? 32 ? 256 ?
 l 1      
  2 4 6 3 l 5 l 7 l
If additional uniformly distributed load is applied to a parabolic cable, the change
in sag is approximately
15 l L
?  (5.219) 2 2 16 ? 5  24? / l
For a rise in temperature t, the change in sag is about
2 2 15 l ct 8 ?
?  1  (5.220) 
  2 2 2 16 ?(5  24? / l) 3l
where c  coefficient of thermal expansion.
Elastic elongation of a parabolic cable is approximately
2 Hl 16 ?
L  1  (5.221) 
 2 ARE 3 l
where A  cross-sectional area of cable
E  modulus of elasticity of cable steel
H  horizontal component of tension in cable
If the corresponding change in sag is small, so that the effect on H is negligible,
this change may be computed from
2 2 2 15 Hl 1  16? /3l
?  (5.222) 2 2 16 ARE? 5  24? / l
For the general case of vertical dead load on a cable, the initial shape of the
cable is given by
MD y  (5.223) D HD
where MD  dead-load bending moment that would be produced by the load in a
simple beam
HD  horizontal component of tension due to dead load
For the general case of vertical live load on the cable, the final shape of the cable
is given by
M  M D L y   (5.224) D H  H D L
5.134 SECTION FIVE
where  vertical deflection of cable due to live load
ML  live-load bending moment that would be produced by the live load in
a simple beam
HL  increment in horizontal component of tension due to live load
Subtraction of Eq. (5.223) from Eq. (5.224) yield
M  H y L LD  (5.225)
H  H D L
If the cable is assumed to take a parabolic shape, a close approximation to HL may
be obtained from
l l H w 1 L D K    dx     dx (5.226)
0 0 AE H 2 D
2 2 2 1 5 16? 16? 3l 4? 16?
K  l  1  log  1  (5.227) 
  
 
 e 2 2 2   4 2 l l 32? l l
where   d2 /dx2.
If elastic elongation and  can be ignored, Eq. (5.226) simplifies to
l  M dx L l
0 3
H   M dx (5.228) L L l
0 2?l  y dx D
0
Thus, for a load uniformly distributed horizontally wL,
l 3 w l L  M dx  (5.229) L
0 12
and the increase in the horizontal component of tension due to live load is
3 2 2 3 w l w l w l 8H w L L L D L H    H (5.230) L D 2 2?l 12 8? 8 w l w D D
When a more accurate solution is desired, the value of HL obtained from Eq. (5.230)
can be used for an initial trial in solving Eqs. (5.225) and (5.226).
(S. P. Timoshenko and D. H. Young, ‘‘Theory of Structures,’’ McGraw-Hill Book
Company, New York: W. T. O’Brien and A. J. Francis, ‘‘Cable Movements under
Two-dimensional Loads,’’ Journal of the Structural Division, ASCE, Vol. 90, No.
ST3, Proceedings Paper 3929, June 1964, pp. 89–123; W. T. O’Brien, ‘‘General
Solution of Suspended Cable Problems,’’ Journal of the Structural Division, ASCE,
Vol. 93, No. ST1, Proceedings Paper 5085, February, 1967, pp. 1–26; W. T.
O’Brien, ‘‘Behavior of Loaded Cable Systems,’’ Journal of the Structural Division,
ASCE, Vol. 94, No. ST10, Proceedings Paper 6162, October 1968, pp. 2281–2302;
G. R. Buchanan, ‘‘Two-dimensional Cable Analysis,’’ Journal of the Structural
Division, ASCE, Vol. 96, No. ST7, Proceedings Paper 7436, July 1970, pp. 1581–
1587).
STRUCTURAL THEORY 5.135
FIGURE 5.102 Cable network.
5.16.2 Cable Systems
Analysis of simple cables is described in Art. 5.16.1. Cables, however, may be
assembled into many types of systems. One important reason for such systems is
that roofs to be supported are two- or three-dimensional. Consequently, threedimensional
cable arrangements often are advantageous. Another important reason
is that cable systems can be designed to offer much higher resistance to vibrations
than simple cables do.
Like simple cables, cable systems behave nonlinearly. Thus, accurate analysis is
difficult, tedious, and time-consuming. As a result, many designers use approximate
methods that appear to have successfully withstood the test of time. Because of the
numerous types of systems and the complexity of analysis, only general procedures
will be outlined in this article.
Cable systems may be stiffened or unstiffened. Stiffened systems, usually used
for suspension bridges are rarely used in buildings. This article will deal only with
unstiffened systems, that is, systems where loads are carried to supports only by
cables.
Often, unstiffened systems may be classified as a network or as a cable truss,
or double-layered plane system.
Networks consist of two or three sets of cables intersecting at an angle (Fig.
5.102). The cables are fastened together at their intersections.
Cable trusses consist of pairs of cables, generally in a vertical plane. One cable
of each pair is concave downward, the other concave upward (Fig. 5.103).
Cable Trusses. Both cables of a cable truss are initially tensioned, or prestressed,
to a predetermined shape, usually parabolic. The prestress is made large enough
that any compression that may be induced in a cable by loads only reduces the
tension in the cable; thus, compressive stresses cannot occur. The relative vertical
position of the cables is maintained by verticals, or spreaders, or by diagonals.
Diagonals in the truss plane do not appear to increase significantly the stiffness of
a cable truss.
Figure 5.103 shows four different arrangements of the cables, with spreaders, in
a cable truss. The intersecting types (Fig. 5.103b and c) usually are stiffer than the
others, for given size cables and given sag and rise.
5.136 SECTION FIVE
FIGURE 5.103 Planar cable systems: (a) completely separated cables; (b) cables intersecting at
midspan; (c) crossing cables; (d ) cables meeting at supports.
FIGURE 5.104 Cable trusses placed radially to support a round
roof.
For supporting roofs, cable trusses often are placed radially at regular intervals
(Fig. 5.104). Around the perimeter of the roof, the horizontal component of the
tension usually is resisted by a circular or elliptical compression ring. To avoid a
joint with a jumble of cables at the center, the cables usually are also connected to
a tension ring circumscribing the center.
Properly prestressed, such double-layer cable systems offer high resistance to
vibrations. Wind or other dynamic forces difficult or impossible to anticipate may
cause resonance to occur in a single cable, unless damping is provided. The probability
of resonance occurring may be reduced by increasing the dead load on a
single cable. But this is not economical, because the size of cable and supports
usually must be increased as well. Besides, the tactic may not succeed, because
future loads may be outside the design range. Damping, however, may be achieved
economically with interconnected cables under different tensions, for example, with
cable trusses or networks.
The cable that is concave downward (Fig. 5.103) usually is considered the loadcarrying
cable. If the prestress in that cable exceeds that in the other cable, the
STRUCTURAL THEORY 5.137
natural frequencies of vibration of both cables will always differ for any value of
live load. To avoid resonance, the difference between the frequencies of the cables
should increase with increase in load. Thus, the two cables will tend to assume
different shapes under specific dynamic loads. As a consequence, the resulting flow
of energy from one cable to the other will dampen the vibrations of both cables.
Natural frequency, cycles per second, of each cable may be estimated from
n
 Tg
w  (5.231) n  l w
where n  integer, 1 for the fundamental mode of vibration, 2 for the second
mode, . . .
l  span of cable, ft
w  load on cable, kips per ft
g  acceleration due to gravity  32.2 ft / s2
T  cable tension, kips
The spreaders of a cable truss impose the condition that under a given load the
change in sag of the cables must be equal. But the changes in tension of the two
cables may not be equal. If the ratio of sag to span ?/ l is small (less than about
0.1). Eq. (5.222) indicates that, for a parabolic cable, the change in tension is given
approximately by
16 AE?
H  ? (5.232) 2 3 l
where ?  change in sag
A  cross-sectional area of cable
E  modulus of elasticity of cable steel
Double cables interconnected with struts may be analyzed as discrete or continuous
systems. For a discrete system, the spreaders are treated as individual members.
For a continuous system, the spreaders are replaced by a continuous diaphragm
that ensures that the changes in sag and rise of cables remain equal under
changes in load. Similarly, for analysis of a cable network, the cables, when treated
as a continuous system, may be replaced by a continuous membrane.
(C. H. Mollman, ‘‘Analysis of Plane Prestressed Cable Structures,’’ Journal of
the Structural Division, ASCE, Vol. 96, No. ST10, Proceedings Paper 7598,
October 1970, pp. 2059–2082; D. P. Greenberg, ‘‘Inelastic Analysis of Suspension
Roof Structures,’’ Journal of the Structural Division, ASCE, Vol. 96, No. ST5,
Proceedings Paper 7284, May 1970, pp. 905–930; H. Tottenham and P. G. Williams,
‘‘Cable Net: Continuous System Analysis,’’ Journal of the Engineering Mechanics
Division, ASCE, Vol. 96, No. EM3, Proceedings Paper 7347, June 1970,
pp. 277–293; A. Siev, ‘‘A General Analysis of Prestressed Nets,’’ Publications,
International Association for Bridge and Structural Engineering, Vol. 23, pp. 283–
292, Zurich, Switzerland, 1963; A. Siev, ‘‘Stress Analysis of Prestressed Suspended
Roofs,’’ Journal of the Structural Division, ASCE, Vol. 90, No. ST4, Proceedings
Paper 4008. August 1964, pp. 103–121; C. H. Thornton and C. Birnstiel, ‘‘Threedimensional
Suspension Structures,’’ Journal of the Structural Division, ASCE, Vol.
93, No. ST2, Proceedings Paper 5196, April 1967, pp. 247–270.)
5.138 SECTION FIVE
5.17 AIR-STABILIZED STRUCTURES
A true membrane is able to withstand tension but is completely unable to resist
bending. Although it is highly efficient structurally, like a shell, a membrane must
be much thinner than a shell and therefore can be made of a very lightweight
material, such as fabric, with considerable reduction in dead load compared with
other types of construction. Such a thin material, however, would buckle if subjected
to compression. Consequently, a true membrane, when loaded, deflects and
assumes a shape that enables it to develop tensile stresses that resist the loads.
Membranes may be used for the roof of a building or as a complete exterior
enclosure. One way to utilize a membrane for these purposes is to hang it with
initial tension between appropriate supports. For example, a tent may be formed by
supporting fabric atop one or more tall posts and anchoring the outer edges of the
stretched fabric to the ground. As another example, a dish-shaped roof may be
constructed by stretching a membrane and anchoring it to the inner surface of a
ring girder. In both examples, loads induce only tensile stresses in the membrane.
The stresses may be computed from the laws of equilibrium, because a membrane
is statically determinate.
Another way to utilize a membrane as an enclosure or roof is to pretension the
membrane to enable it to carry compressive loads. For the purpose, forces may be
applied, and retained as long as needed, around the edges or over the surface of
the membrane to induce tensile stresses that are larger than the larger compressive
stresses that loads will impose. As a result, compression due to loads will only
reduce the prestress and the membrane will always be subjected only to tensile
stresses.
5.17.1 Pneumatic Construction
A common method of pretensioning a membrane enclosure is to pressurize the
interior with air. Sufficient pressure is applied to counteract dead loads, so that the
membrane actually floats in space. Slight additional pressurization is also used to
offset wind and other anticipated loads. Made of lightweight materials, a membrane
thus can span large distances economically. This type of construction, however, has
the disadvantage that energy is continuously required for operation of air compressors
to maintain interior air at a higher pressure than that outdoors.
Pressure differentials used in practice are not large. They often range between
0.02 and 0.04 psi (3 and 5 psf). Air must be continually supplied, because of
leakage. While there may be some leakage of air through the membrane, more
important sources of air loss are the entrances and exits to the structure. Air locks
and revolving doors, however, can reduce these losses.
An air-stabilized enclosure, in effect is a membrane bag held in place by small
pressure differentials applied by environmental energy. Such a structure is analogous
to a soap film. The shape of a bubble is determined by surface-tension forces.
The membrane is stressed equally in all directions at every point. Consequently,
the film forms shapes with minimum surface area, frequently spherical. Because of
the stress distribution, any shape that can be obtained with soap films is feasible
for an air-stabilized enclosure. Figure 5.105c shows a configuration formed by a
conglomeration of bubbles as an illustration of a shape that can be adopted for an
air-stabilized structure.
In practice, shapes of air-stabilized structures often resemble those used for thinshell
enclosures. For example, spherical domes (Fig. 5.105a) are frequently conSTRUCTURAL
THEORY 5.139
FIGURE 5.105 Some shapes for air-supported structures. (Reprinted with permission
from F. S. Merritt, ‘‘Building Engineering and Systems Design,’’ Van Nostrand Reinhold
Company, New York.)
FIGURE 5.106 Inflated dual-wall structure. FIGURE 5.107 Air-supported structure.
structed with a membrane. Also, membranes are sometimes shaped as semi-circular
cylinders with quarter-sphere ends (Fig. 5.105b).
Air-stabilized enclosures may be classified as air-inflated, air-supported, or hybrid
structures, depending on the type of support.
Air-inflated enclosures are completely supported by pressurized air entrapped
within membranes. There are two main types, inflated-rib structures and inflated
dual-wall structures.
In inflated-rib construction, the membrane enclosure is supported by a framework
of air-pressurized tubes, which serve much like arch ribs in thin-shell construction
(Art. 5.15.1). The principle of their action is demonstrated by a water
hose. A flexible hose, when empty, collapses under its own weight on short spans
or under loads normal to its length; but it stiffens when filled with water. The water
pressure tensions the hose walls and enables them to withstand compressive
stresses.
In inflated dual-walled construction, pressurized air is trapped between two concentric
membranes (Fig. 5.106). The shape of the inner membrane is maintained
by suspending it from the outer one. Because of the large volume of air compressed
between the membranes, this type of construction can span longer distances than
can inflated-rib structures.
Because of the variation of air pressure with changes in temperature, provision
must be made for adjustment of the pressure of the compressed air in air-inflated
structures. Air must be vented to relieve excessive pressures, to prevent overtensioning
of the membranes. Also, air must be added to compensate for pressure
drops, to prevent collapse.
Air-supported enclosures consist of a single membrane supported by the difference
between internal air pressure and external atmospheric pressure (Fig. 5.107).
The pressure differential deflects the membrane outward, inducing tensile stresses
in it, thus enabling it to withstand compressive forces. To resist the uplift, the
construction must be securely anchored to the ground. Also, the membrane must
be completely sealed around its perimeter to prevent air leakage.
Hybrid structures consist of one of the preceding types of pneumatic construction
augmented by light metal framing, such as cables. The framing may be merely
5.140 SECTION FIVE
a safety measure to support the membrane if pressure should be lost or a means of
shaping the membrane when it is stretched. Under normal conditions, air pressure
against the membrane reduces the load on the framing from heavy wind and snow
loads.
5.17.2 Membrane Stresses
Air-supported structures are generally spherical or cylindrical because of the supporting
uniform pressure.
When a spherical membrane with radius R, in, its subjected to a uniform radial
internal pressure, p, psi, the internal unit tensile force, lb / in, in any direction, is
given by
pR
T  (5.233)
2
In a cylindrical membrane, the internal unit tensile force, lb / in, in the circumferential
direction is given by
T  pR (5.234)
where R  radius, in, of the cylinder. The longitudinal membrane stress depends
on the conditions at the cylinder ends. For example, with immovable end enclosures,
the longitudinal stress would be small. If, however the end enclosure is
flexible, a tension about half that given by Eq. (5.234) would be imposed on the
membrane in the longitudinal direction.
Unit stress in the membrane can be computed by dividing the unit force by the
thickness, in, of the membrane.
(R. N. Dent, ‘‘Principles of Pneumatic Architecture,’’ John Wiley & Sons, Inc.,
New York; J. W. Leonard, ‘‘Tension Structures,’’ McGraw-Hill Publishing Company,
New York.)
5.18 STRUCTURAL DYNAMICS
Article 5.1.1 notes that loads can be classified as static or dynamic and that the
distinguishing characteristic is the rate of application of load. If a load is applied
slowly, it may be considered static. Since dynamic loads may produce stresses and
deformations considerably larger than those caused by static loads of the same
magnitude, it is important to know reasonably accurately what is meant by slowly.
A useful definition can be given in terms of the natural period of vibration of
the structure or member to which the load is applied. If the time in which a load
rises from zero to its maximum value is more than double the natural period, the
load may be treated as static. Loads applied more rapidly may be dynamic. Structural
analysis and design for such loads are considerably different from and more
complex than those for static loads.
In general, exact dynamic analysis is possible only for relatively simple structures,
and only when both the variation of load and resistance with time are a
convenient mathematical function. Therefore, in practice, adoption of approximate
STRUCTURAL THEORY 5.141
methods that permit rapid analysis and design is advisable. And usually, because
of uncertainties in loads and structural resistance, computations need not be carried
out with more than a few significant figures, to be consistent with known conditions.
5.18.1 Properties of Materials under Dynamic Loading
In general mechanical properties of structural materials improve with increasing
rate of load application. For low-carbon steel, for example, yield strength, ultimate
strength, and ductility rise with increasing rate of strain. Modulus of elasticity in
the elastic range, however, is unchanged. For concrete, the dynamic ultimate
strength in compression may be much greater than the static strength.
Since the improvement depends on the material and the rate of strain, values to
use in dynamic analysis and design should be determined by tests approximating
the loading conditions anticipated.
Under many repetitions of loading, though, a member or connection between
members may fail because of ‘‘fatigue’’ at a stress smaller than the yield point of
the material. In general, there is little apparent deformation at the start of a fatigue
failure. A crack forms at a point of high stress concentration. As the stress is
repeated, the crack slowly spreads, until the member ruptures without measurable
yielding. Though the material may be ductile, the fracture looks brittle.
Some materials (generally those with a well-defined yield point) have what is
known as an endurance limit. This is the maximum unit stress that can be repeated,
through a definite range, an indefinite number of times without causing structural
damage. Generally, when no range is specified, the endurance limit is intended for
a cycle in which the stress is varied between tension and compression stresses of
equal value.
A range of stress may be resolved into two components—a steady, or mean,
stress and an alternating stress. The endurance limit sometimes is defined as the
maximum value of the alternating stress that can be superimposed on the steady
stress an indefinitely large number of times without causing fracture.
Design of members to resist repeated loading cannot be executed with the certainty
with which members can be designed to resist static loading. Stress concentrations
may be present for a wide variety of reasons, and it is not practicable to
calculate their intensities. But sometimes it is possible to improve the fatigue
strength of a material or to reduce the magnitude of a stress concentration below
the minimum value that will cause fatigue failure.
In general, avoid design details that cause severe stress concentrations or poor
stress distribution. Provide gradual changes in section. Eliminate sharp corners and
notches. Do not use details that create high localized constraint. Locate unavoidable
stress raisers at points where fatigue conditions are the least severe. Place connections
at points where stress is low and fatigue conditions are not severe. Provide
structures with multiple load paths or redundant members, so that a fatigue crack
in any one of the several primary members is not likely to cause collapse of the
entire structure.
Fatigue strength of a material may be improved by cold-working the material
in the region of stress concentration, by thermal processes, or by prestressing it in
such a way as to introduce favorable internal stresses. Where fatigue stresses are
unusually severe, special materials may have to be selected with high energy absorption
and notch toughness.
(J. H. Faupel, ‘‘Engineering Design,’’ John Wiley & Sons, Inc., New York;
C. H. Norris et al., ‘‘Structural Design for Dynamic Loads,’’ McGraw-Hill Book
5.142 SECTION FIVE
FIGURE 5.108 Mass on a weightless spring (b) or (d ) may represent
the motion of (a) a beam or (c) a rigid frame in free vibration.
Company, New York; W. H. Munse, ‘‘Fatigue of Welded Steel Structures,’’Welding
Research Council, 345 East 47th Street, New York, NY 10017.)
5.18.2 Natural Period of Vibration
A preliminary step in dynamic analysis and design is determination of this period.
It can be computed in many ways, including by application of the laws of conservation
of energy and momentum or Newton’s second law, F  M(dv/ dt), where F
is force, M mass, v velocity, and t time. But in general, an exact solution is possible
only for simple structures. Therefore, it is general practice to seek an approximate—
but not necessarily inexact—solution by analyzing an idealized representation of
the actual member or structure. Setting up this model and interpreting the solution
require judgment of a high order.
Natural period of vibration is the time required for a structure to go through one
cycle of free vibration, that is, vibration after the disturbance causing the motion
has ceased.
To compute the natural period, the actual structure may be conveniently represented
by a system of masses and massless springs, with additional resistances
provided to account for energy losses due to friction, hysteresis, and other forms
of damping. In simple cases, the masses may be set equal to the actual masses;
otherwise, equivalent masses may have to be computed (Art. 5.18.6). The spring
constants are the ratios of forces to deflections.
For example, a single mass on a spring (Fig. 5.108b) may represent a simply
supported beam with mass that may be considered negligible compared with the
load W at midspan (Fig. 5.108a). The spring constant k should be set equal to the
STRUCTURAL THEORY 5.143
load that produces a unit deflection at midspan; thus, k  48EI/L3, where E is the
modulus of elasticity, psi; I the moment of inertia, in4; and L the span, in, of the
beam. The idealized mass equals W/g, where W is the weight of the load, lb, and
g is the acceleration due to gravity, 386 in / s2.
Also, a single mass on a spring (Fig. 5.108d) may represent the rigid frame in
Fig. 5.108c. In that case, k  2 
 12EI/h3, where I is the moment of inertia, in4,
of each column and h the column height, in. The idealized mass equals the sum of
the masses on the girder and the girder mass. (Weight of columns and walls is
assumed negligible.)
The spring and mass in Fig. 5.108b and d form a one-degree system. The degree
of a system is determined by the least number of coordinates needed to define the
positions of its components. In Fig. 5.108, only the coordinate y is needed to locate
the mass and determine the state of the spring. In a two-degree system, such as
one comprising two masses connected to each other and to the ground by springs
and capable of movement in only one direction, two coordinates are required to
locate the masses.
If the mass with weight W, lb, in Fig. 5.108 is isolated, as shown in Fig. 5.108e
it will be in dynamic equilibrium under the action of the spring force  ky and the
inertia force (d2y/ dt 2)(W/g). Hence, the equation of motion is
2 W d y
 ky  0 (5.235) 2 g dt
where y  displacement of mass, in, measured from rest position. Equation (5.235)
may be written in the more convenient form
2 2 d y kg d y 2  y  y  0 (5.236) 2 2 dt W dt
The solution is
y  A sin t  B cos t (5.237)
where A and B are constants to be determined from initial conditions of the system,
and
kg
 (5.238) W
is the natural circular frequency, rad/ s.
The motion defined by Eq. (5.237) is harmonic. Its natural period, s, is
2
 W
T 2
 (5.239)   kg
Its natural frequency, Hz, is
5.144 SECTION FIVE
1 1 kg
?  (5.240)  T 2
 W
If, at time t  0, the mass has an initial displacement y0 and velocity v0, substitution
in Eq. (5.237) yields A  v0 / and B  y0. Hence, at any time t, the mass
is completely located by
v0 y  sin t  y cos t (5.241) 0 
The stress in the spring can be computed from the displacement y.
Vibrations of Lumped Masses. In multiple-degree systems, an independent differential
equation of motion can be written for each degree of freedom. Thus, in
an N-degree system with N masses, weighing W1, W2, . . . , WN lb, and N2 springs
with constants krj (r  1, 2, . . . , N; j  1, 2, . . . , N), there are N equations of
the form
N 2 W d y r r k y  0 r  1, 2, . . . , N (5.242) 	 rj j 2 g dt j1
Simultaneous solution of these equations reveals that the motion of each mass can
be resolved into N harmonic components. They are called the fundamental, second
third, etc., harmonics. Each set of harmonics for all the masses is called a normal
mode of vibration.
There are as many normal modes in a system as degrees of freedom. Under
certain circumstances, the system could vibrate freely in any one of these modes.
During any such vibration, the ratio of displacement of any two of the masses
remains constant. Hence, the solution of Eqs. (5.242) take the form
N
y  a sin  (t   ) (5.243) 	 r rn n n
n1
where arn and n are constants to be determined from the initial conditions of the
system and n is the natural circular frequency for each normal mode.
To determine n, set y1  A1 sin t; y2  A2 sin t . . . . Then, substitute these
values of yr and their second derivatives in Eqs. (5.242). After dividing each equation
by sin t, the following N equations result:
W1 2 k   A  k A     k A  0 
  11 1 12 2 1N N g
W2 k A  k  A     k A  0 
  21 1 22 2 2N N g
 . . . . . . . . . . . . . . .
kN1A1  kN2A2      AN  0
WN 2 k   
  NN g
(5.244)
If there are to be nontrivial solutions for the amplitudes A1, A2, . . . , AN, the
determinant of their coefficients must be zero. Thus,
STRUCTURAL THEORY 5.145
 W1 2 k   11 g
k21
k12
k22 
W2 2 
g
  
  
k1N
k2N 	  0 (5.245) . .
kN1 kN2   
kNN  2
N
W
g
Solution of this equation for yields one real root for each normal mode. And the
natural period for each normal mode can be obtained from Eq. (5.239).
If  for a normal mode now is substituted in Eqs. (5.244), the amplitudes A1,
A2, . . . , AN for that mode can be computed in terms of an arbitrary value, usually
unity, assigned to one of them. The resulting set of modal amplitudes defines the
characteristic shape for that mode.
The normal modes are mutually orthogonal; that is,
N
W A A  0 (5.246) 	 r rn rm
r1
where Wr is the rth mass out of a total of N, A represents the characteristic amplitude
of a normal mode, and n and m identify any two normal modes. Also, for a
total of S springs
S
k y y  0 (5.247) 	 s sn sm
s1
where ks is the constant for the sth spring and y represents the spring distortion.
When there are many degrees of freedom, this procedure for analyzing free
vibration becomes very lengthy. In such cases, it may be preferable to solve Eqs.
(5.244) by numerical, trial-and-error procedures, such as the Stodola-Vianello
method. In that method, the solution converges first on the highest or lowest mode.
Then, the other modes are determined by the same procedure after elimination of
one of the equations by use of Eq. (5.246). The procedure requires assumption of
a characteristic shape, a set of amplitudes Ar1. These are substituted in one of Eqs.
(5.244) to obtain a first approximation of 2. With this value and with AN1  1,
the remaining N  1 equations are solved to obtain a new set of Ar1. Then, the
procedure is repeated until assumed and final characteristic amplitudes agree.
Because even this procedure is very lengthy for many degrees of freedom, the
Rayleigh approximate method may be used to compute the fundamental mode. The
frequency obtained by this method, however, may be a little on the high side.
The Rayleigh method also starts with an assumed set of characteristic amplitudes
Ar1 and depends for its success on the small error in natural frequency produced
by a relatively large error in the shape assumption. Next, relative inertia forces
acting at each mass are computed: Fr  WrAr1 /AN1, where AN1 is the assumed
displacement at one of the masses. These forces are applied to the system as a
5.146 SECTION FIVE
static load and displacements Br1 due to them calculated. Then, the natural frequency
can be obtained from
N
g FB 	 r r1
r1 2   (5.248) N
2 W B 	 r r1
r1
where g is the acceleration due to gravity, 386 in / s2. For greater accuracy, the
computation can be repeated with Br1 as the assumed characteristic amplitudes.
When the Rayleigh method is applied to beams, the characteristic shape assumed
initially may be chosen conveniently as the deflection curve for static loading.
The Rayleigh method may be extended to determination of higher modes by the
Schmidt orthogonalization procedure, which adjusts assumed deflection curves to
satisfy Eq. (5.246). The procedure is to assume a shape, remove components associated
with lower modes, then use the Rayleigh method for the residual deflection
curve. The computation will converge on the next higher mode. The method is
shorter than the Stodola-Vianello procedure when only a few modes are needed.
For example, suppose the characteristic amplitudes Ar1 for the fundamental mode
have been obtained and the natural frequency for the second mode is to be computed.
Assume a value for the relative deflection of the rth mass Ar2. Then, the
shape with the fundamental mode removed will be defined by the displacements
a  A  c A (5.249) r2 r2 1 r1
where c1 is the participation factor for the first mode.
N
W A A 	 r r2 r1
r1 c  (5.250) 1 N
2 W A 	 r r1
r1
Substitute ar2 for Br1 in Eq. (5.248) to find the second-mode frequency and, from
deflections produced by Fr  Wrar2, an improved shape. (For more rapid covergence,
Ar2 should be selected to make c1 small.) The procedure should be repeated,
starting with the new shape.
For the third mode, assume deflections Ar3 and remove the first two modes:
A  A  c A  c A (5.251) r3 r3 1 r1 2 r2
The participation factors are determined from
N N
W A A W A A 	 	 r r3 r1 r r3 r2
r1 r1 c  c  (5.252) 1 2 N N
2 2 W A W A 	 	 r r1 r r2
r1 r1
Use ar3 to find an improved shape and the third-mode frequency.
Vibrations of Distributed Masses. For some structures with mass distributed
throughout, it sometimes is easier to solve the dynamic equations based on distributed
mass than the equations based on equivalent lumped masses. A distributed
STRUCTURAL THEORY 5.147
mass has an infinite number of degrees of freedom and normal modes. Every particle
in it can be considered a lumped mass on springs connected to other particles.
Usually, however, only the fundamental mode is significant, though sometimes the
second and third modes must be taken into account.
For example, suppose a beam weighs w lb / lin ft and has a modulus of elasticity
E, psi, and moment of inertia I, in4. Let y be the deflection at a distance x from
one end. Then, the equation of motion is
4 2 y w y
EI  0 (5.253) 4 2 x gt
(This equation ignores the effects of shear and rotational inertia.) The deflection yn
for each mode, to satisfy the equation, must be the product of a harmonic function
of time ?n(t) and of the characteristic shape Yn(x), a function of x with undetermined
amplitude. The solution is
? (t)  c sin  t  c cos  t (5.254) n 1 n 2 n
where n is the natural circular frequency and n indicates the mode, and
Y (x)  A sin  x  B cos  x  C sinh  x  D cosh  x (5.255) n n n n n n n n n
where
2 wn 4   (5.256) n EIg
For a simple beam, the boundary (support) conditions for all values of time t
are y  0 and bending moment M  EI 2y/x2  0. Hence, at x  0 and x  L,
the span length, Yn(x)  0 and d2Yn /dx2  0. These conditions require that
n

B  C  D  0   n n n n L
to satisfy Eq. (5.255). Hence, according to Eq. (5.256), the natural circular frequency
for a simply supported beam is
2 2 n 
 EIg
  (5.257) n 2  L w
The characteristic shape is defined by
n
x
Y (x)  sin (5.258) n L
The constants c1 and c2 in Eq. (5.254) are determined by the initial conditions of
the disturbance. Thus, the total deflection, by superposition of modes, is
 n
x
y  A (t) sin (5.259) 	 n L n1
where An(t) is determined by the load (see Art. 5.18.4).
Equations (5.254) to (5.256) apply to spans with any type of end restraints.
Figure 5.109 shows the characteristic shape and gives constants for determination
5.148 SECTION FIVE
FIGURE 5.109 Coefficients for computing natural circular frequencies  and natural periods of
vibration T, s, of prismatic beams. w  weight of beam, lb / lin ft; L  span, ft; E  modulus of
elasticity of the beam material, psi; I  moment of inertia of the beam cross section, in4.
of natural circular frequency  and natural period T for the first four modes of
cantilever simply supported, fixed-end, and fixed-hinged beams. To obtain , select
the appropriate constant from Fig. 5.109 and multiply it by . where L  4 EI/wL
span of beam, ft. To get T, divide the appropriate constant by . 4 EI/wL
To determine the characteristic shapes and natural periods for beams with variable
cross section and mass, use the Rayleigh method. Convert the beam into a
lumped-mass system by dividing the span into elements and assuming the mass of
each element to be concentrated at its center. Also, compute all quantities, such as
deflection and bending moment, at the center of each element. Start with an assumed
characteristic shape and apply Eq. (5.255).
Methods are available for dynamic analysis of continuous beams. (R. Clough
and J. Penzien, ‘‘Dynamics of Structures,’’ McGraw-Hill Book Company, New
York; D. G. Fertis and E. C. Zobel, ‘‘Transverse Vibration Theory,’’ The Ronald
Press Company, New York.) But even for beams with constant cross section, these
procedures are very lengthy. Generally, approximate solutions are preferable.
(J. M. Biggs, ‘‘Introduction to Structural Dynamics,’’ McGraw-Hill Book Company,
New York; N. M. Newmark and E. Rosenblueth, ‘‘Fundamentals of Earthquake
Engineering,’’ Prentice-Hall, Englewood Cliffs, N.J.)
5.18.3 Impact and Sudden Loads
Under impact, there is an abrupt exchange or absorption of energy and drastic
change in velocity. Stresses caused in the colliding members may be several times
larger than stresses produced by the same weights applied statically.
STRUCTURAL THEORY 5.149
An approximation of impact stresses in the elastic range can be made by neglecting
the inertia of the body struck and the effect of wave propagation and
assuming that the kinetic energy is converted completely into strain energy in that
body. Consider a prismatic bar subjected to an axial impact load in tension. The
energy absorbed per unit of volume when the bar is stressed to the proportional
limit is called the modulus of resilience. It is given by ? /2E, where ?y is the yield 2y
stress and E the modulus of elasticity, both in psi.
Below the proportional limit, the unit stress, psi, due to an axial load U, in-lb,
is
2UE
?  (5.260)  AL
where A is the cross-sectional area, in2, and L the length of bar, in. This equation
indicates that, for a given unit stress, energy absorption of a member may be improved
by increasing its length or area. Sharp changes in cross section should be
avoided, however, because of associated high stress concentrations. Also, uneven
distribution of stress in a member due to changes in section should be avoided. For
example, if part of a member is given twice the diameter of another part, the stress
under axial load in the larger portion is one-fourth that in the smaller. Since the
energy absorbed is proportional to the square of the stress, the energy taken per
unit of volume by the larger portion is therefore only one-sixteenth that absorbed
by the smaller. So despite the increase in volume caused by doubling of the diameter,
the larger portion absorbs much less energy than the smaller. Thus, energy
absorption would be larger with a uniform stress distribution throughout the length
of the member.
Impact on Short Members. If a static axial load W would produce a tensile stress
? in the bar and an elongation e, in, then the axial stress produced in a short
member when W falls a distance h, in, is
2h
?  ?  ? 1  (5.261)  e
if ? is within the proportional limit. The elongation due to this impact load is
2h
e  e  e 1  (5.262)  e
These equations indicate that the stress and deformation due to an energy load may
be considerably larger than those produced by the same weight applied gradually.
The same equations hold for a beam with constant cross section struck by a
weight at midspan, except that ? and ? represent stresses at midspan and e and e,
midspan deflections.
According to Eqs. (5.261) and (5.262), a sudden load (h  0) causes twice the
stress and twice the deflection as the same load applied gradually.
Impact on Long Members. For very long members, the effect of wave propagation
should be taken into account. Impact is not transmitted instantly to all parts of
the struck body. At first, remote parts remain undisturbed, while particles struck
accelerate rapidly to the velocity of the colliding body. The deformations produced
5.150 SECTION FIVE
move through the struck body in the form of elastic waves. The waves travel with
a constant velocity, ft / s,
E
c  68.1 (5.263) 
where E  modulus of elasticity, psi
p  density of the struck body, lb/ ft3
If an impact imparts a velocity v, ft / s, to the particles at one end of a prismatic
bar, the stress, psi, at that end is
v
?  E  0.0147v Ep  0.000216pcv (5.264)
c
if ? is in the elastic range. In a compression wave, the velocity of the particles is
in the direction of the wave. In a tension wave, the velocity of the particles is in
the direction opposite the wave.
In the plastic range, Eqs. (6.263) and (5.264) hold, but with E as the tangent
modulus of elasticity. Hence, c is not a constant and the shape of the stress wave
changes as it moves. The elastic portion of the stress wave moves faster than the
wave in the plastic range. Where they overlap, the stress and irrecoverable strain
are constant.
(The impact theory is based on an assumption difficult to realize in practice—
that contact takes place simultaneously over the entire end of the bar.)
At the free end of a bar, a compressive stress wave is reflected as an equal
tension wave, and a tension wave as an equal compression wave. The velocity of
the particles there equals 2v.
At a fixed end of a bar, a stress wave is reflected unchanged. The velocity of
the particles there is zero, but the stress is doubled, because of the superposition
of the two equal stresses on reflection.
For a bar with a fixed end struck at the other end by a moving mass weighing
Wm lb, the initial compressive stress, psi, is
?  0.0147v Ep (5.265) o o
where vo is the initial velocity of the particles, ft / s, at the impacted end of the bar
and E and p, the modulus of elasticity, psi, and density, lb/ ft3, of the bar. As the
velocity of Wm decreases, so does the pressure on the bar. Hence, decreasing compressive
stresses follow the wave front. At any time t 	 2L/c, where L is the length
of the bar, in, the stress at the struck end is
2 t /  ?  ? e (5.266) o
where e  2.71828,  is the ratio of Wb, the weight of the bar, to Wm, and  
2L/c.
When t  , the wave front with stress ?o arrives back at the struck end, assumed
still to be in contact with the mass. Since the velocity of the mass cannot change
suddenly, the wave will be reflected as from a fixed end. During the second interval,
	 t 	 2 , the compressive stress is the sum of two waves moving away from the
struck end and one moving toward this end.
Maximum stress from impact occurs at the fixed end. For  greater than 0.2,
this stress is
STRUCTURAL THEORY 5.151
2  ?  2? (1  e ) (5.267) o
For smaller values of , it is given approximately by
1
? ? 1 (5.268) 
  o 
Duration of impact, time it takes for the impact stress at the struck end to drop
to zero, is approximately

L
T  (5.269)
c
for small values of .
When Wm is the weight of a falling body, velocity at impact is , when it 2gh
falls a distance h, in. Substitution in Eq. (5.265) yields ?o  , since 2EhW /AL b
Wb  pAL is the weight of the bar. Putting Wb  Wm; Wm/A  ?, the stress
produced by Wm when applied gradually, and E  ?L/e, where e is the elongation
for the static load, gives ?o  ? . Then, for values of  smaller than 0.2, 2h /e
the maximum stress, from Eq. (5.268), is
2h  2h
?  ?  (5.270) 
    e e
For larger values of , the stress wave due to gravity acting on Wm during impact
should be added to Eq. (5.267). Thus, for  larger than 0.2,
2h  2  2  ?  2?(1  e )  2? (1  e ) (5.271)  e
Equations (5.270) and (5.271) correspond to Eq. (5.261), which was developed
without wave effects being taken into account. For a sudden load, h  0, Eq. (5.271)
gives for the maximum stress 2?(1  e ), not quite double the static stress, the 2 
result indicated by Eq. (5.261). (See also Art. 5.18.4.)
(S. Timoshenko and J. N. Goodier, ‘‘Theory of Elasticity,’’ McGraw-Hill Book
Company, New York; S. Timoshenko and D. H. Young, ‘‘Engineering Mechanics,’’
John Wiley & Sons, Inc., New York.)
5.18.4 Dynamic Analysis of Simple Structures
Articles 5.181 to 5.18.3 present a theoretic basis for analysis of structures under
dynamic loads. As noted in Art. 5.18.2, an approximate solution based on an idealized
representation of an actual member of structure is advisable for dynamic
analysis and design. Generally, the actual structure may be conveniently represented
by a system of masses and massless springs, with additional resistances to account
for damping. In simple cases, the masses may be set equal to the actual masses;
otherwise, equivalent masses may be substituted for the actual masses (Art. 5.18.6).
The spring constants are the ratios of forces to deflections (see Art. 5.18.2).
Usually, for structural purposes the data sought are the maximum stresses in the
springs and their maximum displacements and the time of occurrence of the max5.152
SECTION FIVE
FIGURE 5.110 One-degree system acted
on by a force varying with time.
imums. This time is generally computed in terms of the natural period of vibration
of the member or structure, or in terms of the duration of the load. Maximum
displacement may be calculated in terms of the deflection that would result if the
load were applied gradually.
The term D by which the static deflection e, spring forces, and stresses are
multiplied to obtain the dynamic effects is called the dynamic load factor. Thus,
the dynamic displacement is
y  De (5.272)
And the maximum displacement ym is determined by the maximum dynamic load
factor Dm, which occurs at time tm.
One-Degree Systems. Consider the one-degree-of-freedom system in Fig. 5.110a.
It may represent a weightless beam with a mass weighing W lb applied at midspan
and subjected to a varying force Fo?(t), or a rigid frame with a mass weighing W
lb at girder level and subjected to this force. The force is represented by an arbitrarily
chosen constant force Fo times F(t), a function of time.
If the system is not damped, the equation of motion in the elastic range is
2 W d y
 ky  F ?(t) (5.273) o 2 g dt
where k is the spring constant and g the acceleration due to gravity, 386 in / s2. The
solution consists of two parts. The first, called the complementary solution, is obtained
by setting ?(t)  0. This solution is given by Eq. (5.237). To it must be
added the second part, the particular solution, which satisfies Eq. (5.273).
The general solution of Eq. (5.273), arrived at by treating an element of the
force-time curve (Fig. 5.111b) as an impulse, is
t vo y  y cos t  sin t  e  ?( ) sin (t  ) d  (5.274) o
0 
where y  displacement of mass from equilibrium position, in
yo  initial displacement of mass (t  0), in
 natural circular frequency of free vibration kg/W
STRUCTURAL THEORY 5.153
FIGURE 5.111 Harmonic motion. (a) Constant force applied to an undamped onedegree
system, such as the one in Fig. 5.110a. (b) Displacements vary with time like
a cosine curve.
k  spring constant  force producing unit deflection, lb / in
vo  initial velocity of mass, in / s
e  Fo /k  displacement under static load, in
A closed solution is possible if the integral can be evaluated.
Assume, for example, the mass is subjected to a suddenly applied force Fo that
remains constant (Fig. 5.111a). If yo and vo are initially zero, the displacement y
of the mass at any time t can be obtained from the integral in Eq. (5.274) by setting
?( )  1:
t
y  e  sin (t  ) d  e(1  cos t) (5.275)
0
This equation indicates that the dynamic load factor D  1  cos t. It has a
maximum value Dm  2 when t  
/ . Figure 5.111b shows the variation of
displacement with time.
Multidegree Systems. A multidegree lumped-mass system may be analyzed by
the modal method after the natural frequencies of the normal modes have been
determined (Art. 5.18.2). This method is restricted to linearly elastic systems in
which the forces applied to the masses have the same variation with time. For other
cases, numerical analysis must be used.
In the modal method, each normal mode is treated as an independent one-degree
system. For each degree of the system, there is one normal mode. A natural frequency
and a characteristic shape are associated with each mode. In each mode,
the ratio of the displacements of any two masses is constant with time. These ratios
define the characteristic shape. The modal equation of motion for each mode is
j
g?(t) F 	 	 r rn 2 d A r1 n 2   A  (5.276) n n j 2 dt 2 W 	 	 r rn
r1
5.154 SECTION FIVE
where An  displacement in the nth mode of an arbitrarily selected mass
n  natural frequency of the nth mode
Fr?(t)  varying force applied to the rth mass
Wr  weight of the rth mass
j  number of masses in the system
	rn  ratio of the displacement in the nth mode of the rth mass to An
g  acceleration due to gravity
We define the modal static deflection as
j
g F	 	 r rn
r1 A  (5.277) n j
2 2  W 	 	 n r rn
r1
Then, the response for each mode is given by
A  D A (5.278) n n n
where Dn  dynamic load factor.
Since Dn depends only on n and the variation of force with time ?(t), solutions
for Dn obtained for one-degree systems also apply to multidegree systems. The total
deflection at any point is the sum of the displacements for each mode, An	rn, at
that point.
Beams. The response of beams to dynamic forces can be determined in a similar
way. The modal static deflection is defined by
L  p(x)	 (x) dx n
0 A  (5.279) n L w 2 2   	 (x) dx n n
0 g
where p(x)  load distribution on the span [p(x)?(x) is the varying force]
	n(x)  characteristic shape of the nth mode (see Art. 5.18.2)
L  span length
w  uniformly distributed weight on the span
The response of the beam then is given by Eq. (5.278), and the dynamic deflection
is the sum of the modal components, An	n(x).
Nonlinear Responses. When the structure does not react linearly to loads, the
equations of motion can be solved by numerical analysis if resistance is a unique
function of displacement. Sometimes, the behavior of the structure can be represented
by an idealized resistance-displacement diagram that makes possible a solution
in closed form. Figure 5.112a shows such a diagram.
Elastic-Plastic Responses. Resistance is assumed linear (R  ky) in Fig. 5.112a
until a maximum Rm is reached. After that, R remains equal to Rm for increases in
y substantially larger than the displacement ye at the elastic limit. Thus, some portions
of the structure deform into the plastic range. Figure 5.112a, therefore, may
be used for ductile structures only rarely subjected to severe dynamic loads. When
STRUCTURAL THEORY 5.155
FIGURE 5.112 Response in the plastic range of a one-degree system with resistance
characteristics indicated in (a) and subjected to a constant force (b) is shown in (c).
this diagram can be used for designing such structures, more economical designs
can be produced than for structures limited to the elastic range, because of the high
energy-absorption capacity of structures in the plastic range.
For a one-degree system, Eq. (5.273) can be used as the equation of motion for
the initial sloping part of the diagram (elastic range). For the second stage, ye 	
y 	 ym, where ym is the maximum displacement, the equation is
2 W d y
 R  F ?(t) (5.280) m o 2 g dt
For the unloading stage, y 	 ym, the equation is
5.156 SECTION FIVE
2 W d y
 R  k(y  y)  F ?(t) (5.281) m m o 2 g dt
Suppose, for example, the one-degree undamped system in Fig. 5.109a behaves
in accordance with the bilinear resistance function of Fig. 5.112a and is subjected
to a suddenly applied constant load (Fig. 5.112b). With zero initial displacement
and velocity, the response in the first stage (y 	 ye), according to Eq. (5.281), is
y  e(1  cos t ) (5.282) 1
dy
 e sin t (5.283) 1 dt
Equation (5.275) also indicates that displacement ye will be reached at a time te
such that cos te  1  ye /e.
For convenience, let t2  t  te be the time in the second stage; thus, t2  0 at
the start of that stage. Since the condition of the system at that time is the same as
at the end of the first stage, the initial displacement is ye and the initial velocity
e sin te.
The equation of motion of the second stage is
2 W d y
 R  F (5.284) m o 2 g dt
The solution, taking into account initial conditions for ye 	 y 	 ym is
g 2 y  (F  R )t  et sin t  y (5.285) o m 2 2 e e 2W
Maximum displacement occurs at the time
We
t  sin t (5.286) m e g(R  R ) m o
and can be obtained by substituting tm in Eq. (5.285).
The third stage, unloading after ym has been reached, can be determined from
Eq. (5.281) and conditions at the end of the second stage. The response, however,
is more easily found by noting that the third stage consists of an elastic, harmonic
residual vibration. In this stage the amplitude of vibration is (Rm  Fo) /k, since
this is the distance between the neutral position and maximum displacement, and
in the neutral position the spring force equals Fo. Hence, the response can be
obtained directly from Eq. (5.275) by substituting ym  (Rm  Fo) /k for e, because
the neutral position, located at y  ym  (Rm  Fo) /k, occurs when t3  
/2,
where t3  t  te  tm. The solution is
R F R  F m o m o y  y   cos t (5.287) m 3 k k
Response in the three stages is shown in Fig. 5.112c. In that diagram, however,
to represent a typical case, the coordinates have been made nondimensional by
expressing y in terms of ye and the time in terms of T, the natural period of vibration.
(J. M. Biggs, ‘‘Introduction to Structural Dynamics,’’ and R. Clough and J. Penzien,
‘‘Dynamics of Structures,’’ McGraw-Hill Book Company, New York; D. G.
Fertis and E. C. Zobel, ‘‘Transverse Vibration Theory,’’ The Ronald Press Company,
STRUCTURAL THEORY 5.157
New York; N. M. Newmark and E. Rosenblueth, ‘‘Fundamentals of Earthquake
Engineering,’’ Prentice-Hall, Englewood Cliffs, N.J.)
5.18.5 Resonance and Damping
Damping in structures, resulting from friction and other causes, resists motion imposed
by dynamic loads. Generally, the effect is to decrease the amplitude and
lengthen the period of vibrations. If damping is large enough, vibration may be
eliminated.
When maximum stress and displacement are the prime concern, damping may
not be of great significance for short-time loads. These maximums usually occur
under such loads at the first peak of response, and damping, unless unusually large,
has little effect in a short period of time. But under conditions close to resonance,
damping has considerable effect.
Resonance is the condition of a vibrating system under a varying load such that
the amplitude of successive vibrations increases. Unless limited by damping or
changes in the condition of the system, amplitudes may become very large.
Two forms of damping generally are assumed in structural analysis, viscous or
constant (Coulomb). For viscous damping, the damping force is taken proportional
to the velocity but opposite in direction. For Coulomb damping, the damping force
is assumed constant and opposed in direction to the velocity.
Viscous Damping. For a one-degree system (Arts. 5.18.2 to 5.18.4), the equation
of motion for a mass weighing W lb and subjected to a force F varying with time
but opposed by viscous damping is
2 W d y dy
 ky  F  c (5.288) 2 g dt dt
where y  displacement of the mass from equilibrium position, in
k  spring constant, lb / in
t  time, s
c  coefficient of viscous damping
g  acceleration due to gravity  386 in / s2
Let us set  cg/2W and consider those cases in which  , the natural circular
frequency [Eq. (5.238)], to eliminate unusually high damping (overdamping). Then,
for initial displacement yo and velocity vo, the solution of Eq. (5.288) with F  0
is
v  y o o t y  e sin  t  y cos  t (5.289) 
  d o d d
where d  and e  2.71828. Equation (5.289) represents a decaying 2 2   
harmonic motion with  controlling the rate of decay and d the natural frequency
of the damped system.
When  
t y  e [v t  (1  t)y ] (5.290) o o
which indicates that the motion is not vibratory. Damping producing this condition
is called critical, and, from the definition of , the critical coefficient is
5.158 SECTION FIVE
2W 2W kW
c  2 (5.291) d  g g g
Damping sometimes is expressed as a percent of critical (  as a percent of ).
For small amounts of viscous damping, the damped natural frequency is approximately
equal to the undamped natural frequency minus 1?2 2 / . For example,
for 10% critical damping (  0.1), d  [1  1?2(0.1)2]  0.995. Hence, the
decrease in natural frequency due to small amounts of damping generally can be
ignored.
Damping sometimes is measured by logarithmic decrement, the logarithm of
the ratio of two consecutive peak amplitudes during free vibration.
2

Logarithmic decrement  (5.292)

For example, for 10% critical damping, the logarithmic decrement equals 0.2
.
Hence, the ratio of a peak to the following peak amplitude is e  1.87. 0.2

The complete solution of Eq. (5.288) with initial displacement yo and velocity
vo is
v  y o o t y  e sin  t  y cos  t 
  d o d d
t 2  (t)  e  ?( )e sin  (t  ) d  (5.293) d
0 d
where e is the deflection that the applied force would produce under static loading.
Equation (5.293) is identical to Eq. (5.274) when  0.
Unbalanced rotating parts of machines produce pulsating forces that may be
represented by functions of the form Fo sin t. If such a force is applied to an
undamped one-degree system. Eq. (5.274) indicates that if the system starts at rest
the response will be
2 F g 1/  o y  sin t  sin t (5.294) 
 
  2 2 W 1   / 
And since the static deflection would be Fo /k  Fog/W2, the dynamic load factor
is
1 
D  sin t  sin t (5.295) 
  2 2 1   / 
If is small relative to , maximum D is nearly unity; thus, the system is practically
statically loaded. If  is very large compared with , D is very small; thus, the
mass cannot follow the rapid fluctuations in load and remains practically stationary.
Therefore, when  differs appreciably from , the effects of unbalanced rotating
parts are not too serious. But if   , resonance occurs; D increases with time.
Hence, to prevent structural damage, measures must be taken to correct the unbalanced
parts to change , or to change the natural frequency of the vibrating mass,
or damping must be provided.
The response as given by Eq. (5.294) consists of two parts, the free vibration
and the forced part. When damping is present, the free vibration is of the form of
STRUCTURAL THEORY 5.159
Eq. (5.289) and is rapidly damped out. Hence, the free part is called the transient
response, and the forced part, the steady-state response. The maximum value of
the dynamic load factor for the steady-state response Dm is called the dynamic
magnification factor. It is given by
1
D  (5.296) m 2 22 22 (1   /  )  (2 /  )
With damping, then, the peak values of Dm occur when    and 2 2 1   / 
are approximately equal to /2 . For example, for 10% critical damping.

D 5 m 0.2
So even small amounts of damping significantly limit the response at resonance.
Coulomb Damping. For a one-degree system with Coulomb damping, the equation
of motion for free vibration is
2 W d y
 ky  
F (5.297) ? 2 g dt
where F is the constant friction force and the positive sign applies when the ve- ?
locity is negative. If initial displacement is yo and initial velocity is zero, the response
in the first half cycle, with negative velocity, is
F F ? ? y  y  cos t  (5.298) 
  o k k
equivalent to a system with a suddenly applied constant force. For the second half
cycle, with positive velocity, the response is
F F 
 ? ? y y  3 cos  t  (5.299) 
  
  o k  k
If the solution is continued with the sign of F changing in each half cycle, the ?
results will indicate that the amplitude of positive peaks is given by yo  4nF /k, ?
where n is the number of complete cycles, and the response will be completely
damped out when t  kyoT/4F , where T is the natural period of vibration, or ?
2
/ .
Analysis of the steady-state response with Coulomb damping is complicated by
the possibility of frequent cessation of motion.
(S. Timoshenko, D. H. Young, and W. Weaver, ‘‘Vibration Problems in Engineering,’’
4th ed., John Wiley & Sons, Inc., New York; D. D. Barkan, ‘‘Dynamics
of Bases and Foundations,’’ McGraw-Hill Book Company; W. C. Hurty and M. F.
Rubinstein, ‘‘Dynamics of Structures,’’ Prentice-Hall, Englewood Cliffs, N.J.)
5.18.6 Approximate Design for Dynamic Loading
Complex analysis and design methods seldom are justified for structures subject to
dynamic loading because of lack of sufficient information on loading, damping,
5.160 SECTION FIVE
resistance to deformation, and other factors. In general, it is advisable to represent
the actual structure and loading by idealized systems that permit a solution in closed
form (see Arts. 5.18.1 to 5.18.5).
Whenever possible, represent the actual structure by a one-degree system consisting
of an equivalent mass with massless spring. For structures with distributed
mass. simplify the analysis in the elastic range by computing the response only for
one or a few of the normal modes. In the plastic range, treat each stage—elastic,
and plastic—as completely independent; for example, a fixed-end beam may be
treated, when in the elastic-plastic stage, as a simply supported beam.
Choose the parameters of the equivalent system to make the deflection at a
critical point, such as the location of the concentrated mass, the same as it would
be in the actual structure. Stresses in the actual structure should be computed from
the deflections in the equivalent system.
Compute an assumed shape factor 	for the system from the shape taken by the
actual structure under static application of the loads. For example, for a simple
beam in the elastic range with concentrated load at midspan, 	may be chosen, for
x 	 L/2, as (Cx/L3)(3L2  4x2), the shape under static loading, and C may be set
equal to 1 to make 	 equal to 1 when x  L/2. For plastic conditions (hinge at
midspan), 	 may be taken as Cx/L, and C set equal to 2, to make 	  1 when
x  L/2.
For a structure with concentrated forces, let Wr be the weight of the rth mass,
	r the value of 	 for a specific mode at the location of that mass, and Fr the
dynamic force acting on Wr. Then, the equivalent weight of the idealized system
is
j
2 W  W 	 (5.300) 	 e r r
r1
where j is the number of masses. The equivalent force is
j
F  F 	 (5.301) 	 e r r
r1
For a structure with continuous mass, the equivalent weight is
2 W   w	 dx (5.302) e
where w is the weight in lb / lin ft. The equivalent force is
F  q	 dx (5.303) e
for a distributed load q, lb/ lin ft.
The resistance of a member or structure is the internal force tending to restore
it to its unloaded static position. For most structures, a bilinear resistance function,
with slope k up to the elastic limit and zero slope in the plastic range (Fig. 5.112a),
may be assumed. For a given distribution of dynamic load, maximum resistance of
the idealized system may be taken as the total load with that distribution that the
structure can support statically. Similarly, stiffness is numerically equal to the total
load with the given distribution that would cause a unit deflection at the point where
the deflections in the actual structure and idealized system are equal. Hence, the
STRUCTURAL THEORY 5.161
equivalent resistance and stiffness are in the same ratio to the actual as the equivalent
forces to the actual forces.
Let k be the actual spring constant, g acceleration due to gravity, 386 in / s2, and
We W  F (5.304)
Fe
where F represents the actual total load. Then, the equation of motion of an
equivalent one-degree system is
2 d y F 2   y  g (5.305) 2 dt W
and the natural circular frequency is
kg
 (5.306) W
The natural period of vibration equals 2
/ . Equations (5.305) and (5.306) have
the same form as Eqs. (5.236), (5.238), and (5.273). Consequently, the response
can be computed as indicated in Arts. 5.18.2 to 5.18.4.
Whenever possible, select a load-time function for F to permit use of a known
solution.
For preliminary design of a one-degree system loaded into the plastic range by
a suddenly applied force that remains substantially constant up to the time of maximum
response, the following approximation may be used for that response:
ye y  (5.307) m 2(1  F /R ) o m
where ye is the displacement at the elastic limit, Fo the average value of the force,
and Rm the maximum resistance of the system. This equation indicates that for
purely elastic response, Rm must be twice Fo; whereas, if ym is permitted to be large,
Rm may be made nearly equal to Fo, with greater economy of material.
For preliminary design of a one-degree system subjected to a sudden load with
duration td less than 20% of the natural period of the system, the following approximation
can be used for the maximum response:
2 1 Fo y  y t  1 (5.308) 
  
 m e d 2 Rm
where Fo is the maximum value of the load and  the natural frequency. This
equation also indicates that the larger ym is permitted to be, the smaller Rm need
be.
For a beam, the spring force of the equivalent system is not the actual force, or
reaction, at the supports. The real reactions should be determined from the dynamic
equilibrium of the complete beam. This calculation should include the inertia force,
with distribution identical with the assumed deflected shape of the beam. For example,
for a simply supported beam with uniform load, the dynamic reaction in
the elastic range is 0.39R  0.11F, where R is the resistance, which varies with
time, and F  qL is the load. For a concentrated load F at midspan, the dynamic
reaction is 0.78R  0.28F. And for concentrated loads F/2 at each third point, it
5.162 SECTION FIVE
is 0.62R  0.12F. (Note that the sum of the coefficients equals 0.50, since the
dynamic-reaction equations must hold for static loading, when R  F.) These expressions
also can be used for fixed-end beams without significant error. If high
accuracy is not required, they also can be used for the plastic range.
5.19 EARTHQUAKE LOADS
The seismic loads on the structure during an earthquake result from inertia forces
which were created by ground accelerations. The magnitude of these loads is a
function of the following factors: mass of the building, the dynamic properties of
the building, the intensity, duration, and frequency content of the ground motion,
and soil-structure interaction. In recent years, a lot of achievements have been made
to incorporate these influential factors into building codes accurately as well as
practically. The basis for IBC 2000 seismic provisions is the 1997 NEHRP ‘‘Recommended
Provisions for the Development of Seismic Regulations for New Buildings
and Other Structures’’ (FEMA 302). The National Earthquake Hazard Reduction
Program (NEHRP) is managed by the Federal Emergency Management Agency
(FEMA).
In IBC 2000, the seismic loads are on a strength level limit state rather than on
a service load level, which was used in UBC 94 and prior versions. The seismic
limit state is based upon system performance, not member performance, and considerable
energy dissipation through repeated cycles of inelastic straining is assumed.
5.19.1 Criteria Selection
In IBC 2000, the following basic information is required to determine the seismic
loads:
1. Seismic Use Group According to the nature of Building Occupancy, each structure
is assigned a Seismic Use Group (I, II, or III) and a corresponding Occupancy
Importance (I) factor (I  1.0, 1.25, or 1.5).
Seismic Use Group I structures are those not assigned to either Seismic Use
Group II or III. Seismic Use Group II are structures whose failure would result
in a substantial public hazard due to occupancy or use. Seismic Use Group III
is assigned to structures for which failure would result in loss of essential facilities
required for post-earthquake recovery and those containing substantial
quantities of hazardous substances.
2. Site Class Based on the soil properties, the site of building is classified as A,
B, C, D, E, or F to reflect the soil-structure interaction. Refer to IBC 2000 for
Site Class definition.
3. Spectral Response Accelerations SS and S1 The spectral response seismic design
maps reflect seismic hazards on the basis of contours. They provide the
maximum considered earthquake spectral response acceleration at short period
SS and at 1-second period S1. They are for Site Class B, with 5% of critical
damping. Refer to the maps in IBC 2000.
4. Basic Seismic-Force-Resisting System Different types of structural system have
different energy-absorbing characteristics. The response modification coefficient
STRUCTURAL THEORY 5.163
R in Table 5.9 is used to account for these characteristics. Systems with higher
ductility have higher R values.
With the above basic parameters available, the following design and analysis criteria
can be determined.
Seismic Design Category. The Seismic Design Category is based on the seismic
group and the design spectral response acceleration coefficients, SDS and SD1, which
will be explained later. The Seismic Design Category for a structure can be determined
in accordance with Tables 5.10 and 5.11.
Seismic Design Categories are used to determine the permissible structural systems,
the limitations on height and irregularity of the structural components that
must be designed for seismic resistance and the types of lateral force analysis that
must be performed.
Seismic Use Groups I and II structures located on sites with mapped maximum
considered earthquake spectral response acceleration at 1-second period S1, equal
to or greater than 0.75g, shall be assigned to Seismic Design Category E. Seismic
Use Group III structures located on such sites shall be assigned to Seismic Design
Category F. A structure assigned to Seismic Design Category E or F shall not be
sited where there is the potential for an active fault to cause rupture of the ground
surface at the structure.
Building Irregularity. Building with irregular shapes, changes in mass from floor
to floor, variable stiffness with height, and unusual setbacks do not perform well
during earthquakes. Thus, for each type of these irregularities, additional design
requirements shall be followed to maintain seismic-resisting capacity. IBC 2000
requires that all buildings be classified as regular or irregular based on the plan and
vertical configuration. See Tables 5.12 and 5.13 for classification and corresponding
requirements.
Design Requirements for Seismic Design Category A. Structures assigned to
Seismic Design Category A need only comply with the following:
• Structure shall be provided with a complete lateral-force-resisting system designed
to resist the minimum lateral force, of 1% floor gravity load.
The gravity load should include the total dead load and other loads listed
below.
• In areas used for storage, a minimum of 25% of the reduced floor live load
(floor live load in public garages and open parking structures need not be included)
• Where an allowance for partition load is included in the floor load design, the
actual partition weight or a minimum weight of 10 psf of floor area (whichever
is greater)
• Total operating weight of permanent equipment
• 20% of flat roof snow load where flat roof snow load exceeds 30 psf
• The direction of application of seismic forces used in design shall be that which
will produce the most critical load effect in each component. The design seismic
forces are permitted to be applied separately in each of two orthogonal directions
and orthogonal effects are permitted to be neglected.
• The effect of this lateral force shall be taken as E in the load combinations.
Special seismic load combinations that include Em need not to be considered.
5.164
TABLE 5.9 Design Coefficients and Factors for Basic Seismic-Force-Resisting Systems
Basic seismic-force-resisting system
Response
modification
coefficient, R
System
overstrength
factor, o
Deflection
amplification
factor, Cd
System limitations and building height limitations
(ft) by seismic design category
A and B C D E F
Bearing wall systems
Ordinary steel braced frames 4 2 31?2 NL NL 160 160 160
Special reinforced concrete shear walls 51?2 21?2 5 NL NL 160 160 100
Ordinary reinforced concrete shear walls 41?2 21?2 4 NL NL NP NP NP
Detailed plain concrete shear walls 21?2 21?2 4 NL NL NP NP NP
Ordinary plain concrete shear walls 11?2 21?2 11?2 NL NP NP NP NP
Special reinforced masonry shear walls 4 21?2 31?2 NL NL 160 160 100
Intermediate reinforced masonry shear walls 31?2 21?2 3 NL NL NP NP NP
Ordinary reinforced masonry shear walls 2 21?2 13?4 NL 160 NP NP NP
Detailed plain masonry shear walls 2 21?2 13?4 NL 160 NP NP NP
Ordinary plain masonry shear walls 11?2 21?2 11?4 NL NP NP NP NP
Light frame walls with shear panels, Wood Structural
Panels
61?2 3 4 NL NL 160 160 100
Light frame walls with shear panels—Gypsum Board 2 21?2 2 NL NL 35 NP NP
Building frame systems
Steel eccentrically braced frames, nonmoment resisting,
connections at columns away from links
7 2 4 NL NL 160 160 100
Special steel concentrically braced frames 6 21?2 5 NL NL 160 160 100
Ordinary steel concentrically braced frames 5 2 41?2 NL NL 160 100 100
Special reinforced concrete shear walls 6 21?2 5 NL NL 160 160 100
5.165 TABLE 5.9 Design Coefficients and Factors for Basic Seismic-Force-Resisting Systems (
Continued)
Basic seismic-force-resisting system
Response
modification
coefficient, R
System
overstrength
factor, o
Deflection
amplification
factor, Cd
System limitations and building height limitations
(ft) by seismic design category
A and B C D E F
Bearing wall systems
Ordinary reinforced concrete shear walls 5 21?2 41?2 NL NL NP NP NP
Detailed plain concrete shear walls 3 21?2 21?2 NL NL NP NP NP
Ordinary plain concrete shear walls 2 21?2 2 NL NP NP NP NP
Composite eccentrically braced frames 8 2 4 NL NL 160 160 100
Composite concentrically braced frames 5 2 41?2 NL NL 160 160 100
Ordinary composite braced frames 3 2 3 NL NL NP NP NP
Composite steel plate shear walls 61?2 21?2 51?2 NL NL 160 160 100
Special composite reinforced concrete shear walls
with steel elements
6 21?2 5 NL NL 160 160 100
Ordinary composite reinforced concrete shear walls
with steel elements
5 21?2 41?2 NL NL NP NP NP
Special reinforced masonry shear walls 5 21?2 4 NL NL 160 160 100
Intermediate reinforced masonry shear walls 41?2 21?2 4 NL NL 160 160 100
Ordinary reinforced masonry shear walls 21?2 21?2 21?4 NL 160 NP NP NP
Detailed plain masonry shear walls 21?2 21?2 21?4 NL 160 NP NP NP
Ordinary plain masonry shear walls 11?2 21?2 11?4 NL NP NP NP NP
Light frame walls with shear panels 7 21?2 41?2 NL NL 160 160 160
5.166
TABLE 5.9 Design Coefficients and Factors for Basic Seismic-Force-Resisting Systems (Continued)
Basic seismic-force-resisting system
Response
modification
coefficient, R
System
overstrength
factor, o
Deflection
amplification
factor, Cd
System limitations and building height limitations
(ft) by seismic design category
A and B C D E F
Moment resisting frame systems
Special steel moment frames 8 3 51?2 NL NL NL NL NL
Special steel truss moment frames 7 3 51?2 NL NL 160 100 NP
Intermediate steel moment frames 6 3 5 NL NL 160 100 NP
Ordinary steel moment frames 4 3 31?2 NL NL 35 NP NP
Special reinforced concrete moment frames 8 3 51?2 NL NL NL NL NL
Intermediate reinforced concrete moment frames 5 3 41?2 NL NL NP NP NP
Ordinary reinforced concrete moment frames 3 3 21?2 NL NP NP NP NP
Special composite moment frames 8 3 51?2 NL NL NL NL NL
Intermediate composite moment frames 5 3 41?2 NL NL NP NP NP
Composite partially restrained moment frames 6 3 51?2 160 160 100 NP NP
Ordinary composite moment frames 3 3 4 NL NP NP NP NP
Masonry wall frames 51?2 3 5 NL NL 160 160 100
Dual systems with special moment frames
Steel eccentrically braced frames, moment-resisting
connections, at columns away from links
8 21?2 4 NL NL NL NL NL
Steel eccentrically braced frames, nonmomentresisting
connections, at columns away from links
7 21?2 4 NL NL NL NL NL
Special steel concentrically braced frames 8 21?2 61?2 NL NL NL NL NL
Ordinary steel concentrically braced frames 6 21?2 5 NL NL NL NL NL
Special reinforced concrete shear walls 8 21?2 61?2 NL NL NL NL NL
5.167
TABLE 5.9 Design Coefficients and Factors for Basic Seismic-Force-Resisting Systems (Continued)
Basic seismic-force-resisting system
Response
modification
coefficient, R
System
overstrength
factor, o
Deflection
amplification
factor, Cd
System limitations and building height limitations
(ft) by seismic design category
A and B C D E F
Ordinary reinforced concrete shear walls 7 21?2 6 NL NL NP NP NP
Composite eccentrically braced frames 8 21?2 4 NL NL NL NL NL
Composite concentrically braced frames 6 21?2 5 NL NL NL NL NL
Composite steel plate shear walls 8 3 61?2 NL NL NL NL NL
Special composite reinforced concrete shear walls
with steel elements
8 3 61?2 NL NL NL NL NL
Ordinary composite reinforced concrete shjear walls
with steel elements
7 3 61?2 NL NL NP NP NP
Special reinforced masonry shear walls 7 3 61?2 NL NL NL NL NL
Intermediate reinforced masonry shear walls 61?2 3 51?2 NL NL NL NP NP
Dual systems with intermediate moment frames
Special steel concentrically braced frames 6 21?2 5 NL NL 160 100 NP
Ordinary steel concentrically braced frames 5 21?2 41?2 NL NL 160 100 NP
Special reinforced concrete shear walls 6 21?2 5 NL NL 160 100 100
Ordinary reinforced concrete shear walls 51?2 21?2 41?2 NL NL NP NP NP
Ordinary reinforced masonry shear walls 3 3 21?2 NL 160 NP NP NP
Intermediate reinforced masonry shear walls 5 3 41?2 NL NL 160 NP NP
Composite concentrically braced frames 5 21?2 41?2 NL NL 160 100 NP
Ordinary composite braced frames 4 21?2 3 NL NL NP NP NP
Ordinary composite reinforced concrete shear walls
with steel elements
5 3 41?2 NL NL NP NP NP
5.168
TABLE 5.9 Design Coefficients and Factors for Basic Seismic-Force-Resisting Systems (Continued)
Basic seismic-force-resisting system
Response
modification
coefficient, R
System
overstrength
factor, o
Deflection
amplification
factor, Cd
System limitations and building height limitations
(ft) by seismic design category
A and B C D E F
Dual systems with intermediate moment frames
Shear Wall-Frame Interactive System with Ordinary
Reinforced Concrete Moment Frames and Ordinary
Reinforced Concrete Shear Walls
51?2 21?2 5 NL NP NP NP NP
Inverted pendulum systems
Special steel moment frames 21?2 2 21?2 NL NL NL NL NL
Ordinary steel moment frames 11?4 2 21?2 NL NL NP NP NP
Special reinforced concrete moment frames 21?2 2 11?4 NL NL NL NL NL
Structural Steel Systems Not Specifically Detailed
for Seismic Resistance
3 3 3 NL NL NP NP NP
NL indicates not limited.
NP indicates not permitted.
STRUCTURAL THEORY 5.169
TABLE 5.10 Seismic Design Category Based on Short Period Response Accelerations
Value of SDS
Seismic Use Group
I II III
SDS 	 0.167g
0.167g  SDS 	 0.33g
0.33g  SDS 	 0.50g
0.50g  SDS
A
B
C
D
A
B
C
D
A
C
D
D
TABLE 5.11 Seismic Design Category Based on 1 Second Period Response Acceleration
Value of SDI
Seismic Use Group
I II III
SDI 	 0.067g
0.067g  SDI 	 0.133g
0.133g  SDI 	 0.20g
0.20g  SDI
A
B
C
D
A
B
C
D
A
C
D
D
Where Em equals the earthquake force where seismic forces and dead loads counteract.
• All parts of the structure between separation joints shall be interconnected, and
the connections shall be capable of transmitting the seismic force induced in the
connection by the parts being connected. Any smaller portion of the structure
shall be tied to the remainder of the structure with 5% the weight of the smaller
portion. A positive connection for resisting horizontal forces acting on the member
shall be provided for each beam, girder, or truss to its support. The connection
shall have strength sufficient to resist 5% of the dead and live load vertical reaction
applied horizontally.
Analysis Procedures for Seismic Design Categories B, C, D, E, and F. For Seismic
Design Categories B and C, IBC 2000 proposed equivalent lateral-load force
procedure shall be used. A more rigorous analysis is permitted, too. However, for
Seismic Design Categories D, E, and F, the analysis procedures are identified in
Table 5.14.
5.19.2 Design Spectral Response Accelerations
Ground motion accelerations, represented by response spectra and coefficients derived
from these spectra, shall be determined in accordance with the general procedure
or the site-specific procedure. The later procedure shall be used for structures
on sites classified as Site Class F.
General Procedure for Determining Maximum Considered Earthquake and Design
Spectral Response Accelerations. The maximum considered earthquake
spectral response accelerations maps only provide values for Site Class B at short
5.170 SECTION FIVE
TABLE 5.12 Plan Structural Irregularities
Irregularities Irregularity type and description
Seismic Design
Category
application
1a Torsional irregularity—to be considered
when diaphragms are not flexible
D, E, and F
Torsional irregularity shall be
considered to exist when the
maximum story drift, computed
including accidental torsion, at one
end of the structure transverse to an
axis is more than 1.2 times the
average of the story drifts at the two
ends of the structure
C, D, E, and F
1b Extreme torsional irregularity—to be
considered when diaphragms are not
flexible
D
Extreme torsional irregularity shall be
considered to exist when the
maximum story drift, computed
including accidental torsion, at one
end of the structure transverse to an
axis is more than 1.4 time the
average of the story drifts at the two
ends of the structure.
C and D
(this irregularity
not permitted in
E or F)
2 Re-entrant corners D
Plan configurations of a structure and
its lateral force-resisting system
contain re-entrant corners, where
both projections of the structure
beyond a re-entrant corner are
greater than 15% of the plan
dimension of the structure in the
given direction.
E and F
3 Diaphragm discontinuity D, E, and F
Diaphragm with abrupt discontinuities
or variations in stiffness, including
those having cutout or open areas
greater than 50% of the gross
enclosed diaphragm area, or changes
in effective diaphragm stiffness of
more than 50% from one story to
the next.
D, E and F
4 Out-of-plane offsets B, C, and D
Discontinuities in a lateral force
resistance path, such as out-of-plane
offsets of the vertical elements.
E and F
STRUCTURAL THEORY 5.171
TABLE 5.13 Vertical Structural Irregularities
Irregularities Irregularity type and description
Seismic Design
Category
application
5 Nonparallel systems C, D, E, and F
The vertical lateral force-resisting elements
are not parallel to or symmetric about the
major orthogonal axes of the lateral forceresisting
system.
1a Stiffness irregularity—soft story D, E, and F
A soft story is one in which the lateral stiffness
is less than 70% of that in the story
above or less than 80% of the average
stiffness of the three stories above.
1b Stiffness irregularity—extreme soft story D
An extreme soft story is one in which the
lateral stiffness is less than 60% of that in
the story above or less than 70% of the
average stiffness of the three stories above.
This irregularity
not permitted
in E or F
2 Weight (mass) irregularity D, E and F
Mass irregularity shall be considered to exist
where the effective mass of any story is
more than 150% of the effective mass of
an adjacent story. A roof is lighter than the
floor below need not be considered.
3 Vertical geometric irregularity D, E, and F
Vertical geometric irregularity shall be
considered to exist where the horizontal
dimension of the laterl-force-resisting
system in any story is more than 130% of
that in an adjacent story.
4 In-plane discontinuity in vertical–lateralforce-
resisting elements
B, C, D, E and
F
An in-plane offset of the lateral-forceresisting
elements greater than the length
of those elements or a reduction in
stiffness of the resisting element in the
story below.
5 Discontinuity in capacity-weak story B, C, and D
A weak story is one in which the story
lateral strength is less than 80% of that in
the story above. The story strength is the
total strength of seismic-resisting elements
sharing the story shear for the direction
under consideration.
This irregularity
not permitted
in E or F
5.172 SECTION FIVE
TABLE 5.14 Analysis Procedures for Seismic Design Categories D, E, and F
Structure description
Minimum allowance analysis
procedure for seismic design
1. Seismic Use Group—1 building of light framed
construction 3 stories or less in height and of
other construction, 2 stories or less in height.
Simplified procedure
2. Regular structures other than those in Item 1
above, up to 240 ft / in height.
Equivalent lateral force procedure
3. Structures that have vertical irregularities of
type 1a, 1b, 2, or 3 in Table 5.13, or plan
irregularities of type 1a or 1b of Table 5.12,
and have a height exceeding 5 stories or 65 ft
and structures exceeding 240 ft in height.
Model analysis procedure
4. Other structures designated as having plan or
vertical irregularities
Equivalent lateral force procedure
with dynamic characteristics
included in the analytical
model
5. Structures with all of the following
characteristics:
• located in an area with SD1 of 0.2 or greater
• located in an area assigned to Site Class E or
F
• with a natural period T of 0.7 seconds or
greater, as determined in equivalent lateral
force procedure
Model analysis procedure. A sitespecific
response spectrum shall
be used but the design base
shear shall not be less than that
determined from simplified
procedure
period (SS) and at 1-second period (S1) and they need to be adjusted for site class
effects, by site coefficient Fa and Fv. (See Tables 5.15 and 5.16.)
The corresponding design spectral response accelerations at short periods and at
1 second are:
2
S  F S (5.309) DS a a 3
2
S  F S (5.310) D1 v 1 3
The general design response spectrum curve is developed as Fig. 5.113, in which
SD1 T  0.2 0 SDS
SD1 T  S SDS
and T is the fundamental period (in seconds) of the structure.
STRUCTURAL THEORY 5.173
TABLE 5.15 Values of Site Coefficient Fa as a Function of Site Class and Mapped
Spectral Response Acceleration at Short Periods (SS)
Site class
Mapped spectral response acceleration at short periods
SS  0.25 SS  0.50 SS  0.75 SS  1.00 SS 
 1.25
A 0.8 0.8 0.8 0.8 0.8
B 1.0 1.0 1.0 1.0 1.0
C 1.2 1.2 1.1 1.0 1.0
D 1.6 1.4 1.2 1.1 1.0
E 2.5 1.7 1.2 0.9 a
F Note a Note a Note a Note a Note a
a Site specific geotechnical investigation and dynamic site response analyses shall be performed to determine
appropriate values.
Note: Use straight-line interpolation for intermediate values of mapped spectral acceleration at short
period, SS.
TABLE 5.16 Values of Site Coefficient Fv as a Function of Site Class and Mapped
Spectral Response Acceleration at 1-Second Periods (S1)
Site class
Mapped spectral response acceleration at 1-second period
S1  0.1 S1  0.2 S1  0.3 S1  0.4 S1  0.5
A 0.8 0.8 0.8 0.8 0.8
B 1.0 1.0 1.0 1.0 1.0
C 1.7 1.6 1.5 1.4 1.3
D 2.4 2.0 1.8 1.6 1.5
E 3.5 3.2 2.8 2.4 a
F Note a Note a Notea Note a Note a
a Site specific geotechnical investigation and dynamic site response analyses shall be performed to determine
appropriate values.
Note: Use straight-line interpolation for intermediate values of mapped spectral acceleration at 1-
second period, S1.
Site Specific Procedures for Determining Design Spectral Response Accelerations
• A site specific study shall account for the regional seismicity and geology; the
expected recurrence rates and maximum magnitudes of events on known faults
and source zones; the location of the site with respect to these; near source effects,
if any; and the characteristics of subsurface site conditions.
• The probabilistic maximum considered earthquake ground motion shall be taken
as that motion represented by an acceleration response spectrum having a 2%
probability of exceedance within a 50-year period. The probabilistic maximum
considered earthquake spectral response acceleration at any period, SaM, shall be
taken from the 2% probability of exceedance within a 50-year period spectrum
(where SaM exceeds the deterministic limit shown in Fig. 5.114.)
5.174 SECTION FIVE
FIGURE 5.113 Design Response Spectrum
FIGURE 5.114 Deterministic Limit on Maximum
Considered Earthquake Response Spectrum
• The maximum considered earthquake ground motion spectrum shall be taken as
the lesser of the probabilistic maximum considered earthquake ground motion or
the deterministic maximum considered earthquake ground motion spectrum S,
but shall not be taken as less than the deterministic limit ground motion as shown
in Fig. 5.114. S is calculated as 150% of the median spectral response accelerations
(SaM) at all periods resulting from a characteristic earthquake on any known
active fault within the region.
The site-specific design spectral response acceleration Sa at any period can be
expressed as
2
S  S (5.311) a aM 3
STRUCTURAL THEORY 5.175
• Sa shall be no less than 80% of the corresponding value as the general design
response on Fig. 5.113.
• The design spectral response acceleration coefficients at short periods, SDS and
the design spectral response acceleration at 1-second period, SD1, shall be taken
the values Sa at periods of 0.2 second and 1.0 second, respectively.
5.19.3 Minimum Design Lateral Force and Related Effects
From Table 5.14, we know that there are several seismic force analysis procedures,
such as simplified procedure, equivalent lateral force procedure, model analysis
procedure. The reader should note that another method, the dynamic analysis procedure,
is not presented here. Different Seismic Design Categories require different
analysis procedures. Among these analysis procedures, the equivalent lateral force
procedure is the most popular approach because of its easy calculation and clear
seismic design concepts. It can also be used as the preliminary design seismic force
for the Seismic Design Categories that require more rigorous analysis procedures.
In this handbook, we will only cover this analysis procedure.
Equivalent Lateral Force Procedure. In this analysis, a building is considered to
be fixed at the base. The seismic base shear, which is equivalent to the total horizontal
forces at the base generated by a seismic force in any direction, can be
expressed as
V  C W (5.312) S
where CS is the response coefficient and W is the effective seismic weight of the
structure, including the total dead load and other loads listed below:
1. In areas used for storage, a minimum of 25% of the reduced floor live load
(floor live load in public garages and open parking structures need not be included)
2. Where an allowance for partition load is included in the floor load design, the
actual partition weight or a minimum weight of 10 psf of floor area (whichever
is greater)
3. Total operating weight of permanent equipment
4. 20% of flat roof snow load where the flat roof snow load exceeds 30 psf
The seismic response coefficient, CS, shall be determined in accordance with the
following formula:
SDS C  (5.313) S R 
  I
where SDS  the design spectral response acceleration at short period
R  the response modification factor from Table 5.9
I  the Occupancy Importance Factor
The value of the seismic response coefficient CS need not exceed the following:
5.176 SECTION FIVE
TABLE 5.17 Coefficient for Upper Limit on Calculated Period
Design spectral response acceleration at 1-second period, SD1 Coefficient Cu

0.4 1.2
0.3 1.3
0.2 1.4
0.15 1.5
0.1 1.7
SDI C  (5.314) S R
T 
  I
but shall not be taken less than:
C  0.44S I (5.315) S D1
For buildings and structures in Seismic Design Categories E or F, and those
buildings and structures for which the 1-second spectral response S1 is equal to or
greater than 0.6g, the value of the seismic response coefficient CS shall not be taken
as less than:
0.5S1 C  (5.316) S R/ I
where I and R are defined above and
SD1  the design spectral response acceleration at 1-second period
T  the fundamental period of the building (seconds)
S1  the maximum considered earthquake spectral response acceleration at 1-
second period
The fundamental period of the building, T in the direction under consideration
shall be established using the structural properties and deformational characteristics
of the resisting elements in a properly substantiated analysis, or shall be taken as
the approximate fundamental period Ta. The calculated fundamental period T shall
not exceed the product of the coefficient for the upper limit on the calculated period
Cu, from Table 5.17, and the approximate fundamental period Ta. The approximate
fundamental Ta shall be determined as:
3 / 4 T  C h (5.317) a T n
STRUCTURAL THEORY 5.177
where CT  building period coefficient (see following list of coefficient values)
• 0.035 for moment resisting frame systems of steel in which the
frames resist 100% of the required seismic force and are not enclosed
or adjoined by more rigid components that will prevent the frames
from deflecting when subjected to seismic forces,
• 0.030 for moments resisting frame systems of reinforced concrete in
which the frames resist 100% of the required seismic force and are
not enclosed or adjoined by more rigid components that will prevent
the frames from deflecting when subjected to seismic forces,
• 0.030 for eccentrically braced steel frames,
• 0.020 for all other building systems.
hn  the height (ft) above the base to the highest level of the building.
Alternately, determination of the approximate fundamental period Ta in seconds,
from the following formula for concrete and steel moment-resisting frame buildings
not exceeding 12 stories in height and having a minimum story height of 10 ft, is
permitted:
T  0.1N (5.318) a
where N is the number of stories.
The base shear V is distributed vertically to the n stories as lateral forces F:
F C V (5.319) x vx
k w h x x C  (5.320) vx n
k wh 	 i i
i1
where C  vx vertical distribution factor,
wi and wx  the portion of the total gravity load of the building, W, located or
assigned to level i or x,
hi and hx  the height (ft) from the base to level i or x, and
k  a distribution exponent related to the building period as follows:
• For buildings having a period of 0.5 seconds or less, k  1
• For buildings having a period of 2.5 seconds or more, k  2
• For buildings having a period between 0.5 and 2.5 seconds, k shall
be 2 or shall be determined by linear interpolation between 1 and
2.
The seismic design story shear in any story, Vx is
n
V  F (5.321) 	 x i
i1
5.178 SECTION FIVE
Rigid Diaphragms. For rigid diaphragms the seismic design story share, Vx shall
be distributed to the various vertical elements of the seismic force-resisting system
in the story under consideration based on the relative lateral stiffness of the vertical
force resisting elements and the diaphragm.
For flexible diaphragms, seismic design story shear, Vx shall be distributed to
various vertical elements based on the tributary area of the diaphragm to each line
of resistance. For the purpose of this section, the vertical elements of the lateral
force-resisting system are permitted to be considered to be in the same line of
resistance, if the maximum out-of-plane offset between each of the elements is less
than 5% of the building dimension perpendicular to the direction of lateral load.
Torsion. Where diaphragms are not flexible, the design shall include the torsional
moment Mt, resulting from the difference in locations of the center of mass and the
center of stiffness. Also where diaphragms are not flexible, in addition to the torsional
moment, the design shall include accidental torsional moments Mta, caused
by assumed displacement of the center of mass, each way from its actual location,
by a distance equal to 5% of the dimension of the building perpendicular to the
direction of the applied forces.
Dynamic Amplification of Torsion. For a structure in Seismic Design Category
C, D, E, or F, where Type 1a or 1b plan torsional irregularity exists, effects of
torsional irregularity shall be accounted for by multiplying the sum of Mt plus Mta
at each level by a torsional amplification factor, Ax, determined from the following
formula:
2 max A  (5.322) 
  x 1.2 avg
where   max the maximum displacement at level x and
  avg the average of the displacement at the extreme points of the structure
at level x
The torsional amplification factor, Ax, is not required to exceed 3.0. The more severe
loading for each element shall be considered for design.
Overturning. The building shall be designed to resist overturning effects caused
by the seismic forces. At any story, the increment of overturning moment in the
story under consideration shall be distributed to the various vertical force-resisting
elements in the same proportion as the distribution of the horizontal shears to those
elements.
The overturning moments at level x, Mx shall be determined from the following
formula:
n
M   F (h  h ) (5.323) 	 x i i x
ix
where Fi  the portion of the seismic base shear V, induced at Level i,
hi and hx  the height from the base to level i or x,
 the Overturning Moment Reduction Factor
The Overturning Moment Reduction Factors are
STRUCTURAL THEORY 5.179
• 1.0 for the top 10 stories,
• 0.8 for the 20th story from the top and below, and
• value between 1.0 and 0.8 determined by a straight line interpolation for stories
between the 20th and 10th stories below the top.
Story Drift Determination. The design story drift shall be computed as the
difference of the deflections at the center of mass at the top and bottom of the story
under consideration. Where allowable stress design is used. shall be computed
using earthquake forces without dividing by 1.4. For structures assigned to Seismic
Design Category C, D, E, or F having plan irregularity types 1a or 1b of Table
5.12, the design story drift shall be computed as the largest difference of the
deflections along any of the edges of the structure at the top and bottom of the
story under consideration.
The deflections of level x, x, shall be determined in accordance with following
formula:
C  d xe   (5.324) x I
where Cd  the deflection amplification factor in Table 5.9,
xe  the deflections determined by an elastic analysis of the seismic force
resisting system, and
I  the Occupancy Importance Factor
For purposes of this drift analysis only, the upper bound limitation specified on
the computed fundamental period, T, in seconds, of the building, shall not apply.
The design story drift shall be increased by the incremental factor relating to
the P-delta effects. When calculating drift, the redundancy coefficient shall be
taken as 1.0.
P-Delta Effects. P-delta effects on story shears and moments the resulting member
forces and moments, and the story drifts induced by these effects are not required
to be considered when the stability coefficient , as determined by the following
formula, is equal to or less than 0.10:
P x  (5.325)
V h C x sx d
where Px  the total unfactored vertical design load at and above level x; when
calculating the vertical design load for purposes of determining Pdelta,
the individual load factors need not exceed 1,0;
  the design story drift occurring simultaneously within Vx;
Vx  the seismic shear force acting between level x and x  1;
hsx  the story height below level x; and
Cd  the deflection amplification factor in Table 5.9
The stability coefficient  shall not exceed max determined as follows:
0.5
   0.25 (5.326) max Cd
where  is the ratio of shear demand to shear capacity for the story between level
x and x  1. Where the ratio  is not calculated, a value of  1.0 shall be used.
5.180 SECTION FIVE
When the stability coefficient  is greater than 0.10 but less than or equal to
 , interstory drifts and element forces shall be computed including P-delta ef- max
fects. To obtain the story drift for including the P-delta effect, the design story drift
shall be multiplied by 1.0 / (1  ). Where  is greater than  the structure is max
potentially unstable and shall be redesigned.
Seismic Load Effect. Where the effects of gravity and seismic loads are additive,
seismic load E shall be defined as:
E  Q  0.2S D (5.327) E DS
and where the effects of gravity counteract the seismic load, seismic load E shall
be defined as
E  Q  0.2S D (5.328) E DS
where E  the combined effect of horizontal and vertical earthquake-induced
forces,
 a reliability factor based on system redundancy,
QE  the effect of horizontal seismic forces,
SDS  the design spectral response acceleration at short periods,
D  the effect of dead load
Where seismic forces and dead loads are additive,
E   Q  0.2S D (5.329) m o E DS
Where seismic forces and dead loads counteract,
E   Q  0.2S D (5.330) m o E DS
Where E, QE, SDS and D are as defined above and o is the system overstrength
factor as given in Table 5.9. The terms oQE need not exceed the maximum force
that can be transferred to the element by the other elements of the lateral forceresisting
system.
Where allowable stress design methodologies are used with the special load
combinations with Em design strengths are permitted to be determined using an
allowable stress increase of 1.7 and a resistance factor 	, of 1.0.
Redundancy. A redundancy coefficient, , shall be assigned to all structures in
accordance with this section, based on the extent of structural redundancy inherent
in the lateral forces resisting system.
For structure assigned to Seismic Design Category A, B, or C, the value of the
redundancy coefficient is 1.0. For structures in Seismic Design Categories D, E,
and F, the redundancy coefficient shall be taken as the largest of the values of i,
calculated at each story i of the structure as follows:
20
  2  (5.331) i r A max i i
STRUCTURAL THEORY 5.181
where r  max the ratio of the design shear resisted by the most heavily loaded single
element in the story to the total story shear, for a given direction of
loading
• For braced frames the value of r is equal to the lateral force maxi
component in the most heavily loaded braced element divided by
the story shear.
• For moment frames, r shall be taken as the maximum of the maxi
sum of the shears in any two adjacent columns in a moment frame
divided by the story shear. For columns common to two bays with
moment resisting connections on opposite sides at the level under
consideration, it is permitted to use 70% of the shear in that column
in the column shear summation.
• For shear walls, r shall be taken as the maximum value of the maxi
product of the shear in the wall or wall pier and 10/ lW, divided by
the story shear, where lW is the length of the wall or wall pier in
feet.
• For dual systems, r shall be taken as the maximum value defined maxi
above, considering all lateral load-resisting elements in the story.
The lateral loads shall be distributed to elements based on relative
rigidities considering the interaction of the dual system. For dual
systems, the value of need not exceed 80% of the value calculated
above.
Ai  the floor area in square feet of the diaphragm level immediately above
the story.
The value of shall not be less than 1.0, and need not exceed 1.5.
For structures with seismic force resisting systems in any direction comprised
solely of special moment frames, the seismic force-resisting system shall be con-
figured such that the value of calculated in accordance with this section does not
exceed 1.25 for structures assigned to Seismic Design Category D, and does not
exceed 1.1 for structures assigned to Seismic Design Category E or F.
Deflections and Drift Limits. The design story drift shall not exceed the allowable
story drift a, as obtained from Table 5.18 for any story. All portions of the
building shall be designed to act as an integral unit in resisting seismic forces unless
separated structurally by a distance sufficient to avoid damaging contact under total
deflection x.
5.19.4 Design Detailing Requirements and Structural Component
Load Effects
In order to provide a more reliable and consistent level of seismic safety in new
building construction, IBC 2000 includes a much larger set of provisions on proportioning
and detailing structural members and system. The Code requirements
are based on Seismic Design Category. These special requirements are for items
such as openings in shear walls and diaphragms, diaphragm design, collector element
design, design of bearing walls and shear walls and their anchorage, direction
5.182 SECTION FIVE
TABLE 5.18 Allowable Story Drift, a
a
Building
Seismic use group
I II III
Building, other than masonry shear wall or
masonry wall frames buildings, four
stories or less in height with interior
walls, partitions, ceilings, and exterior
wall systems that have been designed to
accommodate the story drifts
0.025 h b sx 0.020 hsx 0.015 hsx
Masonry cantilever shear wall buildingsc 0.010 hsx 0.010 hsx 0.010 hxx
Other masonry shear wall buildings 0.007 hxx 0.007 hsx 0.007 hsx
Masonry wall frame buildings 0.013 hsx 0.013 hsx 0.010 hsx
All other buildings 0.020 hsx 0.015 hsx 0.010 hsx
a There shall be no drift for single-story buildings with interior walls, partitions, ceilings, and exterior wall
systems that have been designed to accommodate the story drifts.
b hsx is the story height below Level x.
c Buildings in which the basic structural system consists of masonry shear walls designed as vertical elements
cantilevered from their base or foundation support which are so constructed that moment transfer between
shear walls coupling is negligible.
of seismic load impact, and so on. It is very important that the design engineer be
familiar with requirements.
5.19.5 Seismic Design Requirements on Nonstructural Components
Architectural, mechanical, electrical, and other nonstructural components in structures
shall be designed and constructed to resist equivalent static forces and displacements.
Unless otherwise noted, components shall be considered to have the
same Seismic Design Category as the structure that they occupy or to which they
are attached.
The interrelationship of components and their effect on each other shall be considered
so that the failure of any essential or nonessential architectural, mechanical,
or electrical component shall not cause the failure of another essential architectural,
mechanical, or electrical component.
Component Force Transfer. The component shall be attached such that the component
forces are transferred to the structure of the building. Component seismic
attachments shall be bolted, welded, or otherwise positively fastened without consideration
of frictional resistance produced by the effects of gravity.
The Seismic Force Fp is
0.4 S W z p DS p F  1  2 (5.332) 
  p h Rp 
  Ip
and
STRUCTURAL THEORY 5.183
0.3SDS IpWp  Fp  1.6SDSIpWp
where Fp  Seismic design force centered at the component’s center of gravity and
distributed relative to component’s mass distribution
SDS  Design spectral response acceleration at short period
p  Component amplification factor that varies from 1.00 to 2.50 (select
appropriate value from Tables 5.19 and 5.20)
Ip  Component importance factor that is 1.5 for life safety component and
1.0 for all other components
Wp  Component operating weight
Rp  Component response modification factor that varies from 1.0 to 5.0
(select appropriate value from Tables 5.19 and 5.20)
z  Height in structure at point of attachment of component. For items at
or below the base, z shall be taken as 0.
h  Average roof height of structure relative to the base elevation.
The force Fp shall be applied independently longitudinally and laterally in combination
with service loads associated with the component. Component earthquake
effects shall be determined for combined horizontal and vertical load effects as QE
in E. The redundancy based reliability coefficient, p, is permitted to be taken as
equal to 1.
(J. M. Biggs, ‘‘Introduction to Structural Dynamics,’’ and R. Clough and J. Penzien,
‘‘Dynamics of Structures,’’ McGraw-Hill Publishing Company, New York; E.
Rosenblueth, ‘‘Design of Earthquake-Resistant Structures,’’ Halsted/Wiley, Somerset,
N.J.; N. M. Newmark and E. Rosenblueth, ‘‘Fundamentals of Earthquake
Engineering,’’ Prentice-Hall, Englewood Cliffs, N.J.; S. Okamoto, ‘‘Introduction to
Earthquake Engineering,’’ John Wiley & Sons, Inc., New York, International Building
Code 2000)
5.20 FLOOR VIBRATIONS
Excessive vibration can be characterized as too large for sensitive equipment or too
large for occupant comfort. Determining these permissible levels is an entire research
area in itself; however, some of the more widely accepted levels are discussed
in following paragraphs. These levels are expressed by researchers in terms
of either acceleration, velocity, or displacement amplitudes and are often frequencydependent.
There is no consensus as to the most relevant measure for describing
acceptable levels.
Comfort of the occupants is a function of human perception. This perception is
affected by factors including the task or activity of the perceiver, the remoteness
of the source, and the movement of other objects in the surroundings. A person is
distracted by acceleration levels as small as 0.5% g. Multiple-use occupancies must
therefore be carefully considered.
Webster and Vaicitis describe a facility that has both dining and dancing in a
large open area. The floor was noted to have a first natural frequency of 2.4 Hz,
which is in resonance with the beat of many popular dance song. This resonance
response produced maximum acceleration and displacement levels of 7% g and
0.13 in, respectively. Such levels actually caused sloshing waves in drinks and
noticeable bouncing of the chandeliers. The occupants found these levels to be quite
objectionable.
5.184 SECTION FIVE
TABLE 5.19 Architectural Components Coefficients
Architectural component or element p
a Rp
Interior nonstructural walls and partitions
Plain (unreinforced) masonry walls 1.0 1.25
Other walls and partitions 1.0 2.5
Cantilever elements (unbraced or braced to structural frame below its
center of mass)
Parapets and cantilever interior nonstructural walls 2.5 2.5
Chimneys and stacks when laterally braced or supported by the
structural frame
2.5 2.5
Cantilever elements (braced to structural frame above its center of mass)
Parapets 1.0 2.5
Chimneys and Stacks 1.0 2.5
Exterior Nonstructural Walls 1.0 2.5
Exterior nonstructural wall elements and connections
Wall element 1.0 2.5
Body of wall panel connections 1.0 2.5
Fasteners of the connecting system 1.25 1.0
Veneer
Limited deformity elements and attachments 1.0 2.5
Low deformity elements or attachments 1.0 1.25
Penthouse (except when framed by an extension of the building frame) 2.5 3.5
Ceilings 1.0 2.5
Cabinets
Storage cabinets and laboratory equipment 1.0 2.5
Access floors
Special access floors 1.0 2.5
All other 1.0 1.25
Appendages and ornamentations 2.5 2.5
Signs and billboards 2.5 2.5
Other rigid components
High deformability elements and attachments 1.0 3.5
Limited deformability elements and attachments 1.0 2.5
Low deformability materials and attachments 1.0 1.25
Other flexible components
High deformability elements and attachments 2.5 3.5
Limited deformability elements and attachments 2.5 2.5
Low deformability materials and attachments 2.5 1.25
a Where justified by detailed analyses, a lower value for p is permitted, but shall not be less than 1. The
reduced value of p shall be between 2.5, assigned to flexible or flexibly attached equipment, and 1, assigned
to rigid or rigidly attached equipment.
Many different scales and criteria are available which address the subjective
evaluation of floor vibration. Factors included in these subjective evaluations include
the natural frequency of the floor system, the maximum dynamic amplitude
(acceleration, velocity, or displacement) due to certain excitations, and the amount
of damping present in the floor system. At the present time, most of the design
criteria utilize either a single impact function to assess vibrations, which are tranSTRUCTURAL
THEORY 5.185
TABLE 5.20 Mechanical and Electrical Components Coefficients
Mechanical and electrical component or element p
a Rp
General mechanical
Boilers and furnaces 1.0 2.5
Pressure vessels on skirts and free-standing 2.5 2.5
Stacks 2.5 2.5
Cantilevered chimneys 2.5 2.5
Other 1.0 2.5
Manufacturing and process machinery
General 1.0 2.5
Conveyors (nonpersonnel) 2.5 2.5
Piping systems
High deformability elements and attachments 1.0 3.5
Limited deformability elements and attachments 1.0 2.5
Low deformability elements or attachments 1.0 1.25
HVAC system equipment
Vibration isolated 2.5 2.5
Nonvibration isolated 1.0 2.5
Mounted in-line with ductwork 1.0 2.5
Other 1.0 2.5
Elevator components 1.0 2.5
Escalator component 1.0 2.5
Trussed towers (free-standing or guyed) 2.5 2.5
General electrical
Distributed systems (bus ducts, conduit, cable tray) 2.5 5.0
Equipment 1.0 2.5
Lighting Fixtures 1.0 1.25
a Where justified by detailed analyses, a lower value for p is permitted, but shall not be less than 1. The
reduced value of p shall be between 2.5, assigned to flexible or flexibly attached equipment, and 1, assigned
to rigid or rigidly attached equipment.
sient in nature, or a sinusoidal function to assess steady-state vibrations from rhythmic
activities.
5.21 WISS AND PARMELEE RATING FACTOR
FOR TRANSIENT VIBRATIONS
Wiss and Parmelee also conducted research to refine the findings of Lenzen’s research.
In particular, they attempted to quantify, in a more scientifically rigorous
manner, human perception to transient floor motion. They subjected 40 persons,
standing on a vibrating platform, to transient vibration episodes with different combinations
of frequency (2.5 to 25 Hz), peak displacements (0.0001 to 0.10 in), and
damping (0.1 to 0.16, expressed as a ratio of critical). After each episode, the
subject was asked to rate the vibration on a scale of 1 to 5 with the following
definitions: (1) imperceptible, (2) barely perceptible, (3) distinctly perceptible, (4)
strongly perceptible, and (5) severe. Using regression analysis, an equation was
5.186 SECTION FIVE
FIGURE 5.115 Wiss and Parmelee rating factor scale.17
developed which related the three variables of the vibration episode to the subjective
perception ratings. This equation is presented below.
Wiss and Parmelee rating factor:
0.265 FA
R  5.08
  0.217 D
where R  response rating; 1  imperceptible; 2  barely perceptible; 3  distinctly
perceptible; 4  strongly perceptible; 5  severe.
F  frequency of the vibration episode, Hz
A  maximum displacement amplitude, in
D  damping ratio, expressed as a ratio of critical
A graph of this subjective rating system is shown in Fig. 5.115. It should be
noted that the lines represent a mean for that particular rating. The authors suggest
that the boundaries for each rating lie halfway between the mean lines. The boundaries
defining R  1 and R  5 are not identified by the authors. These ratings are
unbounded; therefore, a mean line cannot be computed.
5.22 REIHER-MEISTER SCALE FOR STEADYSTATE
VIBRATIONS
The scale discussed below and those in Art. 5.21 and 5.23 useful in assessing human
perception to vibration levels. They are presented to provide insight with respect
STRUCTURAL THEORY 5.187
FIGURE 5.116 Modified Reiher-Meister and Reiher-Meister scales.
TABLE 5.21 Estimates of Floor System Damping
Component
Damping
(% of critical) Description
Bare floor 1–3% Lower limit for thin slab of lightweight concrete;
upper limit for thick slab of normal weight
concrete
Ceiling 1–3% Lower limit for hung ceiling; upper limit for
sheetrock on furring attached to beams of
joists
Ductwork and mechanial 1–10% Depends on amount and attachment
Partition 10–20% If attached to the floor system and not spaced
more than every five floor beams of the effective
joist floor width
(Serviceability Considerations for floors and roof systems Chapter 9, ‘‘Steel Design Handbook’’ by
Akbar Tamboli, McGraw-Hill Book Company, New York.)
to the vibration levels which annoy occupants as well as a historical perspective on
the development of floor vibration criteria. Reiher and Meister15 published a frequently
referenced scale concerning human perception to steady-state vibration.
While this scale was not derived specifically for the evaluation of floor systems, it
has been extrapolated by other researchers for such purposes. The scale represented
by the right-hand axis of the graph in Fig. 5.116 was derived from the subjective
evaluations of 10 persons standing on a vibrating platform. The subjects were exposed
to vertical steady-state vibration episodes each lasting approximately 5
minutes, and were asked to classify the vibration as (1) slightly perceptible, (2)
5.188 SECTION FIVE
distinctly perceptible, (3) strongly perceptible, (4) disturbing, and (5) very disturbing.
The frequency and displacement ranges of the episodes were 5 to 70 Hz and
0.001 to 0.40 in, respectively.
5.23 MURRAY CRITERION FOR
WALKING VIBRATIONS
5.23.1 Summary of the Criterion
In the criterion presented by Murray, an acceptable steel floor system is predicted,
with respect to vibration levels due to walking excitation, if the dynamic criterion
below is met. This criterion is applicable to offices and residences with fundamental
natural frequencies below 10 Hz.
Murray criterion:
D  35A ?  2.5 0
where D  damping in floor system, expressed as a percent of critical
A0  maximum initial amplitude of the floor system due to a heel-drop excitation,
in
?  first natural frequency of the floor system, Hz
This criterion is only applicable for the units specified. The reader is cautioned
against using other units.
6.1
SECTION SIX
SOIL MECHANICS AND
FOUNDATIONS
Robert W. Day
Chief Engineer, American Geotechnical
San Diego, California
6.1 INTRODUCTION
6.1.1 Soil Mechanics
Soil mechanics is defined as the application of the laws and principles of mechanics
and hydraulics to engineering problems dealing with soil as an engineering material.
Soil has many different meanings, depending on the field of study. For example,
in agronomy (application of science to farming), soil is defined as a surface deposit
that contains mineral matter that originated from the original weathering of rock
and also contains organic matter that has accumulated through the decomposition
of plants and animals. To an agronomist, soil is that material that has been suffi-
ciently altered and supplied with nutrients that it can support the growth of plant
roots. But to a geotechnical engineer, soil has a much broader meaning and can
include not only agronomic material, but also broken-up fragments of rock, volcanic
ash, alluvium, aeolian sand, glacial material, and any other residual or transported
product of rock weathering. Difficulties naturally arise because there is not a distinct
dividing line between rock and soil. For example, to a geologist a given material
may be classified as a formational rock because it belongs to a definite geologic
environment, but to a geotechnical engineer it may be sufficiently weathered or
friable that it should be classified as a soil.
6.1.2 Rock Mechanics
Rock mechanics is defined as the application of the knowledge of the mechanical
behavior of rock to engineering problems dealing with rock. To the geotechnical
engineer, rock is a relatively solid mass that has permanent and strong bonds between
the minerals. Rocks can be classified as being either sedimentary, igneous,
or metamorphic. There are significant differences in the behavior of soil versus
rock, and there is not much overlap between soil mechanics and rock mechanics.
6.2 SECTION SIX
TABLE 6.1 Problem Conditions Requiring Special Consideration
Problem
type Description Comments
Organic soil, highly plastic
soil
Low strength and high compressibility
Sensitive clay Potentially large strength loss upon large
straining
Micaceous soil Potentially high compressibility
Soil Expansive clay, silt, or slag Potentially large expansion upon wetting
Liquefiable soil Complete strength loss and high deformations
caused by earthquakes
Collapsible soil Potentially large deformations upon wetting
Pyritic soil Potentially large expansion upon oxidation
Laminated rock Low strength when loaded parallel to bedding
Expansive shale Potentially large expansion upon wetting;
degrades readily upon exposure to air and
water
Pyritic shale Expands upon exposure to air and water
Rock
Soluble rock Rock such as limestone, limerock, and gypsum
that is soluble in flowing and standing water
Cretaceous shale Indicator of potentially corrosive groundwater
Weak claystone Low strength and readily degradable upon
exposure to air and water
Gneiss and schist Highly distorted with irregular weathering
profiles and steep discontinuities
Subsidence Typical in areas of underground mining or high
groundwater extraction
Sinkholes Areas underlain by carbonate rock (Karst
topography)
Negative skin friction Additional compressive load on deep
foundations due to settlement of soil
Condition
Expansion loading Additional uplift load on foundation due to
swelling of soil
Corrosive environment Acid mine drainage and degradation of soil and
rock
Frost and permafrost Typical in northern climates
Capillary water Rise in water level which leads to strength loss
for silts and fine sands
Source: ‘‘Standard Specifications for Highway Bridges,’’ 16th ed., American Association of State
Highway and Transporation Officials, Washington, DC.
Table 6.1 presents a list of common soil and rock conditions that require special
consideration by the geotechnical engineer.
6.1.3 Foundation Engineering
A foundation is defined as that part of the structure that supports the weight of
the structure and transmits the load to underlying soil or rock. Foundation engineering
applies the knowledge of soil mechanics, rock mechanics, geology, and
SOIL MECHANICS AND FOUNDATIONS 6.3
structural engineering to the design and construction of foundations for buildings
and other structures. The most basic aspect of foundation engineering deals with
the selection of the type of foundation, such as using a shallow or deep foundation
system. Another important aspect of foundation engineering involves the development
of design parameters, such as the bearing capacity of the foundation. Foundation
engineering could also include the actual foundation design, such as determining
the type and spacing of steel reinforcement in concrete footings. As
indicated in Table 6.2, foundations are commonly divided into two categories: shallow
and deep foundations.
6.2 FIELD EXPLORATION
The purpose of the field exploration is to obtain the following (M. J. Tomlinson,
‘‘Foundation Design and Construction,’’ 5th ed., John Wiley & Sons, Inc., New
York):
1. Knowledge of the general topography of the site as it affects foundation design
and construction, e.g., surface configuration, adjacent property, the presence of
watercourses, ponds, hedges, trees, rock outcrops, etc., and the available access
for construction vehicles and materials.
2. The location of buried utilities such as electric power and telephone cables,
water mains, and sewers.
3. The general geology of the area, with particular reference to the main geologic
formations underlying the site and the possibility of subsidence from mineral
extraction or other causes.
4. The previous history and use of the site, including information on any defects
or failures of existing or former buildings attributable to foundation conditions.
5. Any special features such as the possibility of earthquakes or climate factors
such as flooding, seasonal swelling and shrinkage, permafrost, and soil erosion.
6. The availability and quality of local construction materials such as concrete
aggregates, building and road stone, and water for construction purposes.
7. For maritime or river structures, information on tidal ranges and river levels,
velocity of tidal and river currents, and other hydrographic and meteorological
data.
8. A detailed record of the soil and rock strata and groundwater conditions within
the zones affected by foundation bearing pressures and construction operations,
or of any deeper strata affecting the site conditions in any way.
9. Results of laboratory tests on soil and rock samples appropriate to the particular
foundation design or construction problems.
10. Results of chemical analyses on soil or groundwater to determine possible
deleterious effects of foundation structures.
6.2.1 Document Review
Some of the required information, such as the previous history and use of the site,
can be obtained from a document review. For example, there may be old engi6.4
TABLE 6.2 Common Types of Foundations
Category Common types Comments
Spread footings (also
called pad footings)
Spread footings are often square in plan view, are of uniform reinforced concrete thickness, and
are used to support a single column load located directly in the center of the footing.
Strip footings (also
called wall footings)
Strip or wall footings are often used for load-bearing walls. They are usually long reinforced
concrete members of uniform width and shallow depth.
Combined footings Reinforced concrete combined footings that carry more than one column load are often rectangular
or trapezoidal in plan view.
Shallow foundations Conventional slab-ongrade
A continuous reinforced concrete foundation consisting of bearing wall footings and a slab-ongrade.
Concrete reinforcement often consists of steel re-bar in the footings and wire mesh in the
concrete slab.
Post-tensioned slab-ongrade
A continuous post-tensioned concrete foundation. The post-tensioning effect is created by
tensioning steel tendons or cables embedded within the concrete. Common post-tensioned
foundations are the ribbed foundation, California Slab, and PTI foundation.
Raised wood floor Perimeter footings that support wood beams and a floor system. Interior support is provided by
pad or strip footings. There is a crawl space below the wood floor.
Mat foundation A large and thick reinforced concrete foundation, often of uniform thickness, that is continuous
and supports the entire structure. A mat foundation is considered to be a shallow foundation if it
is constructed at or near ground surface.
6.5
TABLE 6.2 Common Types of Foundations (Continued)
Category Common types Comments
Driven piles Driven piles are slender members, made of wood, steel, or precast concrete, that are driven into
place using pile-driving equipment.
Other types of piles There are many other types of piles, such as bored piles, cast-in-place piles, or composite piles.
Piers Similar to cast-in-place piles, piers are often of large diameter and contain reinforced concrete. Pier
and grade beam support are often used for foundation support on expansive soil.
Caissons Large piers are sometimes referred to as caissons. A caisson can also be a watertight underground
structure within which construction work is carried on.
Deep foundations Mat or raft foundation If a mat or raft foundation is constructed below ground surface or if the mat or raft foundation is
supported by piles or piers, then it should be considered to be a deep foundation system.
Floating foundation A special foundation type where the weight of the structure is balanced by the removal of soil and
construction of an underground basement.
Basement-type
foundation
A common foundation for houses and other buildings in frost-prone areas. The foundation consists
of perimeter footings and basement walls that support a wood floor system. The basement floor
is usually a concrete slab.
Shallow and deep foundations in this table are based on the depth of the soil or rock support of the foundation.
6.6 SECTION SIX
neering reports indicating that the site contains deposits of fill, abandoned septic
systems and leach fields, buried storage tanks, seepage pits, cisterns, mining shafts,
tunnels, or other man-made surface and subsurface works that could impact the
new proposed development. There may also be information concerning on-site utilities
and underground pipelines, which may need to be capped or rerouted around
the project.
During the course of the work, it may be necessary to check reference materials,
such as geologic and topographic maps. Geologic maps can be especially useful
because they often indicate potential geologic hazards (e.g., faults, landslides) as
well as the type of near-surface soil or rock at the site. Both old and recent topographic
maps can also provide valuable site information. Topographic maps are
usually to scale and show the locations of buildings, roads, freeways, train tracks,
and other civil engineering works as well as natural features such as canyons, rivers,
lagoons, sea cliffs, and beaches. The topographic maps can even show the locations
of sewage disposal ponds and water tanks, and by using different colors and shading,
they indicate older versus newer development. But the main purpose of the
topographic map is to indicate ground surface elevations. This information can be
used to determine the major topographic features at the site and for the planning
of subsurface exploration, such as available site access for drilling rigs.
Another important source of information is aerial photographs, which are taken
from an aircraft flying at a prescribed altitude along preestablished lines. Viewing
a pair of aerial photographs, with the aid of a stereoscope, provides a threedimensional
view of the land surface. This view may reveal important geologic
information at the site, such as the presence of landslides, fault scarps, types of
landforms (e.g., dunes, alluvial fans, glacial deposits such as moraines and eskers),
erosional features, general type and approximate thickness of vegetation, and drainage
patterns. By comparing older versus newer aerial photographs, the engineering
geologist can also observe any man-made or natural changes that have occurred at
the site.
6.2.2 Subsurface Exploration
In order for a detailed record of the soil and rock strata and groundwater conditions
at the site to be determined, subsurface exploration is usually required. There are
different types of subsurface exploration, such as borings, test pits, and trenches.
Table 6.3 summarizes the boring, core drilling, sampling, and other exploratory
techniques that can be used by the geotechnical engineer.
A boring is defined as a cylindrical hole drilled into the ground for the purposes
of investigating subsurface conditions, performing field tests, and obtaining soil,
rock, or groundwater specimens for testing. Borings can be excavated by hand (e.g.,
with a hand auger), although the usual procedure is to use mechanical equipment
to excavate the borings.
Many different types of equipment are used to excavate borings. Typical types
of borings are listed in Table 6.3 and include:
Auger Boring. A mechanical auger is a very fast method of excavating a boring.
The hole is excavated by rotating the auger while at the same time applying a
downward pressure on the auger to help obtain penetration of the soil or rock.
There are basically two types of augers: flight augers and bucket augers. Common
available diameters of flight augers are 5 cm to 1.2 m (2 in to 4 ft) and of
bucket augers are 0.3 m to 2.4 m (1 ft to 8 ft). The auger is periodically removed
6.7
TABLE 6.3 Boring, Core Drilling, Sampling, and Other Exploratory Techniques*
Method
(1)
Procedure
(2)
Type of sample
(3)
Applications
(4)
Limitations
(5)
Auger boring, ASTM D
1452
Dry hole drilled with hand
or power auger; samples
preferably recovered from
auger flutes
Auger cuttings, disturbed,
ground up, partially dried
from drill heat in hard
materials
In soil and soft rock; to
identify geologic units and
water content above water
table
Soil and rock stratification
destroyed; sample mixed
with water below the
water table
Test boring, ASTM D 1586 Hole drilled with auger or
rotary drill; at intervals
samples taken 36-mm
(1.4-in) ID and 50-mm (2-
in) OD driven 0.45 m (1.5
ft) in three 150-mm (6-in)
increments by 64-kg (140-
lb) hammer falling 0.76 m
(30 in); hydrostatic
balance of fluid
maintained below water
level
Intact but partially disturbed
(number of hammer blows
for second plus third
increment of driving is
standard penetration
resistance or N)
To identify soil or soft rock;
to determine water
content; in classification
tests and crude shear test
of sample (N-value a
crude index to density of
cohesionless soil and
undrained shear strength
of cohesive soil)
Gaps between samples, 30 to
120 cm (12 to 50 in);
sample too distorted for
accurate shear and
consolidation tests; sample
limited by gravel; N-value
subject to variations,
depending on free fall of
hammer
Test boring of large samples 50- to 75-mm (2- to 3-in) ID
and 63- to 89-mm (2.5- to
3.5-in) OD samplers
driven by hammers up to
160 kg (350 lb)
Intact but partially disturbed
(number of hammer blows
for second plus third
increment of driving is
penetration resistance)
In gravelly soils Sample limited by larger
gravel
Test boring through hollow
stem auger
Hole advanced by hollow
stem auger; soil sampled
below auger as in test
boring above
Intact but partially disturbed
(number of hammer blows
for second plus third
increment of driving is Nvalue)
In gravelly soils (not well
adapted to harder soils or
soft rock)
Sample limited by larger
gravel; maintaining
hydrostatic balance in
hole below water table is
difficult
6.8 TABLE 6.3 Boring, Core Drilling, Sampling, and Other Exploratory Techniques* (
Continued)
Method
(1)
Procedure
(2)
Type of sample
(3)
Applications
(4)
Limitations
(5)
Rotary coring of soil or soft
rock
Outer tube with teeth
rotated; soil protected and
held stationary in inner
tube; cuttings flushed
upward by drill fluid
(examples: Denison,
Pitcher, and Acker
samplers)
Relatively undisturbed
sample, 50 to 200 mm (2
to 8 in) wide and 0.3 to
1.5 m (1 to 5 ft) long in
liner tube
In firm to stiff cohesive soils
and soft but coherent rock
Sample may twist in soft
clays; sampling loose sand
below water table is
difficult; success in gravel
seldom occurs
Rotary coring of swelling
clay, soft rock
Similar to rotary coring of
rock; swelling core
retained by third inner
plastic liner
Soil cylinder 28.5 to 53.2
mm (1.1 to 2.0 in) wide
and 600 to 1500 mm (24
to 60 in) long, encased in
plastic tube
In soils and soft rocks that
swell or disintegrate
rapidly in air (protected
by plastic tube)
Sample smaller; equipment
more complex
Rotary coring of rock,
ASTM D 2113
Outer tube with diamond bit
on lower end rotated to
cut annular hole in rock;
core protected by
stationary inner tube;
cuttings flushed upward
by drill fluid
Rock cylinder 22 to 100 mm
(0.9 to 4 in) wide and as
long as 6 m (20 ft),
depending on rock
soundness
To obtain continuous core in
sound rock (percent of
core recovered depends on
fractures, rock variability,
equipment, and driller
skill)
Core lost in fractured or
variable rock; blockage
prevents drilling in badly
fractured rock; dip of
bedding and joint evident
but not strike
Rotary coring of rock,
oriented core
Similar to rotary coring of
rock above; continuous
grooves scribed on rock
core with compass
direction
Rock cylinder, typically 54
mm (2 in) wide and 1.5 m
(5 ft) long with compass
orientation
To determine strike of joints
and bedding
Method may not be effective
in fractured rock
TABLE 6.3 Boring, Core Drilling, Sampling, and Other Exploratory Techniques* (Continued)
Method
(1)
Procedure
(2)
Type of sample
(3)
Applications
(4)
Limitations
(5)
6.9
Rotary coring of rock, wire
line
Outer tube with diamond bit
on lower end rotated to
cut annular hole in rock;
core protected by
stationary inner tube;
cuttings flushed upward
by drill fluid; core and
stationary inner tube
retrieved from outer core
barrel by lifting device or
‘‘overshot’’ suspended on
thin cable (wire line)
through special largediameter
drill rods and
outer core barrel
Rock cylinder 36.5 to 85
mm (1.4 to 3.3 in) wide
and 1.5 to 4.6 m (5 to 15
ft) long
To recover core better in
fractured rock, which has
less tendency for caving
during core removal; to
obtain much faster cycle
of core recovery and
resumption of drilling in
deep holes
Same as ASTM D 2113 but
to lesser degree
Rotary coring of rock,
integral sampling method
22-mm (0.9-in) hole drilled
for length of proposed
core; steel rod grouted
into hole; core drilled
around grouted rod with
100- to 150-mm (4- to 6-
in) rock coring drill (same
as for ASTM D 2113)
Continuous core reinforced
by grouted steel rod
To obtain continuous core in
badly fractured, soft, or
weathered rock in which
recovery is low by ASTM
D 2113
Grout may not adhere in
some badly weathered
rock; fractures sometimes
cause drift of diamond bit
and cutting rod
Thin-wall tube, ASTM D
1587
75- to 1250-mm (3–50 in)
thin-wall tube forced into
soil with static force (or
driven in soft rock);
retention of sample helped
by drilling mud
Relatively undisturbed
sample, length 10 to 20
diameters
In soft to firm clays, short
(5-diameter) samples of
stiff cohesive soil, soft
rock and, with aid of
drilling mud, in firm to
dense sands
Cutting edge wrinkled by
gravel; samples lost in
loose sand or very soft
clay below water table;
more disturbance occurs if
driven with hammer
6.10
TABLE 6.3 Boring, Core Drilling, Sampling, and Other Exploratory Techniques* (Continued)
Method
(1)
Procedure
(2)
Type of sample
(3)
Applications
(4)
Limitations
(5)
Thin-wall tube, fixed piston 75- to 1250-mm (3- to 50-
in) thin-wall tube, which
has internal piston
controlled by rod and
keeps loose cuttings from
tube, remains stationary
while outer thin-wall tube
forced ahead into soil;
sample in tube is held in
tube by aid of piston
Relatively undisturbed
sample, length 10 to 20
diameters
To minimize disturbance of
very soft clays (drilling
mud aids in holding
samples in loose sand
below water table)
Method is slow and
cumbersome
Swedish foil Samples surrounded by thin
strips of stainless steel,
stored above cutter, to
prevent contact of soil
with tube as it is forced
into soil
Continuous samples 50 mm
(2 in) wide and as long as
12 m (40 ft)
In soft, sensitive clays Samples sometimes damaged
by coarse sand and fine
gravel
Dynamic sounding Enlarged disposable point on
end of rod driven by
weight falling fixed
distance in increments of
100 to 300 mm (4 to 12
in)
None To identify significant
differences in soil strength
or density
Misleading in gravel or
loose saturated fine
cohesionless soils
Static penetration Enlarged cone, 36 mm (1.4
in) diameter and 60
 angle
forced into soil; force
measured at regular
intervals
None To identify significant
differences in soil strength
or density; to identify soil
by resistance of friction
sleeve
Stopped by gravel or hard
seams
6.11
TABLE 6.3 Boring, Core Drilling, Sampling, and Other Exploratory Techniques* (Continued)
Method
(1)
Procedure
(2)
Type of sample
(3)
Applications
(4)
Limitations
(5)
Borehole camera Inside of core hole viewed
by circular photograph or
scan
Visual representation To examine stratification,
fractures, and cavities in
hole walls
Best above water table or
when hole can be
stabilized by clear water
Pits and trenches Pit or trench excavated to
expose soils and rocks
Chunks cut from walls of
trench; size not limited
To determine structure of
complex formations; to
obtain samples of thin
critical seams such as
failure surface
Moving excavation
equipment to site,
stabilizing excavation
walls, and controlling
groundwater may be
difficult
Rotary or cable tool well
drill
Toothed cutter rotated or
chisel bit pounded and
churned
Ground To penetrate boulders, coarse
gravel; to identify
hardness from drilling
rates
Identifying soils or rocks
difficult
Percussion drilling (jack
hammer or air track)
Impact drill used; cuttings
removed by compressed
air
Rock dust To locate rock, soft seams,
or cavities in sound rock
Drill becomes plugged by
wet soil
* Reprinted with permission from ‘‘Landslides: Analysis and Control, Special Report 176,’’ Copyright 1978 by the
National Academy of Sciences. Courtesy of the National Academy Press, Washington, D.C.
Source: G. F. Sowers and D. L. Royster, ‘‘Field Investigation,’’ ch. 4 of ‘‘Landslides: Analysis and Control,
Special Report 176,’’ ed. R. L. Schuster and R. J. Krizek, National Academy of Sciences, Washington, DC.
6.12 SECTION SIX
from the hole, and the soil lodged in the groves of the flight auger or contained
in the bucket of the bucket auger is removed. A casing is generally not used for
auger borings, and the hole may cave-in during the excavation of loose or soft
soils or when the excavation is below the groundwater table. Augers are probably
the most common type of equipment used to excavate borings.
Hollow-Stem Flight Auger. A hollow-stem flight auger has a circular hollow
core which allows for sampling down the center of the auger. The hollow-stem
auger acts like a casing and allows for sampling in loose or soft soils or when
the excavation is below the groundwater table.
Wash-Type Borings. Wash-type borings use circulating drilling fluid, which
removes cuttings from the borehole. The cuttings are created by the chopping,
twisting, and jetting action of the drill bit, which breaks the soil or rock into
small fragments. Casings are often used to prevent cave-in of the hole. Because
drilling fluid is used during the excavation, it can be difficult to classify the soil
and obtain uncontaminated soil samples.
Rotary Coring. This type of boring equipment uses power rotation of the drilling
bit as circulating fluid removes cuttings from the hole. Table 6.3 lists various
types of rotary coring for soil and rock.
Percussion Drilling. This type of drilling equipment is often used to penetrate
hard rock, for subsurface exploration or for the purpose of drilling wells. The
drill bit works much like a jackhammer, rising and falling to break up and crush
the rock material.
In addition to borings, other methods for performing subsurface exploration include
test pits and trenches. Test pits are often square in plan view, with a typical
dimension of 1.2 m by 1.2 m (4 ft by 4 ft). Trenches are long and narrow excavations
usually made by a backhoe or bulldozer. Table 6.4 presents the uses, capabilities,
and limitations of test pits and trenches.
Test pits and trenches provide for a visual observation of subsurface conditions.
They can also be used to obtain undisturbed block samples of soil. The process
consists of carving a block of soil from the side or bottom of the test pit or trench.
Soil samples can also be obtained from the test pits or trenches by manually driving
Shelby tubes, drive cylinders, or other types of sampling tubes into the ground.
(See Art. 6.2.3.)
Backhoe trenches are an economical means of performing subsurface exploration.
The backhoe can quickly excavate the trench, which can then be used to
observe and test the in-situ soil. In many subsurface explorations, backhoe trenches
are used to evaluate near-surface and geologic conditions (i.e., up to 15 ft deep),
with borings being used to investigate deeper subsurface conditions.
6.2.3 Soil Sampling
Many different types of samplers are used to retrieve soil and rock specimens from
the borings. Common examples are indicated in Table 6.3. Figure 6.1 shows three
types of samplers, the ‘‘California Sampler,’’ Shelby tube sampler, and Standard
Penetration Test (SPT) sampler.
The most common type of soil sampler used in the United States is the Shelby
tube, which is a thin-walled sampling tube. It can be manufactured to different
diameters and lengths, with a typical diameter varying from 5 to 7.6 cm (2 to 3 in)
and a length of 0.6 to 0.9 m (2 to 3 ft). The Shelby tube should be manufactured
SOIL MECHANICS AND FOUNDATIONS 6.13
TABLE 6.4 Use, Capabilities, and Limitations of Test Pits and Trenches
Exploration method General use Capabilities Limitations
Hand-excavated test
pits
Bulk sampling, insitu
testing, visual
inspection
Provides data in
inaccessible areas,
less mechanical
disturbance of
surrounding
ground
Expensive, timeconsuming,
limited to depths
above
groundwater level
Backhoe-excavated
test pits and
trenches
Bulk sampling, insitu
testing, visual
inspection,
excavation rates,
depth of bedrock
and groundwater
Fast, economical,
generally less than
4.6 m (15 ft)
deep, can be up to
9 m (30 ft) deep
Equipment access,
generally limited
to depths above
groundwater level,
limited
undisturbed
sampling
Dozer cuts Bedrock
characteristics,
depth of bedrock
and groundwater
level, rippability,
increase depth
capability of
backhoe, level
area for other
exploration
equipment
Relatively low cost,
exposures for
geologic mapping
Exploration limited
to depth above the
groundwater table
Trenches for fault
investigations
Evaluation of
presence and
activity of faulting
and sometimes
landslide features
Definitive location of
faulting,
subsurface
observation up to
9 m (30 ft) deep
Costly, timeconsuming,
requires shoring,
only useful where
dateable materials
are present, depth
limited to zone
above the
groundwater level
Source: NAVFAC DM-7.1, 1982.
to meet exact specifications, such as those stated by ASTM D 1587-94 (1998). The
Shelby tube shown in Fig. 6.1 has an inside diameter of 6.35 cm (2.5 in).
Many localities have developed samplers that have proven successful with local
soil conditions. For example, in southern California, a common type of sampler is
the California Sampler, which is a split-spoon type sampler that contains removable
internal rings, 2.54 cm (1 in) in height. Figure 6.1 shows the California Sampler
in an open condition, with the individual rings exposed. The California Sampler
has a 7.6-cm (3.0 in) outside diameter and a 6.35-cm (2.50-in) inside diameter.
This sturdy sampler, which is considered to be a thick-walled sampler, has proven
successful in sampling hard and desiccated soil and soft sedimentary rock common
in southern California.
Three types of soil samples can be recovered from borings:
6.14 SECTION SIX
FIGURE 6.1 Soil Samplers (no. 1 is the California Sampler in an open condition,
no. 2 is a Shelby Tube, and no. 3 is the Standard Penetration Test sampler.)
1. Altered Soil. During the boring operations, soil can be altered due to mixing
or contamination. For example, if the boring is not cleaned out prior to sampling,
a soil sample taken from the bottom of the borehole may actually consist of cuttings
from the side of the borehole. These borehole cuttings, which have fallen to the
bottom of the borehole, will not represent in-situ conditions at the depth sampled.
In other cases, the soil sample may become contaminated with drilling fluid, which
is used for wash-type borings. These types of soil samples that have been mixed
or contaminated by the drilling process should not be used for laboratory tests
because they will lead to incorrect conclusions regarding subsurface conditions.
Soil that has a change in moisture content due to the drilling fluid or heat generated
during the drilling operations should also be classified as altered soil. Soil that has
been densified by over-pushing or over-driving the soil sampler should also be
considered as altered because the process of over-pushing or over-driving could
squeeze water from the soil.
2. Disturbed Samples. Disturbed soil is defined as soil that has been remolded
during the sampling process. For example, soil obtained from driven samplers, such
as the Standard Penetration Test spilt spoon sampler, or chunks of intact soil brought
to the surface in an auger bucket (i.e., bulk samples), are considered disturbed soil.
Disturbed soil can be used for numerous types of laboratory tests.
SOIL MECHANICS AND FOUNDATIONS 6.15
3. Undisturbed Sample. It should be recognized that no soil sample can be
taken from the ground in a perfectly undisturbed state. However, this terminology
has been applied to those soil samples taken by certain sampling methods. Undisturbed
samples are often defined as those samples obtained by slowly pushing thinwalled
tubes, having sharp cutting ends and tip relief, into the soil. Two parameters,
the inside clearance ratio and the area ratio, are often used to evaluate the disturbance
potential of different samplers, and they are defined as follows:
D 
 D i e inside clearance ratio (%)  100 (6.1)
De
2 2 D 
 D o i area ratio (%)  100 (6.2) 2 Di
where De  diameter at the sampler cutting tip
Di  inside diameter of the sampling tube
Do  outside diameter of the sampling tube
In general, a sampling tube for undisturbed soil specimens should have an inside
clearance ratio of about 1% and an area ratio of about 10% or less. Having an
inside clearance ratio of about 1% provides for tip relief of the soil and reduces
the friction between the soil and inside of the sampling tube during the sampling
process. A thin film of oil can be applied at the cutting edge to also reduce the
friction between the soil and metal tube during sampling operations. The purpose
of having a low area ratio and a sharp cutting end is to slice into the soil with as
little disruption and displacement of the soil as possible. Shelby tubes are manufactured
to meet these specifications and are considered to be undisturbed soil
samplers. As a comparison, the California Sampler has an area ratio of 44% and
is considered to be a thick-walled sampler.
It should be mentioned that using a thin-walled tube, such as a Shelby tube, will
not guarantee an undisturbed soil specimen. Many other factors can cause soil
disturbance, such as:
• Pieces of hard gravel or shell fragments in the soil, which can cause voids to
develop along the sides of the sampling tube during the sampling process
• Soil adjustment caused by stress relief when making a borehole
• Disruption of the soil structure due to hammering or pushing the sampling tube
into the soil stratum
• Expansion of gas during retrieval of the sampling tube
• Jarring or banging the sampling tube during transportation to the laboratory
• Roughly removing the soil from the sampling tube
• Crudely cutting the soil specimen to a specific size for a laboratory test
The actions listed above cause a decrease in effective stress, a reduction in the
interparticle bonds, and a rearrangement of the soil particles. An ‘‘undisturbed’’ soil
specimen will have little rearrangement of the soil particles and perhaps no disturbance
except that caused by stress relief where there is a change from the in-situ
stress condition to an isotropic ‘‘perfect sample’’ stress condition. A disturbed soil
specimen will have a disrupted soil structure with perhaps a total rearrangement of
6.16 SECTION SIX
soil particles. When measuring the shear strength or deformation characteristics of
the soil, the results of laboratory tests run on undisturbed specimens obviously
better represent in-situ properties than laboratory tests run on disturbed specimens.
Soil samples recovered from the borehole should be kept within the sampling
tube or sampling rings. The soil sampling tube should be tightly sealed with end
caps or the sampling rings thoroughly sealed in containers to prevent a loss of
moisture during transportation to the laboratory. The soil samples should be marked
with the file or project number, date of sampling, name of engineer or geologist
who performed the sampling, and boring number and depth.
6.2.4 Field Testing
There are many different types of tests that can be performed at the time of drilling.
The three most common types of field tests are discussed in this section:
Standard Penetration Test (SPT). The Standard Penetration Test (SPT) consists
of driving a thick-walled sampler into a sand deposit. The SPT sampler must have
an inside barrel diameter (Di)  3.81 cm (1.5 in) and an outside diameter (Do) 
5.08 cm (2 in). The SPT sampler is shown in Fig. 6.1. The SPT sampler is driven
into the sand by using a 63.5-kg (140-lb.) hammer falling a distance of 0.76 m (30
in). The SPT sampler is driven a total of 45 cm (18 in), with the number of blows
recorded for each 15 cm (6 in) interval. The ‘‘measured SPT N value’’ (blows per
ft) is defined as the penetration resistance of the sand, which equals the sum of the
number of blows required to drive the SPT sampler over the depth interval of 15
to 45 cm (6 to 18 in). The reason the number of blows required to drive the SPT
sampler for the first 15 cm (6 in) is not included in the N value is that the drilling
process often disturbs the soil at the bottom of the borehole and the readings at 15
to 45 cm (6 to 18 in) are believed to be more representative of the in-situ penetration
resistance of the sand. The data below present a correlation between the measured
SPT N value (blows per ft) and the density condition of a clean sand deposit.
N value (blows per ft) Sand density Relative density
0 to 4 Very loose condition 0 to 15%
4 to 10 Loose condition 15 to 35%
10 to 30 Medium condition 35 to 65%
30 to 50 Dense condition 65 to 85%
Over 50 Very dense condition 85 to 100%
Relative density is defined in Art. 6.3.4. Note that the above correlation is very
approximate and the boundaries between different density conditions are not as
distinct as implied by the table.
The measured SPT N value can be influenced by many testing factors and soil
conditions. For example, gravel-size particles increase the driving resistance (hence
increased N value) by becoming stuck in the SPT sampler tip or barrel. Another
factor that could influence the measured SPT N value is groundwater. It is important
to maintain a level of water in the borehole at or above the in-situ groundwater
level. This is to prevent groundwater from rushing into the bottom of the borehole,
which could loosen the sand and result in low measured N values.
SOIL MECHANICS AND FOUNDATIONS 6.17
Besides gravel and groundwater conditions described above, there are many
different testing factors that can influence the accuracy of the SPT readings. For
example, the measured SPT N value could be influenced by the hammer efficiency,
rate at which the blows are applied, borehole diameter, and rod lengths. The following
equation is used to compensate for these testing factors (A. W. Skempton,
‘‘Standard Penetration Test Procedures,’’ Geotechnique 36):
N  1.67 E C C N (6.3) 60 m b r
where N60  SPT N value corrected for field testing procedures.
Em  hammer efficiency (for U.S. equipment, Em equals 0.6 for a safety
hammer and Em equals 0.45 for a donut hammer)
Cb  borehole diameter correction (Cb  1.0 for boreholes of 65 to 115
mm (2.5 to 4.5 in) diameter, 1.05 for 150-mm diameter (5.9-in), and
1.15 for 200-mm (7.9-in) diameter hole)
Cr  Rod length correction (Cr  0.75 for up to 4 m (13 ft) of drill rods,
0.85 for 4 to 6 m (13 to 20 ft) of drill rods, 0.95 for 6 to 10 m (20
to 33 ft) of drill rods, and 1.00 for drill rods in excess of 10 m (33
ft)
N  measured SPT N value
Even with the limitations and all of the corrections that must be applied to the
measured SPT N value, the Standard Penetration Test is probably the most widely
used field test in the United States. This is because it is relatively easy to use, the
test is economical as compared to other types of field testing, and the SPT equipment
can be quickly adapted and included as part of almost any type of drilling
rig.
Cone Penetration Test (CPT). The idea for the Cone Penetration Test (CPT) is
similar to that for the Standard Penetration Test, except that instead of a thickwalled
sampler being driven into the soil, a steel cone is pushed into the soil. There
are many different types of cone penetration devices, such as the mechanical cone,
mechanical-friction cone, electric cone, and piezocone. The simplest type of cone
is shown in Fig. 6.2. The cone is first pushed into the soil to the desired depth
(initial position) and then a force is applied to the inner rods that moves the cone
downward into the extended position. The force required to move the cone into the
extended position (Fig. 6.2) divided by the horizontally projected area of the cone
is defined as the cone resistance (qc). By continual repetition of the two-step process
shown in Fig. 6.2, the cone resistance data is obtained at increments of depth. A
continuous record of the cone resistance versus depth can be obtained by using the
electric cone, where the cone is pushed into the soil at a rate of 10 to 20 mm/sec
(2 to 4 ft /min). Figure 6.3 presents four simplified examples of cone resistance
(qc) versus depth profiles and the possible interpretation of the soil types and conditions.
A major advantage of the Cone Penetration Test is that by use of the electric
cone, a continuous subsurface record of the cone resistance (qc) can be obtained.
This is in contrast to the Standard Penetration Test, which obtains data at intervals
in the soil deposit. Disadvantages of the Cone Penetration Test are that soil samples
can not be recovered and special equipment is required to produce a steady and
slow penetration of the cone. Unlike the SPT, the ability to obtain a steady and
slow penetration of the cone is not included as part of conventional drilling rigs.
Because of these factors, in the United States the CPT is used less frequently than
the SPT.
6.18 SECTION SIX
FIGURE 6.2 Example of Mechanical Cone Penetrometer Tip (Dutch Mantle
Cone). (Reprinted with permission from the American Society for Testing and Materials,
1998.)
Vane Shear Test (VST). The SPT and CPT are used to correlate the resistance
of driving a sampler (N value) or pushing a cone (qc) with the engineering properties
(such as density condition) of the soil. In contrast, the Vane Test is a different insitu
field test because it directly measures a specific soil property, the undrained
shear strength (su) of clay. Shear strength will be further discussed in Art. 6.3.6.
The Vane Test consists of inserting a four-bladed vane, such as shown in
Fig. 6.4, into the borehole and then pushing the vane into the clay deposit located
at the bottom of the borehole. Once the vane is inserted into the clay, the maximum
torque (Tmax) required to rotate the vane and shear the clay is measured. The undrained
shear strength (su) of the clay can then be calculated by using the following
equation, which assumes uniform end shear for a rectangular vane:
Tmax s  (6.4) u 2 3 (0.5 D H  0.167D )
where Tmax  maximum torque required to rotate the rod which shears the clay
H  height of the vane
D  diameter of the vane
The vane can provide an undrained shear strength (su) that is too high if the vane
is rotated too rapidly. The vane test also gives unreliable results for clay strata that
SOIL MECHANICS AND FOUNDATIONS 6.19
FIGURE 6.3 Simplified examples of CPT cone resistance qc versus depth showing
possible interpretations of soil types and conditions. (From J. H. Schmertmann,
‘‘Guidelines for Cone Penetration Test.’’ U.S. Department of Transportation, Washington,
DC.)
contains sand layers or lenses, varved clay, or if the clay contains gravel or gravelsize
shell fragments.
6.2.5 Exploratory Logs
A log is defined as a written record, prepared during the subsurface excavation of
borings, test pits, or trenches, that documents the observed conditions. Although
logs are often prepared by technicians or even the driller, the most appropriate
individuals to log the subsurface conditions are geotechnical engineers or engineering
geologists who have considerable experience and judgment acquired by
many years of field practice. It is especially important that the subsurface conditions
likely to have the most impact on the proposed project be adequately described.
Figure 6.5 presents an example of a boring log.
6.20 SECTION SIX
FIGURE 6.4 Diagram illustrating the Field Vane Test. (From NAVFAC
DM-7.1, 1982.)
SOIL MECHANICS AND FOUNDATIONS 6.21
FIGURE 6.5 Example of a Boring log. (Reproduced from NAVFAC DM-7.1, 1982.)
6.2.6 Subsoil Profile
The final part of Art. 6.2 presents an example of a subsoil profile. As shown in
Figure 6.6, the subsoil profile summarizes the results of the subsurface exploration.
The results of field and laboratory tests are often included on the subsoil profile.
The development of a subsoil profile is often a required element for geotechnical
and foundation engineering analyses. For example, subsoil profiles are used to deFIGURE
6.6 Subsoil profile. (From J. Lowe and P. F. Zaccheo, ‘‘Subsurface Explorations and Sampling,’’
ch. 1 of ‘‘Foundation Engineering Handbook,’’ ed. H. F. Winterkorn and H.-Y. Fang, Van Nostrand Reinhold
Co., New York.)
SOIL MECHANICS AND FOUNDATIONS 6.23
termine the foundation type (shallow versus deep foundation), calculate the amount
of settlement of the structure, evaluate the effect of groundwater on the project and
develop recommendations for dewatering of underground structures, perform slope
stability analyses for projects having sloping topography, and prepare site development
recommendations.
6.3 LABORATORY TESTING
6.3.1 Introduction
In addition to document review and subsurface exploration, an important part of
the site investigation is laboratory testing. The laboratory testing usually begins
once the subsurface exploration is complete. The first step in the laboratory testing
is to log in all of the materials (soil, rock, or groundwater) recovered from the
subsurface exploration. Then the geotechnical engineer and engineering geologist
prepare a laboratory testing program, which basically consists of assigning specific
laboratory tests for the soil specimens. The actual laboratory testing of the soil
specimens is often performed by experienced technicians, who are under the supervision
of the geotechnical engineer. Because the soil samples can dry out or
changes in the soil structure could occur with time, it is important to perform the
laboratory tests as soon as possible.
Usually at the time of the laboratory testing, the geotechnical engineer and engineering
geologist will have located the critical soil layers or subsurface conditions
that will have the most impact on the design and construction of the project. The
laboratory testing program should be oriented towards the testing of those critical
soil layers or subsurface conditions. For many geotechnical projects, it is also important
to determine the amount of ground surface movement due to construction
of the project. In these cases, laboratory testing should model future expected conditions
so that the amount of movement or stability of the ground can be analyzed.
Laboratory tests should be performed in accordance with standard procedures,
such as those recommended by the American Society for Testing and Materials
(ASTM) or those procedures listed in standard textbooks or specification manuals.
For laboratory tests, it has been stated (M. J. Tomlinson, ‘‘Foundation Design
and Construction,’’ 5th ed., John Wiley & Sons, Inc., New York):
It is important to keep in mind that natural soil deposits are variable in composition
and state of consolidation; therefore it is necessary to use considerable judgment based
on common sense and practical experience in assessing test results and knowing where
reliance can be placed on the data and when they should be discarded. It is dangerous
to put blind faith in laboratory tests, especially when they are few in number. The test
data should be studied in conjunction with the borehole records and the site observations,
and any estimations of bearing pressures or other engineering design data obtained
from them should be checked as far as possible with known conditions and past
experience. Laboratory tests should be as simple as possible. Tests using elaborate
equipment are time-consuming and therefore costly, and are liable to serious error
unless carefully and conscientiously carried out by highly experienced technicians. Such
methods may be quite unjustified if the samples are few in number, or if the cost is
high in relation to the cost of the project. Elaborate and costly tests are justified only
if the increased accuracy of the data will give worthwhile savings in design or will
eliminate the risk of a costly failure.
6.24 SECTION SIX
FIGURE 6.7 Soil element and the soil element separated into phases.
6.3.2 Soil Element
In order to analyze the results of laboratory tests, the concept of the soil element
must be introduced. Figure 6.7 shows an element of soil that can be divided into
three basic parts:
1. Solids—the mineral soil particles
2. Liquids—usually water that is contained in the void spaces between the solid
mineral particles
3. Gas—such as air that is also contained in the void spaces between the solid
mineral particles
As indicated on the right side of Fig. 6.7, the three basic parts of soil can be
rearranged into their relative proportions based on volume and mass. Note that the
symbols as defined in Fig. 6.7 will be used throughout this section.
6.3.3 Index Tests
Index tests are the most basic types of laboratory tests performed on soil samples.
Index tests include the water content (also known as moisture content), specific
gravity tests, unit weight determinations, and particle size distributions and Atterberg
limits, which are used to classify the soil.
Water Content (w). The water content (also known as moisture content) test is
probably the most common and simplest type of laboratory test. This test can be
performed on disturbed or undisturbed soil specimens. The water content test consists
of determining the mass of the wet soil specimen and then drying the soil in
an oven overnight (12 to 16 hr) at a temperature of 110
C (ASTM D 2216-92,
1998). The water content (w) of a soil is defined as the mass of water in the soil
(Mw) divided by the dry mass of the soil (Ms), expressed as a percentage (i.e.,
w  100 Mw/Ms).
SOIL MECHANICS AND FOUNDATIONS 6.25
TABLE 6.5 Formula and Specific Gravity of Common Soil Minerals
Type of mineral Formula
Specific
gravity Comments
Quartz SiO2 2.65 Silicate, most common type of soil
mineral
K Feldspar
Na or Ca Feldspar
KAlSi3O8
NaAlSi3O8
2.54–2.57
2.62–2.76
Feldspars are also silicates and are
the second most common type of
soil mineral.
Calcite CaCO3 2.71 Basic constituent of carbonate rocks
Dolomite CaMg(CO3)2 2.85 Basic constituent of carbonate rocks
Muscovite varies 2.76–3.0 Silicate sheet type mineral (mica
group)
Biotite complex 2.8–3.2 Silicate sheet type mineral (mica
group)
Hematite Fe2O3 5.2–5.3 Frequent cause of reddish-brown
color in soil
Gypsum CaSO42H2O 2.35 Can lead to sulfate attack of concrete
Serpentine Mg3Si2O5(OH)4 2.5–2.6 Silicate sheet or fibrous type mineral
Kaolinite Al2Si2O5(OH)4 2.61–2.66 Silicate clay mineral, low activity
Illite complex 2.60–2.86 Silicate clay mineral, intermediate
activity
Montmorillonite complex 2.74–2.78 Silicate clay mineral, highest activity
NOTE: Silicates are very common and account for about 80% of the minerals at the Earth’s surface.
Values of water content (w) can vary from essentially 0% up to 1200%. A water
content of 0% indicates a dry soil. An example of a dry soil would be near-surface
rubble, gravel, or clean sand located in a hot and dry climate, such as Death Valley,
California. Soil having the highest water content is organic soil, such as fibrous
peat, which has been reported to have a water content as high as 1200%.
Specific Gravity of Soil Solids (G). The specific gravity (G) is a dimensionless
parameter that is defined as the density of solids ( s) divided by the density of
water ( w), or G  s / w. The density of solids ( s) is defined as the mass of solids
(Ms) divided by the volume of solids (Vs). The density of water ( w) is equal to
1 g/cm3 (or 1 Mg/m3) and 62.4 pcf.
For soil, the specific gravity is obtained by measuring the dry mass of the soil
and then using a pycnometer to obtain the volume of the soil. Table 6.5 presents
typical values and ranges of specific gravity versus different types of soil minerals.
Because quartz is the most abundant type of soil mineral, the specific gravity for
inorganic soil is often assumed to be 2.65. For clays, the specific gravity is often
assumed to be 2.70 because common clay particles, such as montmorillonite and
illite, have slightly higher specific gravity values.
Total Unit Weight ( 
t ). The total unit weight (also known as the wet unit weight)
should only be obtained from undisturbed soil specimens, such as those extruded
from Shelby tubes or on undisturbed block samples obtained from test pits and
trenches. The first step in the laboratory testing is to determine the wet density,
defined as t  M/V, where M  total mass of the soil, which is the sum of the
mass of water (Mw) and mass of solids (Ms), and V  total volume of the soil
6.26 SECTION SIX
TABLE 6.6 Unit Weight Relationships*
Parameter Relationships
Total unit weight ( t)
W W G (1  w) s w w   t V 1  e
Dry unit weight ( d )
W G  s w t    d V 1  e 1  w
Saturated unit weight ( sat)
W  V  (G  e)  G (1  w) s vw w w     sat V 1  e 1  G w
Note: The total unit weight ( t) is equal to the saturated unit
weight ( sat) when all the void spaces are filled with
water (i.e., S  100%).
Buoyant unit weight ( b)
   
  b sat w
 (G 
 1)  (G 
 1) w w   b 1  e 1  G w
Note: The buoyant unit weight is also known as the
submerged unit weight.
* See Fig. 6.7 for definition of terms.
Notes:
1. For the equations listed in this table, water content (w) and degree of saturation (S ) must be
expressed as a decimal (not as a percentage).
2. w  density of water (1.0 Mg/m3, 62.4 pcf) and w  unit weight of water (9.81 kN/m3, 62.4 pcf).
sample as defined in Fig. 6.7. The volume (V) is determined by trimming the soil
specimen to a specific size or extruding the soil specimen directly from the sampler
into confining rings of known volume, and then the total mass (M) of the soil
specimen is obtained by using a balance.
The next step is to convert the wet density ( t) to total unit weight ( t). In order
to convert wet density to total unit weight in the International System of Units (SI),
the wet density is multiplied by g (where g  acceleration of gravity  9.81 m/
sec2) to obtain the total unit weight, which has units of kN/m3. For example, in
the International System of Units, the density of water ( w)  1.0 g/cm3 or 1.0
Mg/m3, while the unit weight of water ( w)  9.81 kN/m3.
In the United States Customary System, density and unit weight have exactly
the same value. Thus, the density of water and the unit weight of water are 62.4
pcf. However, for the density of water ( w), the units should be thought of as lbmass
(lbm) per cubic ft, while for unit weight ( w), the units are lb-force (lbf) per
cubic foot. In the United States Customary System, it is common to assume that
1 lbm  1 lbf.
Typical values for total unit weight (t) are 110 to 130 pcf (17 to 20 kN/m3).
Besides the total unit weight, other types of unit weight are used in geotechnical
engineering. For example, the dry unit weight ( d ) refers to only the dry soil per
volume, while the saturated unit weight ( sat) refers to a special case where all the
soil voids are filled with water (i.e., saturated soil). Another commonly used unit
weight is the buoyant unit weight ( b) which is used for calculations involving soil
located below the groundwater table. Table 6.6 presents various equations used to
SOIL MECHANICS AND FOUNDATIONS 6.27
calculate the different types of unit weights. Note in Table 6.6 that w  water
content and G  specific gravity of soil solids. The void ratio (e) and degree of
saturation (S) are discussed in the next article.
6.3.4 Phase Relationships
Phase relationships are the basic soil relationships used in geotechnical engineering.
They are also known as weight-volume relationships. Different types of phase relationships
are discussed below:
Void Ratio (e) and Porosity (n). The void ratio (e) is defined as the volume of
voids (Vv) divided by the volume of solids (Vs). The porosity (n) is defined as
volume of voids (Vv) divided by the total volume (V). As indicated in Fig. 6.7, the
volume of voids is defined as the sum of the volume of air and volume of water
in the soil.
The void ratio (e) and porosity (n) are related as follows:
n e
e  and n  (6.5)
1 
 n 1  e
The void ratio and porosity indicate the relative amount of void space in a soil.
The lower the void ratio and porosity, the denser the soil (and vice versa). The
natural soil having the lowest void ratio is probably till. For example, a typical
value of dry density for till is 2.34 Mg/m3 (146 pcf), which corresponds to a void
ratio of 0.14. A typical till consists of a well-graded soil ranging in particle sizes
from clay to gravel and boulders. The high density and low void ratio are due to
the extremely high stress exerted by glaciers. For compacted soil, the soil type with
typically the lowest void ratio is a well-graded decomposed granite (DG). A typical
value of maximum dry density (Modified Proctor) for a well-graded DG is 2.20
Mg/m3 (137 pcf), which corresponds to a void ratio of 0.21. In general, the factors
needed for a very low void ratio for compacted and naturally deposited soil are as
follows:
1. A well-graded grain-size distribution
2. A high ratio of D100 /D0 (ratio of the largest and smallest grain sizes)
3. Clay particles (having low activity) to fill in the smallest void spaces
4. A process, such as compaction or the weight of glaciers, to compress the soil
particles into dense arrangements
At the other extreme are clays, such as sodium montmorillonite, which at low
confining pressures can have a void ratio of more than 25. Highly organic soil,
such as peat, can have even higher void ratios.
Degree of Saturation (S). The degree of saturation (S) is defined as:
100 Vw S(%)  (6.6)
Vv
The degree of saturation indicates the degree to which the soil voids are filled
6.28 SECTION SIX
with water. A totally dry soil will have a degree of saturation of 0%, while a
saturated soil, such as a soil below the groundwater table, will have a degree of
saturation of 100%. Typical ranges of degree of saturation versus soil condition are
as follows:
Dry: S  0%
Humid: S  1 to 25%
Damp: S  26 to 50%
Moist: S  51 to 75%
Wet: S  76 to 99%
Saturated: S  100%
Relative Density. The relative density is a measure of the density state of a nonplastic
soil. The relative density can only be used for soil that is nonplastic, such
as sands and gravels. The relative density (Dr in %) is defined as:
e 
 e max D (%)  100 (6.7) r e 
 e max min
where emax  void ratio corresponding to the loosest possible state of the soil, usually
obtained by pouring the soil into a mold of known volume
emin  void ratio corresponding to the densest possible state of the soil,
usually obtained by vibrating the soil particles into a dense state
e  the natural void ratio of the soil
The density state of the natural soil can be described as follows:
Very loose condition Dr  0 to 15%
Loose condition Dr  15 to 35%
Medium condition Dr  35 to 65%
Dense condition Dr  65 to 85%
Very dense condition Dr  85 to 100%
The relative density (Dr) should not be confused with the relative compaction
(RC), which will be discussed in Art. 6.10.1.
Useful Relationships. A frequently used method of solving phase relationships is
first to fill in the phase diagram shown in Fig. 6.7. Once the different mass and
volumes are known, the various phase relationships can be determined. Another
approach is to use equations that relate different parameters. A useful relationship
is as follows:
Gw  Se (6.8)
where G  specific gravity of soil solids
w  water content
S  degree of saturation
e  void ratio
Other commonly used relationships are presented in Table 6.7.
SOIL MECHANICS AND FOUNDATIONS 6.29
TABLE 6.7 Mass and Volume Relationships*
Parameter Relationships
Mass
M MGw Mass of solids (M )   GV (1 
 n) s w 1 w eS
eM S s Mass of water (M ) wM  S V w s w v G
Total mass (M)  M  M  M (1  w) s w s
Volume
M V V s v Volume of solids (V )   V(1 
 n)  V 
 (V  V ) s gw G  1 e e w
M SVe w Volume of water (V )  SV e  S V  V 
 V w s v v g  1  e w
(1 
 S)Ve
Volume of gas (V ) (1 
 S)V e  V 
 (V  V )  V 
 V g s s w v w 1  e
V n M Ve s s Volume of voids (V ) V
  V e  V 
 V v s s 1 
n G 1  e w
V V(1  e) s v Total volume (V)   V (1  e)  V  V  V s s g w 1 
n e
*See Fig. 6.7 for definition of terms.
6.3.5 Soil Classification
The purpose of soil classification is to provide the geotechnical engineer with a
way to predict the behavior of the soil for engineering projects. There are many
different soil classification systems in use, and only three of the most commonly
used systems will be discussed in this section.
Unified Soil Classification System (USCS). As indicated in Table 6.8, this classification
system separates soils into two main groups: coarse-grained soils (more
than 50% by weight of soil particles retained on No. 200 sieve) and fine-grained
soils (50% or more by weight of soil particles pass the No. 200 sieve).
The coarse-grained soils are divided into gravels and sands. Both gravels and
sands are further subdivided into four secondary groups as indicated in Table 6.8.
The four secondary classifications are based on whether the soil is well graded,
poorly graded, contains silt-sized particles, or contains clay-sized particles. These
data are obtained from a particle size distribution, also known as a ‘‘grain size
curve,’’ which is obtained from laboratory testing (sieve and hydrometer tests).
Figure 6.8 presents examples of grain size curves.
The Atterberg limits are used to classify fine-grained soil, and they are defined
as follows:
Liquid Limit (LL). The water content corresponding to the behavior change
between the liquid and plastic state of a silt or clay. The liquid limit is deter6.30
TABLE 6.8 Unified Soil Classification System (USCS)
Major divisions Subdivisions
USCS
symbol Typical names Laboratory classification criteria
Coarse-grained
soils
(More than 50%
retained on No.
200 sieve)
Gravels
(More than 50%
of coarse
fraction
retained on
No. 4 sieve)
Sands
(50% or more of
coarse
fraction
passes No. 4
sieve)
GW
GP
GM
GC
SW
SP
SM
SC
Well-graded gravels or gravelsand
mixtures, little or no
fines
Poorly graded gravels or
gravelly sands, little or no
fines
Silty gravels, gravel-sand-silt
mixtures
Clayey gravels, gravel-sandclay
mixtures
Well-graded sands or gravelly
sands, little or no fines
Poorly graded sands or
gravelly sands, little or no
fines
Silty sands, sand-silt mixtures
Clayey sands, sand-clay
mixtures
Less than 5% finesa
Less than 5% finesa
More than 12% finesa
More than 12% finesa
Less than 5% finesa
Less than 5% finesa
More than 12% finesa
More than 12% finesa
Cu  4 and 1  Cc  3
Does not meet Cu and/or Cc
criteria listed above
Minus No. 40 soil plots below
the A-line
Minus No. 40 soil plot on or
above the A-line
Cu  6 and 1  Cc  3
Does not meet Cu and/or Cc
criteria listed above
Minus No. 40 soil plots below
the A-line
Minus No. 40 soil plots on or
above the A-line
6.31
TABLE 6.8 Unified Soil Classification System (USCS) (Continued)
Major divisions Subdivisions
USCS
symbol Typical names Laboratory classification criteria
Fine-grained soils
(50% or more
passes the No.
200 sieve)
Silts and clays
(liquid limit less
than 50)
Silts and clays
(liquid limit 50
or more)
ML
CL
OL
MH
CH
OH
Inorganic silts, rock flour,
silts of low plasticity
Inorganic clays of low
plasticity, gravelly clays,
sandy clays, etc.
Organic silts and organic
clays of low plasticity
Inorganic silts, micaceous
silts, silts of high plasticity
Inorganic highly plastic clays,
fat clays, silty clays, etc.
Organic silts and organic
clays of high plasticity
Inorganic soil
Inorganic soil
Organic soil
Inorganic soil
Inorganic soil
Organic soil
PI  4 or plots below A-line
PI  7 and plots on or above
A-lineb
LL (oven dried) /LL (not
dried)  0.75
Plots below A-line
Plots on or above A-line
LL (oven dried) /LL (not
dried)  0.75
Peat Highly organic PT Peat and other highly organic
soils
Primarily organic matter, dark in color, and organic odor
a ‘‘Fines’’ are those soil particles that pass the No. 200 sieve. For gravels with between 5% to 12% fines, use of
dual symbols required (i.e., GW-GM, GW-GC, GP-GM, or GP-GC). For sands with between 5% to 12% fines, use of
dual symbols required (i.e., SW-SM, SW-SC, SP-SM, or SP-SC).
b If 4  PI  7 and plots above A-line, then dual symbol (i.e., CL-ML) is required.
cCu  D60/D10 and Cc  (D30)2 / [(D10)(D60)] where D60  soil particle diameter corresponding to 60% finer by
weight (from grain size curve).
6.32
FIGURE 6.8 Examples of grain size curves and Atterberg limit test data for different soils. Note that w1 
liquid limit and wp  plastic limit. (Reproduced from M. P. Rollings and R. S. Rollings, ‘‘Geotechnical Materials
in Construction,’’ McGraw-Hill Publishing Co., New York, with permission of McGraw-Hill, Inc.)
SOIL MECHANICS AND FOUNDATIONS 6.33
FIGURE 6.9 Plasticity chart.
mined in the laboratory by using a liquid limit device. The liquid limit is defined
as the water content at which a pat of soil, cut by a groove of standard dimensions,
will flow together for a distance of 12.7 mm (0.5 in) under the impact of
25 blows in a standard liquid limit device.
Plastic Limit (PL). The water content corresponding to the behavior change
between the plastic and semisolid state of a silt or clay. The plastic limit is also
determined in the laboratory and is defined as the water content at which a silt
or clay will just begin to crumble when rolled into a tread approximately 3.2
mm (0.125 in) in diameter.
The plasticity index (PI) is defined as the liquid limit minus the plastic limit
(i.e., PI  LL 
 PL). With both the liquid limit and plasticity index of the finegrain
soil known, the plasticity chart (Fig. 6.9) is then used to classify the soil.
There are three basic dividing lines on the plasticity chart, the LL  50 line, the
A-line, and the U-line. The LL  50 line separates soils into high and low plasticity,
the A-line separates clays from silts, and the U-line represents the upper-limit line
(i.e., uppermost boundary of test data).
As indicated in Table 6.8, symbols (known as ‘‘group symbols’’) are used to
identify different soil types. The group symbols consist of two capital letters. The
first letter indicates the following: G for gravel, S for sand, M for silt, C for clay,
and O for organic. The second letter indicates the following: W for well graded,
which indicates that a coarse-grained soil has particles of all sizes; P for poorly
graded, which indicates that a coarse-grained soil has particles of the same size, or
the soil is skip-graded or gap-graded; M for a coarse-grained soil that has silt-sized
particles; C for a coarse-grained soil that has clay-sized particles; L for a finegrained
soil of low plasticity; and H for a fine-grained soil of high plasticity. An
exception is peat, where the group symbol is PT. Also note in Table 6.8 that certain
soils require the use of dual symbols.
AASHTO Soil Classification System. This classification system was developed
by the American Association of State Highway and Transportation Officials (see
Table 6.9). Inorganic soils are divided into 7 groups (A-1 through A-7), with the
6.34
TABLE 6.9 AASHTO Soil Classification System
Major Divisions Group
AASHTO
symbol Typical names
Sieve analysis
(percent passing) Atterberg limits
Granual
materials
(35% or less
passing No.
200 sieve)
Group A-1
Group A-3
Group A-2
A-1-a
A-1-b
A-3
A-2-4
A-2-5
A-2-6
A-2-7
Stone or gravel fragments
Gravel and sand mixtures
Fine sand that is nonplastic
Silty gravel and sand
Silty gravel and sand
Clayey gravel and sand
Clayey gravel and sand
Percent Passing: No. 10  50%
No. 40  30% No. 200  15%
No. 40  50% No. 200  25%
No. 40  50% No. 200  10%
Percent passing No. 200 sieve  35%
Percent passing No. 200 sieve  35%
Percent passing No. 200 sieve  35%
Percent passing No. 200 sieve  35%
PI  6
PI  6
PI  0 (nonplastic)
LL  40 PI  10
LL  40 PI  10
LL  40 PI  10
LL  40 PI  10
Silt-clay
materials
(More than 35%
passing No.
200 sieve)
Group A-4
Group A-5
Group A-6
Group A-7
A-4
A-5
A-6
A-7-5
A-7-6
Silty soils
Silty soils
Clayey soils
Clayey soils
Clayey soils
Percent passing No. 200 sieve  35%
Percent passing No. 200 sieve  35%
Percent passing No. 200 sieve  35%
Percent passing No. 200 sieve  35%
Percent passing No. 200 sieve  35%
LL  40 PI  10
LL  40 PI  10
LL  40 PI  10
LL  40 PI  LL 
 30
PI  10
LL  40 PI  LL 
 30
PI  10
Highly organic Group A-8 A-8 Peat and other highly
organic soils
Primarily organic matter, dark in color, and organic odor
6.35
Notes:
1. Classification Procedure: First decide which of the three main categories (granular materials, silt-clay materials,
or highly organic) the soil belongs. Then proceed from the top to the bottom of the chart and the first group that
meets the particle size and Atterberg limits criteria is the correct classification.
2. Group Index  (F 
 35)[0.2  0.005(LL 
 40)]  0.01(F 
 15)(PI 
 10), where F  percent passing No.
200 sieve, LL  liquid limit, and PI  plasticity index. Report group index to nearest whole number. For negative
group index, report as zero. When working with A-2-6 and A-2-7 subgroups, use only the PI portion of the
group index equation.
3. Atterberg limits are performed on soil passing the No. 40 sieve. LL  liquid limit, PL  plastic limit, and
PI  plasticity index.
4. AASHTO definitions of particle sizes are as follows: (a) boulders: above 75 mm, (b) gravel: 75 mm to No. 10
sieve, (c) coarse sand: No. 10 to No. 40 sieve, (d) fine sand: No. 40 to No. 200 sieve, and (e) silt-clay size
particles: material passing No. 200 sieve.
5. Example: An example of an AASHTO classification for a clay is A-7-6 (30), or Group A-7, subgroup 6, group
index 30.
6.36 SECTION SIX
eighth group (A-8) reserved for highly organic soils. Soil types A-1, A-2, and
A-7 have subgroups as indicated in Table 6.9. Those soils having plastic fines can
be further categorized by using the group index (defined in Table 6.9). Groups
A-1-a, A-1-b, A-3, A-2-4, and A-2-5 should be considered to have a group index
equal to zero. According to AASHTO, the road supporting characteristics of a
subgrade may be assumed as an inverse ratio to its group index. Thus, a road
subgrade having a group index of 0 indicates a ‘‘good’’ subgrade material that will
often provide good drainage and adequate bearing when thoroughly compacted. A
road subgrade material that has a group index of 20 or greater indicates a ‘‘very
poor’’ subgrade material that will often be impervious and have a low bearing
capacity.
Organic Soil Classification System. Table 6.10 presents a classification system
for organic materials. As indicated in Table 6.10, there are four major divisions, as
follows:
1. Organic Matter. These materials consist almost entirely of organic material.
Examples include fibrous peat and fine-grained peat.
2. Highly Organic Soils. These soils are composed of 30 to 75% organic matter
mixed with mineral soil particles. Examples include silty peat and sandy peat.
3. Organic Soils. These soils are composed of from 5 to 30% organic material.
These soils are typically classified as organic soils of high plasticity (OH, i.e.
LL  50) or low plasticity (OL, i.e., LL  50) and have a ratio of liquid limit
(oven-dried soil) divided by liquid limit (not dried soil) that is less than 0.75
(see Table 6.8).
4. Slightly Organic Soils. These soils typically have less than 5% organic matter.
Per the Unified Soil Classification System, they have a ratio of liquid limit (ovendried
soil) divided by liquid limit (not dried soil) that is greater than 0.75. Often
a modifier, such as ‘‘slightly organic soil,’’ is used to indicate the presence of
organic matter.
Also included in Table 6.10 is the typical range of laboratory test results for the
four major divisions of organic material. Note in Table 6.10 that the water content
(w) increases and the total unit weight ( t) decreases as the organic content increases.
The specific gravity (G) includes the organic matter, hence the low values
for highly organic material. The compression index (Cc) is discussed in Art. 6.5.6.
Other Descriptive Terminology. In addition to the classification of a soil, other
items should also be included in the field or laboratory description of a soil, such
as:
1. Soil Color. Usually the standard primary color (red, orange, yellow, etc.) of the
soil is listed.
2. Soil Texture. The texture of a soil refers to the degree of fineness of the soil.
For example, terms such as smooth, gritty, or sharp can be used to describe
the texture of the soil when it is rubbed between the fingers.
3. Clay Consistency. For clays, the consistency (i.e., degree of firmness) should
be listed. The consistency of a clay varies from ‘‘very soft’’ to ‘‘hard’’ based on
the undrained shear strength of the clay (su). The undrained shear strength can
be determined from the Unconfined Compression Test or from field or laboratory
vane tests. The consistency versus undrained shear strength (su) is as follows:
6.37
TABLE 6.10 Soil Classification for Organic Soil
Major
divisions
Organic
content
USCS
symbol Typical names
Distinguishing characteristics for
visual identification Typical range of laboratory test results
Organic matter
75 to 100%
Organics
(Either
visible or
inferred)
PT
PT
Fibrous peat
(woody,
mats, etc.)
Fine-grained
peat
(amorphous)
Light weight and spongy.
Shrinks considerably on air
drying. Much water squeezes
from sample.
Light weight and spongy.
Shrinks considerably on air
drying. Much water squeezes
from sample.
w  500 to 1200%
t  9.4 to 11 kN/m3 (60 to 70 pcf)
G  1.2 to 1.8
Cc / (1  eo)  0.40
w  400 to 800% PI  200 to 500
t  9.4 to 11 kN/m3 (60 to 70 pcf)
G  1.2 to 1.8
Cc / (1  eo)  0.35
Highly organic
soils
30 to 75%
Organics
(Either
visible or
inferred)
PT
PT
Silty peat
Sandy peat
Relatively light weight, spongy.
Shrinks on air drying.
Usually can readily squeeze
water from sample.
Sand fraction visible. Shrinks
on air drying. Often a
‘‘gritty’’ texture. Usually can
squeeze water from sample.
w  250 to 500% PI  150 to 350
t  10 to 14 kN/m3 (65 to 90 pcf)
G  1.8 to 2.3
Cc / (1  eo)  0.3 to 0.4
w  100 to 400% PI  50 to 150
t  11 to 16 kN/m3 (70 to 100 pcf)
G  1.8 to 2.4
Cc / (1  eo)  0.2 to 0.3
Organic soils
5 to 30%
organics
(Either
visible or
inferred)
OH
OL
Clayey organic
Silt
Organic sand
or Silt
Often has strong hydrogen
sulfide (H2S) odor. Medium
dry strength and slow
dilatency.
Threads weak and friable near
plastic limit, or will not roll
at all. Low dry strength,
medium to high dilatency.
w  65 to 200% PI  50 to 150
t  11 to 16 kN/m3 (70 to 100 pcf)
G  2.3 to 2.6
Cc / (1  eo)  0.2 to 0.35
w  30 to 125% PI  NP to 40
t  14 to 17 kN/m3 (90 to 110 pcf)
G  2.4 to 2.6
Cc / (1  eo)  0.1 to 0.25
Slightly
organic soils
Less than
5%
organics
Use Table
6.8
Soil with
slight
organic
fraction
Depends on the characteristics
of the inorganic fraction.
Depends on the characteristics of the
inorganic fraction.
Source: NAVFAC DM-7.1, 1982, based on unpublished work by Ayers and Plum.
Notes: w  in-situ water content, PI  plasticity index, NP  nonplastic,
t  total unit weight, G  specific
gravity (soil minerals plus organic matter), Cc  compression index, eo  initial void ratio, and Cc / (1  eo)  modified
compression index.
6.38 SECTION SIX
Soil consistency Undrained shear strength (kPa) Undrained shear strength (psf)
Very soft su  12 su  250
Soft 12  su  25 250  su  500
Medium 25  su  50 500  su  1000
Stiff 50  su  100 1000  su  2000
Very stiff 100  su  200 2000  su  4000
Hard su  200 su  4000
4. Sand Density Condition. For sands, the density state of the soil varies from
‘‘very loose’’ to ‘‘very dense.’’ The determination of the density condition is
based on the relative density (Dr in %).
5. Soil Moisture Condition. The moisture condition of the soil should also be
listed. Based on the degree of saturation, the moisture conditions can vary from
a ‘‘dry’’ soil (S  0%) to a ‘‘saturated’’ soil (S  100%).
6. Additional Descriptive Items. The soil classification systems are usually only
applicable for soil and rock particles passing the 75-mm (3-in) sieve. Cobbles
and boulders are larger than the 75 mm (3 in), and if applicable, the words
‘‘with cobbles’’ or ‘‘with boulders’’ should be added to the soil classification.
Typically, cobbles refer to particles ranging from 75 mm (3 in) to 200 mm (8
in) and boulders refer to any particle over 200 mm (8 in).
Other descriptive terminology includes the presence of rock fragments, such as
‘‘crushed shale, claystone, sandstone, siltstone, or mudstone fragments,’’ and unusual
constituents such as ‘‘shells, slag, glass fragments, and construction debris.’’
Soil classification examples are shown on the boring log in Fig. 6.5. Common
types of soil deposits are listed in Table 6.11.
6.3.6 Shear Strength Tests
The shear strength of a soil is a basic geotechnical engineering parameter and is
required for the analysis of foundations, earthwork, and slope stability problems.
This is because of the nature of soil, which is composed of individual soil particles
that slide (i.e., shear past each other) when the soil is loaded.
The shear strength of the soil can be determined in the field (e.g., vane shear
test) or in the laboratory. Laboratory shear strength tests can generally be divided
into two categories:
1. Shear Strength Tests Based on Total Stress. The purpose of these laboratory
tests is to obtain the undrained shear strength (su) of the soil or the failure
envelope in terms of total stresses (total cohesion, c, and total friction angle, 	).
These types of shear strength tests are often referred to as ‘‘undrained’’ shear
strength tests.
2. Shear Strength Tests Based on Effective Stress. The purpose of these laboratory
tests is to obtain the effective shear strength of the soil based on the
failure envelope in terms of effective stress (effective cohesion, c, and effective
friction angle, 	). These types of shear strength tests are often referred to as
‘‘drained’’ shear strength tests. The shear strength of the soil can be defined as
(Mohr-Coulomb failure law):
SOIL MECHANICS AND FOUNDATIONS 6.39
TABLE 6.11 Common Man-made and Geologic Soil Deposits
Main
category Common types of soil deposits Possible engineering problems
Structural fill Dense or hard fill. Often the individual
fill lifts can be identified
Upper surface of structural fill may
have become loose or weathered
Uncompacted
fill
Random soil deposit that can contain
chunks of different types and sizes
of rock fragments
Susceptible to compression and
collapse
Debris fill Contains pieces of debris, such as
concrete, brick, and wood fragments
Susceptible to compression and
collapse
Municipal
dump
Contains debris and waste products
such as household garbage or yard
trimmings
Significant compression and gas
from organic decomposition
Residual soil
deposit
Soil deposits formed by in-place
weathering of rock
Engineering properties are highly
variable
Organic
deposit
Examples include peat and muck
which forms in bogs, marshes, and
swamps
Very compressible and unsuitable
for foundation support
Alluvial
deposit
Soil transported and deposited by
flowing water, such as streams and
rivers
All types of grain sizes, loose
sandy deposits susceptible to
liquefaction
Aeolian
deposit
Soil transported and deposited by
wind. Examples include loess and
dune sands
Can have unstable soil structure
that may be susceptible to
collapse
Glacial
deposit
Soil transported and deposited by
glaciers or their melt water.
Examples include till.
Erratic till deposits and soft clay
deposited by glacial melt water
Lacustrine
deposit
Soil deposited in lakes or other inland
bodies of water
Unusual soil deposits can form,
such as varved silts or varved
clays
Marine
deposit
Soil deposited in the ocean, often
from rivers that empty into the
ocean
Granular shore deposits but
offshore areas can contain soft
clay deposits
Colluvial
deposit
Soil transported and deposited by
gravity, such as talus, hill-wash, or
landslide deposits
Can be geologically unstable
deposit
Pyroclastic
deposit
Material ejected from volcanoes.
Examples include ash, lapilli, and
bombs
Weathering can result in plastic
clay. Ash can be susceptible to
erosion.
NOTE: The first four soil deposits are man-made, all others are due to geologic processes.
	  c   tan 	 (6.9) ? n
where 	  ? shear strength of the soil
c  effective cohesion
  n effective normal stress on the shear surface
	  effective friction angle
The mechanisms that control the shear strength of soil are complex, but in simple
6.40 SECTION SIX
FIGURE 6.10 Direct shear apparatus.
terms the shear strength of soils can be divided into two broad categories: granular
(nonplastic) soils and cohesive (plastic) soils.
Granular Soil. These types of soil are nonplastic and include gravels, sands, and
nonplastic silt such as rock flour. A granular soil develops its shear strength as a
result of the frictional and interlocking resistance between the individual soil particles.
Granular soils, also known as cohesionless soils, can only be held together
by confining pressures and will fall apart when the confining pressure is released
(i.e., c  0). The drained shear strength (effective stress analysis) is of most
importance for granular soils. The shear strength of granular soils is often measured
in the direct shear apparatus, where a soil specimen is subjected to a constant
vertical pressure ( ) while a horizontal force is applied to the top of the shear box n
so that the soil specimen is sheared in half along a horizontal shear surface (see
Fig. 6.10). By plotting the vertical pressure ( ) versus shear stress at failure ( 	? ), n
the effective friction angle (	) can be obtained. Because the test specifications
typically require the direct shear testing of soil in a saturated and drained state, the
shear strength of the soil is expressed in terms of the effective friction angle (	).
Granular soils can also be tested in a dry state, and the shear strength of the soil
is then expressed in terms of the friction angle (	). In a comparison of the effective
friction angle (	) from drained direct shear tests on saturated cohesionless soil
and the friction angle (	) from direct shear tests on the same soil in a dry state, it
has been determined that 	 is only 1 to 2
 lower than 	. This slight difference is
usually ignored and the friction angle (	) and effective friction angle (	) are
typically considered to mean the same thing for granular (nonplastic) soils.
Table 6.12 presents values of effective friction angles for different types of granular
(nonplastic) soils. An exception to the values presented in Table 6.12 are granular
soils that contain appreciable mica flakes. A micaceous sand will often have
a high void ratio and hence little interlocking and a lower friction angle. In summary,
for granular soils, c  0 and the effective friction angle (	) depends on:
1. Soil Type (Table 6.12). Sand and gravel mixtures have a higher effective friction
angle than nonplastic silts.
2. Soil Density. For a given granular soil, the denser the soil, the higher the effective
friction angle. This is due to the interlocking of soil particles, where at a
SOIL MECHANICS AND FOUNDATIONS 6.41
TABLE 6.12 Typical Effective Friction Angles (	) for Different
Cohesionless Soils*
Soil types
Effective friction angles (	) at peak
strength
Loose Medium Dense
Silt (nonplastic) 26 to 30
 28 to 32
 30 to 34

Uniform fine to
medium sand
26 to 30
 30 to 34
 32 to 36

Well-graded sand 30 to 34
 34 to 40
 38 to 46

Sand and gravel
mixtures
32 to 36
 36 to 42
 40 to 48

* Data from B. K. Hough, ‘‘Basic Soils Engineering,’’ 2d ed., John Wiley
& Sons, Inc., New York.
denser state the soil particles are interlocked to a higher degree and hence the
effective friction angle is greater than in a loose state. It has been observed that
in the ultimate shear strength state, the shear strength and density of a loose and
dense sand tend to approach each other.
3. Grain Size Distribution. A well-graded granular soil will usually have a higher
friction angle than a uniform soil. With more soil particles to fill in the small
spaces between soil particles, there is more interlocking and frictional resistance
developed for a well-graded than a uniform granular soil.
4. Mineral Type, Angularity, and Particle Size. Soil particles composed of quartz
tend to have a higher friction angle than soil particles composed of weak carbonate.
Angular soil particles tend to have rougher surfaces and better interlocking
ability. Larger-sized particles, such as gravel-sized particles, typically
have higher friction angles than sand.
5. Deposit Variability. Because of variations in soil types, gradations, particle arrangements,
and dry density values, the effective friction angle is rarely uniform
with depth. It takes considerable judgment and experience in selecting an effective
friction angle based on an analysis of laboratory data.
6. Indirect Methods. For many projects, the effective friction angle of the sand is
determined by indirect means, such as the Standard Penetration Test and the
Cone Penetration Test.
Cohesive Soil. The shear strength of cohesive (plastic) soil, such as silts and clays,
is much more complicated than the shear strength of granular soils. Also, in general
the shear strength of cohesive (plastic) soils tends to be lower than the shear strength
of granular soils. As a result, more shear-induced failures occur in cohesive soils,
such as clays, than in granular (nonplastic) soils.
Depending on the type of loading condition, either a total stress analysis or an
effective stress analysis could be performed for cohesive soil. In general, total stress
analysis (su or c and 	) are used for short-term conditions, such as at the end of
construction. The total stress parameters, such as the undrained shear strength (su),
can be determined from an unconfined compression test or vane tests.
Figure 6.11 presents an example of the undrained shear strength (su) versus
depth for Borings E1 and F1 excavated in an offshore deposit of Orinoco clay
(created by sediments from the Orinoco River, Venezuela). The Orinoco clay can
be generally classified as a clay of high plasticity (CH) and can be considered to
6.42
FIGURE 6.11 Undrained shear strength versus depth for Orinoco clay at Borings E1 and F1.
SOIL MECHANICS AND FOUNDATIONS 6.43
be a relatively uniform soil deposit. The undrained shear strength was obtained
from the Torvane device, laboratory vane, and unconfined compression test (UUC).
Note in Fig. 6.11 that there is a distinct discontinuity in the undrained shear strength
(su) at a depth of 60 ft for Boring E1 and 40 ft for Boring F1. This discontinuity
was due to different sampling procedures. Above a depth of 60 ft at Boring E1 and
40 ft at Boring F1, samplers were hammered into the clay deposit, causing sample
disturbance and a lower shear strength value for the upper zone of clay. For the
deeper zone of clay, a ‘‘WIP’’ sampling procedure was utilized, which produced
less sample disturbance and hence a higher undrained shear strength.
Effective stress analyses (c and 	) are used for long-term conditions, where
the soil and groundwater conditions are relatively constant. Effective shear strength
parameters are often obtained from laboratory triaxial tests, where a saturated soil
specimen is sheared by applying a load to the top of the specimen (see Fig. 6.12).
During shearing, the pore water pressures (u) are measured in order to calculate
the effective friction angle of the soil. Typical values of the effective friction angle
(	) for natural clays range from around 20
 for normally consolidated highly plastic
clays up to 30
 or more for other types of plastic (cohesive) soil. The value of
	 for compacted clay is typically in the range of 25
 to 30
 and occasionally as
high as 35
. In terms of effective cohesion for plastic soil, the value of c for
normally consolidated noncemented clays is very small and can be assumed to be
zero for practical work. These effective friction angles (	) for cohesive soil are
less than the values for granular soil (Table 6.12), and this is the reason there are
more shear failures in cohesive than in granular soil.
6.4 EFFECTIVE STRESS AND STRESS
DISTRIBUTION
It is important to recognize that without adequate and meaningful data from the
field exploration (Art. 6.2) and laboratory testing (Art. 6.3), the engineering analysis
presented in the rest of this chapter will be of doubtful value and may even lead
to erroneous conclusions. The purpose of the engineering analysis is often to develop
site development and foundation design parameters required for the project.
6.4.1 Effective Stress, Total Stress, and Pore Water Pressure
The soil has been described in terms of a written description (soil classification)
and mathematical description (phase relationships). The next step in the analysis is
often to determine the stresses acting on the soil. This is important because most
geotechnical projects deal with a change in stress of the soil. For example, the
construction of a building applies an additional stress onto the soil supporting the
foundation, which results in settlement of the building.
Stress is defined as the load divided by the area over which it acts. In geotechnical
engineering, a compressive stress is considered positive and tensile stress is
negative. Stress and pressure are often used interchangeably in geotechnical engineering.
In the International System of Units (SI), the units for stress are kPa. In
the United States Customary System, the units for stress are psf (lb-force per square
ft). Stress expressed in units of kg/cm2 have been used in the past and are still in
use (e.g., see Fig. 6.11). One kg/cm2 is approximately equal to 100 kPa and one
ton per square ft (tsf).
6.44 SECTION SIX
FIGURE 6.12 Triaxial apparatus.
Effective Stress. An important concept in geotechnical engineering is effective
stress. The effective stress ( ) is defined as follows:
  
 u (6.10)
where  total stress
u  pore water pressure
Many engineering analyses use the vertical effective stress, also known as the effective
overburden stress, which is designated or .   v vo
Total Stress. For the condition of a uniform soil and a level ground surface (geostatic
condition), the total vertical stress ( v) at a depth (z) below the ground surface
is:
  z (6.11) v t
where t  total unit weight of the soil (Table 6.6). For soil deposits having layers
with different total unit weights, the total vertical stress is the sum of the vertical
stress for each individual soil layer.
Pore Water Pressure (u) and Calculation of Vertical Effective Stress ( ). For v
the condition of a hydrostatic groundwater table (i.e., no groundwater flow or excess
pore water pressures), the static pore water pressure (u or us) is:
u   z (6.12) w w
SOIL MECHANICS AND FOUNDATIONS 6.45
where w  unit weight of water
zw  depth below the groundwater table
If the total unit weight of the soil (Eq. 6.11), and the pore water pressure (Eq.
6.12) are known, then the vertical effective stress ( ) can be calculated. An alter- v
native method is to use the buoyant unit weight ( b , see Table 6.6) to calculate the
vertical effective stress. For example, suppose that a groundwater table corresponds
with the ground surface. In this case, the vertical effective stress ( ) is simply the v
buoyant unit weight ( b) times the depth below the ground surface. More often, the
groundwater table is below the ground surface, in which case the vertical total stress
of the soil layer above the groundwater table must be added to the buoyant unit
weight calculations.
6.4.2 Stress Distribution
The previous section described methods used to determine the existing stresses
within the soil mass. This section describes commonly used methods to determine
the increase in stress in the soil deposit due to applied loads. This is naturally
important in settlement analysis because the settlement of the structure is due directly
to its weight, which causes an increase in stress in the underlying soil. In
most cases, it is the increase in vertical stress that is of most importance in settlement
analyses. The symbol z is often used to denote an increase in vertical stress
in the soil, although 
v (change in total vertical stress) is also used.
When dealing with stress distribution, a distinction must be made between onedimensional
and two- or three-dimensional loading. A one-dimensional loading
applies a stress increase at depth that is 100% of the applied surface stress. An
example of a one-dimensional loading would be the placement of a fill layer of
uniform thickness and large areal extent at ground surface. Beneath the center of
the uniform fill, the in-situ soil is subjected to an increase in vertical stress that
equals the following:
  
  h  (6.13) z v t
where h  thickness of the fill layer
t  total unit weight of the fill
In this case of one-dimensional loading, the soil would only be compressed in the
vertical direction (i.e., strain only in the vertical direction).
Another example of one-dimensional loading is the uniform lowering of a
groundwater table. If the total unit weight of the soil does not change as the groundwater
table is lowered, then the one-dimensional increase in vertical stress for the
in-situ soil located below the groundwater table would equal the following:
  
  h  (6.14) z v w
where h  vertical distance that the groundwater table is uniformly lowered
w  unit weight of water
Surface loadings can cause both vertical and horizontal strains, and this is referred
to as two- or three-dimensional loading. Common examples of twodimensional
loading are from strip footings or long embankments (i.e., plane strain
conditions). Examples of three-dimensional loading would be square and rectan6.46
SECTION SIX
FIGURE 6.13 2:1 approximation for the calculation of the increase in vertical
stress at depth due to an applied load (P).
gular footings (spread footings) and round storage tanks. The following two sections
describe methods that can be used to determine the change in vertical stress for
two-dimensional (strip footings and long embankments) and three-dimensional
(spread footings and round storage tanks) loading conditions. In these cases, the
load usually dissipates rapidly with depth. The following methods will yield different
answers for a given set of conditions. The reader is cautioned to follow any
limitations mentioned.
2:1 Approximation. A simple method to determine the increase in vertical stress
with depth is the 2:1 approximation (also known as the 2:1 method). Figure 6.13
illustrates the basic principle of the 2:1 approximation. This method assumes that
the stress dissipates with depth in the form of a trapezoid that has 2:1 (vertical:
horizontal) inclined sides as shown in Fig. 6.13. The purpose of this method is to
approximate the actual ‘‘pressure bulb’’ stress increase beneath a footing.
If there is a strip footing of width B that has a vertical load (P) per unit length
of footing, then, as indicated in Fig. 6.13, the stress applied by the footing ( o)
would be o  P/B where B  width of the strip footing. As indicated in Fig.
6.13, at a depth z below the footing, the vertical stress increase ( z) due to the strip
footing load would be:
P
  
  (6.15) z v B  z
If the footing is a rectangular spread footing having a length  L and a width
 B, then the stress applied by the rectangular footing ( o) would be o  P/ (BL)
where P  entire load of the rectangular spread footing. Based on the 2:1 approximation,
the vertical stress increase ( z) at a depth  z below the rectangular spread
footing would be:
SOIL MECHANICS AND FOUNDATIONS 6.47
P
  
  (6.16) z v (B  z)(L  z)
A major advantage of the 2:1 approximation is its simplicity, and for this reason
it is probably used more often than any other type of stress distribution method.
The main disadvantage with the 2:1 approximation is that the stress increase under
the center of the loaded area equals the stress increase under the corner or side of
the loaded area. The actual situation is that the soil underlying the center of the
loaded area is subjected to a higher vertical stress increase than the soil underneath
a corner or edge of the loaded area. Thus, the 2:1 approximation is often only used
to estimate the average settlement of the loaded area. Different methods, such as
stress distribution based on the theory of elasticity, can be used to calculate the
change in vertical stress between the center and corner of the loaded area.
Equations and Charts Based on the Theory of Elasticity. Equations and charts
have been developed to determine the change in stress due to applied loads based
on the theory of elasticity. The solutions assume an elastic and homogeneous soil
that is continuous and in static equilibrium. The elastic solutions also use a specific
type of applied load, such as a point load, uniform load, or linearly increasing load
(triangular distribution). For loads where the length of the footing is greater than 5
times the width, such as for strip footings, the stress distribution is considered to
be plane strain. This means that the horizontal strain of the elastic soil occurs only
in the direction perpendicular to the long axis of the footing.
Although equations and charts based on the theory of elasticity are often used
to determine the change in soil stress, soil is not an elastic material. For example,
if a heavy foundation load is applied to a soil deposit, there will be vertical deformation
of the soil in response to this load. If this heavy load is removed, the soil
will rebound but not return to its original height because soil is not elastic. However,
it has been stated that as long as the factor of safety against shear failure exceeds
about 3, then stresses imposed by the foundation load are roughly equal to the
values computed from elastic theory.
In 1885, Boussinesq published equations based on the theory of elasticity. For
a surface point load (Q) applied at the ground surface such as shown in Figure
6.14, the vertical stress increase at any depth (z) and distance (r) from the point
load can be calculated by using the following Boussinesq (1885) equation:
3 3Qz
  
  (6.17) z v 2 25/2 2(r  z )
If there is a uniform line load Q (force per unit length), the vertical stress
increase at a depth z and distance r from the line load would be:
3 2Qz
  
  (6.18) z v 2 22 (r  z )
In 1935, Newmark performed an integration of Eq. (6.18) and derived an equation
to determine the vertical stress increase ( z) under the corner of a loaded area.
Convenient charts have been developed based on the Newmark (1935) equation.
For example, Figure 6.15 shows the ‘‘pressure bulbs’’ (also known as isobars) beneath
a square footing and a strip footing. To determine the change in vertical stress
(i.e., z or 
v) at any point below the footing, multiply the value from Figure 6.15
times qo, where qo  uniform applied footing pressure.
6.48 SECTION SIX
FIGURE 6.14 Definition of terms for Eqs. (6.17) and
(6.18).
Figure 6.16 can be easily used to determine the pressure at the edge of a footing
or can be used to determine the pressure under the center of the footing as described
below. The values of m and n must be calculated. The value m is defined as the
width of the loaded area (x) divided by the depth to where the vertical stress increase
( z) is to be calculated. The value n is defined as the length of the loaded
area (y) divided by the depth (z). The chart is entered with the value of n and upon
intersecting the desired m curve, the influence value (I) is then obtained from the
vertical axis. As indicated in Fig. 6.16, vertical stress increase ( z) is then calculated
as the loaded area pressure (qo) times the influence value (I). Figure 6.16 can also
be used to determine the vertical stress increase ( z) below the center of a rectangular
loaded area. In this case, the rectangular loaded area would be divided into
four parts and then Fig. 6.16 would be used to find the stress increase below the
corner of one of the parts. By multiplying this stress by 4 (i.e., 4 parts), the vertical
stress increase ( z) below the center of the total loaded area is obtained. This type
of analysis is possible because of the principle of superposition for elastic materials.
To find the vertical stress increase ( z) outside the loaded area, additional rectangular
areas can be added and subtracted as needed in order to model the loading
condition.
Figure 6.17 presents a chart for determining the change in vertical stress beneath
a uniformly loaded circular area. Figure 6.18 shows a Newmark (1942) chart, which
can be used to determine the vertical stress increase ( z) beneath a uniformly loaded
area of any shape. There are numerous influence charts, each having a different
influence value. Note that the chart in Fig. 6.18 has an influence value (I) of 0.005.
The first step is to draw the loaded area onto the chart, using a scale where AB
SOIL MECHANICS AND FOUNDATIONS 6.49
FIGURE 6.15 Pressure bulb beneath square footing and strip footing. The
curves indicate the values of 
 /qo beneath the footings, where qo  uniform v
footing pressure (Note: applicable only along the line ab from center to edge of
base). (From J. E. Bowles, ‘‘Foundation Analysis and Design,’’ 3d ed., McGraw-
Hill Publishing Co., New York. Reproduced with permission of McGraw-Hill,
Inc.)
equals the depth z. The center of the chart must correspond to the point where the
increase in vertical stress ( z) is desired. The increase in vertical stress ( z) is then
calculated as: z  qoIN where qo  applied stress from the irregular area, I 
influence value (0.005 for Fig. 6.18), and N  number of blocks within the irregular
shaped area plotted on Fig. 6.18. When the value of N is being obtained, portions
of blocks are also counted. Note that the entire procedure must be repeated if the
increase in vertical stress ( z) is needed at a different depth.
6.50 SECTION SIX
FIGURE 6.16 Chart for calculating the increase in vertical stress beneath the
corner of a uniformly loaded rectangular area. (From NAVFAC DM-7.1, 1982,
Reproduced from R. D. Holtz and W. D. Kovacs, ‘‘An Introduction to Geotechnical
Engineering,’’ Prentice-Hall, Inc., Englewood Cliffs, NJ.)
6.5 SETTLEMENT ANALYSES
Settlement can be defined as the permanent downward displacement of the foundation.
There are two basic types of settlement, as follows:
6.5.1 Settlement Due Directly to the Weight of the Structure
The first type of settlement is directly caused by the weight of the structure. For
example, the weight of a building may cause compression of an underlying sand
deposit (Art. 6.5.7) or consolidation of an underlying clay layer (Art. 6.5.6). Often
the settlement analysis is based on the actual dead load of the structure. The dead
load is defined as the structural weight due to beams, columns, floors, roofs, and
SOIL MECHANICS AND FOUNDATIONS 6.51
FIGURE 6.17 Chart for calculating the increase in vertical stress beneath a
uniformly loaded circular area. (From NAVFAC DM-7.1, 1982, Reproduced from
R. D. Holtz and W. D. Kovacs, ‘‘An Introduction to Geotechnical Engineering,’’
Prentice-Hall, Inc., Englewood Cliffs, NJ.)
other fixed members. The dead load does not include nonstructural items. Live
loads are defined as the weight of nonstructural members, such as furniture, occupants,
inventory, and snow. Live loads can also result in settlement of the structure.
For example, if the proposed structure is a library, then the actual weight of
the books (a live load) should be included in the settlement analyses. Likewise, for
a proposed warehouse, it may be appropriate to include the actual weight of anticipated
stored items in the settlement analyses. In other projects where the live loads
represent a significant part of the loading, such as large electrical transmission
towers that will be subjected to wind loads, the live load (wind) may also be
included in the settlement analysis. Considerable experience and judgment are required
to determine the load that is to be used in the settlement analyses.
6.5.2 Settlement Due to Secondary Influences
The second basic type of settlement of a building is caused by secondary influence,
which may develop at a time long after the completion of the structure. This type
of settlement is not directly caused by the weight of the structure. For example, the
foundation may settle as water infiltrates the ground and causes unstable soils to
collapse (i.e., collapsible soil, Art. 6.5.5). The foundation may also settle due to
yielding of adjacent excavations or the collapse of limestone cavities or underground
mines and tunnels. Other causes of settlement that would be included in
this category are natural disasters, such as settlement caused by earthquakes or
undermining of the foundation from floods.
Subsidence is usually defined as a sinking down of a large area of the ground
surface. Subsidence could be caused by the extraction of oil or groundwater that
6.52 SECTION SIX
FIGURE 6.18 Newmark chart for calculating the increase in vertical stress beneath
a uniformly loaded area of any shape. (From N. M. Newmark, ‘‘Influence Charts for
Computation of Stresses in Elastic Foundations,’’ Univ. Illinois Expt. Sta. Bull. 338.
Reproduced from J. E. Bowles, ‘‘Foundation Analysis and Design,’’ 3d ed., McGraw-
Hill Publishing Co., New York.)
SOIL MECHANICS AND FOUNDATIONS 6.53
FIGURE 6.19 Diagram illustrating the definitions of maximum total settlement
( max), maximum differential settlement (
), and maximum angular
distortion ( /L).
leads to a compression of the underlying porous soil or rock structure. Since subsidence
is due to a secondary influence (extraction of oil or groundwater), its effect
on the structure would be included in the second basic type of settlement.
6.5.3 Foundation Design Parameters
Determining the settlement of the structure is one of the primary obligations of the
geotechnical engineer. In general, three parameters are required: maximum total
settlement ( max), maximum differential settlement (
), and rate of settlement. Another
parameter that may be useful in the design of the foundation is the maximum
angular distortion ( /L), defined as the differential settlement between two points
divided by the distance between them. Figure 6.19 illustrates the maximum total
settlement ( max), maximum differential settlement (
), and maximum angular distortion
( /L) of a foundation. Note in Fig. 6.19 that the maximum angular distortion
( /L) does not necessarily occur at the location of maximum differential settlement
(
).
6.5.4 Allowable Settlement
The allowable settlement is defined as the acceptable amount of settlement of the
structure and it usually includes a factor of safety. The allowable settlement depends
on many factors, including the following (D. P. Coduto, ‘‘Foundation Design, Principles
and Practices,’’ Prentice-Hall, Inc., Englewood Cliffs, N.J.):
The Type of Construction. For example, wood-frame buildings with wood siding
would be much more tolerant than unreinforced brick buildings.
6.54 SECTION SIX
TABLE 6.13 Allowable Settlement
Type of movement Limiting factor Maximum settlement
Total settlement
Drainage
Access
Probability of nonuniform settlement:
Masonry walled structure
Framed structures
Smokestacks, silos, mats
15–30 cm (6–12 in)
30–60 cm (12–24 in)
2.5–5 cm (1–2 in)
5–10 cm (2–4 in)
8–30 cm (3–12 in)
Tilting
Stability against overturning
Tilting of smokestacks, towers
Rolling of trucks, etc.
Stacking of goods
Machine operation—cotton loom
Machine operation—turbogenerator
Crane rails
Drainage of floors
Depends on H and W
0.004 L
0.01 L
0.01 L
0.003 L
0.0002 L
0.003 L
0.01–0.02 L
Differential movement
High continuous brick walls
One-story brick mill building, wall cracking
Plaster cracking (gypsum)
Reinforced concrete building frame
Reinforced concrete building curtain walls
Steel frame, continuous
Simple steel frame
0.0005–0.001 L
0.001–0.002 L
0.001 L
0.0025–0.004 L
0.003 L
0.002 L
0.005 L
L  distance between adjacent columns that settle different amounts, or between any two points that
settle differently. Higher values are for regular settlements and more tolerant structures. Lower values are
for irregular settlement and critical structures. H  height and W  width of structure.
Source: G. F. Sowers, ‘‘Shallow Foundations,’’ ch. 6 of ‘‘Foundation Engineerings,’’ ed. G. A. Leonards,
McGraw-Hill Publishing Co., New York.
The Use of the Structure. Even small cracks in a house might be considered
unacceptable, whereas much larger cracks in an industrial building might not
even be noticed.
The Presence of Sensitive Finishes. Tile or other sensitive finishes are much
less tolerant of movements.
The Rigidity of the Structure. If a footing beneath part of a very rigid structure
settles more than the others, the structure will transfer some of the load away
from the footing. However, footings beneath flexible structures must settle much
more before any significant load transfer occurs. Therefore, a rigid structure will
have less differential settlement than a flexible one.
Aesthetic and Serviceability Requirements. The allowable settlement for most
structures, especially buildings, will be governed by aesthetic and serviceability
requirements, not structural requirements. Unsightly cracks, jamming doors and
windows, and other similar problems will develop long before the integrity of
the structure is in danger.
Another example of allowable settlements for buildings is Table 6.13, where the
allowable foundation displacement has been divided into three categories: total settlement,
tilting, and differential movement. Table 6.13 indicates that those structures
that are more flexible (such as simple steel frame buildings) or have more rigid
SOIL MECHANICS AND FOUNDATIONS 6.55
FIGURE 6.20 Laboratory collapse test results for a silty sand. The soil was loaded
in the oedometer to a pressure of 144 kPa and then inundated with distilled water.
foundations (such as mat foundations) can sustain larger values of total settlement
and differential movement.
6.5.5 Collapsible Soil
Collapsible soil can be defined as soil that is susceptible to a large and sudden
reduction in volume upon wetting. Collapsible soil usually has a low dry density
and low moisture content. Such soil can withstand a large applied vertical stress
with a small compression, but then experience much larger settlements after wetting,
with no increase in vertical pressure. Collapsible soil falls within the second basic
category of settlement, which is settlement of the structure due to secondary influences.
In the southwestern United States, collapsible soil is probably the most common
cause of settlement. The category of collapsible soil would include the settlement
of debris, uncontrolled fill, deep fill, or natural soil, such as alluvium or colluvium.
In general, there has been an increase in damage due to collapsible soil, probably
because of the lack of available land in many urban areas. This causes development
of marginal land, which may contain deposits of dumped fill or deposits of natural
collapsible soil. Also, substantial grading can be required to develop level building
pads, which results in more areas having deep fill.
The oedometer (also known as a consolidometer) is the primary laboratory
equipment used to study the settlement behavior of soil. The oedometer test should
only be performed on undisturbed soil specimens, or in the case of studies of fill
behavior, on specimens compacted to anticipated field and moisture conditions.
Figures 6.20 and 6.21 present the results of a collapse test performed on a soil
6.56 SECTION SIX
FIGURE 6.21 Laboratory collapse test results for a silty sand. This plot shows
the vertical deformation versus time after the soil specimen was inundated with
distilled water.
specimen by using the laboratory oedometer equipment. The soil specimen was
loaded in the oedometer to a vertical pressure of 144 kPa (3000 psf) and then
inundated with distilled water. Figure 6.20 shows the load-settlement behavior of
the soil specimen, and Fig. 6.21 shows the amount of vertical deformation (collapse)
as a function of time after inundation. The percent collapse is defined as the change
in height of the soil specimen after inundation divided by the initial height of the
soil specimen.
There are many different methods for dealing with collapsible soil. If there is a
shallow deposit of natural collapsible soil, the deposit can be removed and recompacted
during the grading of the site. In some cases, the soil can be densified (such
as by compaction grouting) to reduce the collapse potential of the soil. Another
method for dealing with collapsible soil is to flood the building footprint or force
water into the collapsible soil stratum by using wells. As the wetting front moves
through the ground, the collapsible soil will densify and reach an equilibrium state.
Flooding or forcing water into collapsible soil should not be performed if there are
adjacent buildings, due to the possibility of damaging these structures. Also, after
the completion of the flooding process, subsurface exploration and laboratory testing
should be performed to evaluate the effectiveness of the process.
There are also foundation options that can be used for sites containing collapsible
soil. A deep foundation system, which derives support from strata below the
collapsible soil, could be constructed. Also, post-tensioned foundations or mat slabs
can be designed and installed to resist the larger anticipated settlement from the
collapsible soil.
SOIL MECHANICS AND FOUNDATIONS 6.57
6.5.6 Settlement of Cohesive and Organic Soils
Cohesive and organic soil can be susceptible to a large amount of settlement from
structural loads. It is usually the direct weight of the structure that causes settlement
of the cohesive or organic soil. The settlement of saturated clay or organic soil can
have three different components: immediate (also known as ‘‘initial settlement’’),
primary consolidation, and secondary compression.
Immediate Settlement. In most situations, surface loading causes both vertical and
horizontal strains. This is referred to as two- or three-dimensional loading. Immediate
settlement is due to undrained shear deformations, or in some cases contained
plastic flow, caused by the two- or three-dimensional loading. Common examples
of three-dimensional loading are from square footings and round storage tanks.
Many different methods are available to determine the amount of immediate settlement
for two- or three-dimensional loadings. Examples include field plate load tests,
equations based on the theory of elasticity, and the stress path method (see R. W.
Day, ‘‘Geotechnical and Foundation Engineering: Design and Construction,’’ Mc-
Graw-Hill Publishing Co., New York).
Primary Consolidation. The increase in vertical pressure due to the weight of the
structure constructed on top of saturated soft clays and organic soil will initially be
carried by the pore water in the soil. This increase in pore water pressure is known
as an excess pore water pressure (ue). The excess pore water pressure will decrease
with time as water slowly flows out of the cohesive soil. This flow of water from
cohesive soil (which has a low permeability) as the excess pore water pressures
slowly dissipate is known as primary consolidation, or simply consolidation. As
the water slowly flows from the cohesive soil, the structure settles as the load is
transferred to the soil particle skeleton, thereby increasing the effective stress of
the soil. Consolidation is a time-dependent process that may take many years to
complete.
Based on the stress history of saturated cohesive soils, they are considered to
be either underconsolidated, normally consolidated, or overconsolidated. The overconsolidation
ratio (OCR) is used to describe the stress history of cohesive soil,
and it is defined as: OCR  / , where: or  maximum past pressure     vm vo vm p
( ), also known as the preconsolidation pressure ( ), which is equal to the   vm p
highest previous vertical effective stress that the cohesive soil was subjected to and
consolidated under, and or  existing vertical effective stress. In terms of   vo v
the stress history of a cohesive soil, there are three possible conditions:
1. Underconsolidated (OCR  1). A saturated cohesive soil is considered underconsolidated
if the soil is not fully consolidated under the existing overburden
pressure and excess pore water pressures (ue) exist within the soil. Underconsolidation
occurs in areas where a cohesive soil is being deposited very rapidly
and not enough time has elapsed for the soil to consolidate under its own weight.
2. Normally Consolidated (OCR  1). A saturated cohesive soil is considered
normally consolidated if it has never been subjected to an effective stress greater
than the existing overburden pressure and if the deposit is completely consolidated
under the existing overburden pressure.
3. Overconsolidated or Preconsolidated (OCR  1): A saturated cohesive soil is
considered overconsolidated if it has been subjected in the past to a vertical
6.58 SECTION SIX
FIGURE 6.22 Example of a consolidation curve. The Casagrande construction
technique for determining the maximum past pressure is also shown on this figure.
effective stress greater than the existing vertical effective stress. An example of
a situation that creates an overconsolidated soil is where a thick overburden
layer of soil has been removed by erosion over time. Other mechanisms, such
as changes in groundwater elevation and changes in soil structure, can create an
overconsolidated soil.
For structures constructed on top of saturated cohesive soil, determining the
overconsolidation ratio of the soil is very important in the settlement analysis. For
example, if the cohesive soil is underconsolidated, then considerable settlement due
to continued consolidation owing to the soil’s own weight as well as the applied
structural load would be expected. On the other hand, if the cohesive soil is highly
overconsolidated, then a load can often be applied to the cohesive soil without
significant settlement.
The oedometer apparatus is used to determine the consolidation properties of
saturated cohesive soil. The typical testing procedure consists of placing an undisturbed
specimen within the apparatus, applying a vertical seating pressure to the
laterally confined specimen, and then submerging the specimen in distilled water.
The specimen is then subjected to an incremental increase in vertical stress, with
each pressure remaining on the specimen for a period of 24 hr. Plotting the vertical
stress versus void ratio of the soil often yields a plot similar to Fig. 6.22. The plot
SOIL MECHANICS AND FOUNDATIONS 6.59
is known as the consolidation curve and consists of two important segments, the
recompression curve (defined by the recompression index Cr) and the virgin consolidation
curve (defined by the compression index Cc). Figure 6.22 also illustrates
the Casagrande construction technique, which can be used to determine the maximum
past pressure ( ). vm
Using the calculated values of Cr and Cc , the primary consolidation settlement
(sc) due to an increase in load (
v) can be determined from the following equations:
1. For underconsolidated soil (OCR  1):
H   
  
 o vo v v s  C log (6.19) c c1  e  o vo
2. For normally consolidated soil (OCR  1):
H   
 o vo v s  C log (6.20) c c1  e  o vo
3. For overconsolidated soil (OCR  1):
Case I:  
   vo v vm
H   
 o vo v s  C log (6.21) c r1  e  o vo
Case II:  
    vo v vm
H  H   
 o vm o vo v s  C log  C log (6.22) c r c 1  e  1  e  o vo o vm
where sc  settlement due to primary consolidation caused by an increase in
load
Cc  compression index, obtained from the virgin consolidation curve
(Fig. 6.22)
Cr  recompression index, obtained from the recompression portion of
the consolidation curve (Fig. 6.22)
Ho  initial thickness of the in-situ saturated cohesive soil layer
eo  initial void ratio of the in-situ saturated cohesive soil layer
  vo initial vertical effective stress of the in-situ soil (see Art. 6.4.1)

  v for an underconsolidated soil (this represents the increase in vertical
effective stress that will occur as the cohesive soil consolidates under
its own weight)
  vm maximum past pressure, also known as the preconsolidation pressure
( ), which is obtained from the consolidation curve using the Cas- p
agrande construction technique (see Fig. 6.22)

v  increase in load, typically due to the construction of a building or
the construction of a fill layer at ground surface
The value of 
v (also known as z) can be obtained from stress distribution
theory as discussed in Art. 6.4.2. Note that a drop in the groundwater table or a
reduction in pore water pressure can also result in an increase in load on the cohesive
soil.
6.60 SECTION SIX
For overconsolidated soil, there are two possible cases that can be used to calculate
the amount of settlement. The first case occurs when the existing vertical
effective stress ( ) plus the increase in vertical stress (
v) due to the proposed vo
building weight does not exceed the maximum past pressure ( ). For this first vm
case, there will only be recompression of the cohesive soil.
For the second case, the sum of the existing vertical effective stress ( ) plus vo
the increase in vertical stress (
v) due to the proposed building weight exceeds
the maximum past pressure ( ). For the second case, there will be virgin con- vm
solidation of the cohesive soil. Given the same cohesive soil and identical field
conditions, the settlement due to the second case will be significantly more than
the first case.
As previously mentioned, primary consolidation is a time-dependent process that
can take many years to complete. The rate of consolidation can be estimated using
the Terzaghi theory of consolidation (see K. Terzaghi and R. B. Peck, ‘‘Soil Mechanics
in Engineering Practice,’’ John Wiley & Sons, Inc., New York):
Secondary Compression. The final component of settlement is due to secondary
compression, which is that part of the settlement that occurs after essentially all of
the excess pore water pressures have dissipated (i.e., settlement that occurs at constant
effective stress). The usual assumption is that secondary compression does not
start until after primary consolidation is complete. The amount of secondary compression
is often neglected because it is rather small compared to the primary
consolidation settlement. However, secondary compression can constitute a major
part of the total settlement for peat or other highly organic soil (see R. D. Holtz
and W. D. Kovacs, ‘‘An Introduction to Geotechnical Engineering,’’ Prentice-Hall,
Inc., Englewood Cliffs, NJ).
The final calculation for estimating the maximum settlement ( max) of the insitu
cohesive soil would be to add together the three components of settlement, or:
  s  s  s (6.23) max i c s
where max  maximum settlement over the life of the structure
si  immediate settlement
sc  primary consolidation settlement
ss  secondary compression settlement
6.5.7 Settlement of Granular Soil
A major difference between saturated cohesive soil and granular soil is that the
settlement of cohesionless soil is not time dependent. Because of the generally high
permeability of granular soil, the settlement usually occurs as the load is applied
during the construction of the building. Many different methods can be used to
determine the settlement of granular soil, such as plate load tests, laboratory testing
of undisturbed soil samples, equations based on the theory of elasticity, and empirical
correlations. For example, Fig. 6.23 shows a chart that presents an empirical
correlation between the measured N value (obtained from the Standard Penetration
Test, see Art. 6.2.4) and the allowable soil pressure (tsf) that will produce a settlement
of the footing of 1 in (2.5 cm).
As an example of the use of Fig. 6.23, suppose a site contains a sand deposit
and the proposed structure can be subjected to a maximum settlement ( max) of
1.0 in (2.5 cm). If the measured N value from the Standard Penetration Test  10
and the width of the proposed footings  5 ft (1.5 m), then the allowable soil
pressure  1 tsf (100 kPa).
SOIL MECHANICS AND FOUNDATIONS 6.61
FIGURE 6.23 Allowable soil bearing pressures for footings on
sand based on the Standard Penetration Test. (From K. Terzaghi and
R. B. Peck, ‘‘Soil Mechanics in Engineering Practice,’’ 2d ed., John
Wiley & Sons, Inc., New York. Reprinted with permission of John
Wiley & Sons, Inc.)
For measured N values other than those for which the curves are drawn in Fig.
6.23, the allowable soil pressure can be obtained by linear interpolation between
curves. According to Terzaghi and Peck, if all of the footings are proportioned in
accordance with the allowable soil pressure corresponding to Fig. 6.23, then the
maximum settlement ( max) of the foundation should not exceed 1 in (2.5 cm) and
the maximum differential settlement (
) should not exceed 0.75 in (2 cm). Figure
6.23 was developed for the groundwater table located at a depth equal to or greater
than a depth of 2B below the bottom of the footing. For conditions of a high
groundwater table close to the bottom of the shallow foundation, the values obtained
from Fig. 6.23 should be reduced by 50%.
6.6 BEARING CAPACITY ANALYSES
A bearing capacity failure is defined as a foundation failure that occurs when the
shear stresses in the soil exceed the shear strength of the soil. Bearing capacity
6.62 SECTION SIX
FIGURE 6.24 General shear foundation failure for soil in a dense or hard state.
(Adapted from A. B. Vesic?, ‘‘Bearing Capacity of Deep Foundations in Sand,’’ Highway
Research Record, no. 39.)
failures of foundations can be grouped into three categories (A. B. Vesic?, ‘‘Bearing
Capacity of Deep Foundations in Sand,’’ Highway Research Record, no. 39):
1. General Shear (Fig. 6.24). As shown in Fig. 6.24, a general shear failure involves
total rupture of the underlying soil. There is a continuous shear failure
of the soil (solid lines) from below the footing to the ground surface. When the
load is plotted versus settlement of the footing, there is a distinct load at which
the foundation fails (solid circle), and this is designated Qult. The value of Qult
divided by the width (B) and length (L) of the footing is considered to be the
‘‘ultimate bearing capacity’’ (qult) of the footing. The ultimate bearing capacity
has been defined as the bearing stress that causes a sudden catastrophic failure
of the foundation. Note in Fig. 6.24 that a general shear failure ruptures and
pushes up the soil on both sides of the footing. For actual failures it the field,
the soil is often pushed up on only one side of the footing with subsequent
tilting of the structure. A general shear failure occurs for soils that are in a dense
or hard state.
2. Punching Shear (Fig. 6.25). As shown in Fig. 6.25, a punching shear failure
does not develop the distinct shear surfaces associated with a general shear
failure. For punching shear, the soil outside the loaded area remains relatively
uninvolved and there is minimal movement of soil on both sides of the footing.
SOIL MECHANICS AND FOUNDATIONS 6.63
FIGURE 6.25 Punching shear foundation failure for soil
in a loose or soft state. (Adapted from A. B. Vesic?, ‘‘Bearing
Capacity of Deep Foundations in Sand,’’ Highway Research
Record, no. 39.)
The process of deformation of the footing involves compression of soil directly
below the footing as well as the vertical shearing of soil around the footing
perimeter. As shown in Fig. 6.25, the load settlement curve does not have a
dramatic break, and for punching shear, the bearing capacity is often defined as
the first major nonlinearity in the load-settlement curve (open circle). A punching
shear failure occurs for soils that are in a loose or soft state.
3. Local Shear Failure (Fig. 6.26). As shown in Fig. 6.26, local shear failure
involves rupture of the soil only immediately below the footing. There is soil
bulging on both sides of the footing, but the bulging is not as significant as in
general shear. Local shear failure can be considered as a transitional phase between
general shear and punching shear. Because of the transitional nature of
local shear failure, the bearing capacity could be defined as the first major nonlinearity
in the load-settlement curve (open circle) or at the point where the
settlement rapidly increases (solid circle). A local shear failure occurs for soils
that have a medium density or firm state.
The documented cases of bearing capacity failures indicate that usually the following
three factors (separately or in combination) are the cause of the failure:
6.64 SECTION SIX
FIGURE 6.26 Local shear foundation failure, which is a transitional phase between
general shear and punching shear failures. (Adapted from A. B. Vesic?, ‘‘Bearing
Capacity of Deep Foundations in Sand,’’ Highway Research Record, no. 39.)
1. There was an overestimation of the shear strength of the underlying soil.
2. The actual structural load at the time of the bearing capacity failure was greater
than that assumed during the design phase.
3. The site was altered, such as the construction of an adjacent excavation, which
resulted in a reduction in support and a bearing capacity failure.
A famous case of a bearing capacity failure is the Transcona grain elevator,
located at Transcona, Manitoba, Canada, near Winnipeg. Figure 6.27 shows the
October 1913 failure of the grain elevator. At the time of failure, the grain elevator
was essentially fully loaded. The foundation had been constructed on clay that was
described as a stiff clay. Note in Fig. 6.27 that the soil has been pushed up on only
one side of the foundation, with subsequent tilting of the structure.
6.6.1 Bearing Capacity for Shallow Foundations
As indicated in Table 6.2, common types of shallow foundations include spread
footings for isolated columns, combined footings for supporting the load from more
than one structural unit, strip footings for walls, and mats or raft foundations constructed
at or near ground surface. Shallow footings often have an embedment that
is less than the footing width.
SOIL MECHANICS AND FOUNDATIONS 6.65
FIGURE 6.27 Transcona grain elevator bearing capacity failure.
Bearing Capacity Equation. The most commonly used bearing capacity equation
is the equation developed by Terzaghi (‘‘Theoretical Soil Mechanics,’’ John Wiley
& Sons, Inc., New York). For a uniform vertical loading of a strip footing, Terzaghi
assumed a general shear failure (Fig. 6.24) in order to develop the following bearing
capacity equation:
Qult 1 q  cN  ?2 BN  D N (6.24) ult c t  t ? q BL
where qult  ultimate bearing capacity for a strip footing
Qult  vertical load causing a general shear failure of the underlying soil
(Fig. 6.24)
B  width of the strip footing
L  length of the strip footing
t  total unit weight of the soil
D?  vertical distance from the ground surface to the bottom of the
strip footing
c  cohesion of the soil underlying the strip footing
Nc, N, and Nq  dimensionless bearing capacity factors
In order to calculate the allowable bearing pressure (qall), the following equation
is used: qall qult /F, where qall  allowable bearing pressure, qult  ultimate bearing
capacity from Eq. (6.24), and F  factor of safety (typically F  3). This allowable
bearing pressure often has to be reduced in order to prevent excessive settlement
of the foundation. In addition, building codes often list allowable bearing pressures
versus soil or rock types, such as Table 6.14, which presents the allowable bearing
pressures (qall) from the ‘‘Uniform Building Code’’ (1997).
6.66 SECTION SIX
TABLE 6.14 Allowable Bearing Pressures
Material type
Allowable bearing
pressurea
Maximum allowable
bearing pressureb
Massive crystalline bedrock 4,000 psf (200 kPa) 12,000 psf (600 kPa)
Sedimentary and foliated rock 2,000 psf (100 kPa) 6,000 psf (300 kPa)
Gravel and sandy gravel (GW, GP) 2,000 psf (100 kPa) 6,000 psf (300 kPa)
Nonplastic soil: sands, silts, and NP silt
(GM, SW, SP, SM)c
1,500 psf (75 kPa) 4,500 psf (220 kPa)
Plastic soil: silts and clays (ML, MH, SC,
CL, CH)c
1,000 psf (50 kPa) 3,000 psf (150 kPa)d
aMinimum footing width and embedment depth equals 1 ft (0.3 m).
bAn increase of 20% of the allowable bearing pressure is allowed for each additional foot (0.3 m) of
width or depth up to the maximum allowable bearing pressures listed in Column 3. An exception is plastic
soil, see note d.
c Group symbols from Table 6.8.
dNo increase in the allowable bearing pressure is allowed for an increase in width of the footing.
For dense or stiff soils, allowable bearing values in this table are generally conservative. For very loose
or very soft soils, the allowable bearing values may be too high.
Source: Data from ‘‘Uniform Building Code’’ (1997)
There are many charts, graphs, and figures that present bearing capacity factors
developed by different engineers and researchers based on varying assumptions. For
example, Fig. 6.28 presents bearing capacity factors Nc, N, and Nq , which automatically
incorporate allowance for punching and local shear failure. Another example
is Fig. 6.29, which presents bearing capacity factors that have not been
adjusted for punching or local shear failure. Figure 6.29 also presents the bearing
capacity equations for square, rectangular, and circular footings. The equations for
granular soil (i.e., cohesionless soil, c  0) and for a total stress analysis for cohesive
soil (i.e., 	 0 and c  su) are also shown in Fig. 6.29.
Other Footing Loads. In addition to the vertical load acting on the footing, it
may also be subjected to a lateral load. A common procedure is to treat lateral
loads separately and resist the lateral loads by using the soil pressure acting on the
sides of the footing (passive pressure) and the frictional resistance along the bottom
of the footing.
It is always desirable to design and construct shallow footings so that the vertical
load is applied at the center of gravity of the footing. For combined footings that
carry more than one vertical load, the combined footing should be designed and
constructed so that the vertical loads are symmetric. There may be design situations
where the footing is subjected to a moment, such as where there is a fixed-end
connection between the building frame and the footing. This moment can be represented
by a load Q that is offset a certain distance (known as the eccentricity)
from the center of gravity of the footing. For other projects, there may be property
line constraints and the load must be offset a certain distance (eccentricity) from
the center of gravity of the footing. Because an eccentrically loaded footing will
create a higher bearing pressure under one side as compared to the opposite side,
one approach is to evaluate the actual pressure distribution beneath the footing. The
usual procedure is to assume a rigid footing (hence linear pressure distribution) and
use the section modulus (1?6B2) in order to calculate the largest and lowest bearing
pressure. For a footing having a width B, the largest (q) and lowest (q) bearing
pressures are as follows:
SOIL MECHANICS AND FOUNDATIONS 6.67
FIGURE 6.28 Bearing capacity factors N and Nq, which automatically
incorporate allowance for punching and local shear failure. (Reproduced
from R. B. Peck, W. E. Hanson, and T. H. Thornburn, ‘‘Foundation
Engineering,’’ John Wiley & Sons, Inc., New York, reproduced
with permission of John Wiley & Sons, Inc.)
Q(B  6e) Q(B 
 6e)
q  q  (6.25) 2 2 B B
where q  largest bearing pressure underneath the footing, which is located along
the same side of the footing as the eccentricity
q  lowest bearing pressure underneath the footing, which is located at the
opposite side of the footing
Q  load applied to the footing (kN per linear m of footing length or lb
per linear ft of footing length)
6.68 SECTION SIX
FIGURE 6.29 Bearing capacity factors N, Nq, and Nc, which do not include allowance for
punching or local shear failure. (Note: for local or punching shear of loose sands or soft clays,
the value of 	 to be used in this figure  tan (0.67 tan 	) and the cohesion used in the bearing 
1
capacity equation  0.67 c). (Reproduced from NAVFAC DM-7.2, 1982.)
SOIL MECHANICS AND FOUNDATIONS 6.69
e  eccentricity of the load Q; i.e., the lateral distance from Q to the center
of gravity of the footing
B  width of the footing
A usual requirement is that the load (Q) must be located within the middle 1?3
of the footing. The above equations are only valid for this condition. The value of
q must not exceed the allowable bearing pressure (qall).
For dense or stiff soils, allowable bearing values in Table 6.14 are generally
conservative. For very loose or very soft soils, the allowable bearing values in Table
6.14 may be too high.
6.6.2 Bearing Capacity for Deep Foundations in Granular Soil
Deep foundations are used when the upper soil stratum is too soft, weak, or compressible
to support the foundation loads. Deep foundations are also used when
there is a possibility of the undermining of the foundation. For example, bridge
piers are often founded on deep foundations to prevent a loss of support due to
flood conditions which could cause river bottom scour. The most common types of
deep foundations are piles and piers that support individual footings or mat foundations
(Table 6.2). Piles are defined as relatively long, slender, column-like members
often made of steel, concrete, or wood that are either driven into place or castin-
place in predrilled holes. Common types of piles are as follows:
Batter Pile. A pile driven in at an angle inclined to the vertical to provide high
resistance to lateral loads.
End-Bearing Pile. A pile whose support capacity is derived principally from
the resistance of the foundation material on which the pile tip rests. End-bearing
piles are often used when a soft upper layer is underlain by a dense or hard
stratum. If the upper soft layer should settle, the pile could be subjected to downdrag
forces, and the pile must be designed to resist these soil-induced forces.
Friction Pile. A pile whose support capacity is derived principally from the
resistance of the soil friction and/or adhesion mobilized along the side of the
pile. Friction piles are often used in soft clays where the end-bearing resistance
is small because of punching shear at the pile tip.
Combined End-Bearing and Friction Pile. A pile that derives its support capacity
from combined end-bearing resistance developed at the pile tip and frictional
and/or adhesion resistance on the pile perimeter.
A pier is defined as a deep foundation system, similar to a cast-in-place pile,
that consists of a column-like reinforced concrete member. Piers are often of large
enough diameter to enable down-hole inspection. Piers are also commonly referred
to as drilled shafts, bored piles, or drilled caissons.
Many other methods are available for forming deep foundation elements. Examples
include earth stabilization columns, such as (NAVFAC DM-7.2, 1982):
Mixed-in-Place Piles. A mixed-in-place soil-cement or soil-lime pile.
Vibro-Replacement Stone Columns. Vibroflotation or other method is used to
make a cylindrical, vertical hole that is filled with compacted gravel or crushed
rock.
6.70 SECTION SIX
Grouted Stone Columns. Similar to the above but includes filling voids with
bentonite-cement or water-sand-bentonite cement mixtures.
Concrete Vibro Columns. Similar to stone columns, but concrete is used instead
of gravel.
Several different items are used in the design and construction of piles, including:
Engineering Analysis. Based on the results of subsurface exploration and laboratory
testing, the bearing capacity of the deep foundation can be calculated in
a similar manner to the previous section on shallow foundations. This section
will describe the engineering analyses for deep foundations in granular and cohesive
soil.
Field Load Tests. Prior to the construction of the foundation, a pile or pier
could be load tested in the field to determine its carrying capacity. Because of
the uncertainties in the design of piles based on engineering analyses, pile load
tests are common. The pile load test can often result in a more economical
foundation than one based solely on engineering analyses.
Application of Pile Driving Resistance. Often the pile driving resistance (i.e.,
blows per ft) is recorded as the pile is driven into place. When the anticipated
bearing layer is encountered, the driving resistance (blows per ft) should substantially
increase.
Specifications and Experience. Other factors that should be considered in the
deep foundation design include governing building code or agency requirements
and local experience.
End Bearing Pile for Granular Soil. For an end bearing pile or pier, the bearing
capacity equation can be used to determine the ultimate bearing capacity (qult).
When we compare the second and third term in Eq. (6.24), the value of B (width
of pile) is much less than the embedment depth (D? ) of the pile. Therefore, the
second term in Eq. (6.24) can be neglected. Assuming granular soil (c  0), Eq.
(6.24) reduces to the following:
Qp q  D N  N (6.26) ult t ? q v q area
where qult  the ultimate bearing capacity of the end-bearing pile or pier
Qp  point resistance force
area  pile tip area (B2 in the case of a square pile and R2 in the case of
a round pile)
  v vertical effective stress at the pile tip
Nq  dimensionless bearing capacity factor
For drilled piers or piles placed in predrilled holes, the value of Nq can be
obtained from Fig. 6.28 or 6.29 based on the friction angle (	) of the granular soil
located at the pile tip. However, for driven piles, the values of Nq listed in Figs.
6.28 and 6.29 are generally too conservative. Figure 6.30 presents a chart that
provides the bearing capacity factor Nq from several different sources. Note in Fig.
6.30 that at 	 30
, Nq varies from about 30 to 150, while at 	 40
, Nq varies
from about 100 to 1000. This is a tremendous variation in Nq values and is related
to the different approaches used by the various researchers, where in some cases
SOIL MECHANICS AND FOUNDATIONS 6.71
FIGURE 6.30 Bearing capacity factor Nq as recommended by various researchers
for deep foundations. (Originally from A. S. Vesic?, ‘‘Ultimate Loads and Settlements
of Deep Foundations in Sand,’’ Duke University, Durham, NC.)
the basis of the relationship shown in Fig. 6.30 is theoretical and in other cases the
relationship is based on analysis of field data such as pile load tests. There is a
general belief that the bearing capacity factor Nq is higher for driven piles than for
shallow foundations. One reason for a higher Nq value is the effect of driving the
pile, which displaces and densifies the cohesionless soil at the bottom of the pile.
The densification could be due to both the physical process of displacing the soil
6.72 SECTION SIX
and the driving vibrations. These actions would tend to increase the friction angle
of the granular soil in the vicinity of the driven pile. Large-diameter piles would
tend to displace and densify more soil than smaller-diameter piles.
Friction Pile for Granular Soil. As the name implies, a friction pile develops its
load carrying capacity due to the frictional resistance between the granular soil and
the pile perimeter. Piles subjected to vertical uplift forces would be designed as
friction piles because there would be no end-bearing resistance as the pile is pulled
from the ground.
Based on a linear increase in frictional resistance with confining pressure, the
average ultimate frictional capacity (qult) can be calculated as follows:
Qs q   tan 	   k tan 	 (6.27) ult h w v w surface area
where qult  the average ultimate frictional capacity for the pile or pier
Qs  ultimate skin friction resistance force
Surface area  perimeter surface area of the pile, which is equal to 4DL for a
square pile and DL for a round pile (D  diameter or width of
pile and L  length of pile)
  h average horizontal effective stress over the length of the pile or pier
  v average vertical effective stress over the length of the pile or pier
k  dimensionless parameter equal to divided by (because of the   h v
densification of the granular soil associated with driven displacement
piles, values of k between 1 and 2 are often assumed)
	w  friction angle between the cohesionless soil and the perimeter of
the pile or pier (degrees)
Commonly used friction angles are 	w  3?4	 for wood and concrete piles and
	w  20
 for steel piles.
In Eq. (6.27), the term tan 	w equals the shear strength ( 	?) between the pile h
or pier surface and the granular soil. This term is identical to Eq. (6.9) (with c 
0), that is, 	?  tan 	. Thus, the frictional resistance force (Qs) in Eq. (6.27) n
is equal to the perimeter surface area times the shear strength of the soil at the pile
or pier surface.
Combined End-Bearing and Friction Pile in Granular Soil. Piles and piers subjected
to vertical compressive loads and embedded in a deposit of granular soil are
usually treated in the design analysis as combined end-bearing and friction piles or
piers. This is because the pile or pier can develop substantial load-carrying capacity
from both end-bearing and frictional resistance. To calculate the ultimate pile or
pier capacity for a condition of combined end-bearing and friction, the value of Qp
from Eq. (6.26) is added to the value of Qs from Eq. (6.27). Usually the ultimate
capacity is divided by a factor of safety of 3 in order to calculate the allowable
pile or pier load.
Pile Groups in Granular Soil. The previous discussion dealt with the load capacity
of a single pile in cohesionless soil. Usually pile groups are used to support
the foundation elements, such as a group of piles supporting a pile cap or a mat
slab. In loose sand and gravel deposits, the load-carrying capacity of each pile in
the group may be greater than that of a single pile because of the densification
effect due to driving the piles. Because of this densification effect, the load capacity
SOIL MECHANICS AND FOUNDATIONS 6.73
of the group is often taken as the load capacity of a single pile times the number
of piles in the group. An exception would be a situation where a weak layer underlies
the cohesionless soil. In this case, group action of the piles could cause
them to punch through the granular soil and into the weaker layer or cause excessive
settlement of the weak layer located below the pile tips.
In order to determine the settlement of the strata underlying the pile group, the
2:1 approximation (see Art. 6.4.2) can be used to determine the increase in vertical
stress (
v) for those soil layers located below the pile tip. If the piles in the group
are principally end-bearing, then the 2:1 approximation starts at the tip of the piles
(L  bottom length of the pile group, B  width of the pile group, and z  depth
below the tip of the piles, see Eq. 6.16). If the pile group develops its load-carrying
capacity principally through side friction, then the 2:1 approximation starts at a
depth of 2?3D, where D  depth of the pile group.
6.6.3 Bearing Capacity for Deep Foundations in Cohesive Soil
The load-carrying capacity of piles and piers in cohesive soil is more complex than
the analysis for granular soil. Some of the factors that may need to be considered
in the analysis are as follows (AASHTO, ‘‘Standard Specifications for Bridges,’’
16th ed., American Association of State Highway and Transportation Officials,
Washington, DC):
• A lower load-carrying capacity of a pile in a pile group as compared to that of
a single pile.
• The settlement of the underlying cohesive soil due to the load of the pile group.
• The effects of driving piles on adjacent structures or slopes. The ground will
often heave around piles driven into soft and saturated cohesive soil.
• The increase in load on the pile due to negative skin friction (i.e., down-drag
loads) from consolidating soil.
• The effects of uplift loads from expansive and swelling clays.
• The reduction in shear strength of the cohesive soil due to construction techniques,
such as the disturbance of sensitive clays or development of excess pore
water pressures during the driving of the pile. There is often an increase in loadcarrying
capacity of a pile after it has been driven into a soft and saturated clay
deposit. This increase with time is known as freeze or setup and is caused primarily
by the dissipation of excess pore water pressures.
• The influence of fluctuations in the elevation of the groundwater table on the
load-carrying capacity when analyzed in terms of effective stresses.
Total Stress Analysis. The ultimate load capacity of a single pile or pier in cohesive
soil is often determined by performing a total stress analysis. This is because
the critical load on the pile, such as from wind or earthquake loads, is a short-term
loading condition and thus the undrained shear strength of the cohesive soil will
govern. The total stress analysis for a single pile or pier in cohesive soil typically
is based on the undrained shear strength (su  c) of the cohesive soil.
The ultimate load capacity of the pile or pier in cohesive soil would equal the
sum of the ultimate end-bearing and ultimate side adhesion components. Using the
Terzaghi bearing capacity equation (Eq. 6.24), the ultimate load capacity (Qult) of
a single pile or pier in cohesive soil equals:
6.74 SECTION SIX
FIGURE 6.31 Ultimate capacity for a single pile or pier in cohesive soil. (Reproduced
from NAVFAC DM-7.2, 1982.)
Q  end bearing  side adhesion ult
 cN (area of tip)  c (surface area) c A
2 Q  c9(R )  c (2RL) ult A
2  9cR  2c RL (6.28) A
or
where Qult  ultimate load capacity of the pile or pier
c  cohesion of the cohesive soil at the pile tip (because it is a total stress
analysis, the undrained shear strength (su  c) is often used)
R  radius of the pile or pier
L  length of the embedment of the pile
cA  adhesion between the cohesive soil and pile or pier perimeter
For Eq. (6.28), the usual assumption is Nc  9. Figure 6.31 can be used to
determine the value of the adhesion (cA) for different types of piles and cohesive
soil conditions. If the pile or pier is subjected to an uplift force, then the first term
in Eq. (6.28) is set equal to zero. Usually the ultimate capacity is divided by a
factor of safety of 3 in order to calculate the allowable pile or pier load.
Pile Groups. The bearing capacity of pile groups in cohesive soils is normally
less than the sum of individual piles in the group, and this reduction in group
SOIL MECHANICS AND FOUNDATIONS 6.75
FIGURE 6.32 Ultimate capacity of a pile group in cohesive soil. (Developed by
Whitaker, reproduced from NAVFAC DM-7.2, 1982.)
capacity must be considered in the analysis. The ‘‘group efficiency’’ is defined as
the ratio of the ultimate load capacity of each pile in the group to the ultimate load
capacity of a single isolated pile. If the spacing between piles in the group is at a
distance that is greater than about 7 times the pile diameter, then the group effi-
ciency is equal to 1 (i.e., no reduction in pile capacity for group action). The group
efficiency decreases as the piles become closer together in the pile group. Figure
6.32 can be used to determine the ultimate load capacity of a pile group in cohesive
soil.
Similar to pile groups in cohesionless soil, the settlement of the strata underlying
the pile group can be evaluated by using the 2:1 approximation (see Art. 6.4.2) to
calculate the increase in vertical stress (
v) for those soil layers located below the
pile tip. If the piles in the group develop their load-carrying capacity principally
by end-bearing in cohesive soil, then the 2:1 approximation starts at the tip of the
piles (L  bottom length of the pile group, B  width of the pile group, and z 
depth below the tip of the piles, see Eq. 6.16). If the pile group develops its loadcarrying
capacity principally through cohesive soil adhesion along the pile perimeter,
then the 2:1 approximation starts at a depth of 2?3 D, where D  depth of the
pile group.
6.76 SECTION SIX
FIGURE 6.33 Common types of retaining walls: (a) Gravity walls of stone,
brick, or plain concrete. Weight provides overturning and sliding stability; (b) cantilevered
wall; (c) counterfort, or buttressed, wall. If backfill covers counterforts,
the wall is termed a counterfort retaining wall; (d ) crib wall; (e) semigravity wall
(often steel reinforcement is used); ( f ) bridge abutment. (Reproduced from J. E.
Bowles, ‘‘Foundation Analysis and Design,’’ 3d ed., McGraw-Hill Publishing Co.,
New York, with permission of McGraw-Hill, Inc.)
6.7 RETAINING WALLS
A retaining wall is defined as a structure whose primary purpose is to provide
lateral support for soil or rock. In some cases, such as basement walls and certain
types of bridge abutments, it may also support vertical loads. The more common
types of retaining walls are shown in Fig. 6.33 and include gravity walls, cantilevered
walls, counterfort walls, and crib walls. Gravity retaining walls are routinely
built of plain concrete or stone, and the wall depends primarily on its massive
SOIL MECHANICS AND FOUNDATIONS 6.77
weight to resist failure from overturning and sliding. Counterfort walls consist of
a footing, a wall stem, and intermittent vertical ribs (called counterforts) that tie
the footing and wall stem together. Crib walls consist of interlocking concrete members
that form cells which are then filled with compacted soil.
Granular soils (sands or gravels) are the standard recommendation for backfill
material. There are several reasons for this recommendation:
1. Predictable Behavior. Import granular backfill generally has a more predictable
behavior in terms of earth pressure exerted on the wall. If silts or clays are used
as backfill material, expansive soil-related forces could be generated by these
soil types.
2. Drainage System. To prevent the build-up of hydrostatic water pressure on the
retaining wall, a drainage system is often constructed at the heel of the wall.
This system will be more effective if highly permeable granular soil is used as
backfill.
3. Frost Action. In cold climates, the formation of ice lenses in the backfill soil
can cause so much lateral movement that the retaining wall will become unusable.
Backfill soil consisting of granular soil and the installation of a drainage
system at the heel of the wall will help to protect the wall from frost action.
6.7.1 Retaining Wall Analyses
Figure 6.34 shows various types of retaining walls and the soil pressures acting on
the walls. Three types of soil pressures act on a retaining wall: (1) active earth
pressure, which is exerted on the back side of the wall, (2) passive earth pressure,
which acts on the front of the retaining wall footing, and (3) bearing pressure,
which acts on the bottom of the retaining wall footing. These three pressures are
individually discussed below.
Active Earth Pressure. In order to calculate the active earth pressure resultant
force (PA), in kN per linear meter of wall or pounds per linear foot of wall, the
following equation is used for granular backfill:
2 1 P  ?2k H (6.29) A A t
where kA  active earth pressure coefficient
t  total unit weight of the granular backfill
H  height over which the active earth pressure acts as defined in Fig. 6.34a
In its simplest form, the active earth pressure coefficient (kA) is equal to:
2 1 k  tan (45
 
 ?2	) (6.30) A
where 	 friction angle of the granular backfill. Equation (6.30) is known as the
active Rankine state, after the British engineer Rankine, who in 1857 obtained this
relationship. Equation (6.30) is valid only for the simple case of a retaining wall
that has a vertical rear face, no friction between the rear wall face and backfill soil,
and the backfill ground surface is horizontal. For retaining walls that do not meet
these requirements, the active earth pressure coefficient (kA) for Eq. (6.29) is often
determined using the Coulomb equation (see Fig. 6.35). Often the wall friction is
neglected (  0
), but if it is included in the analysis, typical values are  3?4	
6.78 SECTION SIX
FIGURE 6.34a Gravity and semigravity
retaining walls. (From NAVFAC DM-7.2,
1982.)
for the wall friction between granular soil and wood or concrete walls and  20

for the wall friction between granular soil and steel walls such as sheet-pile walls.
Note in Fig. 6.35 that when wall friction angle  is used in the analysis, the active
earth pressure resultant force (PA) is inclined at an angle equal to .
Additional important details concerning the active earth pressure are as follows:
1. Sufficient Movement. There must be sufficient movement of the retaining wall
in order to develop the active earth pressure of the backfill. For dense granular
soil, the amount of wall translation to reach the active earth pressure state is
usually very small (i.e., to reach active state, wall translation  0.0005 H, where
H  height of wall).
2. Triangular Distribution. As shown in Figs. 6.34 and 6.35, the active earth
pressure is a triangular distribution and thus the active earth pressure resultant
force (PA) is located at a distance equal to 1?3H above the base of the wall.
3. Surcharge Pressure. If there is a uniform surcharge pressure (Q) acting upon
the entire ground surface behind the wall, then there would be an additional
horizontal pressure exerted upon the retaining wall equal to the product of kA
SOIL MECHANICS AND FOUNDATIONS 6.79
FIGURE 6.34b Cantilever and counterfort
retaining walls. (From NAVFAC DM-7.2,
1982.)
times Q. Thus, the resultant force (P2), in kN per linear m of wall or lb per
linear ft of wall, acting on the retaining wall due to the surcharge (Q) is equal
to P2  QHkA, where Q  uniform vertical surcharge acting upon the entire
ground surface behind the retaining wall, kA  active earth pressure coefficient
(Eq. (6.30) or Fig. 6.35), and H  height of the retaining wall. Because this
pressure acting upon the retaining wall is uniform, the resultant force (P2) is
located at midheight of the retaining wall.
4. Active Wedge: The active wedge is defined as that zone of soil involved in the
development of the active earth pressures upon the wall. This active wedge must
move laterally in order to develop the active earth pressures. It is important that
building footings or other load-carrying members are not supported by the active
wedge, or else they will be subjected to lateral movement. The active wedge is
inclined at an angle of 45
  	/2 from the horizontal.
Passive Earth Pressure. As shown in Fig. 6.34, the passive earth pressure is
developed along the front side of the footing. Passive pressure is developed when
the wall footing moves laterally into the soil and a passive wedge is developed. In
6.80 SECTION SIX
FIGURE 6.34c Design analysis for retaining walls shown in Figs. 6.34a
and 6.34b. (From NAVFAC DM-7.2, 1982.)
order to calculate the passive resultant force (Pp), the following equation is used
assuming that there is cohesionless soil in front of the wall footing:
2 1 P  ?2k D (6.31) p p t
SOIL MECHANICS AND FOUNDATIONS 6.81
FIGURE 6.35 Coulomb’s earth pressure (kA) equation. (From NAVFAC
DM-7.2, 1982.)
where Pp  passive resultant force in kN per linear m of wall or lb per linear ft of
wall
kp  passive earth pressure coefficient
t  total unit weight of the soil located in front of the wall footing
D  depth of the wall footing (vertical distance from the ground surface in
front of the retaining wall to the bottom of the footing)
The passive earth pressure coefficient (kp) is equal to:
2 1 k  tan (45
  ?2	) (6.32) p
where 	  friction angle of the soil in front of the wall footing. Equation (6.32)
is known as the passive Rankine state. In order to develop passive pressure, the
wall footing must more laterally into the soil. The wall translation to reach the
passive state is at least twice that required to reach the active earth pressure state.
Usually it is desirable to limit the amount of wall translation by applying a reduction
factor to the passive pressure. A commonly used reduction factor is 2.0. The soil
engineer routinely reduces the passive pressure by 1?2 (reduction factor  2.0) and
then refers to the value as the allowable passive pressure.
Footing Bearing Pressure. In order to calculate the footing bearing pressure, the
first step is to sum the vertical loads, such as the wall and footing weights. The
vertical loads can be represented by a single resultant vertical force, per linear m
or ft of wall, that is offset by a distance (eccentricity) from the toe of the footing.
This can then be converted to a pressure distribution by using Eq. (6.25). The largest
bearing pressure is routinely at the toe of the footing and it should not exceed the
allowable bearing pressure (Art. 6.6.1).
6.82 SECTION SIX
Retaining Wall Analyses. Once the active earth pressure resultant force (PA) and
the passive resultant force (Pp) have been calculated, the design analysis is performed
as indicated in Fig. 6.34c. The retaining wall analysis includes determining
the resultant location of the forces (i.e., calculate d, which should be within the
middle third of the footing), the factor of safety for overturning, and the factor of
safety for sliding. The adhesion (ca) between the bottom of the footing and the
underlying soil is often ignored for the sliding analysis.
6.7.2 Restrained Retaining Walls
As mentioned in the previous article, in order for the active wedge to be developed,
there must be sufficient movement of the retaining wall. There are many cases
where movement of the retaining wall is restricted. Examples include massive
bridge abutments, rigid basement walls, and retaining walls that are anchored in
nonyielding rock. These cases are often described as restrained retaining walls.
In order to determine the earth pressure acting on a restrained retaining wall,
Eq. (6.29) can be utilized where the coefficient of earth pressure at rest (k0) is
substituted for kA. A common value of k0 for granular soil that is used for restrained
retaining walls is 0.5. Restrained retaining walls are especially susceptible to higher
earth pressures induced by heavy compaction equipment, and extra care must be
taken during the compaction of backfill for restrained retaining walls.
6.7.3 Mechanically Stabilized Earth Retaining Walls
Mechanically stabilized earth retaining walls (also known as MSE retaining
walls) are typically composed of strip- or grid-type (geosynthetic) reinforcement.
Because they are often more economical to construct than conventional concrete
retaining walls, mechanically stabilized earth retaining walls have become very
popular in the past decade. A mechanically stabilized earth retaining wall is composed
of three elements: (1) wall facing material, (2) soil reinforcement, such as
strip- or grid-type reinforcement, and (3) compacted fill between the soil reinforcement.
The design analysis for a mechanically stabilized earth retaining wall is more
complex than for a cantilevered retaining wall. For a mechanically stabilized earth
retaining wall, both the internal and external stability must be checked.
External Stability. The analysis for the external stability is similar to that for a
gravity retaining wall. For example, Figs. 6.36 and 6.37 present the design analysis
for external stability for a level backfill condition and a sloping backfill condition.
In both Figs. 6.36 and 6.37, the zone of mechanically stabilized earth mass is treated
in a similar fashion as a massive gravity retaining wall. The following analyses
must be performed:
1. Allowable bearing pressure: the bearing pressure due to the reinforced soil mass
must not exceed the allowable bearing pressure.
2. Factor of safety of sliding: the reinforced soil mass must have an adequate factor
of safety for sliding.
3. Factor of safety of overturning; the reinforced soil mass must have an adequate
factor of safety for overturning about Point O.
SOIL MECHANICS AND FOUNDATIONS 6.83
FIGURE 6.36 Design analysis for mechanically stabilized earth retaining wall
having horizontal backfill. (Adapted from AASHTO, ‘‘Standard Specifications for
Highway Bridges,’’ 16th ed., American Association of State Highway and Transportation
Officials, Washington, DC.)
FIGURE 6.37 Design analysis for mechanically stabilized earth retaining
wall having sloping backfill. (Adapted from AASHTO, ‘‘Standard Specifi-
cations for Highway Bridges,’’ 16th ed., American Association of State Highway
and Transportation Officials, Washington, DC.)
6.84 SECTION SIX
4. Resultant of vertical forces: the resultant of the vertical forces N must be within
the middle 1?3 of the base of the reinforced soil mass.
5. Stability of reinforced soil mass: the stability of the entire reinforced soil mass
(i.e., shear failure below the bottom of the wall) would have to be checked.
Note in Figure 6.36 that two forces (P1 and P2) are shown acting on the reinforced
soil mass. The first force (P1) is determined from the standard active earth
pressure resultant equation (i.e., Eq. 6.29). The second force (P2) is due to a uniform
surcharge (Q) applied to the entire ground surface behind the mechanically
stabilized earth retaining wall. If the wall does not have a surcharge, then P2 is
equal to zero.
Figure 6.37 presents the active earth pressure force for an inclined slope behind
the retaining wall. Note in Fig. 6.37 that the friction ( ) of the soil along the back
side of the reinforced soil mass has been included in the analysis. The value of kA
would be obtained from Coulomb’s earth pressure equation (Fig. 6.35). As a conservative
approach, the friction angle ( ) can be assumed to be equal to zero and
then PH  PA. Note in both Figs. 6.36 and 6.37 that the minimum width of the
reinforced soil mass must be at least 7?10 the height of the reinforced soil mass.
Internal Stability. To check the stability of the mechanically stabilized zone, a
slope stability analysis can be performed where the soil reinforcement is modeled
as horizontal forces equivalent to its allowable tensile resistance. In addition to
calculation of the factor of safety, the pull-out resistance of the reinforcement along
the slip surface should also be checked.
The analysis of mechanically stabilized earth retaining walls is based on active
earth pressures. It is assumed that the wall will move enough to develop the active
wedge. As with concrete retaining walls, it is important that building footings or
other load carrying members are not supported by the mechanically stabilized earth
retaining wall and the active wedge, or else they could be subjected to lateral
movement.
6.7.4 Sheet Pile Walls
Sheet pile retaining walls are widely used for waterfront construction and consist
of interlocking members that are driven into place. Individual sheet piles come in
many different sizes and shapes. Sheet piles have an interlocking joint that enables
the individual segments to be connected together to form a solid wall.
Many different types of design methods are used for sheet pile walls. Figure
6.38 shows the most common type of design method. In Fig. 6.38, the term H
represents the unsupported face of the sheet pile wall. As indicated in Fig. 6.38,
this sheet pile wall is being used as a waterfront retaining structure and the level
of water in front of the wall is at the same elevation as the groundwater table
elevation behind the wall. For highly permeable soil, such as clean sand and gravel,
this often occurs because the water can quickly flow underneath the wall in order
to equalize the water levels.
In Fig. 6.38, the term D represents that portion of the sheet pile wall that is
anchored in soil. Also shown in Fig. 6.38 is a force designated as Ap. This represents
a restraining force on the sheet pile wall due to the construction of a tieback, such
as by using a rod that has a grouted end or is attached to an anchor block. Tieback
anchors are often used in sheet pile wall construction in order to reduce the bending
SOIL MECHANICS AND FOUNDATIONS 6.85
FIGURE 6.38 Earth pressure diagram for design of
sheet pile wall. (From NAVFAC DM-7.2, 1982.)
moments in the sheet pile. When tieback anchors are used, the sheet pile wall is
typically referred to as an anchored bulkhead, while if no tiebacks are utilized,
the wall is called a cantilevered sheet pile wall.
Sheet pile walls tend to be relatively flexible. Thus, as indicated in Fig. 6.38,
the design is based on active and passive earth pressures. For this analysis, a unit
length (1 m or 1 ft) of sheet pile wall is assumed. The soil behind the wall is
assumed to exert an active earth pressure on the sheet pile wall. At the groundwater
table (Point A), the active earth pressure is equal to kA td1, where kA  active earth
pressure coefficient from Eq. (6.30) (the friction between the sheet pile wall and
the soil is usually neglected in the design analysis), t  total unit weight of the
soil above the groundwater table, and d1  depth from the ground surface to the
groundwater table. At Point B in Fig. 6.38, the active earth pressure equals kA td1
 kA bd2, where b  buoyant unit weight of the soil below the groundwater table
and d2  depth from the groundwater table to the bottom of the sheet pile wall.
For a sheet pile wall having assumed values of H and D (see Fig. 6.38), and using
the calculated values of active earth pressure at Points A and B, the active earth
pressure resultant force (PA), in kN per linear m of wall or lb per linear foot of
wall, can be calculated.
The soil in front of the wall is assumed to exert a passive earth pressure on the
sheet pile wall. The passive earth pressure at Point C in Fig. 6.38 is equal to kp bD,
where the passive earth pressure coefficient (kp) can be calculated from Eq. (6.32).
Similar to the analysis of cantilever retaining walls, if it is desirable to limit the
amount of sheet pile wall translation, then a reduction factor can be applied to the
passive pressure. Once the allowable passive pressure is known at Point C, the
passive resultant force (Pp) can be readily calculated. As an alternative solution for
the passive pressure, Eq. (6.31) can be used to calculate Pp with the buoyant unit
6.86 SECTION SIX
weight ( b) substituted for the total unit weight ( t ) and the depth D as shown in
Fig. 6.38.
Note that a water pressure has not been included in the analysis. This is because
the water level is the same on both sides of the wall and water pressure cancels
itself out. However, if the water level was higher behind than in front of the wall,
then water pressure forces would be generated behind the wall.
The design of sheet pile walls requires the following analyses: (1) evaluation of
the earth pressure resultant forces PA and Pp as previously described, (2) determination
of the required depth D of piling penetration, (3) calculation of the maximum
bending moment (Mmax) which is used to determine the maximum stress in the
sheet pile, and (4) selection of the appropriate piling type, size, and construction
details.
A typical design process is to assume a depth D (Fig. 6.38) and then calculate
the factor of safety for toe failure (i.e., toe kick-out) by the summation of moments
at the tieback anchor (Point D). The factor of safety is defined as the moment due
to the passive force divided by the moment due to the active force. Values of
acceptable factor of safety for toe failure are 2 to 3.
Once the depth D of the sheet pile wall is known, the anchor pull (Ap) must be
calculated. The anchor pull is determined by the summation of forces in the horizontal
direction, or: Ap  PA 
 Pp /F, where PA and Pp are the resultant active and
passive forces and F is the factor of safety that was obtained from the toe failure
analysis. Based on the earth pressure diagram (Fig. 6.38) and the calculated value
of Ap, elementary structural mechanics can be used to determine the maximum
moment in the sheet pile wall. The maximum moment divided by the section modulus
can then be compared with the allowable design stresses.
6.7.5 Temporary Retaining Walls
Temporary retaining walls are often used during construction, such as for the support
of the sides of an excavation that is made below-grade in order to construct
the building foundation. If the temporary retaining wall has the ability to develop
the active wedge, then the basic active earth pressure principles described in the
previous sections can be used for the design of the temporary retaining walls.
Especially in urban areas, movement of the temporary retaining wall may have
to be restricted to prevent damage to adjacent property. If movement of the retaining
wall is restricted, the earth pressures will typically be between the active (kA) and
at-rest (k0) values.
For some projects, the temporary retaining wall may be constructed of sheeting
(such as sheet piles) that are supported by horizontal braces, also known as struts.
Near or at the top of the temporary retaining wall, the struts restrict movement of
the retaining wall and prevent the development of the active wedge. Because of
this inability of the retaining wall to deform at the top, earth pressures near the top
of the wall are in excess of the active (kA) pressures. At the bottom of the wall, the
soil is usually able to deform into the excavation, which results in a reduction in
earth pressure, and the earth pressures at the bottom of the excavation tend to be
constant or even decrease as shown in Fig. 6.39.
The earth pressure distributions shown in Fig. 6.39 were developed from actual
measurements of the forces in struts during the construction of braced excavations.
In Fig. 6.39, case a shows the earth pressure distribution for braced excavations in
sand and cases b and c show the earth pressure distribution for clays. In Fig. 6.39,
SOIL MECHANICS AND FOUNDATIONS 6.87
FIGURE 6.39 Earth pressure distribution on temporary braced walls. (From
NAVFAC DM-7.2 1982, originally developed by K. Terzaghi and R. B. Peck, ‘‘Soil
Mechanics in Engineering Practice,’’ 2d ed., John Wiley & Sons, Inc., New York.)
6.88 SECTION SIX
the distance H represents the depth of the excavation (i.e., the height of the exposed
wall surface). The earth pressure distribution is applied over the exposed height (H)
of the wall surface with the earth pressures transferred from the wall sheeting to
the struts (the struts are labeled with the forces F1, F2, etc.).
Any surcharge pressures, such as surcharge pressures on the ground surface
adjacent the excavation, must be added to the pressure distributions shown in Fig.
6.39. In addition, if the sand deposit has a groundwater table that is above the level
of the bottom of the excavation, then water pressures must be added to the case a
pressure distribution shown in Fig. 6.39.
Because the excavations are temporary (i.e., short-term condition), the undrained
shear strength (su  c) is used for the analysis of the earth pressure distributions
for clay. The earth pressure distributions for clay (i.e., cases b and c) are not valid
for permanent walls or for walls where the groundwater table is above the bottom
of the excavation.
6.8 FOUNDATIONS
This section deals with the selection of the type of foundation. The selection of a
particular type of foundation is often based on a number of factors, such as:
1. Adequate Depth. It must have an adequate depth to prevent frost damage. For
such foundations as bridge piers, the depth of the foundation must be sufficient
to prevent undermining by scour.
2. Bearing Capacity Failure. The foundation must be safe against a bearing capacity
failure (Art. 6.6).
3. Settlement. The foundation must not settle to such an extent that it damages
the structure (Art. 6.5).
4. Quality. The foundation must be of adequate quality so that it is not subjected
to deterioration, such as the sulfate attack of concrete footings.
5. Adequate Strength. The foundation must be designed with sufficient strength
that it does not fracture or break apart under the applied superstructure loads. It
must also be properly constructed in conformance with the design specifications.
6. Adverse Soil Changes. The foundation must be able to resist long-term adverse
soil changes. An example is expansive soil (silts and clays), which could expand
or shrink causing movement of the foundation and damage to the structure.
7. Seismic Forces. The foundation must be able to support the structure during an
earthquake without excessive settlement or lateral movement.
6.8.1 Shallow Foundations
A shallow foundation is often selected when the structural load will not cause
excessive settlement of the underlying soil layers. In general, shallow foundations
are more economical to construct than deep foundations. Common types of shallow
foundations are listed in Table 6.2 and described below:
SOIL MECHANICS AND FOUNDATIONS 6.89
FIGURE 6.40 Examples of shallow foundations: (a) combined footing; (b) combined
trapezoidal footing; (c) cantilever or strap footing; (d ) octagonal footing; (e)
eccentric loaded footing with resultant coincident with area so soil pressure is uniform.
(From J. E. Bowles, ‘‘Foundation Analysis and Design,’’ 2d ed., McGraw-Hill
Publishing Co., New York, with permission of McGraw-Hill, Inc.)
1. Spread Footings, Combined Footings, and Strip Footings. These types of
shallow foundations are probably the most common types of building foundations.
Examples of these types of footings are shown in Fig. 6.40.
2. Mat Foundation. Examples of mat foundations are shown in Fig. 6.41. Based
on economic considerations, mat foundations are constructed for the following
reasons:
(a) Large Individual Footings. A mat foundation is often constructed when
the sum of individual footing areas exceeds about one-half of the total foundation
area.
(b) Cavities or Compressible Lenses. A mat foundation can be used when the
subsurface exploration indicates that there will be unequal settlement caused
by small cavities or compressible lenses below the foundation. A mat foundation
would tend to span over the small cavities or weak lenses and create
a more uniform settlement condition.
(c) Shallow Settlements. A mat foundation can be recommended when shallow
settlements predominate and the mat foundation would minimize differential
settlements.
(d) Unequal Distribution of Loads. For some structures, there can be a large
difference in building loads acting on different areas of the foundation. Conventional
spread footings could be subjected to excessive differential settle6.90
SECTION SIX
FIGURE 6.41 Examples of mat foundations: (a) Flat plate; (b) plate thickened
under columns; (c) beam-and-slab; (d ) plate with pedestals; (e) basement walls as
part of mat. (From J. E. Bowles, ‘‘Foundation Analysis and Design,’’ 2d ed., Mc-
Graw-Hill Publishing Co., New York, with permission of McGraw-Hill, Inc.)
ment, but a mat foundation would tend to distribute the unequal building
loads and reduce the differential settlements.
(e) Hydrostatic Uplift. When the foundation will be subjected to hydrostatic
uplift due to a high groundwater table, a mat foundation could be used to
resist the uplift forces.
3. Post-Tensioned Slabs-on-Grade. Post-tensioned slabs-on-grade are common in
southern California and other parts of the United States. They are an economical
foundation type when there is no ground freezing or the depth of frost penetration
is low. The most common uses of post-tensioned slabs-on-grade are to resist
expansive soil forces or when the projected differential settlement exceeds the
tolerable value for a conventional (lightly reinforced) slabs-on-grade. For example,
post-tensioned slabs-on-grade are frequently recommended if the projected
differential settlement is expected to exceed 2 cm (0.75 in). Installation
and field inspection procedures for post-tensioned slabs-on-grade have been prepared
by the Post-Tensioning Institute (‘‘Design and Construction of Posttensioned
Slabs-on-Ground,’’ 2d ed., Phoenix). Post-tensioned slabs-on-grade
consists of concrete with embedded steel tendons that are encased in thick plastic
sheaths. The plastic sheath prevents the tendon from coming in contact with the
concrete and permits the tendon to slide within the hardened concrete during
the tensioning operations. Usually tendons have a dead end (anchoring plate) in
the perimeter (edge) beam and a stressing end at the opposite perimeter beam
to enable the tendons to be stressed from one end. The Post-Tensioning Institute
SOIL MECHANICS AND FOUNDATIONS 6.91
(‘‘Design and Construction of Post-tensioned Slabs-on-Ground,’’ 2d ed., Phoenix)
provides typical anchorage details for the tendons.
4. Shallow Foundation Alternatives. If the expected settlement for a proposed
shallow foundation is too large, then other options for foundation support or soil
stabilization must be evaluated. Some commonly used alternatives are as follows:
(a) Grading. Grading operations can be used to remove the compressible soil
layer and replace it with structural fill. Usually the grading option is economical
only if the compressible soil layer is near the ground surface and
the groundwater table is below the compressible soil layer or the groundwater
table can be economically lowered.
(b) Surcharge. If the site contains an underlying compressible cohesive soil
layer, the site can be surcharged with a fill layer placed at the ground surface.
Vertical drains (such as wick drains or sand drains) can be installed
in the compressible soil layer to reduce the drainage paths and speed up the
consolidation process. Once the compressible cohesive soil layer has had
sufficient consolidation, the fill surcharge layer is removed and the building
is constructed.
(c) Densification of Soil. Many different methods can be used to densify loose
or soft soil. For example, vibro-flotation and dynamic compaction are often
effective at increasing the density of loose sand deposits. Another option is
compaction grouting, which consists of intruding a mass of very thick consistency
grout into the soil, which both displaces and compacts the loose
soil.
(d) Floating Foundation. A floating foundation is a special type of deep foundation
where the weight of the structure is balanced by the removal of soil
and construction of an underground basement.
6.8.2 Deep Foundations
Probably the most common type of deep foundation is the pile foundation. Table
6.15 presents pile type characteristics and uses. Piles can consist of wood (timber),
steel H-sections, precast concrete, cast-in-place concrete, pressure injected concrete,
concrete filled steel pipe piles, and composite type piles. Piles are either driven into
place or installed in predrilled holes. Piles that are driven into place are generally
considered to be low displacement or high displacement, depending on the amount
of soil that must be pushed out of the way as the pile is driven. Examples of lowdisplacement
piles are steel H-sections and open-ended steel pipe piles that do not
form a soil plug at the end. Examples of high-displacement piles are solid section
piles, such as round timber piles or square precast concrete piles, and steel pipe
piles with a closed end.
A cast-in-place pile is formed by making a hole in the ground and then filling
the hole with concrete. As shown in Fig. 6.42, in its simplest form, the cast-inplace
pile consists of an uncased hole that is filled with concrete. If the soil tends
to cave into the hole, then a shell-type pile can be installed (see Fig. 6.42). This
consists of driving a steel shell or casing into the ground. The casing may be driven
with a mandrel, which is then removed, and the casing is filled with concrete. In
other cases, the casing can be driven into place and then slowly removed as the
hole is filled with concrete.
Figure 6.43 shows typical pile configurations.
6.92
TABLE 6.15 Typical Pile Characteristics and Uses
Pile type Timber Steel
Cast-in-place concrete piles
(shells driven without mandrel)
Cast-in-place concrete piles
(shells withdrawn)
Maximum length 35 m (115 ft) Practically unlimited 45 m (150 ft) 36 m (120 ft)
Optimum length 9–20 m (30–65 ft) 12–50 m (40–160 ft) 9–25 m (30–80 ft) 8–12 m (25–40 ft)
Applicable
material
specifications
ASTM-D25 for piles; PI-54
for quality of creosote; C1-
60 for creosote treatment
(standards of American
Wood Preserves Assoc.)
ASTM-A36 for structural
sections
ASTM-A1 for rail sections
ACI ACIa
Recommended
maximum
stresses
Measured at midpoint of
length: 4–6 MPa (600–900
psi) for cedar, western
hemlock, Norway pine,
spruce, and depending on
code
5–8 MPa (700–1200 psi) for
southern pine, Douglas fir,
oak cypress, and hickory
?s  65 to 140 MPa (9–20
ksi)
?s  0.35–0.5 ?y
0.33 ; 0.4 if shell gauge ? ? c c
 14; shell stress  0.35 ?y
if thickness of shell  3
mm
0.25–0.33?c
Maximum load
for usual
conditions
270 kN (60 kips) Maximum allowable stress 
cross section
900 kN (200 kips) 1300 kN (300 kips)
Optimum-load
range
130–225 kN (30–50 kips) 350–1050 kN (80–240 kips) 450–700 kN (100–150 kips) 350–900 kN (80–200 kips)
Disadvantages Difficult to splice
Vulnerable to damage in hard
driving
Vulnerable to decay unless
treated, when piles are
intermittently submerged
Vulnerable to corrosion
HP section may be damaged or
deflected by major
obstructions
Hard to splice after concreting
Considerable displacement
Concrete should be placed in
dry hole
More than average dependence
on quality of workmanship
6.93
TABLE 6.15 Typical Pile Characteristics and Uses (Continued)
Pile type Timber Steel
Cast-in-place concrete piles
(shells driven without mandrel)
Cast-in-place concrete piles
(shells withdrawn)
Advantages Comparatively low initial cost
Permanently submerged piles
are resistant to decay
Easy to handle
Easy to splice
High capacity
Small displacement
Able to penetrate through light
obstructions
Can be redriven
Shell not easily damaged
Initial economy
Remarks Best suited for friction pile in
granular material
Best suited for end bearing on
rock
Reduce allowable capacity for
corrosive locations
Best suited for friction piles of
medium length
Allowable load on pedestal
pile is controlled by bearing
capacity of stratum
immediately below pile
Typical
illustrations
6.94
TABLE 6.15 Typical Pile Characteristics and Uses (Continued)
Pile type
Concrete filled
steel pipe piles Composite piles
Precast concrete
(including prestressed)
Cast in place
(thin shell driven
with mandrels)
Auger placed
pressure-injected
concrete (grout) piles
Maximum length Practically unlimited 55 m (180 ft) 30 m (100 ft) for precast
60 m (200 ft) for
prestressed
30 m (100 ft) for
straight sections
12 m (40 ft) for tapered
sections
9–25 m (30–80 ft)
Optimum length 12–36 m (40–120 ft) 18–36 m (60–120 ft) 12–15 m (40–50 ft) for
precast
18–30 m (60–100 ft) for
prestressed
12–18 m (40–60 ft) for
straight
5–12 m (16–40 ft) for
tapered
12–18 m (40–60 ft)
Applicable
material
specifications
ASTM A36 for core
ASTM A252 for pipe
ACI Code 318 for
concrete
ACI Code 318 for
concrete
ASTM A36 for
structural section
ASTM A252 for steel
pipe
ASTM D25 for timber
ASTM A15 reinforcing
steel
ASTM A82 cold-drawn
wire
ACI Code 318 for
concrete
ACI See ACIa
Recommended
maximum
stresses
0.40 ?y reinforcement 
205 MPa (30 ksi)
0.50 ?y for core  175
MPa (25 ksi)
0.33 for concrete ?c
Same as concrete in
other piles
Same as steel in other
piles
Same as timber piles for
wood composite
0.33 unless local ?c
building code is less;
0.4 ?y for reinforced
unless prestressed
0.33 ; ?s  0.4 ?y if ?c
shell gauge is  14;
use ?s  0.35 ?y if
shell thickness  3
mm
0.225–0.4?c
Maximum load
for usual
conditions
1800 kN (400 kips)
without cores
18,000 kN (4000 kips)
for large sections with
steel cores
1800 kN (400 kips) 8500 kN (2000 kips) for
prestressed
900 kN (200 kips) for
precast
675 kN (150 kips) 700 kN (160 kips)
Optimum-load
range
700–1100 kN (160–250
kips) without cores
4500–14,000 kN (1000–
3100 kips) with cores
250–725 kN (60–160
kips)
350–3500 kN (80–800
kips)
250–550 kN (60–120
kips)
350–550 kN (80–120
kips)
6.95
TABLE 6.15 Typical Pile Characteristics and Uses (Continued)
Pile type
Concrete filled
steel pipe piles Composite piles
Precast concrete
(including prestressed)
Cast in place
(thin shell driven
with mandrels)
Auger placed
pressure-injected
concrete (grout) piles
Disadvantages High initial cost
Displacement for closedend
pipe
Difficult to attain good
joint between two
materials
Difficult to handle unless
prestressed
High initial cost
Considerable
displacement
Prestressed difficult to
splice
Difficult to splice after
concreting
Redriving not
recommended
Thin shell vulnerable
during driving
Considerable
displacement
Dependence on
workmanship
Not suitable in
compressible soil
Advantages Best control during
installation
No displacement for
open-end installation
Open-end pipe best
against obstructions
High load capacitites
Easy to splice
Considerable length can
be provided at
comparatively low
cost
High load capacities
Corrosion resistance can
be attained
Hard driving possible
Initial economy
Taped sections provide
higher bearing
resistance in granular
stratum
Freedom from noise and
vibration
Economy
High skin friction
No splicing
Remarks Provides high bending
resistance where
unsupported length is
loaded laterally
The weakest of any
material used shall
govern allowable
stresses and capacity
Cylinder piles in
particular are suited
for bending resistance
Best suited for mediumload
friction piles in
granular materials
Patented method
Typical
illustrations
aACI Committee 543, ‘‘Recommendations for Design, Manufacture, and Installation of Concrete Piles,’’ JACI,
August 1973, October 1974.
Sources: NAVFAC DM-7.2, 1982 and J. E. Bowles, ‘‘Foundation Analysis and Design,’’ 3d ed., McGraw-Hill
Publishing, Co., New York.
Stresses given for steel piles and shells are for noncorrosive locations. For corrosive locations estimate possible
reduction in steel cross section or provide protection from corrosion.
6.96 SECTION SIX
FIGURE 6.42 Common types of cast-in-place concrete piles: (a) Uncased pile;
(b) Franki uncased-pedestal pile; (c) Franki cased-pedestal pile; (d ) welded or seamless
pipe pile; (e) cased pile using a thin sheet shell; ( f ) monotube pile; (g) uniform
tapered pile; (h) step-tapered pile. (From J. E. Bowles, ‘‘Foundation Analysis and
Design,’’ 3d ed., McGraw-Hill Publishing Co., New York, with permission of Mc-
Graw-Hill, Inc.)
6.9 FOUNDATION EXCAVATIONS
There are many different types of excavations performed during the construction
of a project. For example, soil may be excavated from the cut or borrow area and
then used as fill (see Art. 6.10). Another example is the excavation of a shear key
or buttress that will be used to stabilize a slope or landslide. Other examples of
excavations are as follows:
1. Footing Excavations. This type of service involves measuring the dimension of
geotechnical elements (such as the depth and width of footings) to make sure
that they conform to the requirements of the construction plans. This service is
often performed at the same time as the field observation to confirm bearing
conditions.
SOIL MECHANICS AND FOUNDATIONS 6.97
FIGURE 6.43 Typical pile configurations. (From J. E. Bowles, ‘‘Foundation Analysis
and Design,’’ 3d ed., McGraw-Hill Publishing Co., New York, with permission
of McGraw-Hill, Inc.)
2. Excavation of Piers. As with the excavation of footings, the geotechnical engineer
may be required to confirm embedment depths and bearing conditions
for piers. Figure 6.44 presents typical steps in the construction of a drilled pier.
3. Open Excavations. An open excavation is defined as an excavation that has
stable and unsupported side slopes. Table 6.16 presents a discussion of the general
factors that control the excavation stability, and Table 6.17 lists factors that
control the stability of excavation slopes in some problem soils.
4. Braced Excavations. A braced excavation is defined as an excavation where
the sides are supported by retaining structures. Figure 6.45 shows common types
of retaining systems and braced excavations. Table 6.18 lists the design considerations
for braced excavations, and Table 6.19 indicates factors that are involved
in the choice of a support system for a deep excavation.
6.10 GRADING AND OTHER SITE
IMPROVEMENT METHODS
Since most building sites start out as raw land, the first step in site construction
work usually involves the grading of the site. Grading is defined as any operation
consisting of excavation, filling, or a combination thereof. A typical grading process
could include some or all of the following:
6.98 SECTION SIX
FIGURE 6.44 Typical steps in the construction of a drilled pier: (a) dry augering
through self-supporting cohesive soil; (b) augering through water bearing cohesionless
soil with aid of slurry; (c) setting the casing.
SOIL MECHANICS AND FOUNDATIONS 6.99
FIGURE 6.44 (d ) dry augering into cohesive soil after sealing; (e) forming a bell.
(After O’Neill and Reese. Reproduced from R. B. Peck, W. E. Hanson, and T. H.
Thornburn, ‘‘Foundation Engineering,’’ John Wiley & Sons, Inc., New York.)
(Continued )
1. Easements. The first step in the grading operation is to determine the location
of any on-site utilities and easements. The on-site utilities and easements often
need protection so that they are not damaged during the grading operation.
2. Clearing, Brushing, and Grubbing. Clearing, brushing, and grubbing are de-
fined as the removal of vegetation (grass, brush, trees, and similar plant types)
by mechanical means. It is important that this debris be removed from the site
and not accidentally placed within the structural fill mass.
3. Cleanouts. This grading process deals with the removal of unsuitable bearing
material at the site, such as loose or porous alluvium, colluvium, peat, muck,
and uncompacted fill.
4. Benching (Hillside Areas). Benching is defined as the excavation of relatively
level steps into earth material on which fill is to be placed.
5. Canyon Subdrain. A subdrain is defined as a pipe and gravel or similar drainage
system placed in the alignment of canyons or former drainage channels.
After placement of the subdrain, structural fill is placed on top of the subdrain.
6. Scarifying and Recompaction. In flat areas that have not been benched, scarifying
and recompaction of the ground surface is performed by compaction
equipment in order to get a good bond between the in-place material and compacted
fill.
6.100 SECTION SIX
TABLE 6.16 General Factors That Control the Stability of the Excavation Slopes
Construction
activity Objectives Comments
Dewatering In order to prevent boiling,
softening, or heave of the
excavation bottom, reduce
lateral pressures on sheeting,
reduce seepage pressures on
face of open cut, and
eliminate piping of fines
through sheeting.
Investigate soil compressibility and
effect of dewatering on settlement of
nearby structures; consider
recharging or slurry wall cutoff.
Examine for presence of lower
aquifer and need to dewater. Install
piezometers if needed. Consider
effects of dewatering in cavity-laden
limestone. Dewater in advance of
excavation.
Excavation
and grading
(also see
Art. 6.10)
Utility trenches, basement
excavations, and site
grading.
Analyze safe slopes or bracing
requirements, and effects of stress
reduction on overconsolidated, soft,
or swelling soils and shales.
Consider horizontal and vertical
movements in adjacent areas due to
excavation and effect on nearby
structures. Keep equipment and
stockpiles a safe distance from the
top of the excavation.
Excavation
wall
construction
To support vertical excavation
walls, and to stabilize
trenching in limited space.
See Art. 6.7 for retaining wall design.
Reduce earth movements and bracing
stresses, where necessary, by
installing lagging on front flange of
soldier pile. Consider effect of
vibrations due to driving sheet piles
or soldier piles. Consider dewatering
requirements as well as wall stability
in calculating sheeting depth.
Movement monitoring may be
warranted.
Blasting To remove or to facilitate the
removal of rock in the
excavation.
Consider the effect of vibrations on
settlement or damage to adjacent
areas. Design and monitor or require
the contractor to design and monitor
blasting in critical areas, and require
a pre-construction survey of nearby
structures.
Anchor or
strut
installation
To obtain support system
stiffness and interaction.
Major excavations require careful
installation and monitoring, e.g., case
anchor holes in collapsible soil,
measure stress in ties and struts, etc.
Sources: NAVFAC DM-7.2, 1982, Clough and Davidson 1977, and Departments of the Army and the
Air Force 1979. G. W. Clough and R. R. Davidson, ‘‘Effects of Construction on Geotechnical Performance,’’
and Department of the Army and the Air Force, ‘‘Soils and Geology, Procedures for Foundation Design.’’
SOIL MECHANICS AND FOUNDATIONS 6.101
TABLE 6.17 Stability of Excavation Slopes in Some Problem Soils
Topic Discussion
General
discussion
The depth and slope of an excavation and groundwater conditions control
the overall stability and movements of open excavations. Factors that
control the stability of the excavation for different material types are as
follows:
1. Rock: For rock, stability is controlled by depths and slopes of
excavation, particular joint patterns, in-situ stresses, and groundwater
conditions.
2. Granular Soils: For granular soils, instability usually does not extend
significantly below the bottom of the excavation provided that seepage
forces are controlled.
3. Cohesive Soils: For cohesive soils, stability typically involves side
slopes but may also include the materials well below the bottom of the
excavation. Instability of the bottom of the excavation, often referred
to as bottom heave, is affected by soil type and strength, depth of cut,
side slope and/or berm geometry, groundwater conditions, and
construction procedures.
Stiff-fissured
clays and
shales
Field shear resistance may be less than suggested by laboratory testing.
Slope failures may occur progressively and shear strengths are reduced
to the residual value compatible with relatively large deformations.
Some case histories suggest that the long-term performance is
controlled by the drained residual friction angle. The most reliable
design would involve the use of local experience and recorded
observations.
Loess and
other
collapsible
soil
Such soils have a strong potential for collapse and erosion of relatively
dry materials upon wetting. Slopes in loess are frequently more stable
when cut vertical to prevent water infiltration. Benches at intervals can
be used to reduce effective slope angles. Evaluate potential for collapse
as described in Art. 6.5.5.
Residual soil Depending on the weathering profile from the parent rock, residual soil
can have a significant local variation in properties. Guidance based on
recorded observations provides a prudent basis for design.
Sensitive
clay
Very sensitive and quick clays have a considerable loss of strength upon
remolding, which could be generated by natural or man-made
disturbance. Minimize disturbance and use total stress analysis based
on undrained shear strength from unconfined compression tests or field
vane tests.
Talus Talus is characterized by loose aggregation of rock that accumulates at
the foot of rock cliffs. Stable slopes are commonly between 1.25:1 to
1.75:1 (horizontal:vertical). Instability is often associated with
abundance of water, mostly when snow is melting.
Loose sands Loose sands may settle under blasting vibrations, or liquefy, settle, and
lose shear strength if saturated. Such soils are also prone to erosion
and piping.
Engineering
evaluation
Slope stability analyses may be used to evaluate the stability of open
excavations in soils where the behavior of such soils can be reasonably
determined by field investigations, laboratory testing, and engineering
analysis. As described above, in certain geologic formations stability is
controlled by construction procedures, side effects during and after
excavation, and inherent geologic planes of weaknesses.
Sources: NAVFAC DM-7.2, 1982 and Clough and Davidson 1977. G. W. Clough and R. R. Davidson,
‘‘Effects of Construction on Geotechnical Performance,’’ and Department of the Army and the Air Force,
‘‘Soils and Geology, Procedures for Foundation Design.’’
6.102 SECTION SIX
FIGURE 6.45 Common types of retaining systems and braced excavations. (From
NAVFAC DM-7.2, 1982.)
7. Cut and Fill Rough Grading Operations. Rough grading operations involve
the cutting of earth materials from high areas and compaction of fill in low
areas, in conformance with grading plans. Other activities could be performed
during rough grading operations, such as:
(a) Ripping or Blasting of Rock. Large rock fragments can be removed from
the site or disposed of in windrows.
(b) Cut-Fill Transition. A cut-fill transition is the location in a building pad
where on one side the pad has been cut down, exposing natural or rock
material, while on the other side fill has been placed. One method to deal
with a cut-fill transition is to over-excavate the cut portion of the pad and
replace it with compacted fill.
(c) Slope Stabilization. Examples of slope stabilization using earth materials
include stabilization fill, buttress fill, drainage buttress, and shear keys.
Such devices should be equipped with backdrain systems.
(d) Fill Slopes. When creating a fill slope, it is often difficult to compact the
outer edge of the fill mass. Because there is no confining pressure, the soil
SOIL MECHANICS AND FOUNDATIONS 6.103
TABLE 6.18 Design Considerations for Braced Excavations
Design factor Comments
Water loads Often greater than earth loads on an impervious wall. Recommend
piezometers during construction to monitor water levels. Should also
consider possible lower water pressures as a result of seepage of water
through or under the wall. Dewatering can be used to reduce the water
loads. Seepage under the wall reduces the passive resistance.
Stability Consider the possible instability in any berm or exposed slope. The sliding
potential beneath the wall or behind the tiebacks should also be
evaluated. For weak soils, deep seated bearing failure due to the weight
of the supported soil should be checked. Also include in stability analysis
the weight of surcharge or weight of other facilities in close proximity to
the excavation.
Piping Piping due to a high groundwater table causes a loss of ground, especially
for silty and fine sands. Difficulties occur due to flow of water beneath
the wall, through bad joints in the wall, or through unsealed sheet pile
handling holes. Dewatering may be required.
Movements Movements can be minimized through the use of a stiff wall supported by
preloaded tiebacks or a braced system.
Dewatering
and
recharge
Dewatering reduces the loads on the wall system and minimizes the
possible loss of ground due to piping. Dewatering may cause settlements
and in order to minimize settlements, there may be the need to recharge
outside of the wall system.
Surcharge Construction materials are usually stored near the wall systems. Allowances
should always be made for surcharge loads on the wall system.
Prestressing
of tieback
anchors
In order to minimize soil and wall movements, it is useful to remove slack
by prestressing tieback anchors.
Construction
sequence
The amount of wall movement is dependent on the depth of the excavation.
The amount of load on the tiebacks is dependent on the amount of wall
movement which occurs before they are installed. Movements of the wall
should be checked at every major construction stage. Upper struts should
be installed as early as possible.
Temperature Struts may be subjected to load fluctuations due to temperature differences.
This may be important for long struts.
Frost
penetration
In cold climates, frost penetration can cause significant loading on the wall
system. Design of the upper portion of the wall system should be
conservative. Anchors may have to be heated. Freezing temperatures also
can cause blockage of flow of water and thus unexpected buildup of
water pressure.
Earthquakes Seismic loads may be induced during an earthquake.
Factors of
safety
The following are suggested minimum factors of safety (F) for overall
stability. Note that these values are suggested guidelines only. Design
factors of safety depend on project requirements.
Earth Berms: Permanent, F  2.0 Temporary, F  1.5
Cut Slopes: Permanent, F  1.5 Temporary, F  1.3
General Stability: Permanent, F  1.5 Temporary, F  1.3
Bottom Heave: Permanent, F  2.0 Temporary, F  1.5
Source: NAVFAC DM-7.2, 1982.
6.104 SECTION SIX
TABLE 6.19 Factors Involved in the Choice of a Support System for an Excavation
Requirements Type of support system Comments
Open excavation
area
Tiebacks or rakers. For shallow
excavation, use cantilever walls.
Consider design items listed in
Table 6.18.
Low initial cost Soldier pile or sheet pile walls.
Consider combined soil slope and
wall.
Consider design items listed in
Table 6.18.
Use as part of
permanent
structure
Diaphragm or pier walls. Diaphragm wall is the most
common type of permanent
wall.
Subsurface
conditions of
deep, soft clay
Struts or rakers that support a
diaphragm or pier wall.
Tieback capacity not adequate
in soft clays.
Subsurface
conditions of
dense, gravelly
sands or clay
Soldier pile, diaphragm wall, or pier
wall.
Sheet piles may lose interlock
on hard driving.
Subsurface
conditions of
overconsolidated
clays
Struts, long tiebacks, or combination
of tiebacks and struts.
High in-situ lateral stresses are
relieved in overconsolidated
soil. Lateral movements may
be large and extend deep
into the soil.
Avoid dewatering Use diaphragm walls or possibly
sheet pile walls in soft subsoils.
Soldier pile wall is too
pervious for this application.
Minimize lateral
movements of
wall
Use high preloads on stiff strutted
or tieback walls.
Analyze the stability of the
bottom of the excavation.
Wide excavation
(greater than 65
ft wide)
Use tiebacks or rackers. Tiebacks are preferable except
in very soft clay soils.
Narrow excavation
(less than 65 ft
wide)
Use cross-excavation struts. Struts are more economical, but
tiebacks still may be
preferred in order to keep the
excavation open.
Note: Deep excavation is defined as an excavation that is more than 20 feet (6 m) below ground surface.
Source: NAVFAC DM-7.2, 1982.
deforms downslope without increasing in density. To deal with this situation,
the slope can be overbuilt and then cut back to the compacted core.
The second-best alternative is to use conventional construction procedures
such as back-rolling techniques or by using a bulldozer to track-walk the
slope.
(e) Revision of Grading Operations. Every grading job is different, and there
could be a change in grading operations based on field conditions.
8. Fine Grading (also known as Precise Grading). At the completion of the
rough grading operations, fine grading is performed to obtain the finish elevations
in accordance with the precise grading plan.
SOIL MECHANICS AND FOUNDATIONS 6.105
9. Slope Protection and Erosion Control. Although this is usually not the responsibility
of the grading contractor, upon completion of the fine grading,
slope protection and permanent erosion control devices are installed.
10. Trench Excavations. Utility trenches are excavated in the proposed road alignments
and building pads for the installation of the on-site utilities. The excavation
and compaction of utility trenches is often part of the grading process.
Once the utility lines are installed, scarifying and recompaction of the road
subgrade is performed and base material is placed and compacted.
11. Footing and Foundation Excavations. Although this is usually not part of the
grading operation, the footing and foundation elements are then excavated (see
Art. 6.9).
6.10.1 Compaction Fundamentals
An important part of the grading of the site often includes the compaction of fill.
Compaction is defined as the densification of a fill by mechanical means. This
physical process of getting the soil into a dense state can increase the shear strength,
decrease the compressibility, and decrease the permeability of the soil. There are
four basic factors that affect compaction:
1. Soil Type. Nonplastic (i.e., granular) soil, such as sands and gravels, can be
effectively compacted by using a vibrating or shaking type of compaction operation.
Plastic (i.e., cohesive) soil, such as silts and clays, is more difficult to
compact and requires a kneading or manipulation type of compaction operation.
If the soil contains oversize particles, such as coarse gravel and cobbles, these
particles tend to interfere with the compaction process and reduce the effectiveness
of compaction for the finer soil particles. Typical values of dry density for
different types of compacted soil are listed in Table 6.20.
2. Material Gradation. Those soils that have a well-graded grain size distribution
can generally be compacted into a denser state than a poorly graded soil that is
composed of soil particles of about the same size. For example, a well-graded
decomposed granite (DG) can have a maximum dry density of 2.2 Mg/m3 (137
pcf), while a poorly graded sand can have a maximum dry density of only 1.6
Mg/m3 (100 pcf, Modified Proctor).
3. Water Content. The water content is an important parameter in the compaction
of soil. Water tends to lubricate the soil particles thus helping them slide into
dense arrangements. However, too much water and the soil becomes saturated
and often difficult to compact. There is an optimum water content at which the
soil can be compacted into its densest state for a given compaction energy.
Typical optimum moisture contents (Modified Proctor) for different soil types
are as follows:
(a) Clay of High Plasticity (CH): optimum moisture content  18%
(b) Clay of Low Plasticity (CL): optimum moisture content  12 to 18%
(c) Well-Graded Sand (SW): optimum moisture content  10%
(d) Well-Graded Gravel (GW): optimum moisture content  7%
Some soils may be relatively insensitive to compaction water content. For
example, open-graded gravels and clean coarse sands are so permeable that water
simply drains out of the soil or is forced out of the soil during the compaction
process. These types of soil can often be placed in a dry state and then vibrated
into dense particle arrangements.
6.106
TABLE 6.20 Characteristics of Compacted Subgrade for Roads and Airfields (from The Unified Soil
Classification System, U.S. Army, 1960)
Major
divisions
(1)
Subdivisions
(2)
USCS
symbol
(3)
Name
(4)
Value as subgrade
(no frost action)
(5)
Potential frost
action
(6)
Coarse-grained soils Gravel and gravelly soils GW Well-graded gravels or gravel-sand mixtures,
little or no fines
Excellent None to very
slight
GP Poorly graded gravels or gravelly sands,
little or no fines
Good to excellent None to very
slight
GM Silty gravels, gravel-sand-silt mixtures Good to excellent Slight to medium
GC Clayey gravels, gravel-sand-clay mixtures Good Slight to medium
Sand and sandy soils SW Well-graded sands or gravelly sands, litttle
or no fines
Good None to very
slight
SP Poorly graded sands or gravelly sands, little
or no fines
Fair to good None to very
slight
SM Silty sands, sand-silt mixtures Fair to good Slight to high
SC Clayey sands, sand-clay mixtures Poor to fair Slight to high
Fine-grained soils Silts and clays with liquid limit
less than 50
ML Inorganic silts, rock flour, silts of low
plasticity
Poor to fair Medium to very
high
CL Inorganic clays of low plasticity, gravelly
clays, sandy clays, etc.
Poor to fair Medium to high
OL Organic silts and organic clays of low
plasticity
Poor Medium to high
Silts and clays with liquid limit
greater than 50
MH Inorganic silts, micaceous silts, silts of high
plasticity
Poor Medium to very
high
CH Inorganic clays of high plasticity, fat clays,
silty clays, etc.
Poor to fair Medium
OH Organic silts and organic clays of high
plasticity
Poor to very poor Medium
Peat Highly organic PT Peat and other highly organic soils Not suitable Slight
6.107
TABLE 6.20 Characterics of Compacted Subgrade for Roads and Airfields (from The Unified Soil
Classification System, U.S. Army, 1960) (Continued)
Compressibility
(7)
Drainage
properties
(8)
Compaction equipment
(9)
Typical dry densities
(10)
pcf Mg/m3
CBR
(11)
Sub. mod.,a
pci
(12)
Almost none Excellent Crawler-type tractor, rubber-tired roller,
steel-wheeled roller
125–140 2.00–2.24 40–80 300–500
Almost none Excellent Crawler-type tractor, rubber-tired roller,
steel-wheeled roller
110–140 1.76–2.24 30–60 300–500
Very slight to slight Fair to very poor Rubber-tired roller, sheepsfoot roller 115–145 1.84–2.32 20–60 200–500
Slight Poor to very poor Rubber-tired roller, sheepsfoot roller 130–145 2.08–2.32 20–40 200–500
Almost none Excellent Crawler-type tractor, rubber-tired roller 110–130 1.76–2.08 20–40 200–400
Almost none Excellent Crawler-type tractor, rubber-tired roller 105–135 1.68–2.16 10–40 150–400
Very slight to medium Fair to poor Rubber-tired roller, sheepsfoot roller 100–135 1.60–2.16 10–40 100–400
Slight to medium Poor to very poor Rubber-tired roller, sheepsfoot roller 100–135 1.60–2.16 5–20 100–300
Slight to medium Fair to poor Rubber-tired roller, sheepsfoot roller 90–130 1.44–2.08 15 or less 100–200
Medium Practically impervious Rubber-tired roller, sheepsfoot roller 90–130 1.44–2.08 15 or less 50–150
Medium to high Poor Rubber-tired roller, sheepsfoot roller 90–105 1.44–1.68 5 or less 50–100
High Fair to poor Sheepsfoot roller, rubber-tired roller 80–105 1.28–1.68 10 or less 50–100
High Practically impervious Sheepsfoot roller, rubber-tired roller 90–115 1.44–1.84 15 or less 50–150
High Practically impervious Sheepsfoot roller, rubber-tired roller 80–110 1.28–1.76 5 or less 25–100
Very high Fair to poor Compaction not practical — — — —
Source: U.S. Army, ‘‘The Unified Soil Classification System.’’
a Subgrade Modulus.
6.108 SECTION SIX
4. Compaction Effort (or Energy). The compactive effort is a measure of the
mechanical energy applied to the soil. Usually, the greater the amount of compaction
energy applied to a soil, the denser the soil will become. There are
exceptions, such as pumping soils (i.e., saturated clays), which can not be densified
by an increased compaction effort. Compactors are designed to use one
or a combination of the following types of compaction effort:
(a) Static weight or pressure
(b) Kneading action or manipulation
(c) Impact or a sharp blow
(d) Vibration or shaking
The laboratory compaction test consists of compacting a soil at a known water
content into a mold of specific dimensions using a certain compaction energy. The
procedure is repeated for various water contents to establish the compaction curve.
The most common testing procedures (compaction energy, number of soil layers in
the mold, etc.) are the Modified Proctor (ASTM D 1557-91, 1998) and the Standard
Proctor (ASTM D 698-91, 1998). The term Proctor is in honor of R. R. Proctor,
who in 1933 showed that the dry density of a soil for a given compactive effort
depends on the amount of water the soil contains during compaction.
For the Modified Proctor (ASTM D 1557-91, 1998, procedure A), the soil is
compacted into a 10.2-cm (4-in) diameter mold that has a volume of 944 cm3
(1/30 ft3), where five layers of soil are compacted into the mold, with each layer
receiving 25 blows from a 44.5-N (10-lbf) hammer that has a 0.46-m (18-in) drop.
The Modified Proctor has a compaction energy of 2700 kN-m/m3 (56,000 ft-lbf /
ft3). The test procedure is to prepare soil at a certain water content, compact the
soil into the mold, and then, by recording the mass of soil within the mold, obtain
the wet density of the compacted soil. By measuring the water content of the
compacted soil, the dry density can be calculated. This compaction procedure is
repeated for the soil at different water contents and then the data are plotted on a
graph in order to obtain the compaction curve.
Figure 6.46 shows the compaction curves for various soils using the Modified
Proctor compaction test. The compaction curves show the relationship between the
dry density (or dry unit weight) and water content for a given compaction effort.
The compaction data presented in Fig. 6.46 were obtained using the Modified Proctor
specifications. The lines to the right of the compaction curves are each known
as a zero air voids curve. These curves represent a condition of saturation (S 
100%) for a specified specific gravity. Note how the right side of the compaction
curves are approximately parallel to the zero air voids curve. This is often the case
for many soil types and can be used as a check on the laboratory test results.
The peak point of the compaction curve is the laboratory maximum dry density
(or the maximum dry unit weight). The water content corresponding to the laboratory
maximum dry density is known as the optimum moisture content. These
laboratory data are important because it tells the grading contractor the best water
content for the most efficient compaction of the soil.
The most common method of assessing the quality of the field compaction is to
calculate the relative compaction (RC) of the fill, defined as: RC  100 d / d max,
where d max  laboratory maximum dry density and d  field dry density. The
maximum dry density ( d max) is the peak point of the laboratory compaction curve.
In order for d to be determined, a field density test must be performed. Field
density tests can be classified as either destructive or nondestructive tests. Probably
the most common destructive method of determining the field dry density is through
SOIL MECHANICS AND FOUNDATIONS 6.109
FIGURE 6.46 Compaction curves for various soils using the Modified Proctor laboratory
test specifications.
the use of the sand cone apparatus. The test procedure consists of excavating a hole
in the ground, filling the hole with sand using the sand cone apparatus, and then
determining the volume of the hole based on the amount of sand required to fill
the hole. Knowing the wet mass of soil removed from the hole divided by the
volume of the hole enables the wet density of the soil to be calculated. The water
content (w) of the soil extracted from the hole can be determined and thus the dry
density ( d ) can then be calculated.
Another type of destructive test for determining the field dry density is the drive
cylinder. This method involves the driving of a steel cylinder of known volume
6.110 SECTION SIX
into the soil. Based on the mass of soil within the cylinder, the wet density can be
calculated. Once the water content (w) of the soil is obtained, the dry density
( d ) of the fill can be calculated.
Probably the most common type of nondestructive field test is the nuclear
method. In this method, the wet density is determined by the attenuation of gamma
radiation. The nuclear method can give inaccurate results (density too high) where
oversize particles are present, such as coarse gravel and cobbles. Likewise, if there
is a large void in the source-detector path, then unusually low density values may
be recorded.
6.10.2 Site Improvement Methods
If the expected settlement for a proposed structure is too large, then different foundation
support or soil stabilization options must be evaluated. As discussed in Art.
6.8.2, one alternative is a deep foundation system that can transfer structural loads
to adequate bearing material in order to bypass a compressible soil layer. Another
option is to construct a floating foundation, which is a special type of deep foundation
where the weight of the structure is balanced by the removal of soil and
construction of an underground basement. Other alternatives include site improvement
methods, such as the following (see Table 6.21):
Soil Replacement. As indicated in Table 6.21, there are basically two types of
soil replacement methods: (1) removal and replacement, and (2) displacement.
The first is the most common approach and consists of the removal of the compressible
soil layer and replacement with structural fill during the grading operations.
Usually the remove and replace grading option is economical only if
the compressible soil layer is near the ground surface and the groundwater table
is below the compressible soil layer or the groundwater table can be economically
lowered.
Water Removal. Table 6.21 lists several different types of water removal site
improvement techniques. If the site contains an underlying compressible cohesive
soil layer, the site can be surcharged with a fill layer placed at ground
surface. Vertical drains (such as wick drains or sand drains) can be installed in
the compressible soil layer to reduce the drainage path and speed up the consolidation
process. Once the compressible cohesive soil layer has had sufficient
consolidation, the fill surcharge layer is removed and the building is constructed.
Site Strengthening. Many different methods can be used to strengthen the onsite
soil (see Table 6.21). For example, deep vibratory techniques are often used
to increase the density of loose sand deposits.
Grouting. In order to stabilize the ground, fluid grout can be injected into the
ground to fill in joints, fractures, or underground voids. For the releveling of
existing structures, one option is mudjacking, which has been defined as a process
whereby a water and soil-cement or soil-lime cement grout is pumped
beneath the slab, under pressure, to produce a lifting force that literally floats
the slab to the desired position. Another commonly used site improvement technique
is compaction grouting, which consists of intruding a mass of very thickconsistency
grout into the soil, which both displaces and compacts the loose
soil. Compaction grouting has proved successful in increasing the density of
poorly compacted fill, alluvium, and compressible or collapsible soil. The advantages
of compaction grouting are less expense and disturbance to the structure
6.111
TABLE 6.21 Site Improvement Methods
Method Technique Principles Suitable soils Remarks
Soil replacement
methods
Remove and replace
Displacement
Excavate weak or undesirable
material and replace with
better soils
Overload weak soils so that
they shear and are displaced
by stronger fill
Any
Very soft
Limited depth and area where
cost-effective; generally  30
ft
Problems with mud-waves and
trapped compressible soil
under the embankment;
highly dependent on specific
site
Water removal
methods
Trenching
Precompression
Precompression with
vertical drains
Electro-osmosis
Allows water drainage
Loads applied prior to
construction to allow soil
consolidation
Shortens drainage path to speed
consolidation
Electric current causes water to
flow to cathode
Soft, fine-grained soils
and hydraulic fills
Normally consolidated
fine-grained soil,
organic soil, fills
Same as above
Normally consolidated
silts and silty clay
Effective depth up to 10 ft;
speed dependent on soil and
trench spacing; resulting
desiccated crust can improve
site mobility
Generally economical; long time
may be needed to obtain
consolidation; effective depth
only limited by ability to
achieve needed stresses
More costly; effective depth
usually limited to 100 ft
Expensive; relatively fast;
usable in confined area; not
usable in conductive soils;
best for small areas
6.112
TABLE 6.21 Site Improvement Methods (Continued)
Method Technique Principles Suitable soils Remarks
Site strengthening
methods
Dynamic compaction
Vibro-compaction
Vibro-replacement
Large impact loads applied by
repeated dropping of a 5- to
35-ton weight; larger weights
have been used
Vibrating equipment densifies
soils
Jetting and vibration used to
penetrate and remove soil;
compacted granular fill then
placed in hole to form
support columns surrounded
by undisturbed soil
Cohesionless best;
possible use for soils
with fines; cohesive
soils below
groundwater table
give poorest results
Cohesionless soils with
20 percent fines
Soft cohesive soils
(su  15 to 50 kPa,
300 to 1000 psf)
Simple and rapid; usable above
and below the groundwater
table; effective depths up to
60 ft; moderate cost; potential
vibration damage to adjacent
structures
Can be efffective up to 100 feet
depth; can achieve good
density and uniformity; grid
spacing of holes critical;
relatively expensive
Relatively expensive
Vibro-displacement Similar to vibro-replacement
except soil is displaced
laterally rather than removed
from the hole
Stiffer cohesive soils
(su  30 to 60 kPa,
600 to 1200 psf)
Relatively expensive
Grouting
Injection of grout
Deep mixing
Fill soil voids with cementing
agents to strengthen and
reduce permeability
Jetting or augers used to
physically mix stabilizer and
soil
Wide spectrum of
coarse- and finegrained
soils
Wide spectrum of
coarse- and finegrained
soils
Expensive; more expensive
grouts needed for finergrained
soils; may use
pressure injection, soil
fracturing, or compaction
techniques
Jetting poor for highly cohesive
clays and some gravelly soils;
deep mixing best for soft
soils up to 165 ft deep
6.113
Thermal
Heat
Freezing
Heat used to achieve
irreversible strength gain and
reduced water susceptibility
Moisture in soil frozen to hold
particles together and
increase shear strength and
reduce permeability
Cohesive soils
All soils below the
groundwater table;
cohesive soils above
the groundwater
table
High energy requirements; cost
limits practicality
Expensive; highly effective for
excavations and tunneling;
high groundwater flows
troublesome; slow process
Geosynthetics Geogrids, geotextiles,
geonets, and
geomembranes
Use geosynthetic materials for
filters, erosion control, water
barriers, drains, or soil
reinforcing (see Art. 6.11)
Effective filters for all
soils; reinforcement
often used for soft
soils
Widely used to accomplish a
variety of tasks; commonly
used in conjunction with
other methods (e.g., strip
drain with surcharge or to
build a construction platform
for site access)
Source: M. P. Rollings and R. S. Rollings, ‘‘Geotechnical Materials in Construction,’’ McGraw-Hill Publishing
Co., New York.
TABLE 6.21 Site Improvement Methods (Continued)
Method Technique Principles Suitable soils Remarks
6.114 SECTION SIX
FIGURE 6.47 Site improvement methods as a function of soil grain size. (Reproduced
from M. P. Rollings and R. S. Rollings, ‘‘Geotechnical Materials in Construction,’’
McGraw-Hill Publishing Co., New York, with permission of McGraw-
Hill, Inc.)
than foundation underpinning, and it can be used to relevel the structure. The
disadvantages are that analyzing the results is difficult, it is usually ineffective
near slopes or for near-surface soils because of the lack of confining pressure,
and the danger exists of filling underground pipes with grout.
Thermal. As indicated in Table 6.21, the thermal site improvement method consists
of either heating or freezing the soil in order to improve its shear strength
and reduce its permeability.
Figure 6.47 presents a summary of site-improvement methods as a function of
soil grain size.
SOIL MECHANICS AND FOUNDATIONS 6.115
FIGURE 6.48 Photograph of a geogrid. (Reproduced from M. P. Rollings and R.
S. Rollings, ‘‘Geotechnical Materials in Construction,’’ McGraw-Hill Publishing Co.,
New York, with permission of McGraw-Hill, Inc.)
6.11 GEOSYNTHETICS
A geosynthetic is defined as a planar product manufactured from polymeric material
and typically placed in soil to form an integral part of a drainage, reinforcement,
or stabilization system. Common types of geosynthetics used during construction
are as follows.
6.11.1 Geogrids
Figure 6.48 shows a photograph of a geogrid, which contains relatively highstrength
polymer grids consisting of longitudinal and transverse ribs connected at
their intersections. Geogrids have a large and open structure and the openings (i.e.,
apertures) are usually 0.5 to 4 in (1.3 to 10 cm) in length and/or width. Geogrids
can be either biaxial or uniaxial, depending on the size of the apertures and shape
of the interconnecting ribs. Geogrids are principally used as soil reinforcement,
such as for subgrade stabilization, slope reinforcement, erosion control, mechanically
stabilized earth retaining walls, and to strengthen the junction between the
top of soft clays and overlying embankments. Geogrids are also used as an overlay
in the construction or repair of asphalt pavements because they tend to reduce
reflective cracking of the pavements.
Compacted soil tends to be strong in compression but weak in tension. The
geogrid is just the opposite, strong in tension but weak in compression. Thus, layers
of compacted soil and geogrid tend to complement each other and produce a soil
mass having both high compressive and tensile strength. The open structure of the
geogrid (see Fig. 6.48) allows the compacted soil to bond in the open geogrid
spaces. Geogrids provide soil reinforcement by transferring local tensile stresses in
the soil to the geogrid. Because geogrids are continuous, they also tend to transfer
6.116 SECTION SIX
and redistribute stresses away from areas of high stress concentrations (such as
beneath a wheel load).
Some of the limitations of geogrid are as follows:
1. Ultraviolet Light. Even geogrids produced of carbon black (i.e., ultraviolet stabilized
geogrids) can degrade when exposed to long-term ultraviolet light. It is
important to protect the geogrid from sunlight and cover the geogrid with fill as
soon as possible.
2. Non-uniform Tensile Strength. Geogrids often have different tensile strengths
in different directions as a result of the manufacturing process. For example, a
Tensar SS-2 (BX1200) biaxial geogrid has an ultimate tensile strength of 2100
lb / ft in the main direction and only 1170 lb / ft in the minor (perpendicular)
direction. It is essential that the engineer always check the manufacturer’s specifications
and determine the tensile strengths in the main and minor directions.
3. Creep. Polymer material can be susceptible to creep. Thus, it is important to
use an allowable tensile strength that does allow for creep of the geosynthetic.
Oftentimes, this allowable tensile design strength is much less than the ultimate
strength of the geogrid. For example, for a Tensar SS-2 (BX1200) biaxial geogrid,
the manufacturer’s recommended tensile strength is about 300 lb / ft, which
is only one-seventh the ultimate tensile strength (2100 lb / ft). The engineer
should never apply an arbitrary factor of safety to the ultimate tensile strength,
but rather obtain the allowable geogrid tensile design strength from the manufacturer.
6.11.2 Geotextiles
Geotextiles are the most widely used type of geosynthetic. Geotextiles are often
referred to as fabric. For example, common construction terminology for geotextiles
includes geofabric, filter fabric, construction fabric, synthetic fabric, and
road-reinforcing fabric. As shown in Figs. 6.49 and 6.50, geotextiles are usually
categorized as either woven or nonwoven, depending on the type of manufacturing
process. Geotextiles are used for many different purposes, as follows:
1. Soil Reinforcement. Used for subgrade stabilization, slope reinforcement, and
mechanically stabilized earth retaining walls. Also used to strengthen the junction
between the top of soft clays and overlying embankments.
2. Sediment Control. Used as silt fences to trap sediment on-site.
3. Erosion Control. Installed along channels, under riprap, and used for shore and
beach protection.
4. Asphalt Overlay. Used in asphalt overlays to reduce reflective cracking.
5. Separation. Used between two dissimilar materials, such as an open graded
base and a clay subgrade, in order to prevent contamination.
6. Filtration and Drainage. Used in place of a graded filter where the flow of
water occurs across (perpendicular to) the plane of the geotextile. For drainage
applications, the water flows within the geotextile.
Probably the most common usage of geotextiles is for filtration (flow of water
through the geotextile). For filtration, the geotextile should be at least 10 times
more permeable than the soil. In addition, the geotextile must always be placed
SOIL MECHANICS AND FOUNDATIONS 6.117
FIGURE 6.49 Photograph of nonwoven geotextiles. The geotextile on the left has
no ultraviolet protection, while the geotextile on the right has ultraviolet protection.
(Reproduced from M. P. Rollings and R. S. Rollings, ‘‘Geotechnical Materials in
Construction,’’ McGraw-Hill Publishing Co., New York, with permission of McGraw-
Hill, Inc.)
FIGURE 6.50 Photograph of a woven geotextile. (Reproduced from M. P. Rollings
and R. S. Rollings, ‘‘Geotechnical Materials in Construction,’’ McGraw-Hill Publishing
Co., New York, with permission of McGraw-Hill, Inc.)
6.118 SECTION SIX
between a less permeable (i.e., the soil) and a more permeable (i.e., the open graded
gravel) material. An inappropriate use of a geotextile would be to wrap it around
a drainage pipe and then cover the geotextile with open-graded gravel. This is
because the geotextile would then have more permeable material on both sides of
the geotextile and it would tend to restrict flow.
Two important design properties for geotextiles used as filtration devices are that
they have an adequate flow capacity and a proper soil retention capability:
1. Flow Capacity. Although specifications have been developed that limit the open
area of the filtration geotextile to 10% or even 5%, it is best to have a larger
open area to develop an adequate flow capacity.
2. Soil Retention Capability. The apparent opening size (AOS), also known as
the equivalent opening size (EOS), determines the soil retention capability. The
AOS is often expressed in terms of opening size (mm) or equivalent sieve size
(e.g., AOS  40–70 indicates openings equivalent to the No. 40 to No. 70
sieves). Obviously, if the geotextile openings are larger than the largest soil
particle diameter, then all of the soil particles will migrate through the geotextile
and clog the drainage system. A common recommendation is that the required
AOS be less than or equal to D85 (grain size corresponding to 85% percent
passing).
Some of the limitations of geotextile are as follows:
1. Ultraviolet Light. Geotextile that has no ultraviolet light protection can rapidly
deteriorate. For example, certain polypropylene geotextiles lost 100% of their
strength after only 8 weeks of exposure.
2. Sealing of Geotextile. When the geotextile is used for filtration, an impermeable
soil layer can develop adjacent the geotextile if it has too low an open area or
too small an AOS.
3. Construction Problems. Some of the more common problems related to construction
with geotextiles are as follows (G. N. Richardson and D. C. Wyant,
‘‘Geotextiles Construction Criteria’’):
(a) Fill placement or compaction techniques damage the geotextile.
(b) Installation loads are greater than design loads, leading to failure during
construction.
(c) Construction environment leads to a significant reduction in assumed fabric
properties, causing failure of the completed project.
(d) Field seaming or overlap of the geotextile fails to fully develop desired
fabric mechanical properties.
(e) Instabilities during various construction phases may render a design inadequate
even though the final product would have been stable.
6.11.3 Geomembranes
Common construction terminology for geomembranes includes liners, membranes,
visqueen, plastic sheets, and impermeable sheets. Geomembranes are used almost
exclusively as barriers to reduce water or vapor migration through soil (see Fig.
6.51). For example, a common usage for geomembranes is for the lining and capping
systems in municipal landfills. For liners in municipal landfills, the thickness
SOIL MECHANICS AND FOUNDATIONS 6.119
FIGURE 6.51 Photograph of a geomembrane, which has a surface texture for
added friction. (Reproduced from M. P. Rollings and R. S. Rollings, ‘‘Geotechnical
Materials in Construction,’’ McGraw-Hill Publishing Co., New York, with permission
of McGraw-Hill, Inc.)
of the geomembrane is usually at least 80 mil. In the United States, one mil is onethousandth
of an inch.
Some of the limitations of geomembranes are as follows:
1. Puncture Resistance. The geomembrane must be thick enough so that it is not
punctured during installation and subsequent usage.
2. Slide Resistance. Slope failures have developed in municipal liners because of
the smooth and low frictional resistance between the geomembrane and overlying
or underlying soil. Textured geomembranes (such as shown in Fig. 6.51)
have been developed to increase the frictional resistance of the geomembrane
surface.
3. Sealing of Seams. A common cause of leakage through geomembranes is due
to inadequate sealing of seams. The following are different methods commonly
used to seal geomembrane seams (M. P. Rollings and R. S. Rollings, ‘‘Geotechnical
Materials in Construction,’’ McGraw-Hill Publishing Co., New York):
(a) Thermal Fusion. Suitable for thermoplastics. Adjacent surfaces are melted
and then pressed together. Commercial equipment is available that uses a
heated wedge (most common) or hot air to melt the materials. Also, ultrasonic
energy can be used for melting rather than heat.
(b) Solvent-Based Systems. Suitable for materials that are compatible with the
solvent. A solvent is used with pressure to join adjacent surfaces. Heating
may be used to accelerate the curing. The solvent may contain some of the
geomembrane polymer already dissolved in the solvent liquid (bodied solvent)
or an adhesive to improve the seam quality.
(c) Contact Adhesive. Primarily suitable for thermosets. Solution is brushed
onto surfaces to be joined, and pressure is applied to ensure good contact.
Upon curing, the adhesive bonds the surfaces together.
6.120 SECTION SIX
FIGURE 6.52 Photograph of a geonet. (Reproduced from M. P. Rollings and R.
S. Rollings, ‘‘Geotechnical Materials in Construction,’’McGraw-Hill Publishing Co.,
New York, with permission of McGraw-Hill, Inc.)
FIGURE 6.53 Photograph of a geocomposite. The geocomposite consists of a
geonet having a textured geomembrane on top, and a filter fabric (geotextile) on the
bottom. (Reproduced from M. P. Rollings and R. S. Rollings, ‘‘Geotechnical Materials
in Construction,’’ McGraw-Hill Publishing Co., New York, with permission of
McGraw-Hill, Inc.)
SOIL MECHANICS AND FOUNDATIONS 6.121
(d) Extrusion Welding. Suitable for all polyethylenes. A ribbon of molten polymer
is extruded over the edge (fillet weld) or between the geomembrane
sheets (flat weld). This melts the adjacent surfaces, which are then fused
together upon cooling.
6.11.4 Geonets and Geocomposites
Geonets are three-dimensional netlike polymeric materials used for drainage (flow
of water within the geosynthetic). Figure 6.52 shows a photograph of a geonet.
Geonets are usually used in conjunction with a geotextile and/or geomembrane and
hence are technically a geocomposite.
Depending on the particular project requirements, different types of geosynthetics
can be combined together to form a geocomposite. For example, a geocomposite
consisting of a geotextile and a geomembrane provides for a barrier that has increased
tensile strength and resistance to punching and tearing. Figure 6.53 shows
a photograph of a geocomposite consisting of a textured geomembrane, geonet, and
geotextile (filter fabric).
6.11.5 Geosynthetic Clay Liners
Geosynthetic clay liners are frequently used as liners for muncipal landfills. The
geosynthetic clay liner typically consists of dry bentonite sandwiched between two
geosynthetics. When moisture infiltrates the geosynthetic clay liner, the bentonite
swells and creates a soil layer having a very low hydraulic conductivity, transforming
it into an effective barrier to moisture migration.
7.1
SECTION SEVEN
STRUCTURAL STEEL
CONSTRUCTION
Bruce Glidden
President, Glidden & Co., Ltd.
Bridgeville, Pennsylvania
Structural steel is an economical construction material for building applications. It
offers high ratios of strength to weight and strength to volume. Thus, structural
steel has the advantage of permitting long clear spans for horizontal members and
requiring less floor space for columns than other common construction materials.
It also can be used in combination with reinforced concrete to provide cost-effective
building components. For large industrial buildings, where the structural frame can
be exposed, it is often the material of choice.
The design of a structural building frame involves the following principal steps:
1. Select the general configuration and type of structure (Sec. 1).
2. Determine the service loads as required by the applicable building code (Art.
5.1.2).
3. Compute the internal forces and moments for the individual members (Sec. 5).
4. Proportion the members and connections.
5. Check performance characteristics, such as deflection, under service conditions.
6. Make a general overall review for economy of function.
7. Prepare complete design drawings delineating all structural steel requirements.
Designers, in addition to performing these steps, should also have an appreciation
of the complete construction cycle to assure a practical and economical design.
This includes understanding the needs of other disciplines and trades, types and
availability of the materials used in steel of construction, applicable codes and
specifications, the role and responsibilities of the fabricator and the erector, and a
designer’s own responsibilities in the area of quality assurance.
The other principal parties involved in structural steel construction are fabricators
and erectors. Erectors frequently act as a subcontractor to the fabricator. Fabrication
operations convert the mill materials into shipping pieces ready for erection at the
jobsite. These operations are generally performed in a shop. The pieces are sized
and shaped to the dimensions shown on detailed shop drawings that are prepared
7.2 SECTION SEVEN
by the fabricator and approved by the structural designer. Shop attachment of detail
pieces (stiffeners, connection materials, etc.) to the individual shipping pieces is
most frequently done by welding. Generally, the fabricator is responsible for moving
the fabricated material to the jobsite. The fabricator determines the size of
shipping pieces, with the concurrence of the designer, at the time the shop drawings
are prepared.
Erectors receive the material and the position and connect the steel into its final
location at the project site. Erectors may have specific equipment on unique projects
with which they are able to perform cost-effective operations. Such equipment may
require attachment points or stiffening of the frame elements, in which case approval
of the designer is requested.
Structural steel consists of hot-rolled steel shapes, steel plates of thickness of 1?8
in or greater, and such fittings as bolts, welds, bracing rods, and turnbuckles. The
owner and the engineer should understand fully what will be furnished by the
fabricator under a contract to furnish ‘‘structural steel.’’ To promote uniformity in
bidding practices, the American Institute of Steel Construction (AISC) has adopted
a ‘‘Code of Standard Practice for Buildings and Bridges’’ (American Institute of
Steel Construction, One East Wacker Drive, Suite 3100, Chicago, IL 60601-2001).
Additional design guides are shown in Table 7.1.
7.1 CODES AND SPECIFICATIONS
Codes, specifications, and standards provide steel designers with sound design procedures
and guidelines. These documents cover selection of service and design
loads, criteria for proportioning members and their connections, procedures for
fabrication and erection, requirements for inspections, and standards for protection
against corrosion and fire. Use of these documents generally ensures safety, economical
designs, and sound operational techniques.
The applicable building code defines the minimum legal requirements for a design.
Most building authorities incorporate in their building code one of the model
building codes (Art. 1.10), but some write their code requirements. Usually, the
basis for the requirements for steel design and construction in building codes are
the American Institute of Steel Construction specifications for structural steel buildings
(Table 7.1). Note that two AISC specifications are available, one applicable to
allowable stress design and plastic design (ASD) and the second to load and resistance
factor design (LRFD).
Table 7.1 also lists other codes and specifications most frequently used by steel
designers. Requirements for special-function buildings, needs of governmental
agencies, and other unique requirements has led to promulgation of many other
codes and specifications. Some of the organizations that publish these standards are
the General Services Administration, U.S. Department of Commerce, Corps of Engineers,
and U.S. Navy Bureau of Yards and Docks.
7.2 MILL MATERIALS
The steel shapes, plates, and bars that make up most of the materials used for
structural steel are produced by mills as hot-rolled products. These products are
made in a batch process; each production run of steel comes from a ‘‘heat.’’ The
STRUCTURAL STEEL CONSTRUCTION 7.3
TABLE 7.1 Basic Steel Construction Codes and Specifications
Organization Document Scope
American Institute of Steel
Construction (AISC)
One East Wacker Drive
Chicago, IL 60601-2001
Code of Standard Practice for
Steel Buildings and
Bridges
Defines structural steel
Plans and specifications
Fabrication
Erection
Quality control
Specification for Structural
Steel Buildings—
Allowable Stress Design
and Plastic Design (ASD)
Specifications for Structural
Steel Buildings—Load and
Resistance Factor Design
(LRFD)
Materials
Loads
Design criteria
Serviceability
Fabrication
Erection
Quality control
American Iron and Steel
Institute (AISI)
1101 17th St., N.W.
Washington, DC 20036
Specification for the Design
of Cold-Formed Steel
Structural Members
Materials
Design criteria
ASTM
100 Barr Harbor Drive
West Conshohocken, PA
19428-2959
ASTM A6
Various ASTM material
specifications
Delivery-shapes / plates
Physical and chemical
requirements
American Welding Society
(AWS)
550 N.W. LeJeune Road
Miami, FL 33126
Structural Welding Code—
Steel (AWS D1.1)
Joint design
Workmanship
Procedures
Inspection
Research Council on Structural
Connections
Engineering Foundation
345 E. 47th St.
New York, NY 10017
Specifications for Structural
Joints Using ASTM A325
or A490 Bolts
Materials
Connection design
Installation
Inspection
Steel Joist Institute (SJI)
3127 10th Ave., North Ext.
Myrtle Beach, SC 29577-6760
Standard Specifications and
Load Tables, Open-Web
Steel Joists
Materials
Design
Steel Structures Painting
Council (SSPC)
40 24th Street, Suite 600
Pittsburgh, PA 15213
Steel Structures Painting
Manual, Vols. 1 and 2
Good practice
Systems
Specifications
specific grade of steel in all mill products is identified by reference to the heat
number.
Through universal acceptance of ASTM specifications (Table 7.1), mill materials
have uniform physical and quality characteristics. There is no significant metallurgical
or physical difference between products ordered to a specific ASTM specifi-
cation and rolled by any U.S. structural mill.
7.4 SECTION SEVEN
TABLE 7.2 Characteristics of Structural Steels
ASTM
specification Thickness, in
Minimum
tensile
strength,
ksi
Minimum
yield
stress,*
ksi
Carbon Steels
A36 To 8 in incl. 58–80† 36
A529 To 1?2 in incl. 60–85† 42
High-strength, low-alloy steels
A441 To 3?4 incl. 70 50
Over 3?4 to 11?2 67 46
Over 11?2 to 4 incl. 63 42
Over 4 to 8 incl. 60 40
A572 Gr 42: to 4 incl. 60 42
Gr 45: to 11?2 incl. 60 45
Gr 50: to 11?2 incl. 65 50
Gr 55: to 11?2 incl. 70 55
Gr 60: to 1 incl. 75 60
Gr 65: to 1?2 incl. 80 65
A242 To 3?4 incl. 70 50
Over 3?4 to 11?2 67 46
Over 11?2 to 4 incl. 63 42
A588 To 4 incl. 70 50
Over 4 to 5 67 46
Over 5 to 8 incl. 63 42
A992 Shapes only 65 50
Heat-treated low-alloy steels
A514 To 3?4 incl. 115–135 100
Over 3?4 to 21?2 115–135 100
Over 21?2 to 4 incl. 105–135 90
*Yield stress or yield strength, whichever shows in the stress-strain curve.
†Minimum tensile strength may not exceed the higher value.
7.2.1 Grades of Steel
Structural steel grades are referred to by their corresponding ASTM designation.
For example, the most commonly used grade of structural steel is A36, which is
produced to meet the requirements of the ASTM A36 specification. This grade
offers a good mix of strength, weldability, and cost. In many designs, this specifi-
cation alone will satisfy designers’ needs. Other specifications, such as A53 for
pipe, provide an equivalent grade of steel for that type of product. However, as
loads on the structural elements becomes larger, other grades of steel may become
more economical because of dimensional limitations or simpler fabrication. These
grades provide greater strength levels at somewhat higher costs per unit weight.
AISC recommends certain grades of steel, all of which have desirable characteristics,
such as weldability and cost-effectiveness, for use where higher strength
levels are required. The specifications covering these grades are listed in Table 7.2.
Several steels have more than one level of tensile strength and yield stress, the
STRUCTURAL STEEL CONSTRUCTION 7.5
TABLE 7.3 Symbols for Structural Shapes
Section Symbol
Wide-flange shapes W
Standard I shapes S
Bearing-pile shapes HP
Similar shapes that cannot be grouped in W, S, or HP M
Structural tees cut from W, S, or M shapes WT, ST, MT
American standard chemicals C
All other channel shapes MC
Angles L
levels being dependent on thickness of material. The listed thicknesses are precise
for plates and nearly correct for shapes. To obtain the precise value for shapes,
refer to an AISC ‘‘Manual of Steel Construction’’ (ASD or LRFD) or to mill catalogs.
Weathering Steels. The A242 and A588 grades of steel offer enhanced corrosion
resistance relative to A36 material. These steels, called weathering steels, form a
thin oxidation film on the surfaces that inhibits further corrosion in ordinary atmospheric
conditions. However, special treatment of construction details is required.
Because of such constraints, and because these grades are more expensive, utilization
of weathering steels in building construction is limited. These grades are
more commonly used in bridge construction.
Steel Grade Identification. Because of the several grades of steel in use, ASTM
specifications require that each piece of hot-rolled steel be properly identified with
vital information, including the heat number. The AISC specifications for structural
steel buildings require fabricators to be prepared to demonstrate, by written procedure
and by actual practice, the visible identification of all main stress-carrying
elements at least through shop assembly. Steel identification include ASTM designation,
heat number (if required), and mill test reports when specifically ordered.
Availability. Because structural steel is produced in a batch process, the less commonly
used shapes and the higher-strength grades are produced less frequently than
commonly used A36 shapes. Furthermore, steel service centers stock the smaller
A36 shapes. As a result, availability of steels can affect construction schedules.
Consequently, steel designers should be aware of the impact of specifying less
commonly used materials and shapes if the project has a tight schedule. Fabricator
representatives can provide needed information.
7.2.2 Structural Shapes
Steel mills have a standard classification for the many products they make, one of
which is structural shapes (heavy). By definition this classification takes in all
shapes having at least one cross-sectional dimension of 3 in or more. Shapes of
lesser size are classified as structural shapes (light) or, more specifically, bars.
Shapes are identified by their cross-sectional characteristics—angles, channels,
beams, columns, tees, pipe, tubing, and piles. For convenience, structural shapes
are simply identified by letter symbols as indicated in Table 7.3. The industry
7.6 SECTION SEVEN
recommended standard (adopted 1970) for indicating a specific size of beam or
column-type shape on designs, purchase orders, shop drawings, etc., specifies listing
of symbol, depth, and weight, in that order. For example, W14 
 30 identifies a
wide-flange shape with nominal depth of 14 in and weight of 30 lb / lin ft. The 
,
read as ‘‘by,’’ is merely a separation.
Each shape has its particular functional use, but the workhorse of building construction
is the wide-flange W section. For all practical purposes, W shapes have
parallel flange surfaces. The profile of a W shape of a given nominal depth and
weight available from different producers is essentially the same, except for the
size of fillets between web and flanges.
7.2.3 Tolerances for Structural Shapes and Plates
Mills are granted a tolerance because of variations peculiar to working of hot steel
and wear of equipment. Limitations for such variations are established by ASTM
specification A6.
Wide-flange beams or columns, for example, may vary in depth by as much as
1?2 in, i.e., 1?4 in over and under the nominal depth. The designer should always
keep this in mind. Fillers, shims, and extra weld metal installed during erection
may not be desirable, but often they are the only practical solution to dimensional
variations from nominal.
Cocked flanges on column members are particularly troublesome to the erector
for it is not until the steel is erected in the field that the full extent of mill variations
becomes evident. This is particularly true for a long series of spans or bays, where
the accumulating effect of dimensional variation of many columns may require
major adjustment. Fortunately, the average variation usually is negligible and nominal
erection clearance allowed for by the fabricator will suffice.
Mill tolerances also apply to beams ordered from the mills cut to length. Where
close tolerance may be desired, as sometimes required for welded connections, it
may be necessary to order the beams long and then finish the ends in the fabricating
shop to precise dimensions. This is primarily the concern of structural detailers.
7.2.4 Cambered Beams
Frequently, designers want long-span beams slightly arched (cambered) to offset
deflection under load and to prevent a flat or saggy appearance. Such beams may
be procured from the mills, the required camber being applied to cold steel. The
AISC Manuals give the maximum cambers that mills can obtain and their prediction
of the minimum cambers likely to remain permanent. Smaller cambers than these
minimums may be specified, but their permanency cannot be guaranteed. Nearly
all beams will have some camber as permitted by the tolerance for straightness,
and advantage may be taken of such camber in shop fabrication.
A method of cambering, not dependent on mill facilities, is to employ heat. In
welded construction, it is commonplace to flame-straighten members that have become
distorted. By the same procedure, it is possible to distort or camber a beam
to desired dimensions.
7.2.5 Steel Plates
Used by fabricators to manufacture built-up structural members, such as columns
and girders, and for detail connection material, plates are identified by the symbol
STRUCTURAL STEEL CONSTRUCTION 7.7
TABLE 7.4 Characteristics of Pipe and Tubular Steels
ASTM
spec. Grade Product
Min
tensile
strength,
ksi
Min
yield
stress,
ksi
A53 B Pipe 60.0 35.0*
A500 A Round 45.0 33.0
A Shaped 45.0 39.0
B Round 58.0 42.0
B Shaped 58.0 46.0
C Shaped 70.0 50.0
A501 . . . All tubing 58.0 36.0
A618 I All tubing 70.0 50.0
II All tubing 70.0 50.0
III All tubing 65.0 50.0
* Use 36.0 for purpose of design.
PL. Cross-sectional dimensions are given in inches (or millimeters). A plate 1?2 in
thick and 2 ft wide is billed as PL 1?2 
 24. Plates may also be specified by weight,
although this is unusual in building construction work.
Mill tolerances for plate products for structural applications are also defined by
ASTM specification A6. There are provisions for thickness, crown, camber, and
length. Consideration of these characteristics are primarily the responsibility of
fabricators. However, steel designers should be aware of how these tolerances affect
the fabricator’s work and permit the design to accommodate these characteristics.
7.2.6 Pipe and Tubular Sections
Pipe meeting the requirements of ASTM specification A53, Types E and S, Grade
B, is comparable to A36 steel, with yield strength Fy  36 ksi. It comes in three
weight classification: standard, extra strong, and double extra strong, and in diameters
ranging up to 26 in.
Several mills produce square and rectangular tubing, known as hollow structural
sections, in sizes from 3 
 2 and 2 
 2 to 12 
 8 and 10 
 10 in, with wall
thickness up to 5?8 in. These flat-sided shapes afford easier connections than pipes,
not only for connecting beams but also for such items as window and door frames.
The main strength properties of several grades of steel used for pipe and tubular
sections are summarized in Table 7.4.
Cautionary Note. Hollow structural sections are not produced to meet the requirements
of ASTM specification A6. Because of this characteristic, the AISC and
the Steel Tube Institute of North America recommended that the nominal wall
thickness of such sections be reduced by 7% when calculating the section properties
of these sections, (area, section modulus, and moment of inertia) so as to maintain
a factor of safety equivalent to that present in other structural steel shapes.
7.8 SECTION SEVEN
FIGURE 7.1 Two main types of construction with high-strength bolts. Although, in general, no
paint is permitted on faying surfaces in slip-critical connections, the following are allowed: scored
galvanized coatings, inorganic zinc-rich paint, and metallized zinc or aluminum coatings.
7.3 FASTENERS
Two basic types of fasteners are typically used in construction, bolts and welds.
Both are used in the fabricating shop and on the job site in connections joining
individual members. Welds are also used to fasten together components of built-up
members. Bolts, however, are more commonly used for field connections, and
welds, for shop work. Rivets, which were once widely used for main connections,
both shop and field, are essentially obsolete.
Many variables affect selection of fasteners. Included among these are economy
of fabrication and erection, availability of equipment, inspection criteria, labor supply,
and such design considerations as fatigue, size and type of connections, continuity
of framing, reuse, and maintenance. It is not uncommon for steel framing
to be connected with such combinations as shop welds and field bolts or to be allwelded.
It is usual to use field welds for column splices with bolted connections
elsewhere. The variables affecting decisions on use of fasteners should be explored
with engineers representing the fabricator and the erector.
7.3.1 High-Strength Bolts
Development of high-strength bolts is vested in the Research Council on Riveted
and Bolted Structural Joints of the Engineering Foundation. Its ‘‘Specification for
Structural Steel Joints Using A325 or A490 Bolts’’ (Table 7.1) was adopted by the
American Institute for Steel Construction. Bolts conforming to ASTM A449 are
acceptable, but their usage is restricted to bearing-type connections (Fig. 7.1) reSTRUCTURAL
STEEL CONSTRUCTION 7.9
quiring bolt diameters greater than 11?2 in. Furthermore, when they are required to
be tightened to more than 50% of their specified minimum tensile strength, hardened
steel washers should be installed under the heads.
When high-strength bolts are used in a connection, they are highly tensioned by
tightening of the nuts and thus tightly clamp together the parts of the connection.
For convenient computation of load capacity, the clamping force and resulting
friction are resolved as shear. Bearing between the bolt body and connected material
is not a factor until loads become large enough to cause slippage between the parts
FIGURE 7.2 Identification markings on heads
and nuts of high-strength bolts.
of the connection. The bolts are assumed
to function in shear following
joint slippage into full bearing.
The clamping and bearing actions
lead to the dual concept: slip-critical
connections and bearing-type connections.
For the latter, the allowable shear
depends on the cross-sectional bolt area
at the shear plane. Hence, two shear values
are assigned, one for the full body
area and one for the reduced area at the
threads.
Identification. There is no difference
in appearance of high-strength bolts intended
for either slip-critical or bearingtype
connections. To aid installers and
inspectors in identifying the several
available grades of steel, bolts and nuts
are manufactured with permanent markings
(Fig. 7.2).
7.3.2 High-Strength Bolt Installation
Washer requirements for high-strength bolted assemblies depend on the method of
installation and type of bolt holes in the connected elements. These requirements
are summarized in Table 7.5.
Bolt Tightening. Specifications require that all high-strength bolts be tightened to
70% of their specified minimum tensile strength, which is nearly equal to the proof
load (specified lower bound to the proportional limit) for A325 bolts, and within
10% of the proof load for A490 bolts. Tightening above these minimum tensile
values does not damage the bolts, but it is prudent to avoid excessive uncontrolled
tightening. The required minimum tension, kips, for A325 and A490 bolts is given
in Table 7.6.
There are three methods for tightening bolts to assure the prescribed tensioning:
Turn-of-Nut. By means of a manual or powered wrench, the head or nut is turned
from an initial snug-tight position. The amount of rotation, varying from one-third
to a full turn, depends on the ratio of bolt length (underside of heat to end of point)
to bolt diameter and on the disposition of the outer surfaces of bolted parts (normal
or sloped not more than 1:20 with respect to the bolt axis). Required rotations are
7.10 SECTION SEVEN
TABLE 7.5 Washer Requirements for High-Strength Bolts
Method of tensioning A325 bolts
A490 bolts
Base material
Fy  40.0*
Base material
Fy  40.0*
Calibrated wrench One washer under
turned element
Two washers One washer
under turned
element
Turn-of-the-nut None Two washers One washer
under turned
element
Both methods, slotted and
oversized holes
Two washers Two washers Two washers
*Fy  specified minimum yield stress, ksi.
TABLE 7.6 Minimum
Tightening Tension, kips, for
High-Strength Bolts
Dia, in A325 A490
5?8 19 24
3?4 28 35
7?8 39 49
1 51 64
11?8 56 80
11?4 71 102
13?8 85 121
11?2 103 148
tabulated in the ‘‘Specification for Structural Steel Joints Using A325 of A490
Bolts.’’
Calibrated Wrench. By means of a powered wrench with automatic cutoff and
calibration on the job. Control and test are accomplished with a hydraulic device
equipped with a gage that registers the tensile stress developed.
Direct Tension Indicator. Special indicators are permitted on satisfactory demonstration
of performance. One example is a hardened steel washer with protrusions
on one face. The flattening that occurs on bolt tightening is measured and correlated
with the induced tension.
7.3.3 Unfinished Bolts
Known in construction circles by several names—ordinary, common, machine, or
rough—unfinished bolts are characterized chiefly by the rough appearance of the
shank. They are covered by ASTM A307. They fit into holes 1?16 in larger in
diameter than the nominal bolt diameter.
STRUCTURAL STEEL CONSTRUCTION 7.11
Unfinished bolts have relatively low load-carrying capacity. This results from
the possibility that threads might lie in shear planes. Thus, it is unnecessary to
extend the bolt body by use of washers.
One advantage of unfinished bolts is the ease of making a connection; only a
wrench is required. On large jobs, however, erectors find they can tighten bolts
more economically with a pneumatic-powered impact wrench. Power tightening
generally yields greater uniformity of tension in the bolts and makes for a betterbalanced
connection.
While some old building codes restrict unfinished bolts to minor applications,
such as small, secondary (or intermediate) beams in floor panels and in certain parts
of one-story, shed-type buildings, the AISC specifications for structural steel buildings,
with a basis of many years of experience, permit A307 bolts for main connections
on structures of substantial size. For example, these bolts may be used for
beam and girder connections to columns in buildings up to 125 ft in height.
There is an economic relation between the strength of a fastener and that of the
base material. So while A307 may be economical for connecting steel with a 36-
ksi yield point, this type of bolt may not be economical with 50-ksi yield-point
steel. The number of fasteners to develop the latter becomes excessive and perhaps
impractical due to size of detail material.
A307 bolts should always be considered for use, even in an otherwise all-welded
building, for minimum-type connections, such as for purlins, girts, and struts.
Locking Devices for Bolts. Unfinished bolts (ASTM A307) and interferencebody-
type bolts (Art 7.3.4) usually come with American Standard threads and nuts.
Properly tightened, connections with these bolts give satisfactory service under
static loads. But when the connections are subjected to vibration or heavy dynamic
loads, a locking device is desirable to prevent the nut from loosening.
Locking devices may be classified according to the method employed: special
threads, special nuts, special washers, and what may be described as field methods.
Instead of conventional threads, bolt may be supplied with a patented self-locking
thread called Dardelet. Sometimes, locking features are built into the nuts. Patented
devices, the Automatic-Nut, Union-Nut, and Pal-Nut, are among the common ones.
Washers may be split rings or specially touched. Field methods generally used
include checking, or distorting, the threads by jamming them with a chisel or locking
by tack welding the nuts.
7.3.4 Other Bolt-Type Fasteners
Interference body of bearing-type bolts are characterized by a ribbed or interrupted-
ribbed shank and a button-shaped head; otherwise, including strength, they
are similar to the regular A325 high-strength bolts. The extreme diameter of the
shank is slightly larger than the diameter of the bolt hole. Consequently, the tips
of the ribs or knurlings will groove the side of the hole, assuring a tight fit. One
useful application has been in high television towers, where minimum-slippage
joints are desired with no more installation effort than manual tightening with a
spud wrench. Nuts may be secured with lock washers, self-locking nuts, or Dardelet
self-locking threads. The main disadvantage of interference body bolts is the need
for accurate matching of truly concentric holes in the members being joined; reaming
sometimes is necessary.
Huckbolts are grooved (not threaded) and have an extension on the end of the
shank. When the bolt is in the hole, a hydraulic machine, similar to a bolting or
7.12 SECTION SEVEN
riveting gun, engages the extension. The machine pulls on the bolt to develop a
high clamping force, then swages a collar into the grooved shank and snaps off the
extension, all in one quick operation.
7.3.5 Welds
Welding is used to fasten together components of a built-up member, such as a
plate girder, and to make connections between members. This technique, which
uses fusion is a controlled atmosphere, requires more highly skilled labor than does
bolting. However, because of cost advantages, welding is widely used in steel construction,
especially in fabricating shops where conditions are more favorable to
closely controlled procedures. When field welding is specified, the availability of
skilled welders and inspection technicians and the use of more stringent qualitycontrol
criteria should be considered.
Any of several welding processes may be used: manual shielded metal arc,
submerged arc, flux cored arc, gas metal arc, electrogas, and electroslag. They are
not all interchangeable, however; each has its advantageous applications.
Many building codes accept the recommendations of the American Welding
Society ‘‘Structural Welding Code’’ (AWS D1.1) (Table 7.1). The AISC specification
incorporates many of this code’s salient requirements.
Weld Types. Practically all welds used for connecting structural steel are of either
of two types: fillet or groove.
Figure 7.3a and b illustrates a typical fillet weld. As stated in Art. 7.27, all
stresses on fillet welds are resolved as shear on the effective throat. The normal
throat dimension, as indicated in Fig. 7.3a and b, is the effective throat for all
welding processes, except the submerged-arc method. The deep penetration characteristic
of the latter process is recognized by increasing the effective throat dimension,
as shown in Fig. 7.3c.
Groove welds (Fig. 7.3d, e, and ?) are classified in accordance with depth of
solid weld metal as either complete or partial penetration. Most groove welds, such
as those in Fig. 7.3d and e, are made complete-penetration welds by the workmanship
requirements: use backup strips or remove slag inclusions and imperfections
(step called back-gouging) on the unshielded side of the root weld. The partialpenetration
groove weld shown in Fig. 7.3? is typical of the type of weld used for
box-type members and column splices. Effective throat depends on the welding
process, welding position, and the chamfer angle 
. The indicated effective throat
(Fig. 7.3?) is proper for the shielded-metal-arc processes and for all welding positions.
(See also Art. 7.27.)
Welding Electrodes. Specifications for all welding electrodes, promulgated by the
American Welding Society (AWS), are identified as A5.1, A5.5, A5.17, etc., depending
on the welding process. Electrodes for manual arc welding, often called
stick electrodes, are designated by the letter E followed by four of five digits. The
first two or three digits designate the strength level; thus, E70XX means electrodes
having a minimum tensile strength of 70.0 ksi. Allowable shear stress on the depositied
weld metal is taken as 0.30 times the electrode strength classification; thus,
0.30 times 70 to an E70 results in an allowable stress of 21.0 ksi. The remaining
digits provide information on the intended usage, such as the particular welding
positions and types of electrode coating.
STRUCTURAL STEEL CONSTRUCTION 7.13
FIGURE 7.3 Effective throats of fillet and groove welds.
Welding Procedures. The variables that affect the quality of a weld are controlled
by welding procedures that must be approved by the structural engineer. Specifi-
cation AWS D1.1 contains several prequalified welding procedures, the use of
which permits fabricators and erectors to avoid the need for obtaining approvals
for specific routine work. Where unusual conditions exist, the specification requires
that formal documentation be submitted for review and approval.
Base-Metal Temperatures. An important requirement in production of quality
welds is the temperature of base metal. Minimum preheat and interpass temperature
as specified by the AWS and AISC standards must be obtained within 3 inches of
the welded joint before welding starts and then maintained until completion. Table
7.7 gives the temperature requirements based on thickness (thickest part of joint)
and welding process for several structural steels. When base metal temperature is
below 32F, it must be preheated to at least 70 and maintained at that temperature
during welding. No welding is permitted when ambient temperature is below 0F.
7.14 SECTION SEVEN
TABLE 7.7 Minimum Preheat and Interpass Temperatures for Base Metal to Be Welded
Steel*
Shielded-metal-arc welding
with other than low-hydrogen
electrodes
Thickness, in Temp, F
Shielded-metal-arc welding
with low-hydrogen electrodes,
gas-metal-arc, and flux-cored
arc welding
Thickness, in Temp, F
A36 To 3?4 in incl. 32 To 3?4 in incl. 32
Over 3?4 to 11?2 150 Over 3?4 to 11?2 50
Over 11?2 to 21?2 225 Over 11?2 to 21?2 150
Over 21?2 300 Over 21?2 225
A242 Not permitted To 3?4 in incl. 32
A441 Over 3?4 to 11?2 70
A588 Over 11?2 to 21?2 150
A572 to Fy  50 Over 21?2 225
A529
*For temperatures for other steels, see AWS D1.1, ‘‘Structural Welding Code,’’ American Welding
Society.
Additional information, including temperature requirements for other structural
steels, is given AWS D1.1 and the AISC specifications for structural steel buildings
(Table 7.1).
Another quality-oriented requirement applicable to fillet welds is minimum leg
size, depending on thickness of steel (Table 7.8). The thicker part connected governs,
except that the weld size need not exceed the thickness of the thinner part.
This rule is intended to minimize the effects of restraint resulting from rapid cooling
due to disproportionate mass relationships.
TABLE 7.8 Minimum Sizes* of Fillet and
Partial-Penetration Welds
Base-metal thickness, in Weld size, in
To 1?4 incl. 1?8
Over 1?4 to 1?2 1?16
Over 1?2 to 3?4 1?4
Over 3?4 to 11?2 5?16
Over 11?2 to 21?2 1?8
Over 21?2 to 6 1?2
Over 6 5?8
*Leg dimension for fillet welds; minimum effective
throat for partial-penetration groove welds.
7.3.6 Inspection of Welds
The quality of welded work is highly dependent upon the close adherence to applicable
welding process and procedural requirements. This, plus attention to diSTRUCTURAL
STEEL CONSTRUCTION 7.15
FIGURE 7.4 Symbols for shop and field bolts.
mensional requirements, will generally result in serviceable welds. As a result, most
welding work incorporated in building construction, other than for major structures,
is inspected using visual inspection techniques. The fabricator’s quality personnel
are responsible for adherence to approved procedures. The owner’s inspector observed
the erector’s operations and may perform any necessary visual inspection of
the finished work.
Four nondestructive testing methods are commonly used to evaluate welded
work. These are (1) magnetic-particle inspection, (2) liquid penetrant inspection,
(3) radiographic inspection, and (4) ultrasonic inspection. The latter two methods
are the most common today. Each of these nondestructive testing methods add to
the cost of construction and should be used where some special service requirement
justifies this added feature. Any such testing must be identified on the drawings or
in the specifications.
7.3.7 Fastener Symbols
Fasteners are indicated on design, shop, and field erection drawings by notes and
symbols. A simple note may suffice for bolts; for example: ‘‘7?8-in A325 bolts,
except as noted.’’ Welds require more explicit information, since their location is
not so obvious as that of holes for bolts.
Symbols are standard throughout the industry. Figure 7.4 shows the symbols for
bolts, Fig. 7.5 the symbols for welds. The welding symbols (Fig. 7.5a) together
with the information key (Fig. 7.5b) are from the American Welding Society ‘‘Symbols
for Welding and Nondestructive Testing, AWS A2.4.
7.3.8 Erection Clearance for Fasteners
All types of fasteners require clearances for proper installation in both shop and
field. Shop connections seldom are a problem, since each member can be easily
manipulated for access. Field connections, however, require careful planning, because
connections can be made only after all members to be connected are aligned
7.16 SECTION SEVEN
FIGURE 7.5 Symbols for shop and field welds.
in final position. This is the responsibility of the fabricator’s engineering staff and
is discharged during the making of shop drawings. However, the basic design con-
figuration must permit the necessary clearances to be developed.
Clearances are required for two reasons: to permit entry, as in the case of bolts
entering holes, and to provide access to the connected elements either to allow the
tightening of bolts with field tools or to permit the movement of manual electrodes
or semiautomatic welding tools in depositing weld metal.
(‘‘Structural Steel Detailing,’’ American Institute of Steel Construction.)
STRUCTURAL STEEL CONSTRUCTION 7.17
7.4 FABRICATION
When considering fabrication, as well as erection of the fabricated product, the
designer must taken into account contractual matters, work by others on the construction
team, schedule implications of the design, and quality assurance matters.
Fortunately, there are well established aids for these considerations. Contractual
questions such as what constitutes structural steel, procedures for preparing and
approving the shop detail drawings, and standard fabrication procedures and tolerances
are all addressed in the AISC’s Code of Standard Practice (Table 7.1).
Insights on economical connection details and the impact of material selection on
mill material deliveries are generally available from the fabricator’s engineering
staff. These engineers are also able to comment on unique erection questions.
Quality assurance questions fall into two categories, fabrication operations and
field operations. Today, sound quality control procedures are in place in most fabrication
shops through an AISC program which prequalifies fabricators. There are
three levels of qualification: I, II and III, with Level III being the most demanding.
Fabricators with either a Level I or Level II certification are suitable for almost all
building work.
Most engineers incorporate the AISC’s Code of Standard Practice in their project
specification.
7.4.1 Shop Detail Drawings
Detail drawings are prepared by the fabricator to delineate to his work force the
fabrication requirements. Because each shop has certain differences in equipment
and/or procedures, the fabricator develops details which, when matched with his
processes, are the most economical. To accomplish this end, the design drawings
need to be complete, showing all structural steel requirements, and should include
design information on the forces acting at connections. Designers should avoid
specifying deck openings and beam penetrations through notes on the drawings.
This is a frequent cause of extra costs on fabrication contracts.
7.4.2 Fabrication Processes
Mill material is cut to length by sawing, shearing, or flame cutting. Columns may
also be milled to their final length. Holes for fasteners are drilled or punched.
Punched and reamed holes are seldom used in building construction. Cuts for weld
preparation, web openings, and dimensional clearances are flame cut. AISC guidelines
for each of these processes are associated with the AISC’s fabricator prequalification
program. Welding for building construction is performed in accordance
with the provisions of the AWS Structural Welding Code, D1.1. Most requirements
can be satisfied using pre-qualified welding procedures.
7.5 QUALITY ASSURANCE
Concepts for improving and maintaining quality in the constructed project stress
the participation of the design professional in the project team consisting of the
7.18 SECTION SEVEN
owner, design professional, and general contractor. While the structural engineer
plays a varying role in the major phases of a project—that is, conceptual, preliminary,
and final design; bidding; and construction—his or her participation is vital
to achieving the appropriate level of quality.
Those activities of the structural engineer that have the greatest impact on quality
are materials selection, determination of workmanship quality levels, quality control
(QC) requirements, preparation of clear and complete contract documents, and review
of the contractor’s work. One aspect of the last item that is particularly important
in steel construction is the review and approval of the fabricator’s shop
drawings. Because the fabricator’s engineers design connections to meet the criteria
provided by the design professional, the review and approval process must assure
that connection designs and details are compatible with the intent and requirements
of the basic design.
(‘‘Quality in the Constructed Project,’’ American Society of Civil Engineers.)
STRUCTURAL FRAMING SYSTEMS
Steel construction may be classified into three board categories: wall-bearing, skeleton,
and long-span framing. Depending on the needs of the building, one or more
of these categories may be incorporated.
In addition to the main building elements—floors, roofs, walls—the structural
system must include bracing members that provide lateral support for main members
as well as for other bracing members, resistance to lateral loads on the building,
redundant load paths, and stiffness to the structure limit deflections. An economical
and safe design properly integrates these systems into a completed structure.
7.6 WALL-BEARING FRAMING
Probably the oldest and commonest type of framing, wall-bearing (not to be confused
with bearing-wall construction), occurs whenever a wall of a building, interior
or exterior, is used to support ends of main structural elements carrying roof or
floor loads. The walls must be strong enough to carry the reaction from the supported
members and thick enough to ensure stability against any horizontal forces
that may be imposed. Such construction often is limited to relatively low structures,
because load-bearing walls become massive in tall structures. Nevertheless, a wallbearing
system may be advantageous for tall buildings when designed with reinforcing
steel.
A common application of wall-bearing construction may be found in many
single-family homes. A steel beam, usually 8 or 10 in deep, is used to carry the
interior walls and floor loads across the basement with no intermediate supports,
the ends of the beam being supported on the foundation walls. The relatively shallow
beam depth affords maximum headroom for the span. In some cases, the spans
may be so large that an intermediate support becomes necessary to minimize de-
flection. Usually a steel pipe column serves this purpose.
Another example of wall-bearing framing is the member used to support masonry
over windows, doors, and other openings in a wall. Such members, called
lintels, may be a steel angle section (commonly used for brick walls in residences)
STRUCTURAL STEEL CONSTRUCTION 7.19
FIGURE 7.6 Lintels supporting masonry.
or, on longer spans and for heavier walls, a fabricated assembly. A variety of
frequently used types is shown in Fig. 7.6. In types b, c, and e, a continuous plate
is used to close the bottom, or soffit, of the lintel, and to join the load-carrying
beams and channels into a single shipping unit. The gap between the toes of the
channel flanges in type d may be covered by a door frame or window trim, to be
installed later. Pipe and bolt separators are used to hold the two channels together
to form a single member for handling.
Bearing Plates. Because of low allowable pressures on masonry, bearing plates
(sometimes called masonry plates) are usually required under the ends of all beams
that rest on masonry walls, as illustrated in Fig. 7.7. Even when the pressure on
the wall under a member is such that an area no greater than the contact portion
of the member itself is required, wall plates are sometimes prescribed, if the member
is of such weight that it must be set by the steel erector. The plates, shipped
loose and in advance of steel erection, are then set by the mason to provide a
satisfactory seat at the proper elevation.
Anchors. The beams are usually anchored to the masonry. Government anchors,
as illustrated in Fig. 7.7, are generally preferred.
Nonresidential Uses. Another common application for the wall-bearing system is
in one-story commercial and light industrial-type construction. The masonry side
walls support the roof system, which may be rolled beams, open-web joists, or light
7.20 SECTION SEVEN
FIGURE 7.7 Wall-bearing beam.
trusses. Clear spans of moderate size are usually economical, but for longer spans
(probably over 40 ft), wall thickness and size of buttresses (pilasters) must be built
to certain specified minimum proportions commensurate with the span—a requirement
of building codes to assure stability. Therefore, the economical aspect should
be carefully investigated. It may cost less to introduce steel columns and keep wall
size to the minimum permissable. On the other hand, it may be feasible to reduce
the span by introducing intermediate columns and still retain the wall-bearing system
for the outer end reactions.
Planning for Erection. One disadvantage of wall-bearing construction needs emphasizing:
Before steel can be set by the ironworkers, the masonry must be built
up to the proper elevation to receive it. When these elevations vary, as is the case
at the end of a pitched or arched roof, then it may be necessary to proceed in
alternate stages, progress of erection being interrupted by the work that must be
performed by the masons, and vice versa. The necessary timing to avoid delays is
seldom obtained. A few columns or an additional rigid frame at the end of a building
may cost less than using trades to fit an intermittent and expensive schedule.
Remember, too, that labor-union regulations may prevent the trades from handling
any material other than that belonging to their own craft. An economical rule may
well be: Lay out the work so that the erector and ironworkers can place and connect
all the steelwork in one continuous operation.
(F. S. Merritt and R. Brockenbrough, ‘‘Structural Steel Designers Handbook,’’
2d ed., McGraw-Hill Publishing Company, New York.)
7.7 SKELETON FRAMING
In skeleton framing all the gravity loadings of the structure, including the walls are
supported by the steel framework. Such walls are termed nonbearing or curtain
walls. This system made the skyscraper possible. Steel, being so much stronger
STRUCTURAL STEEL CONSTRUCTION 7.21
FIGURE 7.8 Typical beam-and-column steel framing, shown in plan.
FIGURE 7.9 Typical steel spandrel beams.
7.22 SECTION SEVEN
than all forms of masonry, is capable of sustaining far greater load in a given space,
thus obstructing less of the floor area in performing its function.
With columns properly spaced to provide support for the beams spanning between
them, there is no limit to the floor and roof area that can be constructed with
this type of framing, merely by duplicating the details for a single bay. Erected tier
upon tier, this type of framing can be built to any desired height. Fabricators refer
to this type of construction as ‘‘beam and column.’’ A typical arrangement is illustrated
in Fig. 7.8.
The spandrel beams, marked B1 in Fig. 7.8, are located in or under the wall so
as to reduce eccentricity caused by wall loads. Figure 7.9 shows two methods for
connecting to the spandrel beam the shelf angle that supports the outer course of
masonry over window openings 6 ft or more in width. In order that the masonry
contractor may proceed expeditiously with the work, these shelf angles must be in
alignment with the face of the building and at the proper elevation to match a
masonry joint. The connection of the angles to the spandrel beams is made by
bolting; shims are provided to make the adjustments for line and elevation.
Figure 7.9a illustrates a typical connection arrangement when the outstanding
leg of the shelf angle is about 3 in or less below the bottom flange of the spandrel
beam; Fig. 7.9b illustrates the corresponding arrangement when the outstanding leg
of the shelf angle is more than about 3 in below the bottom flange of the spandrel
beam. In the cases represented by Fig. 7.9b, the shelf angles are usually shipped
attached to the spandrel beam. If the distance from the bottom flange to the horizontal
leg of the shelf angle is greater than 10 in, a hanger may be required.
In some cases, as over door openings, the accurate adjustment features provided
by Fig. 7.9a and b may not be needed. It may then be more economical to simplify
the detail, as shown in Fig. 7.9c. The elevation and alignment will then conform
to the permissible tolerances associated with the steel framework.
(E. H. Gaylord, Jr., et al., ‘‘Design of Steel Structures,’’ 3rd ed.; R. L. Brockenbrough
and F. S. Merritt, ‘‘Structural Steel Designers Handbook,’’ 2d ed.,
McGraw-Hill Publishing Company, New York.)
7.8 LONG-SPAN FRAMING
Large industrial buildings, auditoriums, gymnasiums, theaters, hangars, and exposition
buildings require much greater clear distance between supports than can be
supplied by beam and column framing. When the clear distance is greater than can
be spanned with rolled beams, several alternatives are available. These may be
classified as girders, simple trusses, arches, rigid frames, cantilever-suspension
spans, and various types of space frames, such as folded plates, curvilinear grids,
thin-shell domes, two-way trusses, and cable networks.
Girders are the usual choice where depths are limited, as over large unobstructed
areas in the lower floors of tall buildings, where column loads from floors above
must be carried across the clear area. Sometimes, when greater strength is required
than is available in rolled beams, cover plates are added to the flanges (Fig. 7.10a)
to provide the additional strength.
When depths exceed the limit for rolled beams, i.e., for spans exceeding about
67 ft (based on the assumption of a depth-span ratio of 1:22 with 36-in-deep Ws),
the girder must be built up from plates and shapes. Welded girders are used instead
of the old-type conventional riveted girds (Fig. 7.10b), composed of web plate,
angles, and cover plates.
STRUCTURAL STEEL CONSTRUCTION 7.23
FIGURE 7.10 Typical built-up girders.
Welded girders generally are composed
of three plates (Fig. 7.10c). This
type offers the most opportunity for simple
fabrication, efficient use of material,
and least weight. Top and bottom flange
plates may be of different size (Fig.
7.10d), an arrangement advantageous in
composite construction, which integrates
a concrete floor slab with the
girder flange, to function together.
Heavy girders may use cover-plated
tee sections (Fig. 7.10e). Where lateral
loads are a factor, as in the case of girders
supporting cranes, a channel may be
fastened to the top flange (Fig. 7.10?).
In exceptionally heavy construction, it is
not unusual to use a pair of girders diaphragmed
together to share the load
(Fig. 7.10g).
The availability of high-strength,
weldable steels resulted in development
of hybrid girders. For example, a highstrength
steel, say A572 Grade 50, whose yield stress is 50 ksi, may be used in a
girder for the most highly stressed flanges, and the lower-priced A36 steel, whose
yield stress is 36 ksi, may be used for lightly stressed flanges and web plate and
detail material. The AISC specification for allowable-stress design requires that the
top and bottom flanges at any cross section have the same cross-sectional area, and
that the steel in these flanges be of the same grade. The allowable bending stress
may be slightly less than that for conventional homogeneous girders of the highstrength
steel, to compensate for possible overstress in the web at the junction with
the flanges. Hybrid girders are efficient and economical for heavy loading and long
spans and, consequently, are frequently employed in bridgework.
Trusses. When depth limits permit, a more economical way of spanning long
distances is with trusses, for both floor and roof construction. Because of their
greater depth, trusses usually provide greater stiffness against deflection when compared
pound for pound with the corresponding rolled beam or plate girder that
otherwise would be required. Six general types of trusses frequently used in building
frames are shown in Fig. 7.11 together with modifications that can be made to
suit particular conditions.
Trusses in Fig. 7.11a to d and k may be used as the principal supporting members
in floor and roof framing. Types e to j serve a similar function in the framing
of symmetrical roofs having a pronounced pitch. As shown, types a to d have a
top chord that is not quite parallel to the bottom chord. Such an arrangement is
used to provide for drainage of flat roofs. Most of the connections of the roof
beams (purlins), which these trusses support, can be identical, which would not be
the case if the top chord were dead level and the elevation of the purlins varied.
When used in floors, truss types a to d have parallel chords.
Properly proportioned, bow string trusses (Fig. 7.11j) have the unique characteristic
that the stress in their web members is relatively small. The top chord,
which usually is formed in the arc of a circle, is stressed in compression, and the
bottom chord is stressed in tension. In spite of the relatively expensive operation
7.24 SECTION SEVEN
FIGURE 7.11 Types of steel trusses.
of forming the top chord, this type of truss has proved very popular in roof framing
on spans of moderate lengths up to about 100 ft.
The Vierendeel truss (Fig. 7.11k) generally is shop welded to the extent possible
to develop full rigidity of connections between the verticals and chords. It is useful
where absence of diagonals is desirable to permit passage between the verticals.
Trusses also may be used for long spans, as three-dimensional trusses (space
frames) or as grids. In two-way girds, one set of parallel lines of trusses is interSTRUCTURAL
STEEL CONSTRUCTION 7.25
FIGURE 7.12 Some examples of structures with truss roofs.
sected at 90 by another set of trusses so that the verticals are common to both
sets. Because of the rigid connections at the intersections, loads are distributed
nearly equally to all trusses. Reduced truss depth and weight savings are among
the apparent advantages of such grids.
Long-span joists are light trusses closely spaced to support floors and flat roofs.
They conform to standard specifications (Table 7.1) and to standard loading. Both
Pratt and Warren types are used, the shape of chords and webs varying with the
fabricator. Yet, all joists with the same designation have the same guaranteed loadsupporting
capacity. The standard loading tables list allowable loads for joists up
to 72 in deep and with clear span up to 144 ft. The joists may have parallel or
sloping chords or other configuration.
Truss Applications. Cross sections through a number of buildings having roof
trusses of the general type just discussed are shown diagrammatically in Fig. 7.12.
Cross section a might be that of a storage building or a light industrial building. A
Fink truss provides a substantial roof slope. Roofs of this type are often designed
7.26 SECTION SEVEN
to carry little loading, if any, except that produced by wind and snow, since the
contents of the building are supported on the ground floor. For light construction,
the roof and exterior wall covering may consist of thin, cold-formed metal panels.
Lighting and ventilation, in addition to that provided by windows in the vertical
side walls, frequently are furnished by means of sash installed in the vertical side
of a continuous monitor, framing for which is indicated by the dotted lines in the
sketch.
Cross section b shows a scissors truss supporting the high roof over the nave of
a church. This type of truss is used only when the roof pitch is steep, as in ecclesiastical
architecture.
A modified Warren truss, shown in cross section c, might be one of the main
supporting roof members over an auditorium, gymnasium, theater, or other assembly-
type building where large, unobstructed floor space is required. Similar trusses,
including modified Pratt, are used in the roofs of large garages, terminal buildings,
and airplane hangars, for spans ranging from about 80 up to 500 ft.
The Pratt truss (Fig. 7.12d) is frequently used in industrial buildings, while e
depicts a type of framing often used where overhead traveling cranes handle heavy
loads from one point on the ground to another.
Arches. When very large clear spans are needed, the bent framing required to
support walls and roof may take the form of solid or open-web arches, of the kind
shown in Fig. 7.13. A notable feature of bents a and b is the heavy steel pins at
points A, B, and C, connecting the two halves of the arch together at the crown
and supporting them at the foundation. These pines are designed to carry all the
reaction from each half arch, and to function in shear and bearing much as a single
bolt is assumed to perform when loaded in double shear.
Use of hinge pins offers two advantages in long-span frames of the type shown
in Fig. 7.13. In the first place, they simplify design calculations. Second, they
simplify erection. All the careful fitting can be done and strong connections required
to develop the needed strength at the ends of the arch can be made in the shop,
instead of high above ground in the field. When these heavy members have been
raised in the field about in their final position, the upper end of each arch is adjusted,
upward or downward, by means of jacks near the free end of the arch. When the
holes in the pin plates line up exactly, the crown pins is slipped in place and secured
against falling out by the attachment of keeper plates. The arch is then ready to
carry its loading. Bents of the type shown in Fig. 7.13a and b are referred to as
three-hinged arches.
When ground conditions are favorable and foundations are properly designed,
and if the loads to be carried are relatively light, as, for example, for a large
gymnasium, a hingeless arch similar to the one shown diagrammatically in Fig.
7.13c may offer advantage in overall economy.
In many cases, the arches shown in Fig. 7.13a and b are designed without the
pins at B (two-hinged arch). Then, the section at B must be capable of carrying
the moment and shear present. Therefore, the section at B may be heavier than for
the three-hinged arch, and erection will be more exacting for correct closure.
Rigid Frames. These are another type of long-span bent. In design, the stiffness
afforded by beam-to-column connections is carefully evaluated and counted on in
the design to relieve some of the bending moment that otherwise would be assumed
as occurring with maximum intensity at midspan. Typical examples of rigid frame
bents are shown in Fig. 7.14. When complete assembled in place in the field, the
STRUCTURAL STEEL CONSTRUCTION 7.27
FIGURE 7.13 Steel arches: (a) and (b) three-hinged; (c) fixed.
frames are fully continuous throughout their entire length and height. A distinguishing
characteristic of rigid frames is the absence of pins or hinges at the crown, or
midspan.
In principle, single-span rigid-frame bents are either two-hinged or hingeless
arches. For hingeless arches, the column bases are fully restrained by large rigid
foundations, to which they are attached by a connection capable of transmitting
moment as well as shear. Since such foundations may not be economical or even
possible when soil conditions are not favorable, the usual practice is to consider
the bents hinged at each reaction. However, this does not imply the necessity of
expensive pin details; in most cases, sufficient rotation of the column base can be
obtained with the ordinary flat-ended base detail and a single line of anchor bolts
7.28 SECTION SEVEN
FIGURE 7.14 Steel rigid frames: (a) single bent; (b) continuous frame with
underfloor tie; (c) connection of tie to a column; (d ) with two-hinged.
placed perpendicular to the span on the column center line. Many designers prefer
to obtain a hinge effect by concentrating the column load on a narrow bar, as shown
in Fig. 7.14c; this refinement is worthwhile in larger spans.
Regardless of how the frame is hinged, there is a problem in resisting the horizontal
shear that the rigid frame imparts to the foundation. For small spans and
light thrusts, it may be feasible to depend on the foundation to resist lateral displacement.
However, more positive performance and also reduction in costs are
usually obtained by connecting opposite columns of a frame with tie rods, as illustrated
in Fig. 7.14b, thus eliminating these horizontal forces from the foundation.
For ties on small spans, it may be possible to utilize the reinforcing bars in the
floor slab or floor beams, by simply connecting them to the column bases. On
larger spans, it is advisable to use tie rods and turnbuckles, the latter affording the
opportunity to prestress the ties and thus compensate for elastic elongation of the
rods when stressed. Prestressing the rod during erection to 50% of its value has
been recommended for some major installations; but the foundations should be
checked for resisting some portion of the thrust.
Single-story, welded rigid frames often are chosen where exposed steelwork is
desired for such structures as churches, gymnasiums, auditoriums, bowling alleys,
STRUCTURAL STEEL CONSTRUCTION 7.29
and shopping centers, because of attractive appearance and economy. Columns may
be tapered, girders may vary in depth linearly or parabolically, haunches (knees)
may be curved, field joints may be made inconspicuous, and stiffness may simply
be plates.
Field Splices. One problem associated with long-span construction is that of locating
field splices compatible with the maximum sizes of members that can be
shipped and erected. Field splices in frames are generally located at or near the
point of counterflexure, thus reducing the splicing material to a minimum. In general,
the maximum height for shipping by truck is 8 ft, by rail 10 ft. Greater overall
depths are possible, but these should always be checked with the carrier; they vary
with clearances under bridges and through tunnels.
Individual shipping pieces must be stiff enough to be handled without buckling
or other injury, light enough to be lifted by the raising equipment, and capable of
erection without interference from other parts of the framework. This suggests a
study of the entire frame to ensure orderly erection, and to make provisions for
temporary bracing of the members, to prevent jackknifing, and for temporary guying
of the frame, to obtain proper alignment.
Hung-Span Beams. In some large one-story buildings, an arrangement of cantilever-
suspension (hung) spans (Fig. 7.15) has proved economical and highly effi-
cient. This layout was made so as to obtain equal maximum moments, both negative
and positive, for the condition of uniform load on all spans. A minimum of three
spans is required; that is, a combination of two end spans (A) and one intermediate
span (C). The connection at the end of the cantilever (point D) must be designed
as a shear connection only. If the connection is capable of transmitting moment as
well as shear, it will change the design to one of continuity and the dimensions in
Fig. 7.15 will not apply. This scheme of cantilever and suspended spans is not
necessarily limited to one-story buildings.
As a rule, interior columns are separate elements in each story. Therefore, horizontal
forces on the building must be taken solely by the exterior columns.
(E. H. Gaylord, Jr., et al., ‘‘Design of Steel Structures,’’ 3d ed.; and F. S. Merritt
and R. L. Brockenbrough, ‘‘Structural Steel Designer’s Handbook,’’ 2d ed.,
McGraw-Hill Publishing Company, New York.)
FIGURE 7.15 Hung- or suspended-span steel construction.
7.9 STEEL AND CONCRETE FRAMING
In another type of framing system, different from those described in Arts. 7.7 and
7.8, a partial use of structural steel has an important role, namely, composite framing
of reinforced concrete and structural steel.
7.30 SECTION SEVEN
Composite construction actually occurs whenever concrete is made to assist steel
framing in carrying loads. The term composite, however, often is used for the
specific cases in which concrete slabs act together with flexural members.
Reinforced-concrete columns of conventional materials when employed in tall
buildings and for large spans become excessively large. One method of avoiding
this objectionable condition is to use high-strength concrete and high-strength reinforcing
bars. Another is to use a structural-steel column core. In principle, the
column load is carried by both the steel column and the concrete that surrounds
the steel shape. Building codes usually contain an appropriate formula for this
condition.
A number of systems employ a combination of concrete and steel in various
ways. One method features steel columns supporting a concrete floor system by
means of a steel shearhead connected to the columns at each floor level. The shallow
grillage is embedded in the floor slab, thus obtaining a smooth ceiling without
drops or capitals.
Another combination system is the lift-slab method. In this system, the floor
slabs are cast one on top of another at ground level. Jacks, placed on the permanent
steel columns, raise the slabs, one by one, to their final elevation, where they are
made secure to the columns. When fireproofing is required, the columns may be
boxed in with any one of many noncombustible materials available for that purpose.
The merit of this system is the elimination of formwork and shoring that are essential
in conventional reinforced-concrete construction.
For high-rise buildings, structural-steel framing often is used around a central,
load-bearing, concrete core, which contains elevators, stairways, and services. The
thick walls of the core, whose tubular configuration may be circular, square, or
rectangular, are designed as shear walls to resist all the wind forces as well as
gravity loads. Sometimes, the surrounding steel framing is cantilivered from the
core, or the perimeter members are hung from trusses or girders atop the core and
possibly also, in very tall buildings, at midheight of the core.
FRAME AND MEMBER BRACING SYSTEMS
7.10 BRACING DESIGN CONSIDERATIONS
Bracing as it applies to steel structures includes secondary members incorporated
into the system of main members to serve these principal functions:
1. Slender compression members, such as columns, beams, and truss elements
are braced, or laterally supported, so as to restrain the tendency to buckle in a
direction normal to the stress path. The rigidity, or resistance to buckling, of an
individual member is determined from its length and certain physical properties of
its cross section. Economy and size usually determine whether bracing is to be
employed.
2. Since most structures are assemblies of vertical and horizontal members forming
rectangular (or square) panels, they possess little inherent rigidity. Consequently,
additional rigidity must be supplied by a secondary system of members or by rigid
or semi-rigid joints between members. This is particularly necessary when the
framework is subject to lateral loads, such as wind, earthquakes, and moving loads.
Exempt from this second functional need for bracing are trusses, which are basically
STRUCTURAL STEEL CONSTRUCTION 7.31
an arrangement of triangles possessing in their planes an inherent ideal rigidity both
individually and collectively.
3. There frequently is a need for bracing to resist erection loads and to align or
prevent overturning, in a direction normal to their planes, of trusses, bents, or frames
during erection. Such bracing may be temporary; however, usually bracing needed
for erection is also useful in supplying rigidity to the structure and therefore is
permanently incorporated into the building. For example, braces that tie together
adjoining trusses and prevent their overturning during erection are useful to prevent
sway—even though the swaying forces may not be calculable.
7.11 FRAME BRACING
Design of bracing to resist forces induced by wind, seismic disturbances, and moving
loads, such as those caused by cranes, is not unlike, in principle, design of
members that support vertical dead and live loads. These lateral forces are readily
calculable. They are collected at points of application and then distributed through
the structural system and delivered to the ground. Wind loads, for example, are
collected at each floor level and distributed to the columns that are selected to
participate in the system. Such loads are cumulative; that is, columns resisting wind
shears must support at any floor level all the wind loads on the floors above the
one in consideration.
FIGURE 7.16 Wind bracing for multistory
buildings.
7.11.1 Bracing Tall Buildings
If the steel frame of the multistory
building in Fig. 7.16a is subjected to lateral
wind load, it will distort as shown
in Fig. 7.16b, if the connections of columns
and beams are of the standard
type, for which rigidity (resistance to rotation)
is nil. One can visualize this
readily by assuming each joint is connected
with a single pin. Naturally, the
simplest method to prevent this distortion
is to insert diagonal members—
triangles being inherently rigid, even if
all the members forming the triangles
are pin-connected.
Braced Bents. Bracing of the type in Fig. 7.16c, called X bracing, is both efficient
and economical. Unfortunately, X bracing is usually impracticable because of interference
with doors, windows, and clearance between floor and ceiling. Usually,
for office buildings large column-free areas are required. This offers flexibility of
space use, with movable partitions. But about the only place for X bracing in this
type of building is in the elevator shaft, fire tower, or wherever a windowless wall
is required. As a result, additional bracing must be supplied by other methods. On
the other hand, X bracing is used extensively for bracing industrial buildings of the
shed or mill type.
7.32 SECTION SEVEN
FIGURE 7.17 Typical wind connections for beams to columns.
Moment-Resisting Frames. Designers have a choice of several alternatives to X
bracing. Knee braces, shown in Fig. 7.16d, or portal frames, shown in Fig. 7.16e,
may be used in outer walls, where they are likely to interfere only with windows.
For buildings with window walls, the bracing often used is the bracket type (Fig.
7.16?). It simply develops the end connection for the calculated wind moment.
Connections vary in type, depending on size of members, magnitude of wind moment,
and compactness needed to comply with floor-to-ceiling clearances.
Figure 7.17 illustrates a number of bracket-type wind-braced connections. The
minimum type, represented in Fig. 7.17e, consists of angles top and bottom: They
are ample for moderate-height buildings. Usually the outstanding leg (against the
column) is of a size that permits only one gage line. A second line of fasteners
would not be effective because of the eccentricity. When greater moment resistance
is needed, the type shown in Fig. 7.17b should be considered. This is the type that
has become rather conventional in field-bolted construction. Figure 7.17c illustrates
the maximum size with beam stubs having flange widths that permit additional
gage lines, as shown. It is thus possible on larger wide-flange columns to obtain
16 fasteners in the stub-to-column connection.
The resisting moment of a given connection varies with the distance between
centroids of the top and bottom connection piece. To increase this distance, thus
increasing the moment, an auxiliary beam may be introduced as shown in Fig.
7.17d, if it does not create an interference.
STRUCTURAL STEEL CONSTRUCTION 7.33
All the foregoing types may be of welded construction, rather than bolted. In
fact, it is not unusual to find mixtures of both because of the fabricator’s decision
to shop-bolt and field-weld, or vice versa. Welding, however, has much to offer in
simplifying details and saving weight, as illustrated in Fig. 7.17e, ?, and g. The
last represents the ultimate efficiency with respect to weight saving, and furthermore,
it eliminates interfering details.
Deep wing brackets (Fig. 7.17h and i) are sometimes used for wall beams and
spandrels designed to take wind stresses. Such deep brackets are, of course, acceptable
for interior beam bracing whenever the brackets do not interfere with
required clearances.
Not all beams need to wind-braced in tall buildings. Usually the wind load is
concentrated on certain column lines, called bents, and the forces are carried
through the bents to the ground. For example, in a wing of a building, it is possible
to concentrate the wind load on the outermost bent. To do so may require a stiff
floor or diaphragm-like system capable of distributing the wind loads laterally. Onehalf
these loads may be transmitted to the outer bent, and one-half to the main
building to which the wing connects.
Braced bents are invariably necessary across the narrow dimension of a building.
The question arises as to the amount of bracing required in the long dimension,
since wind of equal unit intensity is assumed to act on all exposed faces of structures.
In buildings of square or near square proportions, it is likely that braced bents
will be provided in both directions. In buildings having a relatively long dimension,
as compared with width, the need for bracing diminishes. In fact, in many instances,
wind loads are distributed over so many columns that the inherent rigidity of the
whole system is sufficient to preclude the necessity of additional bracing.
Column-to-column joints are treated differently for wind loads. Columns are
compression members and transmit their loads, from section above to section below,
by direct bearing between finished ends. It is not likely, in the average building,
for the tensile stresses induced by wind loads ever to exceed the compressive pressure
due to dead loads. Consequently, there is no theoretical need for bracing a
column joint. Actually, however, column joints are connected together with nominal
splice plates for practical considerations—to tie the columns during erection and
to obtain vertical alignment.
This does not mean that designers may always ignore the adequacy of column
splices. In lightly loaded structures, or in exceptionally tall but narrow buildings,
it is possible for the horizontal wind forces to cause a net uplift in the windward
column because of the overturning action. The commonly used column splices
should then be checked for their capacity to resist the maximum net tensile stresses
caused in the column flanges. This computation and possible heaving up of the
splice material may not be thought of as bracing; yet, in principle, the column joint
is being ‘‘wind-braced’’ in a manner similar to the wind-braced floor-beam connections.
7.11.2 Shear Walls
Masonary walls enveloping a steel frame, interior masonry walls, and perhaps some
stiff partitions can resist a substantial amount of lateral load. Rigid floor systems
participate in lateral-force distribution by distributing the shears induced at each
floor level to the columns and walls. Yet, it is common design practice to carry
wind loads on the steel frame, little or no credit being given to the substantial
resistance rendered by the floors and walls. In the past, some engineers deviated
from this conversatism by assigning a portion of the wind loads to the floors and
7.34 SECTION SEVEN
walls; nevertheless, the steel frame carried the major share. When walls of glass or
thin metallic curtain walls, lightweight floors, and removable partitions are used,
this construction imposes on the steel frame almost complete responsibility for
transmittal of wind loads to the ground. Consequently, windbracing is critical for
tall steel structures.
In tall, slender buildings, such as hotels and apartments with partitions, the
cracking of rigid-type partitions is related to the wracking action of the frame
caused by excessive deflection. One remedy that may be used for exceptionally
slender frames (those most likely to deflect excessively) is to supplement the normal
bracing of the steel frame with shear walls. Acting as vertical cantilevers in resisting
lateral forces, these walls, often constructed of reinforced concrete, may be arranged
much like structural shapes, such as plates, channels, Ts, Is, or Hs. (See also Arts.
3.2.4 and 5.12.) Walls needed for fire towers, elevator shafts, divisional walls, etc.,
may be extended and reinforced to serve as shear walls, and may relieve the steel
frame of cumbersome bracing or avoid uneconomical proportions.
7.11.3 Bracing Industrial-Type Buildings
Bracing of low industrial buildings for horizontal forces presents fewer difficulties
than bracing of multistory buildings, because the designer usually is virtually free
FIGURE 7.18 Relative stiffness of bents depends
on restraints on columns.
to select the most efficient bracing without
regard to architectural considerations
or interferences. For this reason,
conventional X bracing is widely
used—but not exclusively. Knee braces,
struts, and sway frames are used where
needed.
Wind forces acting on the frame
shown in Fig. 7.18a, with hinged joints
at the top and bottom of supporting columns,
would cause collapse as indicated
in Fig. 7.18b. In practice, the joints
would not be hinged. However, a minimum-
type connection at the truss connection
and a conventional column base
with anchor bolts located on the axis
transverse to the frame would approximate
this theoretical consideration of
hinged joints. Therefore, the structure
requires bracing capable of preventing
collapse or unacceptable deflection.
In the usual case, the connection between
truss and columns will be stiffened
by means of knee braces (Fig. 7.18c). The rigidity so obtained may be supplemented
by providing partial rigidity at the column base by simply locating the
anchor bolts in the plane of the bent.
In buildings containing overhead cranes, the knee braced may interfere with
crane operation. Then, the interference may be eliminated by fully anchoring the
column base so that the column may function as a vertical cantilever (Fig. 7.18d).
The method often used for very heavy industrial buildings is to obtain substantial
rigidity at both ends of the column so that the behavior under lateral load will
STRUCTURAL STEEL CONSTRUCTION 7.35
FIGURE 7.20 Braced bays in a one-story building transmit wind loads to the ground.
resemble the condition illustrated in Fig. 7.18e. In both (d) and (e), the footings
must be designed for such moments.
FIGURE 7.19 Braced bays in framing for an
industrial building.
A common assumption in wind distribution
for the type of light mill building
shown in Fig. 7.19 is that the windward
columns take a large share of the
load acting on the side of the building
and deliver the load directly to the
ground. The remaining wind load on the
side is delivered by the same columns
to the roof systems, where the load joins
with the wind forces imposed directly
on the roof surface. Then, by means of
diagonal X bracing, working in conjunction
with the struts and top chords
of the trusses, the load is carried to the
eave struts, thence to the gables and,
through diagonal bracing, to the foundations.
Because wind may blow from any direction, the building also must be braced
for the wind load on the gables. This bracing becomes less important as the building
increases in length and conceivably could be omitted in exceptionally long structures.
The stress path is not unlike that assumed for the transverse wind forces. The
load generated on the ends is picked up by the roof system and side framing,
delivered to the eave struts, and then transmitted by the diagonals in the end
sidewall bays to the foundation.
No distribution rule for bracing is intended in this discussion; bracing can be
designed many different ways. Whereas the foregoing method would be sufficient
for a small building, a more elaborate treatment may be required for larger structures.
Braced bays, or towers, are usually favored for structures such as that shown in
Fig. 7.20. There, a pair of transverse bents are connected together with X bracing
in the plane of the columns, plane of truss bottom chords, plane of truss top chords,
and by means of struts and sway frames. It is assumed that each such tower can
carry the wind load from adjacent bents, the number depending on assumed rigid7.36
SECTION SEVEN
ities, size, span, and also on sound judgment. Usually every third or fourth bent
should become a braced bay. Participation of bents adjoining the braced bay can
be assured by insertion of bracing designated ‘‘intermediate’’ in Fig. 7.20b. This
bracing is of greater importance when knee braces between trusses and columns
cannot be used. When maximum lateral stiffness of intermediate bents is desired,
it can be obtained by extending the X bracing across the span; this is shown with
broken lines in Fig. 7.20b.
Buildings with flat or low-pitched roofs, shown in Fig. 7.12d and e, require little
bracing because the trusses are framed into the columns. These columns are designed
for the heavy moments induced by wind pressure against the building side.
The bracing that would be provided, at most, would consist of X bracing in the
plane of the bottom chords for purpose of alignment during erection and a line or
two of sway frames for longitudinal rigidity. Alignment bracing is left in the structure
since it affords a secondary system for distributing wind loads.
7.11.4 Bracing Craneway Structures
All building framing affected by overhead cranes should be braced for the thrusts
induced by sidesway and longitudinal motions of the cranes. Bracing used for wind
or erection may be assumed to sustain the lateral crane loadings. These forces are
usually concentrated on one bent. Therefore, normal good practice dictates that
adjoining bents share in the distribution. Most effective is a system of X bracing
located in the plane of the bottom chords of the roof trusses.
In addition, the bottom chords should be investigated for possible compression,
although the chords normally are tension members. A heavily loaded crane is apt
to draw the columns together, conceivably exerting a greater compression stress
than the tension stress obtainable under dead load alone. This may indicate the need
for intermediate bracing of the bottom chord.
7.11.5 Bracing Rigid Frames
Rigid frames of the type shown in Fig. 7.14 have enjoyed popular usage for gymnasiums,
auditoriums, mess halls, and with increasing frequency, industrial buildings.
The stiff knees at the junction of the column with the rafter imparts excellent
transverse rigidity. Each bent is capable of delivering its share of wind load directly
to the footings. Nevertheless, some bracing is advisable, particularly for resisting
wind loads against the end of the building. Most designers emphasize the importance
of an adequate eave strut; it usually is arranged so as to brace the inside
flange (compression) of the frame knee, the connection being located at the midpoint
of the transition between column and rafter segments of the frame. Intermediate
X bracing in the plane of the rafters usually is omitted.
7.12 BRACING FOR INDIVIDUAL MEMBERS
For an ideally straight, exactly concentrically loaded beam or column, only a small
force may be needed from an intermediate brace to reduce the unbraced length of
STRUCTURAL STEEL CONSTRUCTION 7.37
a column or the unsupported length of the compression flange of a beam. But there
is no generally accepted method of calculating that force.
The principal function of a brace is to provide a node in the buckled configuration.
Hence, rigidity is the main requirement for the brace. But actual members
do contain nonuniform residual stresses and slight initial crookedness and may be
slightly misaligned, and these eccentricities create deformations that must be resisted
by the brace.
A rule used by some designers that has proved satisfactory is to design the brace
for 2% of the axial load of columns, or 2% of the total compressive stress in beam
flanges. Studies and experimental evidence indicate that this rule is conservative.
7.12.1 Column Bracing
Interior columns of a multistory building are seldom braced between floor connections.
Bracing of any kind generally interferes with occupancy requirements and
architectural considerations. Since the slenderness ratio l / r in the weak direction
usually controls column size, greatest economy is achieved by using only wide-
flange column sections or similar built-up sections.
It is frequently possible to reduce the size of wall columns by introducing knee
braces or struts in the plane of the wall, or by taking advantage of deep spandrels
or girts that may be otherwise required. Thus the slenderness ratio of the weak and
strong axis can be brought into approximate balance. The saving in column weight
may not always be justified; one must take into account the weight of additional
bracing and cost of extra details.
Column bracing is prevalent in industrial buildings because greater vertical clearances
necessitate longer columns. Tall slender columns may be braced about both
axes to obtain an efficient design.
Undoubtedly, heavy masonry walls afford substantial lateral support to steel
columns embedded wholly or partly in the wall. The general practice, however, is
to disregard this assistance.
An important factor in determining column bracing is the allowable stress or
load for the column section (Art. 7.19). Column formulas for obtaining this stress
are based on the ratio of two variables, effective length Kl and the physical property
called radius of gyration r.
The question of when to brace (to reduce the unsupported length and thus slenderness
ratio) is largely a matter of economics and architectural arrangements; thus
no general answer can be given.
7.12.2 Beam Bracing
Economy in size of member dictates whether laterally unsupported beams should
have additional lateral support between end supports. Lateral support at intermediate
points should be considered whenever the allowable stress obtained from the reduction
formulas for large l / rt falls below some margin, say 25%, of the stress
allowed for the fully braced condition. There are cases, however, where stresses as
low as 4.0 ksi have been justified, because intermediate lateral support was impractical.
The question often arises: When is a steel beam laterally supported? There is
no fixed rule in specifications (nor any intended in this discussion) because the
7.38 SECTION SEVEN
FIGURE 7.21 Methods of providing lateral support for beams.
answer requires application of sound judgment based on experiences. Tests and
studies that have been made indicate that it takes rather small forces to balance the
lateral thrusts of initial buckling.
Figure 7.21 illustrates some of the common situations encountered in presentday
practice. In general, positive lateral support is provided by:
(a) and (b) All types of cast-in-place concrete slabs (questionable for vibrating
loads and loads hung on bottom flange).
(c) Metal and steel plate decks, with welded connections.
(d) Wood decks nailed securely to nailers bolted to the beam.
(e) and (?) Beam flange tied or braced to strut system, either as shown in (e)
or by means of cantilever tees, as shown in (?); however, struts should be adequate
to resist rotation.
(g) Purlins used as struts, with tees acting as cantilevers (common in rigid
frames and arches). If plate stiffness are used, purlins should be connected to
them with high-strength bolts to ensure rigidity.
STRUCTURAL STEEL CONSTRUCTION 7.39
(h) Open-web joists tack-welded (or the equivalent) to the beams, but the joists
themselves must be braced together (bridging), and the flooring so engaged with
the flanges that the joists, in turn, are adequately supported laterally.
(i) Purlins connected close to the compression flange.
(k) Tees (part of cast-in-place gypsum construction) welded to the beams.
Doubtful lateral support is provided by:
( j ) Purlins seated on beam webs, where the seats are distant from the critical
flange
(l ) Precast slabs not adequately fastened to the compression flange.
FIGURE 7.22 Lateral bracing systems; (a)
without and (b) with X bracing.
The reduction formulas for large l / r,
given in Fig. 7–31 do not apply to steel
beams fully encased in concrete, even
though no other lateral support is provided.
Introducing a secondary member to
cut down the unsupported length does
not necessarily result in adequate lateral
support. The resistive capacity of the
member and its supports must be traced
through the system to ascertain effectiveness.
For example the system in Fig.
7.22a may be free to deflect laterally as
shown. This can be prevented by a rigid
floor system that acts as a diaphragm, or
in the absence of a floor, it may be necessary
to X-brace the system as shown
in Fig. 7.22b.
FLOOR AND ROOF SYSTEMS
7.13 FLOOR-FRAMING
DESIGN CONSIDERATIONS
Selection of a suitable and economical floor system for a steel-frame building involves
many considerations: load-carrying capacity, durability, fire resistance, dead
weight, overall depth, facility for installing power, light, and telephones, facility for
installing aid conditioning, sound transmission, appearance, maintenance, and construction
time.
Building codes specify minimum design live loads for floor and roof systems.
In the absence of a code regulation, one may use ‘‘Minimum Design Loads in
Buildings and Other Structures,’’ ASCE 7-93, American Society of Civil Engineers.
See also Art. 5.1.2. Floors should be designed to support the actual loading or these
minimum loads, whichever is larger. Most floors can be designed to carry any given
load. However, in some instances, a building code may place a maximum load limit
on particular floor systems without regard to calculated capacity.
7.40 SECTION SEVEN
Resistance to lateral forces should not be disregarded, especially in areas of
seismic disturbances or for perimeter windbents. In designs for such conditions,
floors may be employed as horizontal diaphragms to distribute lateral forces to
walls or vertical framing; those elements then transmit the lateral forces to the
foundations. When using lightweight floor systems, special reinforcement in the
floor slab may be necessary at those points where the floor diaphragm transfers the
horizontal forces to the frame elements.
Durability becomes a major consideration when a floor is subject to loads other
than static or moderately kinetic types of forces. For example, a light joist system
may be just the floor for an apartment or an office building but may be questionable
for a manufacturing establishment where a floor must resist heavy impact and severe
vibrations. Shallow floor systems deflect more than deep floors; the system selected
should not permit excessive or objectionable deflections.
Fire resistance and fire rating are very important factors, because building codes
in the interest of public safety, specify the degree of resistance that must be provided.
Many floor systems are rated by the codes or by fire underwriters for purposes
of satisfying code requirements or basing insurance rates.
The dead weight of the floor system, including the framing, is an important
factor affecting economy of construction. For one thing, substantial saving in the
weight and cost of a steel frame may result with lightweight floor systems. In
addition, low dead weight may also reduce foundation costs.
Joist systems, either steel or concrete, require no immediate support, since they
are obtainable in lengths to meet normal bay dimensions in tier building construction.
On the other hand, concrete arch and cellular-steel floors are usually designed
with one or two intermediate beams within the panel. The elimination of secondary
beams does not necessarily mean overall economy just because the structural-steel
contract is less. These beams are simple to fabricate and erect and allow much
duplication. An analysis of contract price shows that the cost per ton of secondary
beams will average 20% under the cost per ton for the whole steel structure; or
viewed another way, the omission of secondary beams increases the price per ton
on the balance of the steelwork by 31?2% on the average. This fact should be taken
into account when making a cost analysis of several systems.
Sometimes, the depth of a floor system is important. For example, the height of
a building may be limited for a particular type of fire-resistant construction or by
zoning laws. The thickness of the floor system may well be the determining factor
limiting the number of stories that can be built. Also, the economy of a deep floor
is partly offset by the increase in height of walls, columns, pipes, etc.
Another important consideration, particularly for office buildings and similartype
occupancies, is the need for furnishing an economical and flexible electrical
wiring system. With the accent on movable partitions and ever-changing office
arrangements, the readiness and ease with which telephones, desk lights, computers,
and other electric-powered business machines can be relocated are of major importance.
Therefore, the floor system that by its makeup provides large void spaces
or cells for concealing wiring possesses a distinct advantage over competitive types
of solid construction. Likewise, accommodation of recessed lighting in ceilings may
disclose an advantage for one system over another. Furthermore, for economical air
conditioning and ventilation, location of ducts and method of support warrant study
of several floor systems.
Sound transmission and acoustical treatments are other factors that need to be
evaluated. A wealth of data are available in reports of the National Institute of
Standards and Technology. In general, floor systems of sandwich type with air
spaces between layers afford better resistance to sound transmission than solid sysSTRUCTURAL
STEEL CONSTRUCTION 7.41
FIGURE 7.23 Open-web steel joist construction.
tems, which do not interrupt sound waves. Although the ideal soundproof floor is
impractical, because of cost, several reasonably satisfactory systems are available.
Much depends on type of occupancy, floor coverings, and ceiling finish—acoustical
plaster or tile.
Appearance and maintenance also should be weighed by the designer and the
owner. A smooth, neat ceiling is usually a prerequisite for residential occupancy;
a less expensive finish may be deemed satisfactory for an institutional building.
Speed of construction is essential. Contractors prefer systems that enable the
follow-up trades to work immediately behind the erector and with unimpeded ef-
ficiency.
In general, either rolled beams or open-web joists are used to support the floor
elements. The most common types of flooring are (a) concrete fill on metal deck,
(b) pre-cast concrete plank, and (c) cast-in-place concrete floors with integral joist.
Metal decks may be cellular or plain and are usually stud-welded to the supporting
elements to provide composite action. Cast-in-place concrete floors, or concretepan
floors, are becoming less common than in the past. In addition to the systems
described, there are several adaptations of these as well as other proprietary systems.
7.13.1 Steel Joist Floors
The lightest floor system in common use is the open-web steel joist construction
shown in Fig. 7.23. It is popular for all types of light occupancies, principally
because of initial low cost.
Many types of open-web joists are available. Some employ bars in their makeup,
while others are entirely of rolled shapes; they all conform to standards and goodpractice
specifications promulgated by the Steel Joist Institute and the American
Institute of Steel Construction (see Table 7.1). All joists conform to the standard
loading tables and carry the same size designation so that designers need only
indicate on project drawings the standard marking without reference to manufacturer,
just as for a steel beam or column section.
Satisfactory joists construction is assured by adhering to SJI and AISC recommendations.
Joists generally are spaced 2 ft c to c. They should be adequately
braced (with bridging) during construction to prevent rotation or buckling, and to
avoid ‘‘springy’’ floors, they should be carefully selected to provide sufficient depth.
This system has many advantages: Falsework is eliminated. Joists are easily
handled, erected, and connected to supporting beams—usually by tack welding.
7.42 SECTION SEVEN
FIGURE 7.24 Cellular-steel floor construction.
Temporary coverage and working platforms are quickly placed. The open space
between joists, and through the webs, may be utilized for ducts, cables, light fixtures,
and piping. A thin floor slab may be cast on steel lath, corrugated-steel sheets,
or wire-reinforced paper lath laid on top of the joists. A plaster ceiling may be
suspended or attached directly to the bottom flange of the joists.
Lightweight beams, or so-called ‘‘junior’’ beams, are also used in the same
manner as open-web joists, and with the same advantages and economy, except
that the solid webs do not allow as much freedom in installation of utilities. Beams
may be spaced according to their safe load capacity; 3- and 4-ft spacings are common.
As a type, therefore, the lightweight-steel-beam floor is intermediate between
concrete arches and open-web joists.
7.13.2 Cellular-Steel Floors
Cold-formed steel decking is frequently used in office buildings. One type is illustrated
in Fig. 7.24. Other manufacturers make similar cellular metal decks, the
primary difference being in the shape of the cells. Often, decking with half cells is
used. These are open ended on the bottom, but flat sheets close those cells that
incorporate services. Sometimes, cells are enlarged laterally to transmit air for air
conditioning.
Two outstanding advantages of cellular floors are rapidity of erection and ease
with which present and future connections can be made to telephone, computer,
light, and power wiring, each cell serving as a conduit. Each deck unit becomes a
working platform immediately on erection, thus enabling the several finishing trades
to follow right behind the steel erector.
Although the cost of the steel deck system may be larger than that of other floor
systems, the cost differential can be narrowed to competitive position when equal
consideration for electrical facility is imposed on the other systems; e.g., the addition
of 4 in of concrete fill to cover embedded electrical conduit on top of a
concrete flat-slab floor.
In earlier floors of this type, the steel decking was assumed to be structurally
independent. In that case, the concrete fill served only to provide fire resistance
and a level floor. Most modern deckings, however, are bonded or locked to the
concrete, so that the two materials act as a unit in composite construction. Usually,
only top-quality stone concrete (ASTM C33 aggregates) is used, although lightweight
concrete made with ASTM C330 aggregates is an acceptable alternative.
STRUCTURAL STEEL CONSTRUCTION 7.43
Usage of cellular deck in composite construction is facilitated by economical
attachment of shear connectors to both the decking and underlying beams. For
example, when welded studs are used, a welding gun automatically fastens the studs
through two layers of hot-dipped galvanized decking to the unpainted top flanges
of the steel beams. This construction is similar to composite concrete-steel beams
(Art. 7.13.3)
The total floor weight of cellular steel construction is low, comparable to openweb
steel joists. Weight savings of about 50% are obtained in comparison with allconcrete
floors; 30% savings in overall weight of the building. However, a big cost
saving in a high-labor-rate area results from elimination of costly formwork needed
for concrete slabs, since the steel decking serves as the form.
Fire resistance for any required rating is contributed by the fill on top of the
cells and by the ceiling below (Fig. 7.24). Generally, removable panels for which
no fire rating is claimed are preferred for suspended ceilings. In this case, fireproofing
materials are applied directly to the underside of the metal deck and all exposed
surfaces of steel floor beams, a technique often called spray-on fireproofing.
7.13.3 Composite Concrete-Steel Beams
In composite construction, the structural concrete slab is made to assist the steel
beams in supporting loads. Hence, the concrete must be bonded to the steel to
ensure shear transfer. When the steel beams are completely encased in the concrete,
the natural bond is considered capable of resisting horizontal shear. But that bond
generally is disregarded when only the top flange is in contact with the concrete.
Consequently, shear connectors are used to resist the horizontal shear. Commonly
used connectors are welded studs, hooked or headed, and short lengths of channels.
Usually, composite construction is most efficient for heavy loading, long spans,
large beam spacing, and restricted depths. Because the concrete serves much like
a cover plate, lighter steel beams may be used for given loads, and deflections are
smaller than for noncomposite construction.
7.13.4 Concrete-Pan Floors
FIGURE 7.25 Concrete joist floor.
Concrete floors cast on removable metal
forms or pans, which form the joists, are
frequently used with steel girders. Since
the joists span the distance between columns,
intermediate steel beams are not
needed (Fig. 7.25). This floor generally
weighs less than the arch system (reinforced
concrete slabs on widely spaced
beams), but still considerably more than
the lightest types.
There are a number of variations of
the concrete-joist system, such as the
‘‘gird’’ or ‘‘waffle’’ system, where the
floor is cast on small, square, removable
pans, or domes, so that the finished
product becomes a two-way joist system.
Other systems employ permanent
7.44 SECTION SEVEN
filler blocks—usually a lightweight tile. Some of these variations fall in the heaviest
floor classification; also the majority require substantial forms and shoring.
7.14 ROOF FRAMING SYSTEMS
These are similar in many respects to the floor types, discussed in Arts. 7.13 and
7.13.1. In fact, for flat-top tier buildings, the roof may be just another floor. However,
when roof loads are smaller than floor loads, as is usually the case, it may be
economical to lighten the roof construction. For example, steel joists may be spaced
farther apart. Where roof decking is used, the spacing of the joists is determined
by the load-carrying ability of the applied decking and of the joists.
Most of the considerations discussed for floors in Art. 7.13 also are applicable
to roof systems. In addition, however, due thought should be given to weather
resistance, heat conductance and insulation, moisture absorption and vapor barriers,
and especially to maintenance.
Many roof systems are distinctive as compared with the floor types; for example,
the corrugated sheet-metal roofing commonly employed on many types of industrial
or mill buildings. The sheets rest on small beams, channels, or joists, called purlins,
which in turn are supported by trusses. Similar members on the sidewalls are called
girts.
DESIGN OF MEMBERS
In proportioning of members, designers should investigate one or more or a combination
of five basic stress or strength conditions: axial tension, axial compression,
bending, shearing, and member element crippling. Other conditions that should be
investigated under special conditions are local buckling, excessive deflection, torsion
and fatigue. Until the early 1990s, such analyses were based on allowable
stress design (ASD). More recently, a method known as load and resistance factor
design (LRFD) has come into use because it permits a more rational design. It takes
into account the probability of loading conditions and statistical variations in the
strength, or resistance capability, of members and connection materials.
The use of LRFD design procedures will result in a savings of material, generally
in the range of 15 to 20%, and on major structures, some elements may show a
savings of up to 25%. Such weight savings generally means a lesser cost for the
structural steel. However, except for major structures, when serviceability factors
such as deflection and vibration are considered in the proportioning of the individual
members, the nominal savings of LRFD procedures versus ASD procedures is more
likely to be approximately 5%.
7.15 BASES FOR ASD AND LRFD
ASD is based on elastic theory. Design limits the maximum unit stress a member
is permitted to bear under service loads to a level determined by a judgmental, but
STRUCTURAL STEEL CONSTRUCTION 7.45
experience-based, safety factor. Building codes establish allowable unit stresses,
which are normally related to the minimum yield stress for each grade of steel.
Plastic design is based on the ultimate strength of members. A safety factor,
comparable to that established for elastic design, is applied to the design load to
determine the ultimate-load capacity required of a member.
LRFD is based on the concept that no applicable limit state should be exceeded
when the structure, or any member or element, is subject to appropriate combinations
of factored loads.
A limit state is defined as a condition in which a structure or structural component
becomes unfit for further structural service. A structural member can have
several limit states.
Strength limit states relate to maximum load-carrying capacity.
Serviceability limit states relate to performance under normal service conditions
with respect to such factors as deflection and vibration.
Design specifications establish load factors to be applied to each type of service
load, such as dead, live, and wind loads, the values of the factors depending on the
specific combination of loads to be imposed on a structure (Art. 5.1.3).
The AISC ‘‘Load and Resistance Factor Design Specification for Structural Steel
Buildings’’ requires that structures be designed so that, under the most critical
combination of factored loads, the design strength of the structures or their individual
elements is not exceeded. For each strength limit state, the design strength
is the product of the nominal strength and a resistance factor , given in the specification.
Derived with the use of probability theory, provides an extra margin of
safety for the limit state being investigated. Nominal strength of a member depends
on its geometric properties, yield or ultimate strength, and type of loading to be
resisted, such as tension, compression, or flexure.
The AISC LRFD specification permits structural analysis based on either elastic
or plastic behavior. Elastic theory is most commonly used. Where plastic theory is
used for complex structures, all possible mechanisms that may form in the structure
should be investigated. The collapse mechanism is the one that requires the lightest
load for collapse to occur.
Numerous computer programs for analysis and design of members or structures
are available. If data input describing the structure and loading are accurate, most
of these programs yield a quick and accurate design. For complex structures, care
should be taken in use of computer programs to check the results to ensure that
they are logical, since a critical input error may not be easily found. If a program
can produce a plot of the configuration of the loaded structure based on the data
input, the plot should be used as a check, inasmuch as omission of a member or
other errors in connectivity data can be readily discerned from the plot.
(‘‘Plastic Design in Steel—A Guide and Commentary,’’ M & R No. 41, American
Society of Civil Engineers.)
7.16 DESIGN AIDS AND REFERENCES
Design procedures using either the ASD or the LRFD specifications require the use
of many numerical values which represent the section properties of the individual
shapes or plates under consideration. Several publications in the form of handbooks
have been developed by the industry to provide the designer with this and other
useful information. In addition, many steel producers publish handbooks which
7.46 SECTION SEVEN
TABLE 7.9 Handbooks and Design Guides
Publisher Title Content
American Institute of Steel
Construction (AISC)
One East Wacker Drive
Chicago, IL 60601-2001
ASD Manual of Steel
Construction
Design specification
Section properties
Dimensional data
Design aids
LRFD Manual of Steel
Construction—Vol. I
Design specification
Section properties
Dimensional data
Design aids
LRFD Manual of Steel
Construction—Vol. I
Design aids
Suggested design details
Dimensional data
Design Guide No. 1
Column Base Plates
Theory and examples of base
plate and anchor bolt
design
Design Guide No. 2
Steel and Composite Beams
with Web Openings
Theory and examples of web
penetration design
Design Guide No. 3
Serviceability Design
Considerations for Low-Rise
Buildings
Design criteria
Design Guide No. 5
Design of Low- and
Medium-Rise Steel
Buildings
Synopsis of design criteria
and design details
Design Guide No. 7
Industrial Buildings: Roof
to Column Anchorage
Industrial building design
Seismic Provisions for
Structural Steel Buildings
Design criteria
Design details
American Institute of Steel
Construction (address
above) or
Steel Tube Institute of
North America
8500 Station Street
Suite 270
Mentor, OH 44060
Hollow Structural Sections
Connections Manual
Section properties
Dimensional data
Fabrication
Detail design criteria
Steel Joist Institute (SJI)
3127 10th Ave.
No. Ext.
No. Myrtle Beach, SC
29577-6760
Standard Specifications and
Load Tables, Open-Web
Steel Joist
Dimensional data
Load capacity
STRUCTURAL STEEL CONSTRUCTION 7.47
TABLE 7.10 Guide to Selection of Beam Depths and Deflection Limits
Yield stress Fy, ksi
36.0 42.0 45.0 50.0
Maximum stress, ksi
0.60Fy 0.66Fy
Specific beam condition Minimum depth-span ratio
Maximum ratio of
deflection to span
Heavy shock or vibration 1
18
1
15.5
1
14.5
1
13
1
357
1
324
Heavy pedestrian traffic 1
20
1
17
1
16
1
14.5
1
320
1
291
Normal loading 1
22
1
19
1
18
1
16
1
290
1
264
Beams for flat roofs* 1
25
1
21.5
1
20
1
18
1
258
1
232
Roof purlins, except for flat
roofs*
1
28
1
24
1
22
1
20
1
232
1
210
* Investigate for stability against ponding.
provide section property values for the products they market. Table 7.9 lists several
handbooks widely used by design professionals, as well as other design guides
which address specific design features.
7.17 SERVICEABILITY CRITERIA
Experienced designers are aware of certain practical limitations on the size of individual
members. Flexural members which have marginal or too shallow a depth
can cause deflections that can damage other building elements, as well as cause
vibrations under moving loads that disturb a building’s occupants. Almost all building
code leave stiffness design criteria to the designer. Experienced designers have
found that to specify limits for all possible variations loads, occupancies, and types
of construction is impracticable.
This section outlines various criteria, originally based on experience but up-dated
on the basis of testing, which the designer can incorporate to develop a serviceable
design. The ASD specification (Table 7.1) restricts the maximum live-load deflection
of beams and girders supporting plaster ceilings to 1?360 of the span. This
requirement is not applicable to less rigid construction details. The AISC LRFD
specification contains no numerical limits for serviceability criteria. Table 7.10 may
be used to set limits on deflections of flexural members frequently encountered in
building design.
Minimum Depth-Span Ratios. Also, as a guide, Table 7.10 lists suggested minimum
depth-span ratios for various loading conditions and yield strengths of steel
up to Fy  50.0 ksi. These may be useful for estimating or making an initial design
selection. Since maximum deflection is a straight-line function of maximum bend7.48
SECTION SEVEN
ing stress ?b and therefore is nearly proportional to Fy, a beam of steel with Fy 
100.0 ksi would have to be twice the depth of a beam of steel with Fy  50.0 ksi
when each is stressed to allowable values and has the same maximum deflection.
Vibration of large floor areas that are usually free of physical dampeners, such
as partitions, may occur in buildings such as shopping centers and department
stores, where pedestrian traffic is heavy. The minimum depth-span ratios in Table
7.10 suggested for ‘‘heavy pedestrian traffic’’ are intended to provide an acceptable
solution.
One rule of thumb that may be used to determine beam depth quickly is to
choose a depth, in, not less than 1.5% of Fy times the span, ft. Thus, for A36 steel
depth, in, should be at least half the span, ft.
Ponding. Beams for flat roofs may require a special investigation to assure stability
against water accumulation, commonly called ponding, unless there is adequate
provision for drainage during heavy rainfall. The AISC specification gives
these criteria for stable roofs:
C  0.9C  0.25 (7.1) p s
4 25S
I  (7.2) d 6 10
where Cp  32Ls /107 Ip
4 Lp
Cs  32 /107 Is
4 SLs
Lp  column spacing in direction of girder, ft (length of primary members)
Ls  column spacing perpendicular to direction of girder, ft (length of secondary
member)
S  spacing of secondary members, ft
Ip  moment of inertia for primary members, in4
Is  moment of inertia for secondary members, in4. Where a steel deck is
supported on primary members, it is considered the secondary member.
Use 0.85Is for joists and trusses
Id  moment of inertia of a steel deck supported on secondary members,
in4 / ft
Uniform-Load Deflections. For the common case of a uniformly loaded simple
beam loaded to the maximum allowable bending stress, the deflection in inches
may be computed from
5 F l b  (7.3)
24 Ed/ l
where Fb  the allowable bending stress, ksi
l  the span, in
E  29,000 ksi
d/ l  the depth-span ratio
Drift. AISC Design Guide No. 3 (Table 7.9) suggests that the lateral deflection
of a building frame (drift) be limited to a value which does not damage other
structural or architectural components when subject to a 10-year recurrence interval
wind pressure. The 10-year wind pressure can be reasonably estimated at 75% of
the 50-year wind pressure.
STRUCTURAL STEEL CONSTRUCTION 7.49
Camber. Trusses of 80-ft or greater span should be cambered to offset dead-load
deflections. Crane girders 75 ft or more in span should be cambered for deflection
under dead load plus one-half live load.
7.18 TENSION MEMBERS
These are proportioned so that their gross and net areas are large enough to resist
imposed loads. The criteria for determining the net area of a tension member with
bolt holes is the same for allowable stress design and load-and-resistance-factor
design. In determination of net area, the width of a bolt hole should be taken 1?16
in larger than the nominal dimension of the hole normal to the direction of applied
stress. Although the gross section for a tension member without holes should be
taken normal to the direction of applied stress, the net section for a tension member
with holes should be chosen as the one with the smallest area that passes through
any chain of holes across the width of the member. Thus, the net section may pass
through a chain of holes lying in a plane normal to the direction of applied stress
or through holes along a diagonal of zigzag line.
Net section for a member with a chain of holes extending along a diagonal or
zigzag line is the product of the net width and thickness. To determine net width,
deduct from the gross width the sum of the diameters of all the holes in the chain,
then add, for each gage space in the chain, the quantity
2 s
4g
where s  longitudinal spacing (pitch, in) of any two consecutive holes and g 
transverse spacing (gage, in) of the same two holes.
The critical net section of the member is obtained from that chain with the least
net width.
When a member axially stressed in tension is subjected to nonuniform transfer
of load because of connections through bolts to only some of the elements of the
cross section, as in the case of a W, M, or S shape connected solely by bolts through
the flanges, the net area should be reduced as follows: 10% if the flange width is
at least two-thirds the beam depth and at least three fasteners lie along the line of
stress; 10% also for structural tees cut from such shapes; 15% for any of the preceding
shapes that do not meet those criteria and for other shapes that have at least
three fasteners in line of stress; and 25% for all members with only two fasteners
in the line of stress.
7.18.1 ASD of Tension Members
Unit tensile stress Ft on the gross area should not exceed 0.60Fy, where Fy is the
minimum yield stress of the steel member (see Table 7.11). Nor should Ft exceed
0.50Fu, where Fu is the minimum tensile strength of the steel member, when the
allowable stress is applied to the net area of a member connected with fasteners
requiring holes. However, if the fastener is a large pin, as used to connect eyebars,
pin plates, etc., Ft is limited to 0.45Fy on the net area. Therefore, for the popular
7.50 SECTION SEVEN
TABLE 7.11 Tension on Gross Area
Allowable tensile
stress (ASD)
Fy, ksi Ft, ksi
Unit design tensile
strength (LRFD)
Fy, ksi Pn /Ag
36 21.6 36 32.4
42 25.2 42 37.8
45 27.0 45 30.5
50 30.0 50 45.0
55 33.0 55 49.5
60 36.0 60 54.0
A36 steel, the allowable tension stresses for gross and net areas are 22.0 and 29.0
ksi, respectively, and in the case of pin plates, 16.2 ksi.
7.18.2 LRFD of Tension Members
Design tensile strength Pn, kips, of the gross area Ag, in2, should not exceed
0.90Fy, where Fy is the minimum yield stress of the steel (Table 7.9) and Pn 
AgFy. Nor should the design tensile strength Pn, kips, exceed 0.75Fu on the net
area Ae, in2, of the member. Other criteria control the design tensile strength of pinconnected
members. (Refer to the AISC specification for LRFD.)
7.19 COLUMNS AND OTHER
COMPRESSION MEMBERS
The principal factors governing the proportioning of members carrying compressive
forces are overall column buckling, local buckling, and gross section area. The
effect of overall column buckling depends on the slenderness ratio Kl/ r, where Kl
is the effective length, in, of the column, l is the unbraced length, and r is the least
radius of gyration, in, of the cross section. The effect of local buckling depends on
the width-thickness ratios of the individual elements of the member cross section.
W shapes with depths of 8, 10, 12, and 14 in are most commonly used for
building columns and other compression members. For unbraced compression
members, the most efficient shape is one where the value of ry with respect to the
minor axis approaches the value of rx with respect to the major axis.
When built-up sections are used as compression members, the element joining
the principal load-carrying elements, such as lacing bars, should have a shear capacity
of at least 2% of the axial load.
7.19.1 Effective Column Length
Proper application of the column capacity formulas for ASD or LRFD depends on
judicious selection of K. This term is defined as the ratio of effective column length
to actual unbraced length.
STRUCTURAL STEEL CONSTRUCTION 7.51
FIGURE 7.27 Values of effective column length K for idealized conditions.
FIGURE 7.26 Configurations of members of
a rigid frame caused by sidesway.
For a pin-ended column with translation
of the ends prevented, K  1. But
in general, K may be greater or less than
unity. For example, consider the columns
in the frame in Fig. 7.26. They are
dependent entirely on their own stiffness
for stability against sidesway. If enough
axial load is applied to them, their effective
length will exceed their actual
length. But if the frame were braced to
prevent sidesway, the effective length
would be less than the actual length because
of the resistance to end rotation
provided by the girder.
Theoretical values of K for six idealized
conditions in which joint rotation
and translation are either fully realized
or nonexistent are given in Fig. 7.27.
Also noted are values recommended by the Column Research Council for use in
design when these conditions are approximated. Since joint fixity is seldom fully
achieved, slightly higher design values than theoretical are given for fixed-end columns.
Specifications do not provide criteria for sidesway resistance under vertical loading,
because it is impossible to evaluate accurately the contribution to stiffness of
the various components of a building. Instead, specifications cite the general conditions
that have proven to be adequate.
7.52 SECTION SEVEN
TABLE 7.12 Slenderness Ratio at
Maximum Stress for Elastic Buckling
Failure
Fy, ksi Cc Fy, ksi Cc
36.0 126.1 60.0 97.7
42.0 166.7 65.0 93.8
45.0 112.8 90.0 79.8
50.0 107.0 100.0 75.7
55.0 102.0
Constructions that inhibit sidesway in building frames include substantial masonry
walls, interior shear walls; braced towers and shafts; floors and roofs providing
diaphragm action—that is, stiff enough to brace the columns to shear walls or
bracing systems; frames designed primarily to resist large side loadings or to limit
horizontal deflection; and diagonal X bracing in the planes of the frames. Compression
members in trusses are considered to be restrained against translation at
connections. Generally, for all these constructions, K may be taken as unity, but a
value less than one is permitted if proven by analysis.
When resistance to sidesway depends solely on the stiffness of the frames; for
example, in tier buildings with light curtain walls or with wide column spacing,
and with no diagonal bracing systems or shear walls, the designer may use any of
several proposed rational methods for determining K. A quick estimate, however,
can be made by using the alignment chart in an AISC ‘‘Manual of Steel Construction.’’
The effective length Kl of compression members, in such cases, should not
be less than the actual unbraced length.
7.19.2 ASD of Compression Members
The allowable compressive stress on the gross section of axially loaded members
is given by formulas determined by the effective slenderness ratios Kl/ r of the
members. A critical value, designated Cc, occurs at the slenderness ratio corresponding
to the maximum stress for elastic buckling failure (Table 7.12). This is
illustrated in Fig. 7.28. An important fact to note: when Kl/ r exceeds Cc  126.1,
the allowable compressive stress is the same for A36 and all higher-strength steels.
C  
2	;s2E/F (7.4) c y
where E  modulus of elasticity of the steel  29,000 ksi and Fy  specified
minimum yield stress, ksi.
When Kl/ r for any unbraced segments is less than Cc, the allowable compressive
stress, ksi is
2 2 [1  (Kl/ r) /2C ]F c y F  (7.5) a FS
where FS is the safety factor, which varies from 1.67 when Kl/ r  0 to 1.92 when
Kl/ r  Cc.
STRUCTURAL STEEL CONSTRUCTION 7.53
FIGURE 7.28 Allowable stresses for axial compression.
3 5 3Kl/ r (Kl/ r)
FS   (7.6) 3 3 8C 8C c c
When Kl/ r is greater than Cc:
2 12	 E 149,000
F  (7.7) a 2 2 23(Kl/ r) (Kl/ r)
This is the Euler column formula for elastic buckling with a constant safety factor
of 1.92 applied.
Increased stresses are permitted for bracing and secondary members with l / r
greater than 120. (K is taken as unity.) For such members, the allowable compressive
stress is
Fa F  (7.8) as 1.6  l /200r
where Fa is given by Eq. (7.5) or (7.6). The higher stress is justified by the relative
7.54
FIGURE 7.29 Maximum width-thickness ratios for allowable stress design of compression members.
7.55
FIGURE 7.29 Maximum width-thickness ratios for allowable stress design of compression members.
(Continued )
7.56 SECTION SEVEN
unimportance of these members and the greater restraint likely at their end connections.
The full unbraced length should always be used for l.
Tables giving allowable stresses for the entire range of Kl/ r appear in the AISC
ASD ‘‘Manual of Steel Construction.’’ Approximate values may be obtained from
Fig. 7.28. Allowable stresses are based on certain minimum sizes of structural
members and their elements that make possible full development of strength before
premature buckling occurs. The higher the allowable stresses the more stringent
must be the dimensional restrictions to preclude buckling or excessive deflections.
The AISC ASD specification for structural steel buildings limits the effective
slenderness ratio Kl/ r to 200 for columns, struts, and truss members, where K is
the ratio of effective length to actual unbraced length l, and r is the least radius of
gyration.
A practical rule also establishes limiting slenderness ratios l / r for tension members:
For main members 240
For bracing and secondary members 300
But this does not apply to rods or other tension members that are drawn up tight
(prestressed) during erection. The purpose of the rule is to avoid objectionable
slapping or vibration in long, slender members.
The AISC ASD specification also specifies several restricting ratios for compression
members. One set applies to projecting elements subjected to axial compression
or compression due to bending. Another set applies to compression elements
supported along two edges.
Figure 7.29 lists maximum width-thickness ratios, b/ t, for commonly used elements
and grades of steel. Tests show that when b/ t of elements normal to the
direction of compressive stress does not exceed these limits, the member may be
stressed close to the yield stress without failure by local buckling. Because the
allowable stress increases with Fy, the specified yield stress of the steel, widththickness
ratios are less for higher-strength steels.
These b/ t ratios should not be confused with the width-thickness ratios described
in Art. 7.20. There, more restrictive conditions are set in defining compact sections
qualified for higher allowable stresses.
7.19.3 LRFD of Compression Members
When the elements of the cross section of a compression member have widththickness
ratios that do not exceed the limits tabulated in Table 7.13, the design
compressive strength is cPn. The resistance factor c should be taken as 0.85. The
nominal strength is given by Pn  AgFcr, where Ag is the cross-sectional area, in2,
and Fcr is the critical compressive stress, ksi. Formulas for Fct are based on a
parameter c.
F F Kl Kl y y
  (7.9) c   r	 E r 286,220
where E  modulus of elasticity, ksi  29,000 ksi. For c  1.5,
2 c F  0.658 F (7.10) cr y
For c  1.5,
STRUCTURAL STEEL CONSTRUCTION 7.57
TABLE 7.13 Limiting Width-Thickness Ratios for LRFD of Columns
Compression elements
Width
thickness
ratio
Limiting width-thickness ratio r
General A36 steel A50 steel
Flanges of W and other I shapes
and channels; outstanding legs of
pairs of angles in continuous
contact
b/ t 95/
Fy 15.8 13.4
Flanges of square and rectangular
box sections; flange cover plates
and diaphragm plates between
lines of fasteners or welds
b/ t 238/
F  F* y r 47.7 (rolled)
53.9
(welded)
37.6
(rolled)
41.1
(welded)
Legs of single angle struts and
double angle struts with
separators; unstiffened elements
(i.e., supported along one edge)
b/ t 76/
Fy 12.7 10.7
Stems of tees d/ t 127/
Fy 21.2 18.0
All other stiffened elements
(elements supported along two
edges)
b/ t
hc / tw
253/
Fy 42.2 35.8
*Fy  compressive residual stress in flange: 10 ksi for rolled shapes, 16.5 ksi for welded sections.
2 F  (0.877/  )F (7.11) cr c y
Computations can be simplified by use of column load tables in the AISC LRFD
‘‘Steel Construction Manual.’’
For design of columns with elements having width-thickness ratios exceeding
the limits in Table 7.13, refer to the AISC LRFD specification.
(T. V. Galambos, ‘‘Guide to Design Criteria for Metal Compression Members,’’
4th ed., John Wiley & Sons, Inc., New York.)
7.20 BEAMS AND OTHER FLEXURAL MEMBERS
The capacity of members subject to bending depends on the cross-section geometry,
AISC ASD and LRFD procedures incorporate the concept of compact and noncompact
sections.
7.20.1 ASD of Flexural Members
Beams classified as compact are allowed a bending stress, ksi, Fb  0.66Fy for the
extreme surfaces in both tension and compression, where Fy, is the specified yield
stress, ksi. Such members have an axis of symmetry in the plane of loading, their
compression flange is adequately braced to prevent lateral displacement, and they
develop their full plastic moment (section modulus times yield stress) before buckling.
7.58 SECTION SEVEN
FIGURE 7.30 Requirements for laterally supported compact beam sections in ASD.
STRUCTURAL STEEL CONSTRUCTION 7.59
FIGURE 7.30 Requirements for laterally supported compact beam sections in ASD.
(Continued )
7.60 SECTION SEVEN
Compactness Requirements. To qualify as compact, members must meet the following
conditions:
1. The flanges must be continuously connected to the web or webs.
2. The width-thickness ratio of unstiffened projecting elements of the compression
flange must not exceed For computation of this ratio, with b equals 65.0/
F . y
one-half the full flange width of I-shaped sections, or the distance from the free
edge to the first row of fasteners (or welds) for projecting plates, or the full width
of legs of angles, flanges of zees of channels, or tee stems.
3. The web depth-thickness ratio d/tw must not exceed 640(1  3.74a /Fy)/
F
when ?a, the computed axial stress, is equal to or less than 0.16Fy, or 257/
Fy
when ?a  0.16Fy.
4. The width-thickness ratio of stiffened compression flange plates in box sections
and that part of the cover plates for beams and built-up members that is
included between longitudinal lines of bolts or welds must not exceed 190/
F . y
5. For the compression flange of members not box shaped to be considered
supported, unbraced length between lateral supports should not exceed
or 20,000 A? /Fyd, where b? is the flange width, A? the flange area, and 76.0b /
F ? y
d the web depth.
6. The unbraced length for rectangular box-shaped members with depth not
more than 6 times the width and with flange thickness not more than 2 times the
web thickness must not exceed (1950  1200 M1 /M2)b/Fy. The unbraced length
in such cases, however, need not be less than 1200b/Fy. M1 is the smaller and M2
the larger of bending moments at points of lateral support.
7. The diameter-thickness ratio of hollow circular steel sections must not exceed
300/Fy.
Allowable Bending Stresses for Compact Beams. Most sections used in building
framing, including practically all rolled W shapes of A36 steel and most of those
with Fy  50 ksi, comply with the preceding requirements for compactness, as
illustrated in Fig. 7.30. Such sections, therefore, are designed with Fb  0.66Fy.
Excluded from qualifying are hybrid girders, tapered girders, and sections made
from A514 steel.
Braced sections that meet the requirements for compactness, and are continuous
over their supports or rigidly framed to columns, are also permitted a redistribution
of the design moments. Negative gravity-load moments at supports may be reduced
10%. But then, the maximum positive moment must be increased by 1% of the
average negative moments. This moment redistribution does not apply to cantilevers,
hybrid girders, or members of the A514 steel.
Allowable Bending Stresses for Noncompact Beams. Many other beam-type
members, including nearly compact sections that do not meet all seven requirements,
are accorded allowable bending stresses, some higher and some considerably
lower than 0.66Fy, depending on such conditions as shape factor, direction of loading,
inherent resistance to torsion or buckling, and external lateral support. The
common conditions and applicable allowable bending stresses are summarized in
Fig. 7.31. In the formulas,
STRUCTURAL STEEL CONSTRUCTION 7.61
FIGURE 7.31 Allowable bending stresses for sections not qualifying as compact.
l  distance, in, between cross sections braced against twist or lateral displacement
of the compression flange
rt  radius of gyration, in, of a section comprising the compression flange plus
one-third of the compression web area, taken about an axis in the plane of
the web
A?  area of the compression flange, in2
The allowable bending stresses Fb, ksi, for values often used for various grades
of steel are listed in Table 7.14.
7.62 SECTION SEVEN
TABLE 7.14 Allowable Bending Stresses,
ksi
Fy 0.60Fy 0.66Fy 0.75Fy
36.0 22.0 24.0 27.0
42.0 25.2 27.7 31.5
45.0 27.0 29.7 33.8
50.0 30.0 33.0 37.5
55.0 33.0 36.3 41.3
60.0 36.0 39.6 45.0
65.0 39.0 42.9 48.8
Lateral Support of Beams. In computation of allowable bending stresses in compression
for beams with distance between lateral supports exceeding requirements,
a range sometimes called laterally unsupported, the AISC ASD formulas contain a
moment factor Cb in recognition of the beneficial effect of internal moments, both
in magnitude and direction, at the points of support. For the purpose of this summary,
however, the moment factor has been taken as unity and the formulas simplified
in Fig. 7.31. The formulas are exact for the case in which the bending
moment at any point within an unbraced length is larger than that at both ends of
this length. They are conservative for all other cases. Where more refined values
are desired, see Art. 7.20.2 or refer to the AISC ASD specification for structural
steel buildings.
Limits on Beam Width-Thickness Ratios. For flexural members in which the
width-thickness ratios of compression elements exceed the limits given in Fig. 7.31
and which are usually lightly stressed, appropriate allowable bending stresses are
suggested in ‘‘Slender Compression Elements,’’ Appendix C, AISC specification.
For additional discussion of lateral support, see Art. 7.12.2. Also, addition information
on width-thickness ratios of compression elements is given in Fig. 7.29.
ASD for Shear in Flexural Members. The shear strength of a flexural member
may be computed by dividing the total shear force at a section by the web area,
the product of the web thickness and overall member depth. Whereas flexural
strength normally controls selection of rolled shapes, shear strength can be critical
when the web has cutouts or holes that reduce the net web area of when a shortspan
beam carries a large concentrated load. Also, in built-up members, such as
plate girders or rigid frame elements, shear often controls web thickness.
The web depth-thickness ratio permitted without stiffeners, h/ t  for 380/
Fy
ASD and h/ t  for LRFD, is satisfied by the W shapes of A36 steel. 418/
Fy
Furthermore, only the lightest one or two W sections in each depth fail to satisfy
these criteria for 50-ksi material.
For members with h/ t  , the unit shear stress on the gross section 380/
Fy
should not be greater than Fv  0.40Fy, where Fy is the minimum yield point of
the web steel ksi (Table 7.15). Members with higher h/ t ratios require stiffeners
(see Art. 7.21.1).
Beams with web angle or shear-bar end connections and a coped top flange
should be checked for shear on the critical plane through the holes in the web. In
this case, the allowable unit shear stress is Fv  0.30Fu, where Fu is the minimum
tensile strength of the steel, ksi.
STRUCTURAL STEEL CONSTRUCTION 7.63
TABLE 7.15 Allowable Shear on Gross Area, ksi
For ASD
when h/ t  380/
Fy
Fy Fu
For LRFD
when h/ t  418/
Fy
Fy Vn
36.0 14.5 36.0 19.4
42.0 17.0 42.0 22.7
45.0 18.0 45.0 24.3
50.0 20.0 50.0 27.0
55.0 22.0 55.0 29.7
60.0 24.0 60.0 32.4
A special case occurs when a web lies in a plane common to intersecting members;
for example, the knee of a rigid frame. Then, shear stresses generally are high.
Such webs, in elastic design, should be reinforced when the web thickness is less
than 32M/AbcFy, where M is the algebraic sum of clockwise and counterclockwise
moments (in ft-kips) applied on opposite sides of the connection boundary, and Abc
is the planar area of the connection web, in2 (approximately the product of the
depth of the member introducing the moment and the depth of the intersecting
member). In plastic design, this thickness is determined from 23Mp /AbcFy, where
Mp is the plastic moment, or M times a load factor of 1.70. In this case, the total
web shear produced by the factored loading should not exceed the web area (depth
times thickness) capacity in shear. Otherwise, the web must be reinforced with
diagonal stiffeners or a doubler plate.
For deep girder webs, allowable shear is reduced. The reduction depends on the
ratio of clear web depth between flanges to web thickness and an aspect ratio of
stiffener spacing to web depth. In practice, this reduction does not apply when the
ratio of web depth to thickness is less than . 380/
Fy
7.20.2 LRFD of Flexural Members
The AISC LRFD specification for structural steel buildings permits plastic analysis
for steels with yield stress not exceeding 65 ksi. Negative moments induced by
gravity loading may be reduced 10% for compact beams, if the positive moments
are increased by 10% of the average of the negative moments.
Design strength in bending of flexural members is defined as bMn, where the
resistance b  0.90 and Mn is the nominal flexural strength. Mn depends on several
factors, including the geometry of the section, the unbraced length of the compression
flange, and properties of the steel. Beams may be compact, noncompact, or
slender-element sections. For compact beams, the AISC specification sets limits on
the width-thickness ratios of section elements to restrict local buckling. These limits
are listed in Table 7.16.
For a compact section bent about the major axis, the unbraced length Lb of the
compression flange where plastic hinges may form at failure may not exceed Lpd
given by Eqs. (7.12) and (7.13). For beams bent about the minor axis and square
and circular beams, Lb is not restricted for plastic analysis.
For I-shaped beams that are loaded in the plane of the web and are symmetric
about major and minor axes or symmetric about the minor axis but with the compression
flange larger than the tension flange, including hybrid girders,
7.64 SECTION SEVEN
TABLE 7.16 Limiting Width-Thickness Ratios for LRFD of Beams
Beam element
Width-thickness
ratio
Limiting width-thickness
ratio, p
General A36 steel A50 steel
Flanges of W and other I shapes
and channels
b/ t 65/
Fy 10.8 9.2
Flanges of square and rectangular
box sections; flange cover
plates and diaphragm plates
between lines of fasteners or
welds
b/ t 190/
Fy 31.7 26.9
Webs in flexural compression hc / tw 640/
Fy 106.7 90.5
3600  2200(M /M ) 1 p L  r (7.12) pd y Fyc
where Fyc  minimum yield stress, ksi, of compression flange
M1  smaller of the moments, in-kips, at the end of the unbraced length of
the beam.
Mp  plastic moment, in-kips
ry  radius of gyration, in, about minor axis
For homogeneous sections, Mp  FyZ, where Z is the plastic section modulus, in3.
(For hybrid girders, Z may be computed from the fully plastic distribution.) M1 /
Mp is positive for beams with reverse curvature, negative for single curvature.
For solid rectangular bars and symmetric box beams,
5000  3000(M /M ) 1 p L  r (7.13) pd y Fy
The flexural design strength 0.90Mn is determined by the limit state of lateral
torsional buckling and should be calculated for the region of the last hinge to form
and for regions not adjacent to a plastic hinge. For compact sections bent about the
major axis, Mn depends on the following unbraced lengths:
Lb  distance, in, between points braced against lateral displacement of the compression
flange or between points braced to prevent twist
Lp  limiting laterally unbraced length, in, for full plastic bending capacity
 300ry / for I shapes and channels 
Fy?
 3750(ry /Mp) / for box beams and solid rectangular bars 
JA
Fy?  flange yield stress, ksi
J  torsional constant, in4 (see AISC LRFD ‘‘Manual of Steel Construction’’)
A  cross-sectional area, in2
Lr  limiting laterally unbraced length, in, for inelastic lateral buckling
For I-shaped beams symmetric about the major or minor axis or symmetric about
the minor axis with the compression flange larger than the tension flange, and
channels loaded in the plane of the web,
STRUCTURAL STEEL CONSTRUCTION 7.65
r X y 1 2 L  1  
1  X (F  F ) (7.14) r 2 yw r  (F  F ) yw r
where Fyw  specified minimum yield stress of web, ksi
Fr  compressive residual stress in flange  10 ksi for rolled shapes, 16.5
ksi for welded sections
X1  (	/Sx) 
EGJA/2
X2  (4Cw/ Iy) (Sx /GJ)2
E  elastic modulus of the steel  29,000 ksi
G  shear modulus of elasticity  11,200 ksi
Sx  section modulus about major axis, in3 (with respect to the compression
flange if that flange is larger than the tension flange)
Cw  warping constant, in6 (see AISC Manual—LRFD)
Iy  moment of inertia about minor axis, in4
7.20.3 Limit-State Moments
For the aforementioned shapes, the limiting buckling moment Mr, ksi, may be
computed from
M  (F  F )S (7.15) r yw r x
For compact beams with Lb  Lr , bent about the major axis,
L  L b p M C M  (M  M )  M (7.16)   n b p p r p L  L r p
where Cb  1.75  1.05(M1 /M2)  0.3(M1 /M2)2  2.3, where M1 is the smaller
and M2 the larger end moment in the unbraced segment of the beam;
M1 /M2 is positive for reverse curvature
 1.0 for unbraced cantilevers and beams with moment over much of
the unbraced segment equal to or greater than the larger of the segment
end moments (see T. V. Galambos ‘‘Guide to Stability Design Criteria
for Metal Structures,’’ 4th ed., John Wiley & Sons, Inc., New York,
for use of larger values of Cb)
For solid rectangular bars bent about the major axis,
L  57,000(r /M ) 
JA (7.17) r y r
and the limiting buckling moment is given by
M  F S (7.18) r y x
For symmetric box sections loaded in the plane of symmetry and bent about the
major axis, Mr should be determined from Eq. (7.15) and Lr from Eq. (7.17).
For compact beams with Lb  Lr , bent about the major axis,
M  M  C M (7.19) n cr b r
where Mcr  critical elastic moments, kip-in. For shapes to which Eq. (17.11)
applies,
7.66 SECTION SEVEN
2 M  C (	/L ) 
EI GJ  I C (	E/L ) (7.20) cr b b y y w b
For solid rectangular bars and symmetric box sections,
M  57,000C 
JA/ (L / r ) (7.21) cr b b y
Noncompact Beams. The nominal flexural strength Mn for noncompact beams is
the least value determined from the limit states of
1. Lateral-torsional buckling (LTB)
2. Flange local buckling (FLB)
3. Web local buckling (WLB)
The AISC LRFD specification for structural steel buildings presents formulas for
determining limit-state moments. In most cases, LRFD computations for flexural
members can be simplified by use of tables in the AISC ‘‘Manual of Steel Construction—
LRFD.’’ See also Art. 7.21.
LRFD for Shear in Flexural Members. The design shear strength is VVn, where
V  0.90, and for rolled shapes and built-up members without stiffeners is governed
by the web depth-thickness ratio. The design shear strength may be computed
from
h 418
V  0.90 
 0.6F A  0.54F A  (7.22) n yw y w t 
Fy
418/
F 418/
F y y 418 h 523
V  0.90 
 0.6  0.54F A   (7.23) n yw b/t h/t t 
F 
F y y
132,000 119,000 h 523
V  0.90 
 A   (7.24) n w 2 2 (h/ t) (h/ t) t 
Fy
where Vn  nominal shear strength, kips
Aw  area of the web, in2  dt
d  overall depth, in
t  thickness of web, in
h  the following web dimensions, in: clear distance between fillets for
rolled shapes; clear distance between flanges for welded sections
Fy  specified minimum yield stress, ksi, of web steel
See also Art. 7.21.2.
7.20.4 Beam Penetrations
Certain designs, especially buildings with minimal floor-to-floor heights, require
penetrations, or openings, in the webs of beams to permit the routing of ductwork
or piping. In general, such penetrations can safely be made at locations where the
beam shear loading is low if the penetration height is limited to half the beam
depth. The central span region of a beam carrying a uniform load is an example
of a typical situation. The penetration should be centered on the mutual axis of the
member and all re-entrant corners should have a generous radius.
STRUCTURAL STEEL CONSTRUCTION 7.67
FIGURE 7.32 Typical beam penetrations.
When penetrations are necessary at locations with higher shear loadings, it may
be necessary to reinforce the web with longitudinal stiffeners. Figure 7.32 shows
typical configurations with (a) being unreinforced and (b) reinforced. Design of
such reinforcement is done by considering a free-body of the section of the beam
containing the penetration. Further information on beam penetrations is available
in AISC Design Guide No. 2 (Table 7.9).
7.21 PLATE GIRDERS
Plate girders may have either a box or an I shape. Main components are plates or
plates and angles, arranged so that the cross section is either singly or doubly
symmetrical. Generally, the elements are connected by continuous fillet welds. In
existing construction, the connection may have been made with rivets or bolts
through plates and angles. Fig. 7.33 depicts typical I-shape girders.
Plate girders are commonly used for long spans where they cost less than rolled
W shapes or where members are required with greater depths or thinner webs than
those available with rolled W shapes. The AISC LRFD ‘‘Specification for Structural
Steel for Buildings’’ distinguished between a plate girder and a beam in that a plate
7.68 SECTION SEVEN
FIGURE 7.33 Plate girders: (a) welded (b) bolted.
girder has web stiffeners or a web with hc / tw  970/ or both, where hc is 
F , y
twice the distance from the neutral axis to (1) the inside face of the compression
flange when it is welded to the web or (2) the nearest line of fasteners to the
compression flange when the web-flange connection is bolted.
7.21.1 ASD Procedure for Plate Girders
Allowable stresses for tension, compression, bending, and shear are the same for
plate girders as those given in Arts. 7.18 to 7.20, except where stiffeners are used.
But reductions in allowable stress are required under some conditions, and there
are limitations on the proportions of girder components.
Web Depth-Thickness Limits. The ratio of the clear distance h between flanges,
in, to web thickness t, in, is limited by
h 14,000
 (7.25)
t 
F (F  16.5) y y
where Fy is the specified yield stress of the compression flange steel, ksi (Table
7.17). When, however, transverse stiffeners are provided at spacings not exceeding
1.5 times the girder depth, the limit on h/ t is increased to
h 2,000
 (7.26)
t 
Fy
STRUCTURAL STEEL CONSTRUCTION 7.69
TABLE 7.17 Limiting Depth-Thickness Ratios for ASD of Plate-Girder Webs
Fy, ksi
h/ t
Eq. (7.25)
h/ t
Eq. (7.26) Fy, ksi
h/ t
Eq. (7.25)
h/ t
Eq. (7.26)
36.0 322 333 60.0 207 258
42.0 282 309 65.0 192 248
45.0 266 298 90.0 143 211
50.0 243 283 100.0 130 200
55.0 223 270
General Design Method. Plate girders may be proportioned to resist bending on
the assumption that the moment of inertia of the gross cross section is effective.
No deductions need be made for fastener holes, unless the holes reduce the gross
area of either flange by more than 15%. When they do, the excess should be
deducted.
Hybrid girders, which have higher-strength steel in the flanges than in the web,
may also be proportioned by the moment of inertia of the gross section when they
are not subjected to an axial force greater than 15% of the product of yield stress
of the flange steel and the area of the gross section. At any given section, the
flanges must have the same cross-sectional area and be made of the same grade of
steel.
The allowable compressing bending stress Fb for plate girders must be reduced
from that given in Art. 7.20 where h/ t exceeds For greater values of this 760/
F . b
ratio, the allowable compressive bending stress, except for hybrid girders, becomes
A h 760 w F	  F 1  0.0005  (7.27)    b b A t 
F ? b
where Aw  the web area, in2 and A?  the compression flange area, in2.
For hybrid girders, not only is the allowable compressive bending stress limited
to that given by Eq. (7.24), but also the maximum stress in either flange may not
exceed
3 12  (A /A )(3
 
 ) w ? F	  F (7.28)   b b 12  2(A /A ) w ?
where a  ratio of web yield stress to flange yield stress.
Flange Limitations. The projecting elements of the compression flange must
comply with the limitations for b/ t given in Art. 7.21. The area of cover plates,
where used, should not exceed 0.70 times the total flange area. Partial-length cover
plates (Fig. 7.33b) should extend beyond the theoretical cutoff point a sufficient
distance to develop their share of bending stresses at the cutoff point. Preferably
for welded-plate girders, the flange should consist of a series of plates, which may
differ in thickness and width, joined end to end with complete-penetration groove
welds (Fig. 7.33a).
Bearing Stiffeners. These are required on girder webs at unframed ends. They
may also be needed at concentrated loads, including supports. Set in pairs, bearing
stiffeners may be angles or plates placed on opposite sides of the web, usually
normal to the bending axis. Angles are attached with one leg against the web. Plates
7.70 SECTION SEVEN
are welded perpendicular to the web. The stiffeners should have close bearing
against the flanges through which they receive their loads, and should extend nearly
to the edges of the flanges.
These stiffeners are designed as columns, with allowable stresses as given in
Art. 7.19. The column section is assumed to consist of a pair of stiffeners and a
strip of girder web with width 25 times web thickness for interior stiffeners and 12
times web thickness at ends. In computing the effective slenderness ratio Kl/ r, use
an effective length Kl of at least 0.75 the length of the stiffeners.
Intermediate Stiffeners. With properly spaced transverse stiffeners strong enough
to act as compression members, a plate-girder web can carry loads far in excess of
its buckling load. The girders acts, in effect, like a Pratt truss, with the stiffeners
as struts and the web forming fields of diagonal tension. The following formulas
for stiffeners are based on this behavior. Like bearing stiffeners, intermediate stiffeners
are placed to project normal to the web and the bending axis, but they may
consist of a single angle or plate. They may be stopped short of the tension flange
a distance up to 4 times the web thickness. If the compression flange is a rectangular
plate, single stiffeners must be attached to it to prevent the plate from twisting.
When lateral bracing is attached to stiffeners, they must be connected to the compression
flange to transmit at least 1% of the total flange stress, except when the
flange consists only of angles.
The total shear force, kips, divided by the web area, in2, for any panel between
stiffeners should not exceed the allowable shear Fv given by Eqs. (7.29a) and
(7.29b).
Except for hybrid girders, when Cv is less than unity:
F 1  C y v F  C   0.4F (7.29a)   v v y 3 2.89 1.15 
1  (a/h)
For hybrid girders or when Cv is more than unity or when intermediate stiffeners
are omitted:
F C y v F   0.4F (7.29b) v y 2.89
where a  clear distance between transverse stiffeners, in
h  clear distance between flanges within an unstiffened segment, in
Cv  when Cv is less than 0.8
45,000k
2 F (h/ t) y
 when Cv is more than 0.8
190 k  h/t Fv
t  web thickness, in
k  5.34  4(a/h)2 when a/h  1
 4  5.34(a/h)2 when a/h  1
Stiffeners for an end panel or for any panel containing large holes and for
adjacent panels should be so spaced that the largest average web shear ?v in the
panel does not exceed the allowable shear given in Eq. (7.29b).
Intermediate stiffeners are not required when h/ t is less than 260 and ?v is less
than the allowable stress given by Eq. (7.29b). When these criteria are not satisfied,
stiffeners should be spaced so that the applicable allowable shear, Eq. (7.29a) or
STRUCTURAL STEEL CONSTRUCTION 7.71
FIGURE 7.34 Plate girder web design. Chart shows the relationship between allowable shears
in web of plate girders, with yield stress Fy  36 ksi, and web thickness, distance between
flanges, and stiffener spacing.
(7.29b), is not exceeded, and in addition, so that a/h is not more than [260/ (h/ t)]2
or 3.
Solution of the preceding formulas for stiffener spacing requires assumptions of
dimensions and trials. The calculations can be facilitated by using tables in the
AISC ‘‘Manual of Steel Construction.’’ Also, Fig. 7.34 permits rapid selection of
the most efficient stiffener arrangement, for webs of A36 steel. Similar charts can
be drawn for other steels.
If the tension field concept is to apply to plate girder design, care is necessary
to ensure that the intermediate stiffeners function as struts. When these stiffeners
are spaced to satisfy Eq. (7.29a), their gross area, in2 (total area if in pairs) should
be at least
7.72 SECTION SEVEN
2 1 C a (a/h) v A  YDht (7.30)   st 2 2 h 
1  (a/h)
where Y  ratio of yield stress of web steel to yield stress of stiffener steel
D  1.0 for stiffeners in pairs
 1.8 for single-angle stiffeners
 2.4 for single-plate stiffeners
When the greatest shear stress ?v in a panel is less than Fv determined from Eq.
(7.29a), the gross area of the stiffeners may be reduced in the ratio ?v /Fv.
The moment of inertia of a stiffener or pair of stiffeners, about the web axis,
should be at least (h/50)4. The connection of these stiffeners to the web should be
capable of developing shear, in kips per lineal inch of single stiffener or pair, of at
least
3 Fyw ?  h (7.31)   vs  340
where Fyw is the yield stress of the web steel (Table 7.18). This shear also may be
reduced in the ratio ?v /Fv as above.
TABLE 7.18 Required Shear Capacity of
Intermediate-Stiffener Connections to Girder
Web
Fyw, ksi
?vg, kips
per lin in Fyw, ksi
?vg, kips
per lin in
36.0 0.034h 60.0 0.074h
42.0 0.043h 65.0 0.084h
45.0 0.048h 90.0 0.136h
50.0 0.056h 100.0 0.160h
55.0 0.065h
Combined Stresses in Web. A check should be made for combined shear and
bending in the web where the tensile bending stress is approximately equal to the
maximum permissible. When ?v, the shear force at the section divided by the web
area, is greater than that permitted by Eq. (7.29a), the tensile bending stress in the
web should be limited to no more than 0.6Fyw or Fyw(0.825  0.375?v /Fv), where
Fv is the allowable web shear given by Eq. (7.29a). For girders with steel flanges
and webs with Fy exceeding 65 ksi, when the flange bending stress is more than
75% of the allowable, the allowable shear stress in the web should not exceed that
given by Eq. (7.22).
Also, the compressive stresses in the web should be checked (see Art. 7.22).
7.21.2 LRFD Procedure for Plate Girders
Plate girders are normally proportioned to resist bending on the assumption that
the moment of inertia of the gross section is effective. The web must be proporSTRUCTURAL
STEEL CONSTRUCTION 7.73
tioned such that the maximum web depth-thickness ratio h/ t does not exceed h/ t
given by (7.32) or (7.33), whichever is applicable.
If a/h  1.5,
h 2000
 (7.32)
t 
Fy?
If a/h  1.5,
h 14,000
 (7.33)
t 
F ( F  F ) y? y? r
where a  clear distance between transverse stiffeners, in
t  web thickness, in
Fy?  specified minimum yield stress of steel, ksi
Fr  compressive residual stress in flange  16.5 ksi for plate girders
Web stiffeners are frequently required to achieve an economical design. However,
web stiffeners are not required if h/ t  260 and adequate shear strength is provided
by the web. The criteria for the design of plate girders are given in the AISC LRFD
Specification.
Design Flexural Strength. The design flexural strength is bMn, where b  0.90.
If hc / t  970 determine the nominal flexural strength as indicated in Art. 
F , y
7.15, for either compact or noncompact shapes. If hc / t  970 Mn is governed 
F , y
by the limit states of tension-flange yielding or compression-flange buckling.
The design strength is the smaller of the values of bMn for yielding of the
tension flange, which is
M  0.90S R R F (7.34) b n xt PG e yt
and for buckling of the compression flange, which is
M  0.90S R RF (7.35) b n xc PG e cr
where RPG  plate-girder bending-strength reduction factor
 1  0.0005ar(hc / t  970/ )  1.0 
Fcr
Re  hybrid girder factor
 1  0.1(1.3  ar)(0.81  m)  1.0
 1 for nonhybrid girders
ar  ratio of web area to compression-flange area
m  ratio of web yield stress to flange yield stress or to Fcr
Fcr  critical compression-flange stress, ksi
Fyt  yield stress of tension flange, ksi
Sxt  section modulus, in3, with respect to the tension flange
Sxc  section modulus, in3, with respect to the compression flange
The critical stress Fcr is different for different limit states. Its value is computed
from the values of parameters that depend on the type of limit state: plate girder
coefficient CPG, slenderness parameter , limiting slenderness parameter p for a
compact element, and limiting slenderness parameter , for a noncompact element.
Thus, Fcr may be computed from one of Eqs. (7.34) to (7.36) for the limit states
7.74 SECTION SEVEN
of lateral-torsional buckling and flange local buckling. The limit state of local buckling
of web does not apply.
F  F   (7.36) cr y? p
  1 p F  C F 1   F     (7.37)    cr b y? y? p r 2    r p
2 F  C /   (7.38) cr PG r
where Fy?  specified minimum flange yield stress, ksi
Cb  bending coefficient dependent on moment gradient
 1.75  1.05(M1 /M2)  0.3(M1 /M2)2 for lateral-torsional buckling
 1 for flange local buckling
CPG  286,000/Cb for lateral torsional buckling
 11,200 for flange local buckling
 Lb / rT for lateral-torsional buckling
 b?/2t? for flange local buckling
Lb  laterally unbraced length of girder, in
rT  radius of gyration, in, of compression flange plus one-sixth the web
b?  flange width, in
t?  flange thickness, in
p  300/ for lateral-torsional buckling 
Fy?
 65/ for flange local buckling 
Fy?
r  756/ for lateral-torsional buckling 
Fy?
 150/ for flange local buckling 
Fy?
Design Shear Strength. This is given by vVn, where v  0.90. With tension-
field action, in which the web is permitted to buckle due to diagonal compression
and the web carries stresses in diagonal tension in the panels between vertical
stiffeners, the design shear strength is larger than when such action is not permitted.
Tension-field action is not allowed for end panels in nonhybrid plate girders, for
all panels in hybrid girders and plate girders with tapered webs, and for panels in
which the ratio of panel width to depth a/h exceeds 3.0 or [260(h/ t)]2, where t is
the web thickness. For these conditions, the design shear strength is given by
 V  0.90 
 0.6A F C  0.54A F C (7.39) n n w yw v w yw v
where Aw  web area, in2
Fyw  specified web yield stress, ksi
Cv  ratio of critical web stress, in the linear buckling theory, to the shear
yield stress of the web steel
For tension-field action, the design shear strength depends on the ratio of panel
width to depth a/h. For h/ t  187
k/F , yw
V  0.54A F (7.40) v n w yw
For h/ t  187
k/F , yw
STRUCTURAL STEEL CONSTRUCTION 7.75
1  Cv V  0.54A F C  (7.41)   v n w yw v 2 1.15
1  (a/h)
where k  web buckling coefficient
5 if a/h  0.3 or a/h  [260/ (h/ t)]2
 5  5/(a/h)2 otherwise
Cv  when 187  h/ t 
187
k/Fyw 
k/F 234
k/F yw yw h/ t
 when h/ t 
44,000 k
234
k/Fyw 2 (h/ t) Fy
Web Stiffeners. Transverse stiffeners are required if the web shear strength without
stiffeners is inadequate, if h/ t  or if h/ t does not meet the re- 418/
F , yw
quirements of Eqs. (7.30) and (7.31). Where stiffeners are required, the spacing of
stiffeners should be close enough to maintain the shear within allowable limits.
Also, the moment of inertia Ist, in4, of a transverse stiffener should be at least that
computed from
3 I  at j (7.42) st
where j  2.5/(a/h)2  2.
The moment of inertia for a pair of stiffeners should be taken about an axis
through the center of the web. For a single stiffener, Ist should be taken about the
web face in contact with the stiffener. In addition, for design for tension-field action,
the stiffener area Ast, in2, should be at least that computed from
F V yw u 2 A  0.15Dht(1  C )  18t  0 (7.43)   st v F  V ys u n
where Fys  specified yield stress of stiffener, ksi
Vu  required shear strength at stiffener, kips, calculated for the factored
loads
D  1.0 for a pair of stiffeners
 1.8 for a single-angle stiffener
 2.4 for a single-plate stiffener
Bending and Shear Interaction. Plate girders should also be proportioned to satisfy
Eq. (7.43) if they are designed for tension-field action, stiffeners are required,
and Vu /Mu lies between 60 and 133% of Vn /Mn.
M V u u  0.625  1.24 (7.44)
M V n n
where Mn  design flexural strength
Mu  required flexural strength calculated for the factored loads but may
not exceed 0.90Mn
Vn  design shear strength
Vu  required shear strength calculated for the factored loads but may not
exceed 0.90Vn
7.76 SECTION SEVEN
7.22 WEB OR FLANGE LOAD-BEARING
STIFFENERS
Members subject to large concentrated loads within their length or large end reactions
should be proportioned so that the forces on the web or flange cannot cause
local failure or the webs or flanges should be stiffened to carry the concentrated
loads. Both ASD and LRFD procedures include design criteria.
7.22.1 ASD for Load-Bearing Stiffeners
Webs of rolled beams and plate girders should be so proportioned that the compressive
stress, ksi, at the web toe of the fillets does not exceed
F  0.66F (7.45) a y
where Fy  specified minimum yield stress, ksi.
Web failure probably would be in the form of buckling caused by concentrated
loading, either at an interior load or at the supports. The capacity of the web to
transmit the forces safely should be checked.
FIGURE 7.35 Web crippling in a simple
beam. The critical web section is assumed to
occur at the fillet.
Load Distribution. Loads are resisted
not only by the part of the web directly
under them but also by the parts immediately
adjacent. A 45 distribution
usually is assumed, as indicated in Fig.
7.35 for two common conditions. The
distance k is determined by the point
where the fillet of the flange joins the
web; it is tabulated in the beam tables
of the AISC ‘‘Manual of Steel Construction.’’
Fa is applicable to the horizontal
web strip of length b  k at the end
support or b  2k under an interior load.
Bearing stiffeners are required when Fa
is exceeded.
Bearing atop Webs. The sum of the compression stresses resulting from loads
bearing directly on or through a flange on the compression edge of a plate-girder
web should not exceed the following:
When the flange is restrained against rotation, the allowable compressive stress,
ksi, is
4 10,000
F  5.5  (7.46)   a 2 2 (a/h) (h/ t)
When the flange is not restrained against rotation,
4 10,000
F  2  (7.47)   a 2 2 (a/h) (h/ t)
STRUCTURAL STEEL CONSTRUCTION 7.77
FIGURE 7.36 Web crippling in a column at a welded joint with a beam.
where a  clear distance between transverse stiffeners, in
h  clear distance between flanges, in
t  web thickness, in
The load may be considered distributed over a web length equal to the panel
length (distance between vertical stiffeners) or girder depth, whichever is less.
Web Stiffeners on Columns. The web of a column may also be subject to crippling
by the thrust from the compression flange of a rigidly connected beam, as
shown at point a in Fig. 7.36. Likewise, to ensure full development of the beam
plastic moment, the column flange opposite the tensile thrust at point b may require
stiffening.
When stiffeners having a combined cross-sectional area Ast, in2, are required on
the column whenever Ast computed from Eq. (7.48) is positive
P  F t(t  5k) yc b A  (7.48) st Fys
where t  thickness of column web, in
tb  thickness, in, of beam flange delivering concentrated load
Fyc  column steel yield stress, ksi
Fys  stiffener steel yield stress, ksi
P  computed force delivered by beam flange or connection plate multiplied
by 5?3 when force is a result of dead and live loads, or by 4?3 when it is
a result of wind or earthquake forces, kips
k  distance from face of column to edge of fillet on rolled sections (use
equivalent for welded sections)
Regardless of the preceding requirement, a single or double stiffener is needed
opposite the compression force delivered to the column at point a when
7.78 SECTION SEVEN
3 4100 t 
Fyc d  (7.49) c P
where dc  clear distance, in, between column flanges (clear of fillets). Also, a pair
of stiffeners is needed opposite the tension force at point b when
P
t  0.4 (7.50) ? Fyc
where t?  thickness of column flange, in.
The thickness of a stiffener should not be less than one-half the thickness of the
beam flange or plate that delivers force P to the column. Stiffener width should not
be less than one-third of the flange or plate width.
7.22.2 LRFD for Load-Bearing Stiffeners
Six limit states should be considered at locations where a large concentrated force
acting on a member introduces high local stresses. These limit states are local flange
bending, local web yielding, web crippling, sidesway web buckling, compression
buckling of the web, and high shear in column web panels. Detailed requirements
for determining the design strength for each of these limit states are contained in
the AISC LRFD ‘‘Specification for Structural Steel for Buildings.’’
When web stiffeners are required to prevent web crippling or compression buckling
of the web, they are designed as columns with an effective length of Kl 
0.75h, where h is the clear distance between flanges. The effective cross section is
the area of the stiffeners plus 25t for interior stiffeners for 12t for stiffeners at the
end of a member, where t is the web thickness.
7.23 BEARING
For bearing on finished surfaces, such as milled ends and ends of fitted bearing
stiffeners, or on the projected area of pins in finished holes, the allowable stress in
ASD is
F  0.90F (7.51) p y
where Fy is the specified minimum yield stress of the steel, ksi. When the parts in
contact have different yield stresses, use the smaller Fy (Table 7.19).
The allowable bearing stress on expansion rollers and rockers, kip/ in, is
F  13 y F  0.66d (7.52) p 20
where d is the diameter of roller or rocker, in (Table 7.20).
Allowable bearing stresses on masonry usually can be obtained from a local or
state building code, whichever governs. In the absence of such regulations, however,
the values in Table 7.21 may be used.
STRUCTURAL STEEL CONSTRUCTION 7.79
TABLE 7.19 Bearing on Finished
Surfaces, ksi
Allowable
stress (ASD)
Fy Fp
Design strength
(LRFD)
Fy Rn /Apb
36 32.4 36 54.0
42 37.8 42 63.0
45 40.5 45 67.5
50 45.0 50 75.0
55 49.5 55 82.5
60 54.0 60 90.0
TABLE 7.20 Allowable Bearing Loads on
Expansion Rollers or Rockers, kips per in
of Bearing
Allowable
load (ASD)
Fy Fp
Design strength
(LRFD)
Fy R*n
36 0.76d 36 1.30d
42 0.96d 42 1.64d
45 1.06d 45 1.81d
50 1.22d 50 2.08d
55 1.39d 55 2.37d
60 1.55d 60 2.64d
* d is the diameter, in. of the roller or rocker.
TABLE 7.21 Allowable Bearing on Masonry, ksi
On sandstone and limestone 0.40
On brick in cement mortar 0.25
On the full area of concrete 0.35?	c
On less than full concrete area 0.35?	 
A /A  0.7?	 c 2 1 c
where  ?	c specified compressive strength, ksi, of the concrete
A1  bearing area
A2  concrete area
LRFD Procedure for Bearing. The design strength in bearing on the projected
bearing area for finished surfaces, such as milled ends and ends of bearing stiffeners,
or on the projected area of pins in finished holes, is Rn, where  0.75.
R  2.0F A (7.53) n y pb
where Fy is the lesser minimum yield stress, ksi, of the steel (Table 7.19) and Apb
is the projected bearing area, in2.
7.80 SECTION SEVEN
For expansion rollers and rockers, Rn, kips, is given by
R  1.5(F  13)Ld/20 (7.54) n y
where L is the length, in, of bearing, and d is the diameter, in (see Table 7.20).
7.24 COMBINED AXIAL COMPRESSION AND
BENDING
A member carrying both axial and bending forces is subjected to secondary bending
moments resulting from the axial force and the displacement of the neutral axis.
This effect is referred to as the P- effect. Such secondary bending moments are
more critical in members where the axial force is a compressive force, because the
P- secondary moment increases the deflection of the member. In ASD, the effects
of these secondary moments may be neglected where the axial force is a tensile
force or where the actual compressive stress is less than 15% of the allowable
compressive stress. LRFD does not include this concept.
The following design criteria apply to singly and doubly symmetrical members.
7.24.1 ASD for Compression and Bending
When the computed axial stress, ?a is less than 15% of Fa, the stress that would
be permitted if axial force alone were present, a straight-line interaction formula
may be used. Thus, when ?a /Fa  0.15:
? ? ? a bx by    1.0 (7.55)
F F F a bx by
where subscripts x and y indicate, respectively, the major and minor axes of bending
(if bending is about only one axis, then the term for the other axis is omitted), and
?b  computed compressive bending stress, ksi, at point under consideration
Fb  compressive bending stress, ksi, that is allowed if bending alone existed
When ?a /Fa  0.15, the effect of the secondary bending moment should be
taken into account and the member proportioned to satisfy Eqs. (7.56a) and (7.56b)
where, as before, subscripts x and y indicates axes of bending:
? C ? C ? a mx bx my by    1.0 (7.56a)
F [1  ? /F	 ]F [1  ? /F	 ]F a a ex bx a ey by
? ? ? a bx by    1.0 (7.56b)
0.60F F F y bx by
2 12	 E
F	  (7.57) e 2 23(Kl / r ) b b
where E  modulus of elasticity, 29,000 ksi
Ib  actual unbraced length, in, in the plane of bending
STRUCTURAL STEEL CONSTRUCTION 7.81
rb  corresponding radius of gyration, in
K  effective-length factor in the plane of bending
Cm  reduction factor determined from the following conditions:
1. For compression members in frames subject to joint translation (sidesway),
Cm  0.85.
2. For restrained compression members in frames braced against joint translation
and not subject to transverse loading between their supports in the plane of bending,
Cm  0.6  0.4M1 /M2, but not less than 0.4. M1 /M2 is the ratio of the smaller to
larger moments at the ends of that portion of the member unbraced in the plane of
bending under consideration. M1 /M2 is positive when the member is bent in reverse
curvature, and negative when it is bent in single curvature.
3. For compression members in frames braced against joint translation in the
plane of loading and subjected to transverse loading between their supports, the
value of Cm may be determined by rational analysis. Instead, however, Cm may be
taken as 0.85 for members whose ends are restrained, and 1.0 for ends unrestrained.
In wind and seismic design may be increased one-third. The resultant section, F	e
however, should not be less than that required for dead and live loads alone without
the increase in allowable stress.
Additional information, including illustrations of the foregoing three conditions
for determining the value of Cm, is given in the AISC ‘‘Commentary’’ on the AISC
ASD ‘‘Specification for Structural Steel for Buildings.’’
7.24.2 LRFD for Compression and Bending
Members subject to both axial compression and bending stresses should be proportioned
to satisfy Eq. (7.58) or (7.59), whichever is applicable.
For (Pu / cPn)  0.2,
M P 8 M uy u ux    1.0 (7.58)    P 9 M M c n b nx b ny
For (Pu / cPn)  0.2,
M P M uy u ux    1.0 (7.59)   2 P M M c n b nx b ny
where Pu  required compressive strength, kips, calculated for the factored axial
loads
Mu  required flexural strength, kip-in calculated for primary bending and
P- effects
cPn  design compressive strength (Art. 7.19.3)
bMn  design flexural strength (Art. 7.20.2)
Mu may be determined for the factored loads from a second-order elastic analysis.
The AISC LRFD specification, however, permits Mu to be determined from
Eq. (7.60) with the variables in this equation determined from a first-order analysis.
M  B M  B M (7.60) u 1 nt 2 lt
7.82 SECTION SEVEN
where Mnt  required flexural strength, kip-in, with no relative displacement of the
member ends; for example, for a column that is part of a rigid frame,
drift is assumed prevented
Mlt  required flexural strength, kip-in, for the effects only of drift as determined
from a first-order analysis
B1  magnification factor for Mnt to account for the P- effects

Cm
1  P /P u e
Cm  reduction factor defined for Eq. (7.57)
B2  magnification factor for Mlt to account for the P- effects
B2 may be calculated from either Eq. (7.61) or (7.62), the former usually being the
simpler to evaluate.
1
B  (7.61) 2 1  (	P /	HL) u oh
1
B  (7.62) 2 1  	P /	P u e
where 	Pu  sum of the axial-load strengths, kips, of all the columns in a story
Pe  AgFy / 2 c
Ag  gross area of member, in2
Fy  specified yield stress, ksi
c 
F F Kl Kl y y    r	 E r 286,220
K  effective column length factor in the plane of bending, to be determined
by structural analysis, but not to exceed unity in calculation
of B1 and not to be less than unity in calculation of B2
r  governing radius of gyration, in, about the plane of buckling
oh  drift, in, of the story in which the column is located
L  story height, in
	H  sum of all the horizontal forces on the story that cause oh
7.25 COMBINED AXIAL TENSION AND
BENDING
For ASD, members subject to both axial tension and bending stresses should be
proportioned to satisfy Eq. (7.55), with ?b and Fb, respectively, as the computed
and allowable bending tensile stress. But the compressive bending stresses must not
exceed the values given in Art. 7.20.1.
LRFD for Tension and Bending. Symmetric members subject to both axial tension
and bending stresses should be proportioned to satisfy either Eq. (7.58) or Eq.
(7.59), whichever is applicable.
STRUCTURAL STEEL CONSTRUCTION 7.83
FIGURE 7.37 Steel-concrete composite-beam construction: (a) and (b) with welded-stud
shear connectors; (c) with encasement in concrete.
7.26 COMPOSITE CONSTRUCTION
In composite construction, rolled or built-up steel shapes are combined with reinforced
concrete to form a structural member. Examples of this type of construction
include: (a) concrete-encased steel beams (Fig. 7.37c), (b) concrete decks interactive
with steel beams (Fig. 7.37a and b), (c) concrete encased steel columns, and (d)
concrete filled steel columns. The most common use of this type of construction is
for composite beams, where the steel beam supports and works with the concrete
slab to form an economical building element.
Design procedures require that a decision be made regarding the use of shoring
for the deck pour. (Procedures for ASD and LRFD differ in this regard.) If shoring
is not used, the steel beam must carry all dead loads applied until the concrete
hardens, even if full plastic capacity is permitted for the composite section afterward.
The assumed composite cross section is the same for ASD and LRFD procedures.
The effective width of the slab is governed by beam span and beam spacing
or edge distance (Fig. 7.37a and b).
Slab compressive stresses are seldom critical for interior beams but should be
investigated, especially for edge beams. Thickening the slab key and minimum
requirements for strength of concrete can be economical.
7.84 SECTION SEVEN
FIGURE 7.38 Steel-concrete composite-beam construction with formed steel decking: (a) ribs
parallel to beam; (b) ribs transverse to beam [refer to (a) for applicable requirements].
Connector Details. In composite construction, shear connectors welded to the top
flange of the steel beam are typically used to ensure composite action by transferring
shear between the concrete deck and steel beam. Location, spacing, and size
limitations for shear connectors are the same for ASD and LRFD procedures. Connectors,
except those installed in ribs of formed steel decks, should have a minimum
lateral concrete cover of 1 in. The diameter of a stud connector, unless located
directly over the beam web, is limited to 2.5 times the thickness of the beam flange
to which it is welded. Minimum center-to-center stud spacing is 6 diameters along
the longitudinal axis, 4 diameters transversely. Studs may be spaced uniformly,
rather than in proportion to horizontal shear, inasmuch as tests show a redistribution
of shear under high loads similar to the stress redistribution in large bolted joints.
Maximum spacing is 8 times the slab thickness.
Formed Steel Decking. Concrete slabs are frequently cast on permanent steel
decking with a ribbed, corrugated, cellular, or blended cellular cross section (see
Sec. 8). Two distinct composite-design configurations are inherent: ribs parallel or
ribs perpendicular to the supporting beams or girders (Fig. 7.38) The design procedures,
for both ASD and LRFD, prescribed for composite concrete-slab and steelbeam
construction are also applicable for systems utilizing formed steel decking,
subject to additional requirements of the AISC ‘‘Specification for Structural Steel
for Buildings’’ and as illustrated in Fig. 7.38.
STRUCTURAL STEEL CONSTRUCTION 7.85
Shear and Deflection of Composite Beams. In ASD and LRFD, shear forces are
assumed to be resisted by the steel beam. Deflections are calculated based on composite
section properties. It should be noted that, because of creep of the concrete,
the actual deflections of composite beams under long-term loads, such as dead load,
will be greater than those computed.
7.26.1 ASD of Encased Beams
Two design methods are allowed for encased beams. In one method, stresses are
computed on the assumption that the steel beam alone supports all the dead load
applied prior to concrete hardening (unless the beam is temporarily shored), and
the composite beam supports the remaining dead and live loads. Then, for positive
bending moments, the total stress, ksi, on the steel-beam bottom flange is
M M D L ?   0.66F (7.63) b y S St
where Fy  specified yield stress of the steel, ksi
MD  dead-load bending moment, kip-in
ML  live-load bending moment, kip-in
S  section modulus of steel beam, in3
St  section modulus of transformed section, in3. To obtain the transformed
equivalent steel area, divide the effective concrete area by the modular
ratio n (modulus of elasticity of steel divided by modulus of elasticity
of concrete). In computation of effective concrete area, use effective
width of concrete slab (Fig. 7.37a and b)
The stress 0.66Fy is allowed because the steel beam is restrained against lateral
buckling.
The second method stems from a ‘‘shortcut’’ provision contained in many building
codes. This provision simply permits higher bending stresses in beams encased
in concrete. For example,
M  M D L ?   0.76F (7.64) b y S
This higher stress would not be realized, however, because of composite action.
7.26.2 ASD of Beams with Shear Connectors
For composite construction where shear connectors transfer shear between slab and
beam, the design is based on behavior at ultimate load. It assumes that all loads
are resisted by the composite section, even if shores are not used during construction
to support the steel beam until the concrete gains strength. For this case, the computed
stress in the bottom flange for positive bending moment is
M  M D L ?   0.66F (7.65) b y St
where St  section modulus, in3, of transformed section of composite beam. To
7.86 SECTION SEVEN
prevent overstressing the bottom flange of the steel beam when temporary shoring
is omitted, a limitation is placed on the value of St used in computation of ?b with
Eq. (7.65):
ML S  1.35  0.35 S (7.66)   t s MD
where MD  moment, kip-in, due to loads applied prior to concrete hardening (75%
cured)
ML  moment, kip-in, due to remaining dead and live loads
Ss  section modulus, in3, of steel beam alone relative to bottom flange
Shear on Connectors. Shear connectors usually are studs or channels. The total
horizontal shear to be taken by the connectors between the point of maximum
positive moment and each end of a simple beam, or the point of counterflexure in
a continuous beam, is the smaller of the values obtained from Eqs. (7.67) and (7.68).
0.85?	A c c V  (7.67) h 2
A F s y V  (7.68) h 2
 where ?	c specified strength of concrete, ksi
Ac  actual area of effective concrete flange, as indicated in Fig. 7.36a and
b, in2
As  area of steel beam, in2
In continuous composite beams, where shear connectors are installed in negativemoment
regions, the longitudinal reinforcing steel in the concrete slab may be
considered to act compositely with the steel beam in those regions. In such cases,
the total horizontal shear to be resisted by the shear connectors between an interior
support and each adjacent infection point is
A F sr yr V  (7.69) h 2
where Asr  total area, in2, of longitudinal reinforcing steel within the effective
width of the concrete slab at the interior support
Fyr  specified yield stress of the reinforcing steel, ksi
These formulas represent the horizontal shear at ultimate load divided by 2 to
approximate conditions at working load.
Number of Connectors. The minimum number of connectors N1, spaced uniformly
between the point of maximum moment and adjacent points of zero moment,
is Vh /q, where q is the allowable shear load on a single connector, as given in
Table 7.22. Values in this table, however, are applicable only to concrete made with
aggregates conforming to ASTM C33. For concrete made with rotary-kiln-produced
aggregates conforming to ASTM C330 and with concrete weight of 90 pcf or more,
the allowable shear load for one connector is obtained by multiplying the values
in Table 7.22 by the factors in Table 7.23.
STRUCTURAL STEEL CONSTRUCTION 7.87
TABLE 7.22 Allowable Horizontal-Shear Loads, q, for Connectors, kips
(Applicable only to concrete made with ASTM C33 aggregates)
Connector  3.0 ?	c  3.5 ?	c  4.0 ?	c
1?2-in dia. 
 2-in hooked or headed stud* 5.1 5.5 5.9
5?8-in dia. 
 21?2-in hooked or headed stud* 8.0 8.6 9.2
3?4-in dia. 
 3-in hooked or headed stud* 11.5 12.5 13.3
7?8-in dia. 
 31?2-in hooked or headed stud* 15.6 16.8 18.0
3-in channel, 4.1 lb 4.3w† 4.7w† 5.0w†
4-in channel, 5.4 lb 4.6w† 5.0w† 5.3w†
5-in channel, 6.7 lb 4.9w† 5.5w† 5.6w†
* Length given is minimum.
†w  length of channel, in.
TABLE 7.23 Shear-Load Factors for Connectors in Lightweight Concrete
Air dry weight, pcf, of concrete 90 95 100 105 110 115 120
Factors for  4.0 ksi ?	c 0.73 0.76 0.78 0.81 0.83 0.86 0.88
Factors for  5.0 ksi ?	c 0.82 0.85 0.87 0.91 0.93 0.96 0.99
If a concentrated load occurs between the points of maximum and zero moments,
the minimum number of connectors required between the concentrated load and
the point of zero moment is given by
V SM/M  S h t c s N  (7.70)   2 q S S t s
where M  maximum moment, in-kips
Mc  moment, in-kips, at concentrated load  M
Ss  section modulus, in3, of steel beam relative to bottom flange
St  section modulus, in3, of transformed section of composite beam relative
to bottom flange but not to exceed St computed from Eq. (7.66).
The allowable shear loads for connectors incorporate a safety factor of about
2.5 applied to ultimate load for the commonly used concrete strengths. Not to be
confused with shear values for fasteners given in Art. 7.30, the allowable shear
loads for connectors are applicable only with Eqs. (7.67) to (7.69).
The allowable horizontal shear loads given in Tables 7.22 and 7.23 may have
to be adjusted for use with formed steel decking. For decking with ribs parallel to
supports (Fig. 7.38a), the allowable loads should be reduced when w/h is less than
1.5 by multiplying the tabulated values by
w H
0.6  1  1 (7.71)    h h
where w  average width of concrete rib, in
h  nominal rib height, in
7.88 SECTION SEVEN
H  length of stud after welding, in, but not more than (h  3) for computations
For decking with ribs perpendicular to supports, the reduction factor is:
0.85 w H
 1  1 (7.72)     h h 
N
where N  number of studs on a beam and in one rib, but three studs are the
maximum that may be considered effective.
7.26.3 LRFD of Encased Beams
Two methods of design are allowed, the difference being whether or not shoring is
used. In both cases, the design strength is bMn, where b  0.90. Mn is calculated
for the elastic stress distribution on the composite section if shoring is used or the
plastic stress distribution on the steel section alone if shoring is not used.
7.26.4 LRFD of Composite Beams
As with ASD, the use of shoring to carry deal loads prior to the time the concrete
has hardened determines which design procedures are used. For composite construction
where the steel beams are exposed, the design flexural strength for positive
moment (compression in the concrete) is bMn. It is dependent on the depththickness
ratio hc / tw of the steel beam, where tw is the web thickness and, for webs
of rolled or formed sections, hc is twice the distance from the neutral axis to the
toe of the fillet at the compression flange, and for webs of built-up sections, hc is
twice the distance from the neutral axis to the nearest line of fasteners at the
compression flange or the inside face of a welded compression flange.
When hc / tw  b  0.85 and Mn is calculated for plastic stress dis- 640/
F , y
tribution on the composite section. If hc / tw  b  0.90 and Mn is 640/
F , y
calculated for elastic stress distribution, with consideration of the effects of shoring.
When the member is subject to negative moment, the practical design approach is
to neglect the composite section and use the requirements for beams in flexure, as
given in Art. 7.20.2.
LRFD of Beams with Shear Connectors. The concepts described in Art. 7.26.2
for ASD apply also to LRFD of beams with shear connectors. Inasmuch as factored
loads are used for LRFD, however, the equations used in the two types of design
differ.
In regions of positive moment, the total horizontal shear Vh, kips, to be carried
by the shear connectors between the point of maximum moment and the point of
zero moment is the smallest value computed from Eqs. (7.73) to (7.75).
V  0.85?	A (7.73) h c c
V  A F (7.74) h s y
V  	Q (7.75) h n
STRUCTURAL STEEL CONSTRUCTION 7.89
where  ?	c 28-day compressive strength of concrete, ksi
Ac  area of concrete slab within the effective width, in2
As  area of the cross section, in2, of steel beam
Fy  specified minimum yield stress of the steel
	Qn  sum of the nominal strengths, kips, of the shear connectors between
the point of maximum moment and the point of zero moment
The number of shear connectors n must equal or exceed Vh /Qn, where Qn is the
nominal strength of one shear connector.
The nominal strength, kips, of one stud shear connector embedded in a solid
concrete slab is
Q  0.5A 
?	E  A F (7.76) n sc c c sc u
where Asc  cross-sectional area of a stud shear connector, in2
 ?	c 28-day compressive strength of concrete, ksi
Fu  minimum specified tensile strength of a stud shear connector, ksi
Ec  modulus of elasticity of the concrete, ksi
The nominal strength, kips, of one channel shear connector embedded in a solid
concrete slab is
Q  0.3(t  0.5t )L 
?	E (7.77) n ? w c c c
where t?  flange thickness of channel shear connector, in
tw  web thickness of channel, in
Lc  length of channel, in
As in ASD, the shear capacity of stud connectors may have to be reduced if they
are used with formed metal decking. The reduction factors, Eqs. (7.71) and (7.72),
also apply to LRFD.
7.27 MEMBERS SUBJECT TO TORSION
This is a special type of load application, since in normal practice eccentric loads
on beams are counterbalanced to the point where slight eccentricities may be neglected.
For example, spandrel beams supporting a heavy masonry wall may not
be concentric with the load, thus inducing torsional stresses, but these will largely
be canceled out by the equally eccentric loads of the floor, partitions, attached
beams, and similar restraints. For this reason, one seldom finds any ill effects from
torsional stresses.
It is during the construction phase that torsion may be in evidence, usually the
result of faulty construction procedure. In Fig. 7.39 are illustrated some of the bad
practices that have caused trouble in the field: when forms for concrete slabs are
hung on one edge of a beam (usually the light secondary beam) the weight of the
wet concrete may be sufficient to twist the beam. Figure 7.39 shows the correct
method, which reduces torsion. Likewise for spandrels, the floor ties, if any, forms
or the slab itself should be placed prior to the construction of the eccentric wall
(Fig. 7.39b). Connectors for heavy roofing sheets when located on one side of the
7.90 SECTION SEVEN
FIGURE 7.39 Steel beams subject to torsion—good and bad practice.
purlin may distort the section; the condition should be corrected by staggering, as
indicated in Fig. 7.39c.
Equations for computing torsion stresses are given in Art. 5.4.2. Also, see Bibliography,
Art. 7.55.
7.28 MEMBERS SUBJECT TO CYCLIC LOADING
Relatively few structural members in a building are ever subjected to large, repeated
variations of stress or stress reversals (tension to compression, and vice versa) that
could cause fatigue damage to the steel. Members need not be investigated for this
possibility unless the number of cycles of such stresses exceeds 20,000, which is
nearly equivalent to two applications every day for 25 years.
DESIGN OF CONNECTIONS
Design of connections and splices is a critical aspect of the design process. Because
each fabricator has unique equipment and methods, the detailed configuration of
STRUCTURAL STEEL CONSTRUCTION 7.91
connections plays an important part in determining the cost of the fabricated product.
Consequently, the detailed design of these elements is a part of the work
performed by the fabricator. In the industry, this work is known as detailing.
Usually, the structural engineer indicates the type of connections and type and
size of fasteners required; for example, ‘‘framed connections with 7?8-in A325 bolts
in bearing-type joints,’’ or the type of connection with reference to AWS D1.1
requirements. For beams, the design drawings should specify the reactions. If, however,
the reactions are not noted, the detailer will determine the reactions from the
uniform-load capacity (tabulated in the AISC Manual), giving due consideration to
the effect of large concentrated loads near the connection. For connections resisting
lateral loads, live, wind, or seismic, the design drawing should stipulate the forces
and moments to be carried. Generally, the design should also include a sketch
showing the type of moment connection desired.
Design Criteria for Connections. Either ASD or LRFD may be used to design
the connections of a structure. Selection of the design procedure, however, must be
consistent with the method used to proportion the members. When LRFD procedures
are used, the loads and load factors discussed in Arts. 7.15 to 7.28 should
be incorporated. The AISC Manual, Vol. II, Connections, provides many design
aids for both design procedures.
7.29 COMBINATIONS OF FASTENERS
The AISC ASD and LRFD ‘‘Specification for Structural Steel for Buildings’’ distinguish
between existing and new framing in setting conditions for use of fasteners
in connection design.
In new work, A307 bolts or high-strength bolts in bearing-type connections
should not be considered as sharing the load with welds. If welds are used, they
should be designed to carry the load in the connection. However, when one leg of
a connection angle is connected with one type of fastener and the other leg with a
different type, this rule does not apply. The load is transferred across each joint by
one type of fastener. Such connections are commonly used, since one type of fastener
may be selected for shop work and a different type for field work.
High-strength bolts in slip-critical joints may share the load with welds on the
same connection interface if the bolts are fully tightened before the welds are made.
For connections in existing frames, existing rivets and high-strength bolts may
be used for carrying stresses from existing dead loads, and welds may be provided
for additional dead loads and design live loads. This provision assumes that whatever
slip that could occur in the existing joint has already occurred.
7.30 LOAD CAPACITY OF BOLTS
Under service conditions, bolts may be loaded in tension, shear, or a combination
of tension and shear. The load capacities specified in AISC ASD and LRFD specifications
are closely related and are based on the ‘‘Specification for Structural Joints
Using ASTM A325 or A490 Bolts,’’ Research Council on Structural Connections
of the Engineering Foundation. Both bearing-type and slip-critical bolted connections
are proportional for the shear forces on the gross area of bolts.
7.92 SECTION SEVEN
TABLE 7.24 Allowable Stresses, ksi, for Bolts and Threaded Partsa
Fasteners
Shear in slip-critical connections b Fv
Standardsize
holes
Oversize
and shortslot
holes
Long-slot holes
Transverse
loadc
Parallel
loadc
Bearing-type connections
Shear
Fv
Tension Ft, including
reduction for shear stress
d ?v
A407 bolts 10.0e,? 26  1.8?v  20
Threaded Parts and
A449 bolts,
threadedg not
excluded from shear
planes
0.17 h Fv 0.43Fv  1.8?v  0.33 h,i Fv
Threaded parts and
A449 bolts, threads
excluded from shear
planesg
0.22 h Fv 0.43 Fv  1.4?v  0.33 h Fv
A325 bolts, when
threads are not
excluded from shear
planes
17.0 15.0 12.0 10.0 21.0? 2 2 
(44)  4.39?v
A325 bolts, when
threads are excluded
from shear planes
17.0 15.0 12.0 10.0 30.0? 2 2 
(44)  2.15?v
A490 bolts, when
threads are not
excluded from shear
planes
21.0 18.0 15.0 13.0 28.0? 2 2 
(54)  3.75?v
A490 bolts, when
threads are excluded
from shear planes
21.0 18.0 15.0 13.0 40.0? 2 2 
(54)  1.82?v
aFor wind or seismic loading, acting alone or in combination with design dead and live loads, allowable stresses
the table may be increased one-third, if the required section then is at least that required for design, dead, live, and
impact loads without this increase. For tension combined with shear, the coefficients of ?v in the tabulated formulas
could not be changed.
b Assumes clean mill scale and blast-cleaned surfaces with Class A coatings (slip coefficient 0.33). For special
faying-surface conditions, see the Research Council on Structural Connections specification.
c Relative to the long axis of the slotted hole.
d Static loading only. For fatigue conditions, see the AISC ASD ‘‘Specification for Structural Steel for Buildings.’’
e Threads permitted in shear planes.
? Reduce 20% for bolts in bearing-type splices of tension members if the fastener pattern has a length, parallel to
the line of force, exceeding 50 in.
g Applicable to threaded parts meeting the requirements of ASTM A36, A242, A441, A529, A572, A588, A709,
A852 and to A449 bolts in bearing-type connections requiring bolt diameters exceeding 11?2 in.
hFv  minimum tensile strength, ksi, of bolts.
iFor the threaded portion of an upset rod, AbFt should be larger than 0.60AsFy, where Ab is the area at the major
lead diameter, As is the nominal body area before upsetting, and Fv is the specified yield stress, ksi.
7.30.1 ASD for Bolts
Allowable tension and shear stresses for bolts are listed in Table 7.24. The allowable
bearing load at a bolt hole is 1.5Fudt, where Fu is the specified tensile strength, d
is the nominal bolt diameter, and t  thickness of connected part.
Table 7.25 tabulates maximum sizes for standard, oversize, and slotted bolt
holes. Oversize holes are permitted only in slip-critical connections. In slip-critical
connections, slots may be formed without regard to the direction of loading; but in
bearing-type connections, slot length should be placed normal to the direction of
STRUCTURAL STEEL CONSTRUCTION 7.93
TABLE 7.25 Maximum Bolt-Hole Sizes, in*
Bolt
diameter, in
Diameter
of standard
hole
Diameter
of oversize
hole
Short-slot
hole
(width 
 length)
Long-slot
hole
(width 
 length)
1?2 9?16 5?8 9?16 
 11?16 9?16 
 11?4
5?8 11?16 13?16 11?16 
 7?8 11?16 
 19?16
3?4 13?16 15?16 13?16 
 1 13?16 
 17?8
7?8 15?16 11?16 15?16 
 11?8 15?16 
 23?16
1 11?16 11?4 11?16 
 15?16 11?16 
 21?2
11?8 d  1?16 d  5?16 (d  1?16) 
 (d  3?8) (d  1?16) 
 (2.5 
 d)
* Approval of the designer is required for use of oversize or slotted holes. Larger holes than those listed in
the table, if required for tolerance in location of anchor bolts in concrete foundations, may be used in
column base details.
loading. Washers, hardened when used with high-strength bolts, should be placed
over oversize and short-slot holes.
Long-slot holes may be used in only one ply of the connected parts at an individual
faying surface. When the slot is in an outer ply, plate washers or a continuous
bar with standard holes should be installed to cover the entire slot. Washers
or bars for A325 or A490 bolts should be 5?16 in or more thick but need not be
hardened. If hardened washers are required, they should be placed over the outer
surface of a plate washer or bar.
7.30.2 LRFD for Bolts
The design strength of bolts or threaded parts is Rn (tabulated in Table 7.26)
applied to the nominal body area of bolts and threaded parts except upset rods (see
footnote h for Table 7.26). The applied load is the sum of the factored external
loads plus the tension, if any resulting from prying action caused by deformation
of connected parts. If high-strength bolts are required to support the applied loads
by direct tension, they should be proportioned so that the average required strength
(not including initial bolt tightening force) applied to the nominal bolt area will not
exceed the design strength.
The design strength in tension for a bolt or threaded part subject to combined
tension and shear stresses is also listed in Table 7.26. The value of ?v, the shear
caused by the factored loads producing tensile stress, should not exceed the values
for shear alone given in Table 7.26.
Table 7.25 lists maximum dimensions for standard, oversize, and slotted bolt
holes. The limitations on these are the same as those for ASD (Art. 7.26.1).
The design bearing strength at a bolt hole may be taken as Rn  3.0dtFu, or
with  0.75, as 2.25dtFu, where d is the nominal bolt diameter, t is the thickness
of the connected part, and Fu is the tensile strength of the connected part.
7.31 LOAD CAPACITY OF WELDS
For welds joining structural steel elements, the load capacity depends on type of
weld, strength of electrode material, and strength of the base metal. Fillet or groove
7.94 SECTION SEVEN
TABLE 7.26 Design Strength, ksi, for Bolts and Threaded Parts
Fasteners
Shear in slip-critical connections a Fv
Standardsize
holes
Oversized
and shortslot
holes
Long-slot
holes
Transverse
loadsa
Parallel
loadb
Bearing-type connections
Design
shear
strength
Pn
Tension Ft, including
reduction for shear stress
c ?v
A307 bolts 16.2d,e 39  1.8?v  30
Threaded parts and A449
bolts, threads? not
excluded from shear
planes
0.45 g Fu 0.73Fu  1.8?v  0.56 g,h Fu
Threaded parts and A449
bolts, threads excluded
from shear planes?
0.60 g Fu 0.73Fu  1.4?v  0.56 g Fu
A325 bolts, when threads
are not excluded from
shear planes
17.0 15.0 12.0 10.0 35.1e 85  1.8?v  68
A325 bolts, when threads
are excluded from shear
planes
17.0 15.0 12.0 10.0 46.8e 85  1.4?v  68
A490 bolts, when threads
are not excluded from
shear planes
21.0 18.0 15.0 13.0 43.9e 106  1.8?v  84
A490 bolts, when threads
are excluded from shear
planes
21.0 18.0 15.0 13.0 58.5e 106  1.4?v  84
a Assumes clean mill scale and blast-cleaned surfaces with Class A coatings (slip coefficient 0.33). For special
faying-surface conditions, see the Research Council on Structural Connections LRFD specification for structural joints.
b Relative to the long axis of the slotted holes.
c Static loading only. For fatigue conditions, see the AISC ASD ‘‘Specification for Structural Steel for Buildings.’’
d  0.60. Threads permitted in shear planes.
e   0.65. Reduce design shear strength 20% for bolts in bearing-type splices of tension members if the fastener
pattern has a length, parallel to the line of force, exceeding 50 in.
? Applicable to threaded parts meeting the requirements of ASTM A36, A242, A441, A529, A572, A588, A709, or
A852 and to A449 bolts in bearing-type connections requiring bolt diameters exceeding 11?2 in.
gFu  minimum tensile strength, ksi, of bolts.
hFor the threaded portion of an upset rod, AbRn should be larger than AsFy, where Ab is the area at the major thread
diameter, As is the nominal body area before upsetting, Fy is the specified yield stress, ksi, and Rn is the design tensile
strength, where  0.65.
welds (Fig. 7.43) are commonly used for steel connections. Groove welds are classified
as complete or partial penetration. (See Art. 7.3.5.)
A significant characteristic of fillet-welded joints is that all forces, regardless of
the direction in which they act, are resolved as shear on the effective throat of the
weld. For instance, when joining elements such as a girder flange to a web, fillet
welds are designed to carry the horizontal shear without regard to the tensile or
compressive stresses in the elements.
For computation of load capacity, the effective area of groove and fillet welds
is the effective length times the effective throat thickness. The effective area for a
plug or slot weld is the nominal cross-sectional area of the hole or slot in the plane
of the faying surface.
Except for fillet welds in holes or slots, the effective length of a fillet weld is
the overall length of weld, including the return. For a groove weld, the effective
length should be taken as the width of the part joined.
STRUCTURAL STEEL CONSTRUCTION 7.95
TABLE 7.27 Design Shear Strength for Welds, ksi*
Types of weld and stress Material
LRFD
Resistance
factor 
Nominal strength†
FBM or Fw
ASD
Allowable stress
Complete penetration groove weld
Tension normal to effective area Base 0.90 Fy Same as base metal
Compression normal to effective area Base 0.90 Fy Same as base metal
Tension or compression parallel to axis of weld
Shear on effective area Base 0.90 0.60Fy 0.30 
 nominal tensile strength
of weld metal
Weld electrode 0.80 0.60FEXX
Partial penetration groove welds
Compression normal to effective area
Tension or compression parallel to axis of weld† Base 0.90 Fy Same as base metal
Shear parallel to axis of weld Base
Weld electrode
0.75 0.60FEXX 0.30 
 nominal tensile strength
of weld metal
Tension normal to effective area Base 0.90 Fy 3.0 
 nominal tensile strength
of weld metal
Weld electrode 0.80 0.60FEXX
Fillet welds
Shear on effective area Base
Weld electrode
0.75 0.60FEXX 0.30 
 nominal tensile strength
of weld metal
Tension or compression parallel to axis of
weld†
Base 0.90 Fy
Plug or slot welds
Shear parallel to faying surfaces (on effective
area)
Base
Weld electrode
0.75 0.60FEXX 3.0 
 nominal tensile strength
of weld metal
* Reprinted with permission from F. S. Merritt and R. L. Brockenbrough, ‘‘Structural Steel Designers Handbook,’’
2d ed., McGraw-Hill, Inc., New York.
† Design strength is the smaller of FBM and Fu:
FBM  nominal strength of base metal to be welded, ksi.
Fw  nominal strength of weld electrode material, ksi.
Fy  specified minimum yield stress of base metal, ksi.
FEXX  classification strength of weld metal, as specified in appropriate AWS specification, ksi.
The effective throat thickness of a fillet weld is the shortest distance from the
root of the joint to the nominal face of the weld (Fig. 7.3). For fillet welds made
by the submerged-arc process, however, the effective throat should be taken as the
leg size for welds 3?8 in and smaller but as the theoretical throat plus 0.11 in for
larger fillet welds.
For a complete-penetration groove weld, the effective throat is the thickness of
the thinnest part joined. For partial-penetration groove welds, the effective throat
thickness depends on the included angle at the root of the groove. For all J or U
joints and for bevel or V joints with an included angle of 60 or more, the effective
throat thickness may be taken as the depth of the chamfer. When the included angle
for bevel or V joints is between 45 and 60, the effective throat thickness should
be the depth of chamfer minus 1?8 in. For flare bevel and flare V-groove welds when
flush to the surface of a bar or a 90 bend in a formed section, the effective throat
thickness is 5?6 and 1?2 the radius of the bar or bend, respectively. When the radius
is 1 in or more, for gas metal arc welding, the effective thickness is 1?4 the radius.
Welds subject to static loads should be proportioned by ASD for the allowable
stresses and by LRFD for the design strengths in Table 7.27. If connections will
7.96 SECTION SEVEN
FIGURE 7.40 Bolted connection in shear and bearing: (a) with bolt in
single shear; (b) with bolt in double shear (two shearing planes).
be subject to fatigue from stress fluctuations, load capacity should be reduced as
provided in the AISC ‘‘Specification for Structural Steel for Buildings.’’
7.32 BEARING-TYPE BOLTED CONNECTIONS
When some slip, although very small, may occur between connected parts, the
fasteners are assumed to function in shear. The presence of paint on contact surfaces
is therefore of no consequence. Fasteners may be A307 bolts or high-strength bolts
or any other similar fastener not dependent on development of friction on the contact
surfaces.
Single shear occurs when opposing forces act on a fastener as shown in Fig.
7.39a, tending to slide on their contact surfaces. The body of the fastener resists
this tendency; a state of shear then exists over the cross-sectional area of the fastener.
Double-shear takes place whenever three or more plates act on a fastener as
illustrated in Fig. 7.40b. There are two or more parallel shearing surfaces (one on
each side of the middle plate in Fig. 7.40b). Accordingly, the shear strength of the
fastener is measured by its ability to resist two or more single shears.
Bearing on Base Metal. This is a factor to consider; but calculation of bearing
stresses in most joints is useful only as an index of efficiency of the net section of
tension members.
Edge Distances. The AISC ‘‘Specification for Structural Steel for Buildings,’’
ASD and LRFD, recommends minimum edge distances, center of hole to edge of
connected part, as given in Table 7.28. In addition, the edge distance, in, when in
the direction of force should not be less than 2P/Fut for ASD or P/ Fut for LRFD,
where p is the force, kips, transmitted by one fastener to the part for which the
edge distance is applicable;  0.75; Fu is the specified minimum tensile strength
of the part (not the fastener), ksi; and t is the thickness of the part, in.
A special rule applies to beams with framed connections that are usually designed
for the shear due to beam reactions. The edge distance for the beam web,
with standard-size holes, should be not less than 2PR /Fut for ASD or PR / Fut for
STRUCTURAL STEEL CONSTRUCTION 7.97
TABLE 7.28 Minimum Edge Distance for Punched, Reamed, or
Drilled Holes, in
Fastener
diameter, in At sheared edges
At rolled edges of plates, shapes
or bars or gas-cut edges†
1?2 7?8 3?4
5?8 11?8 7?8
3?4 11?4 1
7?8 11?2* 11?8
1 13?4* 11?4
11?8 2 11?2
11?4 21?4 14?8
Over 11?4 13?4 
 diameter 11?4 
 diameter
* These may be 11?4 in at the ends of beam connection angles.
† All edge distances in this column may be reduced 1?8 in when the hole is at
a point where stress does not exceed 25% of the maximum allowed stress in the
element.
LRFD, where PR is the beam reaction per bolt, kips. This rule, however, need not
be applied when the bearing stress transmitted by the fastener does not exceed
0.90Fu.
The maximum distance from the center of a fastener to the nearest edge of parts
in contact should not exceed 6 in or 12 times the part thickness.
Minimum Spacing. The AISC specification also requires that the minimum distance
between centers of bolt holes be at least 22?3 times the bolt diameter. But at
least three diameters is desirable. Additionally, the hole spacing, in, when along
the line of force, should be at least 2P/Fut  d/2 for ASD or P/ Fut  d/2 for
LRFD, where P, Fu, and t are as previously defined for edge distance and d 
nominal diameter of fastener, in. Since this rule is for standard-size holes, appropriate
adjustments should be made for oversized and slotted holes. In no case should
the clear distance between holes be less than the fastener diameter.
Eccentric Loading. Stress distribution is not always as simple as for the joint in
Fig. 7.40a where the fastener is directly in the line of significant. Sometimes, the
load is applied eccentrically, as shown in Fig. 7.41. For such connections, tests
show that use of actual eccentricity to compute the maximum force on the extreme
fastener is unduly conservative because of plastic behavior and clamping force
generated by the fastener. Hence, it is permissible to reduce the actual eccentricity
to a more realistic ‘‘effective’’ eccentricity.
For fasteners equally spaced on a single gage line, the effective eccentricity in
inches is given by
1  2n
l  l  (7.78) eff 4
where l  the actual eccentricity and n  the number of fasteners. For the bracket
in Fig. 7.41b the reduction applied to l1 is (1  2 
 6)/4  3.25 in.
For fasteners on two or more gage lines
7.98 SECTION SEVEN
FIGURE 7.41 Eccentrically loaded fastener groups: (a) with bolts in shear only; (b)
with bolts in combined tension and shear.
1  n
l  l  (7.79) eff 2
when n is the number of fasteners per gage line. For the bracket in Fig. 7.41a, the
reduction is (1  4)/2  2.5 in.
In Fig. 7.41a, the load P can be resolved into an axial force and a moment:
Assume two equal and opposite forces acting through the center of gravity of the
fasteners, both forces being equal to and parallel to P. Then, for equal distribution
on the fasteners, the shear on each fastener caused by the force acting in the direction
of P is ?v  P/n, where n is the number of fasteners.
The other force forms a couple with P. The shear stress ?e due to the couple is
proportional to the distance from the center of gravity and acts perpendicular to the
line from the fastener to the center. In determining ?e, it is convenient to first express
it in terms of x, the force due to the moment Pleff on an imaginary fastener at unit
distance from the center. For a fastener at a distance a from the center, ?e  ax,
and the resisting moment is ?ea  a2x. The sum of the moments equals Pleff. This
STRUCTURAL STEEL CONSTRUCTION 7.99
FIGURE 7.42 Fasteners in tension. Prying action on the connection causes a
moment M  Pe /n on either side, where P  applied load, e its eccentricity, as
shown above, and n the number of fasteners resisting the moment.
equation enables x to be evaluated and hence, the various values of ?e. The resultant
R of ?e and ?v can then be found; a graphical solution usually is sufficiently accurate.
The stress so obtained must not exceed the allowable value of the fastener
in shear (Art. 7.30).
For example, in Fig. 7.41a, ?v  P/8. The sum of the moments is
2 2 4a x  4a x  Pl 1 2 eff
Pleff x  2 2 4a x  4a x 1 2
Then, ?e  a2x for the most distant fastener, and R can be found graphically as
indicated in Fig. 7.41a.
Tension and Shear. For fastener group B in Fig. 7.41b, use actual eccentricity l2
since these fasteners are subjected to combined tension and shear. Here too, the
load P can be resolved into an axial shear force through the fasteners and a couple.
Then, the stress on each fastener caused by the axial shear is P/n, where n is the
number of fasteners. The tensile forces on the fasteners vary with distance from
the center of rotation of the fastener group.
A simple method, erring on the safe side, for computing the resistance moment
of group B fasteners assumes that the center of rotation coincides with the neutral
axis of the group. It also assumes that the total bearing pressure below the neutral
7.100 SECTION SEVEN
axis equals the sum of the tensile forces on the fasteners above the axis. Then, with
these assumptions, the tensile force on the fastener farthest from the neutral axis is
d Pl max 2 ?  (7.80) t 2 	Ad
where d  distance of each fastener from the neutral axis
dmax  distance from neutral axis of farthest fastener
A  nominal area of each fastener
The maximum resultant stresses ?t and ?v  P/n are then plotted as an ellipse
and R is determined graphically. The allowable stress is given as the tensile stress
Ft as a function of the computer shear stress ?v. (In Tables 7.24 and 7.26, allowable
stresses are given for the ellipse approximated by three straight lines.)
Note that the tensile stress of the applied load is not additive to the internal
tension (pretension) generated in the fastener on installation. On the other hand,
the AISC Specification does require the addition to the applied load of tensile
stresses resulting from prying action, depending on the relative stiffness of fasteners
and connection material. Prying force Q (Fig. 7.42b) may vary from negligible to
a substantial part of the total tension in the fastener. A method for computing this
force is given in the AISC Manual.
The old method for checking the bending strength of connection material ignored
the effect of prying action. It simply assumed bending moment equal to P/n times
e (Fig. 7.42). This procedure may be used for noncritical applications.
7.33 SLIP-CRITICAL BOLTED CONNECTIONS
Design of this type of connection assumes that the fastener, under high initial
tensioning, develops frictional resistance between the connected parts, preventing
slippage despite external load. Properly installed A307 bolts provide some friction,
but since it is not dependable it is ignored. High-strength steel bolts tightened nearly
to their yield strengths, however, develop substantial, reliable friction. No slippage
will occur at design loads if the contact surfaces are clean and free of paint or have
only scored galvanized coatings, inorganic zinc-rich paint, or metallized zinc or
aluminum coatings.
The AISC ‘‘Specification for Structural Steel for Buildings,’’ ASD and LRFD,
lists allowable shear for high-strength bolts in slip-critical connections. Though
there actually is not shear on the bolt shank, the shear concept is convenient for
measuring bolt capacity.
Since most joints in building construction can tolerate tiny slippage, bearingtype
joints, which are allowed much higher shears for the same high-strength bolts
when the threads are not in shear planes, may, for reasons of economy, lessen the
use of slip-critical joints.
The capacity of a slip-critical connection does not depend on the bearing of the
bolts against the sides of their holes. Hence, general specification requirements for
protection against high bearing stresses or bending in the bolts may be ignored.
If the fasteners B in Fig. 7.41b are in a slip-critical connection, the bolts above
the neutral axis will lose part of their clamping force; but this is offset by a compressive
force below the neutral axis. Consequently, there is no overall loss in
frictional resistance to slippage.
STRUCTURAL STEEL CONSTRUCTION 7.101
FIGURE 7.43 Two main types of weld—fillet and grove. Grove welds may be complete or partial
penetration.
When it is apparent that there may be a loss of friction (which occurs in some
type of brackets and hangers subject to tension and shear) and slip under load
cannot be tolerated, the working value in shear should be reduced in proportion to
the ratio of residual tension to initial tension.
Slip-critical connections subjected to eccentric loading, such as that illustrated
in Fig. 7.41, are analyzed in the same manner as bearing-type connections (Art.
7.32).
7.34 ECCENTRICALLY LOADED WELDED
CONNECTIONS
Welds are of two general types, fillet (Fig. 7.43a) and groove (Fig. 7.43b), with
allowable stresses dependent on grade of weld and base steels. Since all forces on
a fillet weld are resisted as shear on the effective throat (Art. 7.31), the strength of
connections resisting direct tension, compression and shear are easily computed on
the basis that a kip of fillet shear resists a kip of the applied forces. Many connections,
some of which are shown in Fig. 7.44, are not that simple because of eccentricity
of applied force with respect to the fillets. In designing such joints it is
customary to take into account the actual eccentricity.
The underlying design principles for eccentric welded connections are similar
to those for eccentric bolted connections (Art. 7.32). Consider the welded bracket
in Fig. 7.45. The first step is to compute the center of gravity of the weld group.
Then, the load P can be resolved into an equal and parallel load through the center
of gravity and a couple. The load through the center of gravity is resisted by a
uniform shear on the welds; for example, if the welds are all the same size, shear
per linear inch is ?v  P/n where n is the total linear inches of weld. The moment
Pl of the couple is resisted by the moment of the weld group. The maximum stress,
which occurs on the weld element farthest from the center of gravity, may be
expressed as ?e  Pl/S, where S is the polar section modulus of the weld group.
To find S, first compute the moments of inertia Ix of the welds about the XX
axis and IY about the perpendicular YY axis. (If the welds are all the same size,
their lengths, rather than their relative shear capacities, can be conveniently used
in all moment calculations.) The polar moment of inertia J  IX  UY, and the
polar section modulus S  J/a, where a is the distance from the center of gravity
to the farthest weld element. The resultant R of ?v and ?e, which acts normal to the
7.102 SECTION SEVEN
FIGURE 7.44 Typical eccentric welded connections.
FIGURE 7.45 Stresses on
welds caused by eccentricity.
STRUCTURAL STEEL CONSTRUCTION 7.103
FIGURE 7.46 Typical bolted framed connections.
line from the center of gravity to the weld element for which the stress is being
determined, should not exceed the capacity of the weld element (Art. 7.31).
7.35 TYPES OF BEAM CONNECTIONS
In general, all beam connections are classified as either framed or seated. In the
framed type, the beam is connected to the supporting member with fittings (short
angles are common) attached to the beam web. With seated connections, the ends
of the beam rest on a ledge or seat, in much the same manner as if the beam rested
on a wall.
7.35.1 Bolted Framed Connections
When a beam is connected to a support, a column or a girder, with web connection
angles, the joint is termed ‘‘framed.’’ Each connection should be designed for the
end reaction of the beam, and type, size and strength of the fasteners, and bearing
strength of base materials should be taken into account. To speed design, the AISC
Manual lists a complete range of suitable connections with capacities depending
on these variables. Typical connections for beam or channels ranging in depth from
3 to 30 in are shown in Fig. 7.46.
To provide sufficient stability and stiffness, the length of connection angles
should be at least half the clear depth of beam web.
For economy, select the minimum connection adequate for the load. For example,
assume an 18-in beam is to be connected. The AISC Manual (ASD) lists
three- and four-row connections in addition to the five-row type shown in Fig. 7.46.
Total shear capacity ranges from a low of 26.5 kips for 3?4-in-diam A307 bolts in
a three-row regular connection to a high of 263.0 kips for 1-in-diam A325 bolts in
a five-row heavy connection, bearing type. This wide choice does not mean that
all types of fasteners should be used on a project, but simply that the tabulated data
cover many possibilities, enabling an economical selection. Naturally, one type of
fastener should be used throughout, if practical; but shop and field fasteners may
be different.
Bearing stresses on beam webs should be checked against allowable stresses
(Arts. 7.30.1 and 7.30.2), except for slip-critical connections, in which bearing is
7.104 SECTION SEVEN
FIGURE 7.47 Typical bolted seated connections: (a) stiffened seat; (b)
unstiffened seat.
not a factor. Sometimes, the shear capacity of the field fasteners in bearing-type
connections may be limited by bearing on thin webs, particularly where beams
frame into opposite sides of a web. This could occur where beams frame into
column or girder webs.
One side of a framed connection usually is shop connected, the other side field
connected. The capacity of the connection is the smaller of the capacities of the
shop or field group of fasteners.
In the absence of specific instructions in the bidding information, the fabricator
should select the most economical connection. Deeper and stiffer connections, if
desired by the designer, should be clearly specified.
7.35.2 Bolted Seated Connections
Sizes, capacities, and other data for seated connections for beams, shown in Fig.
7.47, are tabulated in the AISC Manual. Two types are available, stiffened seats
(Fig. 7.47a) and unstiffened seats (Fig. 7.47b).
Unstiffened Seats. Capacity is limited by the bending strength of the outstanding
horizontal leg of the seat angle. A 4-in leg 1 in thick generally is the practical limit.
In ASD, an angle of A36 steel with these dimensions has a top capacity of 60.5
kips for beams of A36 steel, and 78.4 kips when Fy  50 ksi for the beam steel.
Therefore, for larger end reactions, stiffened seats are recommended.
The actual capacity of an unstiffened connection will be the lesser of the bending
strength of the seat angle, the shear resistance of the fasteners in the vertical leg,
or the bearing strength of the beam web. (See also Art. 7.22 for web crippling
stresses.) Data in the AISC Manual make unnecessary the tedious computations of
balancing the seat-angle bending strength and beam-web bearing.
The nominal setback from the support of the beam to be seated is 1?2 in. But
tables for seated connections assume 3?4 in to allow for mill underrun of beam
length.
STRUCTURAL STEEL CONSTRUCTION 7.105
Stiffened Seats. These may be obtained with either one or two stiffener angles,
depending on the load to be supported. As a rule, stiffeners with outstanding legs
having a width less than 5 in are not connected together; in fact, they may be
separated, to line up the angle gage line (recommended centerline of fasteners) with
that of the column.
The capacity of a stiffened seat is the lesser of the bearing strength of the fitted
angle stiffeners or the shear resistance of the fasteners in the vertical legs. Crippling
strength of the beam web usually is not the deciding factor, because of ample seat
area. When legs larger than 5 in wide are required, eccentricity should be considered,
in accordance with the technique given in Art. 7.32. The center of the beam
reaction may be taken at the midpoint of the outstanding leg.
Advantages of Seated Connections. For economical fabrication, the beams
merely are punched and are free from shop-fastened details. They pass from the
punching machine to the paint shed, after which they are ready for delivery. In
erection, the seat provides an immediate support for the beam while the erector
aligns the connection hole. The top angle is used to prevent accidental rotation of
the beam. For framing into column webs, seated connections allow more erection
clearance for entering the trough formed by column flanges than do framed connections.
A framed beam usually is detailed to whim 1?16 in of the column web.
This provides about 1?8 in total clearance, whereas a seated beam is cut about 1?2 in
short of the column web, yielding a total clearance of about 1 in. Then, too, each
seated connection is wholly independent, whereas for framed beams on opposite
sides of a web, there is the problem of aligning the holes common to each connection.
Frequently, the angles for framed connections are shop attached to columns.
Sometimes, one angle may be shipped loose to permit erection. This detail, however,
cannot be used for connecting to column webs, because the column flanges
may obstruct entering or tightening of bolts. In this case, a seated connection has
a distinct advantage.
7.35.3 Welded Framed Connections
The AISC Manual tabulates sizes and capacities of angle connections for beams
for three conditions: all welded, both legs (Fig. 7.48); web leg shop welded, outstanding
leg for hole-type fastener; and web leg for hole-type fastener installed in
shop, outstanding leg field welded. Tables are based on E70 electrodes. Thus, the
connections made with A36 steel are suitable for beams of both carbon and highstrength
structural steels.
Eccentricity of load with respect to the weld patterns causes stresses in the welds
that must be considered in addition to direct shear. Assumed forces, eccentricities,
and induced stresses are shown in Fig. 7.48b. Stresses are computed as in the
example in Art. 7.34, based on vector analysis that characterizes elastic design. The
capacity of welds A or B that is smaller will govern design.
If ultimate strength (plastic design) of such connections is considered, many of
the tabulated ‘‘elastic’’ capacities are more conservative than necessary. Although
AISC deemed it prudent to retain the ‘‘elastic’’ values for the weld patterns, recognition
was given to research results on plastic behavior by reducing the minimum
beam-web thickness required when welds A are on opposite sides of the web. As
a result, welded framed connections are now applicable to a larger range of rolled
beams than strict elastic design would permit.
7.106 SECTION SEVEN
FIGURE 7.48 Welded framed connections on beam web:
(a) weld locations along connection angles; (b) forces on
welds.
Shear stresses in the supporting web for welds B should also be investigated,
particularly when beams frame on opposite side of the web.
7.35.4 Welded-Seat Connections
Also tabulated in the AISC Manual, welded-seat connections (Fig. 7.49) are the
welded counterparts of bolted-seat connections for beams (Art. 7.35.2). As for
welded frame connections (Art. (7.35.3), the load capacities for seats, taking into
account for eccentricity of loading on welds, are computed by ‘‘elastic’’ vector
analysis. Assumptions and the stresses involved are shown in Fig. 7.49c.
In ASD, an unstiffened seat angle of A36 steel has a maximum capacity of 60.5
kips for supporting beams of A36 steel, and 78.4 kips for steel with Fy  50 ksi
(Fig. 7.49a). For heavier loads, a stiffened seat (Fig. 7.49b) should be used.
Stiffened seats may be a beam stub, a tee section, or two plates welded together
to form a tee. Thickness of the stiffener (vertical element) depends on the strengths
of beam and seat materials. For a seat of A36 steel, stiffener thickness should be
at least that of the supported beam web when the web is A36 steel, and 1.4 times
thicker for web steel with Fy  50 ksi.
STRUCTURAL STEEL CONSTRUCTION 7.107
FIGURE 7.49 Welded-seat connections: (a) unstiffened seat; (b) stiffened
seat; (c) stresses in the welds.
When stiffened seats are on line on opposite sides of a supporting web of A36
steel, the weld size made with E70 electrodes should not exceed one-half the web
thickness, and for web steel with Fy  50 ksi, two-thirds the web thickness.
Although top or side lug angles will hold the beam in place in erection, it often
is advisable to use temporary erection bolts to attach the bottom beam flange to
the seat. Usually, such bolts may remain after the beam flange is welded to the
seat.
7.35.5 End-Plate Connections
The art of welding makes feasible connections that were not possible with oldertype
fasteners, e.g., end-plate connections (Fig. 7.50).
7.108 SECTION SEVEN
FIGURE 7.50 End-plate connection between beam and column flange.
Of the several variations, only the flexible type (Fig. 7.50c) has been ‘‘standardized’’
with tabulated data in the AISC Manual. Flexibility is assured by making
the end plate 1?4 in thick wherever possible (never more than 3?8 in). Such connections
in tests exhibit rotations similar to those for framed connections.
The weld connecting the end plate to the beam web is designed for shear. There
is no eccentricity. Weld size and capacity are limited by the shear strength of the
beam web adjoining the weld. Effective length of weld is reduced by twice the
weld size to allow for possible deficiencies at the ends.
As can be observed, this type of connection requires accurate cutting of the
beam to length. Also the end plates must be squarely positioned so as to compensate
for mill and shop tolerances.
The end plate connection is easily adapted for resisting beam moments (Fig.
7.50b, c and d). One deterrent, however, to its use for tall buildings where column
flanges are massive and end plates thick is that the rigidity of the parts may prevent
drawing the surfaces into tight contact. Consequently, it may not be easy to make
such connections accommodate normal mill and shop tolerances.
7.35.6 Special Connections
In some structural frameworks, there may be connections in which a standard type
(Arts. 7.35.1 to 7.35.5) cannot be used. Beam centers may be offset from column
centers, or intersection angles may differ from 90, for example.
For some skewed connections the departure from the perpendicular may be taken
care of by slightly bending the framing angles. When the practical limit for bent
angles is exceeded, bent plates may be used (Fig. 7.51a).
Special one-sided angle connections, as shown in Fig. 7.51b, are generally acceptable
for light beams. When such connections are used, the eccentricity of the
fastener group in the outstanding leg should be taken into account. Length l may
be reduced to the effective eccentricity (Art. 7.32).
Spandrel and similar beams lined up with a column flange may be conveniently
connected to it with a plate (Fig. 7.51c and d). The fasteners joining the plate to
the beam web should be capable of resisting the moment for the full lever arm l
for the connection in Fig. 7.51c. For beams on both sides of the column with equal
STRUCTURAL STEEL CONSTRUCTION 7.109
FIGURE 7.51 Examples of special connections.
reactions, the moments balance out. But the case of live load on one beam only
must be considered. And bear in mind the necessity of supporting the beam reaction
as near as possible to the column center to relieve the column of bending stresses.
When spandrels and girts are offset from the column, a Z-type connection (Fig.
7.51e) may be used. The eccentricity for beam-web fasteners should be taken as
l1, for column-flange fasteners as l2, and for fasteners joining the two connection
angles as l3 when l3 exceeds 21?2 in; smaller values of l3 may be considered negligible.
7.35.7 Simple, Rigid, and Semirigid Connections
Moment connections are capable of transferring the forces in beam flanges to the
column. This moment transfer, when specified, must be provided for in addition to
7.110 SECTION SEVEN
FIGURE 7.52 Methods of constructing flexible welded connections.
and usually independent of the shear connection needed to support the beam reaction.
Framed, seated, and end-plate connections (Arts. 7.35.1 to 7.35.5) are examples
of shear connections. Those in Fig. 7.17 (p. 7.32), are moment connections.
In Fig. 7.17a to g, flange stresses are developed independently of the shear connections,
whereas in h and i, the forces are combined and the entire connection
resolved as a unit.
Moment connections may be classified according to their design function: those
resisting moment due to lateral forces on the structure, and those needed to develop
continuity, with or without resistance to lateral forces.
The connections generally are designed for the computed bending moment,
which often is less than the beam’s capacity to resist moment. A maximum connection
is obtained, however, when the beam flange is developed for its maximum
allowable stress.
The ability of a connection to resist moment depends on the elastic behavior of
the parts. For example, the light lug angle shown connected to the top flange of
the beam in Fig. 7.52b is not designed for moment and accordingly affords negligible
resistance to rotation. In contrast, full rigidity is expected of the direct welded
flange-to-column connection in Fig. 7.52a. The degree of fixity, therefore, is an
important factor in design of moment connections.
Fixity of End Connections. Specifications recognize three types of end connections:
simple, rigid, and semirigid. The type designated simple (unrestrained) is
intended to support beams and girders for shear only and leave the ends free to
STRUCTURAL STEEL CONSTRUCTION 7.111
rotate under load. The type designated rigid (known also as rigid-frame, continuous,
restrained frame) aims at not only carrying the shear but also providing sufficient
rigidity to hold virtually unchanged the original angles between members connected.
Semirigid, as the name implies, assumes that the connections of beams and
girders possess a dependable and known moment capacity intermediate in degree
between the simple and rigid types. Figure 7.54 illustrates these three types together
with the uniform-load moments obtained with each type.
Although no definite relative rigidities have been established, it is generally
conceded that the simple or flexible type could vary from zero to 15% (some
researchers recommend 20%) end restraint and that the rigid type could vary from
90 to 100%. The semirigid types lie between 15 and 90%, the precise value assumed
in the design being largely dependent on experimental analysis. These percentages
of rigidity represent the ratio of the moment developed by the connection, with no
column rotation, to the moment developed by a fully rigid connection under the
same conditions, multiplied by 100.
Framed and seated connections offer little or no restraint. In addition, several
other arrangements come within the scope of simple-type connections, although
they appear to offer greater resistance to end rotations. For example, in Fig. 7.52a,
a top plate may be used instead of an angle for lateral support, the plate being so
designed that plastic deformation may occur in the narrow unwelded portion. Naturally,
the plate offers greater resistance to beam rotation than a light angle, but it
can provide sufficient flexibility that the connection can be classified as a simple
type. Plate and welds at both ends are proportional for about 25% of the beam
moment capacity. The plate is shaped so that the metal across the least width is at
yield stress when the stresses in the wide portion, in the butt welds, and in the fillet
welds are at allowable working values. The unwelded length is then made from 20
to 50% greater than the least width to assure ductile yielding. This detail can also
be developed as an effective moment-type connection.
Another flexible type is the direct web connection in Fig. 7.52b. Figured for
shear loads only, the welds are located on the lower part of the web, where the
rotational effect of the beam under load is the least. This is a likely condition when
the beam rests on erection seats and the axis of rotation centers about the seat rather
then about the neutral axis.
Tests indicate that considerable flexibility also can be obtained with a property
proportioned welded top-plate detail as shown in Fig. 7.52c without narrowing it
as in Fig. 7.52a. This detail is usually confined to wind-braced simple-beam designs.
The top plate is designed for the wind moment on the joint, at the increased
stresses permitted for wind loads.
The problem of superimposing wind bracing on what is otherwise a clear-cut
simple beam with flexible connections is a complex one. Some compromise is
usually effected between theory and actual design practice. Two alternatives usually
are permitted by building codes:
1. Connections designed to resist assumed wind moments should be adequate
to resist the moments induced by the gravity loading and the wind loading, at
specified increased unit stresses.
2. Connections designed to resist assumed wind moments should be so designed
that larger moments, induced by gravity loading under the actual condition of restraint,
will be relieved by deformation of the connection material.
Obviously, these options envisage some nonelastic, but self-limiting, deformation
of the structural-steel parts. Innumerable wind-braced buildings of riveted, bolted,
7.112 SECTION SEVEN
FIGURE 7.53 Methods of constructing welded rigid connections.
or welded construction have been designed on this assumption of plastic behavior
and have proved satisfactory in service.
Fully rigid, bolted beam end connections are not often used because of the
awkward, bulky details, which, if not interfering with architectural clearances, are
often so costly to design and fabricate as to negate the economy gained by using
smaller beam sections. In appearance, they resemble the type shown in Fig. 7.17
for wind bracing; they are developed for the full moment-resisting capacity of the
beam.
Much easier to accomplish and more efficient are welded rigid connections (Fig.
7.53). They may be connected simply by butt welding the beam flanges to the
columns—the ‘‘direct’’ connection shown in Fig. 7.53a and b. Others may prefer
the ‘‘indirect’’ method, with top plates, because this detail permits ordinary mill
tolerance for beam length. Welding of plates to stiffen the column flanges, when
necessary, is also relatively simple.
In lieu of the erection seat angle in Fig. 7.53b, a patented, forged hook-and-eye
device, known as Saxe erection units, may be used. The eye, or seat, is shop welded
to the column, and the hook, or clip, is shop welded to the underside of the beam
bottom flange. For deep beams, a similar unit may be located on the top flange to
prevent accidental turning over of the beams. Saxe units are capable of supporting
normal erection loads and deadweight of members; but their contribution to the
strength of the connection is ignored in computing resistance to shear.
STRUCTURAL STEEL CONSTRUCTION 7.113
FIGURE 7.54 Effect of rigidity of connections on end moments.
A comparison of fixities intermediate between full rigidity and zero restrain in
Fig. 7.54 reveals an optimum condition attainable with 75% rigidity; end and centerspan
moments are equal, each being WL/ 16, or one-half the simple-beam moment.
The saving in weight of beam is quite apparent.
Perhaps the deterrent to a broader usage of semirigid connections has been the
proviso contained in specifications: ‘‘permitted only upon evidence that the connections
to be used are capable of resisting definite moments without overstress of
the fasteners.’’ As a safeguard, the proportioning of the beam joined by such connections
is predicated upon no greater degree of end restraint than the minimum
known to be effected by the connection. Suggested practice, based on research with
welded connections, is to design the end connections for 75% rigidity but to provide
a beam sized for the moment that would result from 50% restraint; i.e., WL/ 12.
(‘‘Report of Tests of Welded Top Plate and Seat Building Connections,’’ The Welding
Journal, Research Supplement 146S–165S, 1944.) The type of welded connection
in Fig. 7.52c when designed for the intended rigidity, is generally acceptable.
End-plate connections (Fig. 7.50) are another means of achieving negligible,
partial, and full restraint.
7.36 BEAM SPLICES
These are required in rigid frames, suspended-span construction, and continuous
beams. Such splices are usually located at points of counterflexure or at points
where moments are relatively small. Therefore, splices are of moderate size. Flanges
and web may be spliced with plates or butt welded.
7.114 SECTION SEVEN
FIGURE 7.55 Welded beam splices.
For one reason or another it is sometimes
expedient to make a long beam
from two short lengths. A welded joint
usually is selected, because the beams
can be joined together without splice
plates and without loss of section because
of bolt holes. Also, from the viewpoint
of appearance, the welded joint is
hardly discernible.
Usually, the joint must be 100% ef-
ficient, to develop the full section. Figure
7.55 illustrates such a detail. The back side of the initial weld is gouged or
chipped out; access holes in the beam webs facilitate proper edge preparation and
depositing of the weld metal in the flange area in line with the web. Such holes
are usually left open, because plugs would add undesirable residual stresses to the
joint.
7.37 COLUMN SPLICES
Column-to-column connections are usually determined by the change in section. In
general, a change is made at every second floor level, where a shop or field splice
is located. From an erection viewpoint, as well as for fabrication and shipment,
splices at every third floor may be more economical because of the reduced number
of pieces to handle. This advantage is partly offset by extra weight of column
material, because the column size is determined by loads on the lowest story of
each tier, there being an excess of section for the story or two above.
Splices are located just above floor-beam connections, usually about 2 to 3 ft
above the floor. Because column stresses are transferred from column to column
by bearing, the splice plates are of nominal size, commensurate with the need for
safe erection and bending moments the joint may be subjected to during erection.
From the viewpoint of moment resistance, a conventional column splice develops
perhaps 20% of the moment capacity of the column.
Figure 7.56 illustrates the common types of column splices made with high
strength bolts. In Fig. 7.56a and b, the upper column bears directly on the lower
column; filler plates are supplied in (b) when the differences in depth of the two
columns are greater than can be absorbed by erection clearance.
As a rule, some erection clearance should be provided. When columns of the
same nominal depth are spliced, it is customary to supply a 1?8-in fill under each
splice plate on the lower column, or, as an alternate, to leave the bolt holes open
on the top gage line below the finished joint until the upper shaft is erected. The
latter procedure permits the erector to spring the plates apart to facilitate entry of
the upper column.
When the upper column is of such dimension that its finished end does not
wholly bear on the lower column, one of two methods must be followed: In Fig.
7.56c, stresses in a portion of the upper column not bearing on the lower column
are transferred by means of flange plates that are finished to bear on the lower
column. These bearing plates must be attached with sufficient single-shear bolts to
develop the load transmitted through bearing on the finished surface.
When the difference in column size is pronounced, the practice is to use a
horizontal bearing plate as shown in Fig. 7.56d. These plates, known as butt plates,
STRUCTURAL STEEL CONSTRUCTION 7.115
FIGURE 7.56 Slip-critical bolted column splices.
may be attached to either shaft with tack welds or clip angles. Usually it is attached
to the upper shaft, because a plate on the lower shaft may interfere with erection
of the beams that frame into the column web.
Somewhat similar are welded column splices. In Fig. 7.57a, a common case,
holes for erection purposes are generally supplied in the splice plates and column
flanges as shown. Some fabricators, however, prefer to avoid drilling and punching
of thick pieces, and use instead clip angles welded on the inside flanges of the
columns, one pair at diagonally opposite corners, or some similar arrangement,
Figure 7.57b and c corresponds to the bolted splices in Fig. 7.56c and d. The shop
and field welds for the welded butt plate in Fig. 7.57c may be reversed, to provide
erection clearance for beams seated just below the splice. The erection clip angles
would then be shop welded to the underside of the butt plate, and the field holes
would pierce the column web.
The butt-weld splice in Fig. 7.57d is the most efficient from the standpoint of
material saving. The depth of the bevel as given in the illustration is for the usual
column splice, in which moment is unimportant. However, should the joint be
subjected to considerable moment, the bevel may be deepened; but a 1?8-in minimum
shoulder should remain for the purpose of landing and plumbing the column. For
full moment capacity, a complete-penetration welded joint would be required.
STEEL ERECTION
A clear understanding of what the fabricator furnishes or does not furnish to the
erector, particularly on fabrication contracts that may call for delivery only, is all7.116
SECTION SEVEN
FIGURE 7.57 Welded column splices.
important—and in many instances fabricated steel is purchased on delivery basis
only.
Purchasing structural steel is simplified by the ‘‘Code of Standard Practice for
Buildings and Bridges,’’ (Table 7.1). A provision in the construction contract making
the code a part of the contract is often used, since it establishes a commonly
accepted and well-defined line of demarcation between what is, and what is not, to
be furnished under the contract. Lacking such a provision, the contract, to avoid
later misunderstandings, must enumerate in considerable detail what is expected of
both parties to the contract.
Under the code—and unless otherwise specifically called for in the contract
documents—such items as steel sash, corrugated-iron roofing or siding, and openweb
steel joists, and similar items, even if made of steel and shown on the contract
design drawings, are not included in the category ‘‘structural steel.’’ Also, such
items as door frames are excluded, even when made of structural shapes, if they
are not fastened to the structure in such way as to comply with ‘‘constituting part
of the steel framing.’’ On the other hand, loose lintels shown on design plans or in
separate scheduling are included.
According to the code, a fabricator furnishes with ‘‘structural steel,’’ to be
erected by someone else, the field bolts required for fastening the steel. The fabSTRUCTURAL
STEEL CONSTRUCTION 7.117
ricator, however, does not furnish the following items unless specified in the invitation
to bid: shims, fitting-up bolts, drift pins, temporary cables, welding electrodes,
or thin leveling plates for column bases.
The code also defines the erection practices. For example, the erector does not
paint field boltheads and nuts, field welds, or touch up abrasions in the shop coat,
or perform any other field painting unless required in specifications accompanying
the invitation to bid.
7.38 ERECTION EQUIPMENT
If there is a universal piece of erection equipment, it is the crane. Mounted on
wheels or tractor threads, it is extremely mobile, both on the job and in moving
from job to job. Practically all buildings are erected with this efficient raising device.
The exception, of course, is the skyscraper whose height exceeds the reach of the
crane. Operating on ground level, cranes have been used to erect buildings of about
20 stories, the maximum height being dependent on the length of the boom and
width of building.
The guy derrick is a widely used raising device for erection of tall buildings.
Its principal asset is the ease by which it may be ‘‘jumped’’ from tier to tier as
erection proceeds upward. The boom and mast reverse position; each in turn serves
to lift up the other. It requires about 2 h to make a two-story jump.
Stiff-leg derricks and gin poles are two other rigs sometimes used, usually in
the role of auxiliaries to cranes or guy derricks. Gin poles are the most elementary—
simply a guyed boom. The base must be secure because of the danger of
kicking out. The device is useful for the raising of incidental materials, for dismantling
and lowering of larger rigs, and for erection of steel on light construction
where the services of a crane are unwarranted.
Stiff-leg derricks are most efficient where they may be set up to remain for long
periods of time. They have been used to erect multistory buildings but are not in
popular favor because of the long time required to jump from tier to tier. Among
the principal uses for stiff legs are (1) unloading steel from railroad cars for transfer
to trucks, (2) storage and sorting, and (3) when placed on a flat roof, raising steel
to roof level, where it may be sorted and placed within each of a guy derrick.
Less time for ‘‘jumping’’ the raising equipment is needed for cranes mounted
on steel box-type towers, about three stories high, that are seated on interior elevator
wells or similar shafts for erecting steel. These tower cranes are simply jacked
upward hydraulically or raised by cables, with the previously erected steel-work
serving as supports. In another method, a stiff-leg derrick is mounted on a trussed
platform, spanning two or more columns, and so powered that it can creep up the
erected exterior columns. In addition to the advantage of faster jumps, these methods
permit steel erection to proceed as soon as the higher working level is reached.
7.39 CLEARANCE FOR ERECTING BEAMS
Clearances to permit tightening bolts and welding are discussed in Art. 7.3.7. In
addition, designers also must provide sufficient field clearance for all members so
as to permit erection without interference with members previously erected. The
7.118 SECTION SEVEN
FIGURE 7.58 Erection
clearance for beams.
shop drafter should always arrange the details so that the members can be swung
into their final position with shifting the members to which they connect from their
final positions. The following examples illustrate the conditions most frequently
encountered in building work:
FIGURE 7.59 Alternative method for providing
erection clearance.
In framed beam connections (Fig.
7.58), the slightly shorter distance outto-
out of connection angles (B—1?8 in),
as compared with the face-to-face distance
between supporting members, is
usually sufficient to allow forcing the
beam into position. Occasionally, however,
because the beam is relatively
short, or because heavy connection angles
with wide outstanding legs are required,
the diagonal distance A may exceed
the clearance distance B. If so, the
connection for one end must be shipped
bolted to the framed beam to permit its
removal during erection.
An alternative solution is to permanently
fasten on connection angle of
each pair to the web of the supporting
beam, temporarily bolting the other angle
to the same web for shipment, as shown in Fig. 6.59. The beam should be
investigated for the clearance in swinging past permanently bolted connection angles.
Attention must also be paid to possible interference of stiffeners in swinging
the beam into place when the supporting member is a plate girder.
Another example is that of a beam seated on column-web connections (Fig.
7.60). The first step is to remove the top angles and shims temporarily. Then, while
hanging from the derrick sling, the beam is tilted until its ends clear the edges of
the column flanges, after which it is rotated back into a horizontal position and
landed on the seats. The greatest diagonal length G of the beam should be about
1?8 in less than the face-to-face distance F between column webs. It must also be
such as to clear any obstruction above; e.g., G must be equal to or less than C, or
the obstructing detail must be shipped bolted for temporary removal. To allow for
possible overrun, the ordered length L of the beam should be less than the detailing
length E by at least the amount of the permitted cutting tolerance.
Frequently, the obstruction above the beam connection may be the details of a
column splice. As stated in Art. 7.37, it may be necessary to attach the splice
STRUCTURAL STEEL CONSTRUCTION 7.119
FIGURE 7.60 Clearance for beam seated on
column-web connections.
material on the lower end of the upper shaft, if erection of the beam precedes
erection of the column in the tier above.
7.40 ERECTION SEQUENCE
The order in which steel is to be fabricated and delivered to the site should be
planned in advance so as not to conflict with the erector’s methods or construction
schedule. For example, if steel is to be erected with derricks, the approximate
locations at which the derricks will be placed will determine the shipping installments,
or sections, into which the frame as a whole must be segregated for orderly
shipment. When installments are delivered to the site at predetermined locations,
proper planning will eliminate unnecessary rehandling. Information should be conveyed
to the drafting room so that the shipping installments can be indicated on
the erection plans and installments identified on the shipping lists.
In erection of multistory buildings with guy derricks, the practice is to hoist and
place all columns in each story first, spandrel beams and wall bracing next, and
interior beams and wall bracing next, and interior beams with filler beams last.
More specifically, erection commences with bays most distant from the derrick and
progresses toward the derrick, until it is closed in. Then, the derrick is jumped to
the top and the process is repeated for the next tier. Usually, the top of the tier is
planked over to obtain a working platform for the erectors and also to afford protection
for the trades working below. However, before the derrick is jumped, the
corner panels are plumbed; similarly when panels are erected across the building,
cables are stretched to plumb the structure.
7.120 SECTION SEVEN
There is an established sequence for completing the connections. The raising
gang connects members together with temporary fitting-up bolts. The number of
bolts is kept to a minimum, just enough to draw the joint up tight and take care of
the stresses caused by deadweight, wind, and erection forces. Permanent connections
are made as soon as alignment is within tolerance limits. Usually, permanent
bolting or welding follows on the heels of the raising gang. Sometimes, the latter
moves faster than the gang making the permanent connections, in which case it
may be prudent to skip every other floor, thus obtaining permanent connections as
close as possible to the derrick—a matter of safe practice.
Some erectors prefer to use permanent high-strength (A325 and A490) bolts for
temporary fitting up. Because bolts used for fit-up are not tightened to specified
minimum tension, they may be left in place and later tightened as required for
permanent installation.
7.41 FIELD-WELDING PROCEDURES
The main function of a welding sequence is to control distortion due primarily to
the effects of welding heat. In general, a large input of heat in a short time tends
to produce the greatest distortion. Therefore, it is always advisable, for large joints,
to weld in stages, with sufficient time between each stage to assure complete dispersal
of heat, except for heat needed to satisfy interpass-temperature requirements
(Art. 7.3.5). Equally important, and perhaps more efficient from the erector’s viewpoint,
are those methods that balance the heat input in such a manner that the
distortional effects tend to cancel out.
Welding on one flange of a column tends to leave the column curled toward the
welded side cooling, because of shrinkage stresses. A better practice for beams
connecting to both sides of a column is to weld the opposite connections simultaneously.
Thus the shrinkage of each flange is kept in balance and the column remain
plumb.
If simultaneous welding is not feasible, then the procedure is to weld in stages.
About 60% of the required weld might be applied on the first beam, then the joint
on the opposite flange might be completely welded, and finally, welded on the first
beam would be completed. Procedures such as this will go far to reduce distortion.
FIGURE 7.61 Indication of sequence in welding
a connection.
Experience has shown that it is good
practice to commence welding at or near
the center of a building and work outward.
Columns should be checked frequently
for vertical alignment, because
shrinkage in the welds tends to shorten
the distance between columns. Even
though the dimensional change at each
joint may be very small, it can accumulate
to an objectionable amount in a
long row of columns. One way to reduce
the distortion is to allow for
shrinkage at each joint, say, 1?16 in for a
20-ft bay, by tilting or spreading the columns.
Thus, a spread of 1?8 in for the two ends of a beam with flanges butt welded
to the columns may be built in at the fabricating shop; for example, by
STRUCTURAL STEEL CONSTRUCTION 7.121
increasing the spacing of erection-bolt holes in the beam bottom flange. Control in
the field, however, is maintained by guy wires until all points are welded.
Shortening of bays can become acute in a column row in which beams connect
to column flanges, because the shrinkage shortening could possibly combine with
the mill underrun in column depths. Occasionally, in addition to spreading the
columns, it may be necessary to correct the condition by adding filler plates or
building out with weld metal.
Some designers of large welded structures prefer to detail the welding sequence
for each joint. For example, on one project, the procedure for the joint shown in
Fig. 7.61 called for four distinct operations, or stages: first, the top 6 inches of the
shear weld on the vertical connection was made; second, the weld on the top flange;
third, the bottom-flange weld; and fourth, the remaining weld of the vertical connection.
The metal was allowed to return to normal temperature before starting each
stage. One advantage of this procedure is the prestressing benefits obtained in the
connecting welds. Tensile stresses are developed in the bottom-flange weld on cooling;
compressive stresses of equal magnitude consequently are produced in the top
flange. Since these stresses are opposite to those caused by floor loads, welding
stresses are useful in supporting the floor loads. Although this by-product assistance
may be worthwhile, there are no accepted methods for resolving the alleged benefits
into design economy.
Multistory structures erected with equipment supported on the steelwork as it
rises will be subjected by erection loads to stresses and strains. The resulting deformations
should be considered in formulating a field-welding sequence.
7.42 ERECTION TOLERANCES
Dimensional variations in the field often are a consequence of permissible variations
in rolling of steel and in shop fabrication. Limits for mill variations are prescribed
in ASTM A6, ‘‘General Requirements for Delivery of Rolled Steel Plates, Shapes,
Sheet Piling, and Bars for Structural Use.’’ For example, wide-flange beams are
considered straight, vertically or laterally, if they are within 1?8 in for each 10 ft of
length. Similarly, columns are straight if the deviation is within 1?8 in per 10 ft,
with a maximum deviation of 3?8 in.
It is standard practice to compensate in shop details for certain mill variations.
The adjustments are made in the field, usually with clearances and shims.
Shop-fabrication tolerance for straightness of columns and other compression
members often is expressed as a ratio, 1:1000, between points of lateral support.
(This should be recognized as approximately the equivalent of 1?8 in per 10 ft, and
since such members rarely exceed 30 ft in length, between lateral supports, the 3?8-
in maximum deviation prevails.) Length of fabricated beams have a tolerance of
1?16 in up to 30 ft and 1?8 in over 30 ft. Length of columns finished to bear on their
ends have a tolerance of 1?32 in.
Erected beams are considered level and aligned if the deviation does not exceed
1:500. Similarly, columns are plumb and aligned if the deviation of individual
pieces, between splices in the usual multistory building, does not exceed 1:500.
The total or accumulative displacement for multistory columns cannot exceed the
limits prescribed in the American Institute of Steel Construction ‘‘Code of Standard
Practice.’’ For convenience, these are indicated in Fig. 7.62. Control is placed only
on the exterior columns and those in the elevator shaft.
7.122 SECTION SEVEN
FIGURE 7.62 Permissible deviations from plumb for columns. Limits shown are based on the
assumption that the center of the column base coincides with the established column line.
Field measurements to determine whether columns are plumb should always be
made at night or on cloudy days, never in sunshine. Solar radiation induces differential
thermal strains, which cause the structure to curl away from the sun by an
amount that renders plumbing measurements useless.
If beam flanges are to be field welded (Fig. 7.56a) and the shear connection is
a high-strength-bolted, slip-critical joint, the holes should be made oversize or horSTRUCTURAL
STEEL CONSTRUCTION 7.123
izontal slotted (Art. 7.3.1), thus providing some built-in adjustment to accommodate
mill and shop tolerances for beams and columns.
Similarly, for beams with framed connections (Fig. 7.46 and 7.47) that will be
field bolted to columns, allowance should be made in the details for finger-type
shims, to be used where needed for column alignment.
Because of several variables, bearing of column joints is seldom in perfect contact
across the entire cross-sectional area. The AISC recommends acceptance if
gaps between the bearing surfaces do not exceed 1?16 in. Should a gap exceed 1?16
in and an engineering investigation shows need for more contact area, the gap may
be filled with mild steel shims.
Tolerance for placing machinery directly on top of several beams is another
problem occasionally encountered in the field. The elevation of beam flanges will
vary because of permissible variations for mill rolling, fabrication, and erection.
This should be anticipated and adequate shims provided for field adjustments.
7.43 ADJUSTING LINTELS
Lintels supported on the steel frame (sometimes called shelf angles) may be permanently
fastened in the shop to the supporting spandrel beam, or they may be
attached so as to allow adjustment in the field (see Fig. 7.9, p. 7.21). In the former
case, the final position is solely dependent on the alignment obtained for the spandrel
itself, whereas for the latter, lintels may be adjusted to line and grade independently
of the spandrel. Field adjustment is the general rule for all multistory
structures. Horizontal alignment is obtained by using slotted holes in the connection
clip angles. Vertical elevation (grade) is obtained with shims.
When walls are of masonry construction, a reasonable amount of variation in
the position of lintels may be absorbed without much effort by masons. So the
erector can adjust the lintels immediately following the permanent fastening of the
spandrels to the columns. This procedure is ideal for the steel erector, because it
allows him to complete his contract without costly delays and without interference
with other trades. Subsequent minor variations in the position of the lintels, because
of deflection or torsional rotation of the spandrel when subjected to deadweight of
the floor slab, are usually absorbed without necessitating further lintel adjustment.
With lightweight curtain walls, however, the position of the lintels is important,
because large paneled areas afford less latitude for variation. As a rule, the steel
erector is unable to adjust the lintels to the desired accuracy at the time the main
framework is erected. If the erector has contracted to do the adjusting, this work
must wait until the construction engineer establishes the correct lines and grades.
In the usual case, floor slabs are concreted immediately after the steelwork is inspected
and accepted. The floor grades then determined become the base to which
the lintels can be adjusted. At about the same time, the wall contractor has scaffolds
in place, and by keeping pace with wall construction, the steel erector, working
from the wall scaffolds, adjusts the lintels.
In some cases, the plans call for concrete encasement of the spandrel beams, in
which case concreting is accomplished with the floor slab. The construction engineer
should ensure that the adjustment features provided for the lintels are not
frozen in the concrete. One suggestion is to box around the details, thus avoiding
chopping out concrete. In some cases, it may be possible to avoid the condition
entirely by locating the connection below the concrete encasement, where the adjustment
is always accessible.
7.124 SECTION SEVEN
The whole operation of lintel adjustment is one of coordination between the
several trades. That this be carried out in an orderly fashion is the duty of the
construction engineer. Furthermore, the desired procedure should be carefully
spelled out in the job specifications so that erection costs can be estimated fairly.
Particularly irksome to the construction engineer is the lintel located some distance
below the spandrel and supported on flexible, light steel hangers. This detail
can be troublesome because it has no capacity to resist torsion. Avoid this by
developing the lintel and spandrel to act together as a single member.
CORROSION PROTECTION
Protection of steel surfaces has been, since the day steel was first used, a vexing
problem for the engineers, paint manufacturers, and maintenance personnel. Over
the years, there have been many developments, the result of numerous studies and
research activities. Results are published in the ‘‘Steel Structures Painting Manual.’’
This work is in two volumes—Vol. 1, ‘‘Good Painting Practice,’’ and Vol. II, ‘‘Systems
and Specifications’’ (Steel Structures Painting Council, 40 24th Street, Suite
600, Pittsburgh, PA 15213). Each of the paint systems covers the method of cleaning
surfaces, types of paint to be used, number of coats to be applied, and techniques
to be used in their applications. Each surface treatment and paint system is
identified by uniform nomenclature, e.g., Paint System Specification SSPC-PS7.00-
64T, which happens to be the identity of the minimum-type protection as furnished
for most buildings.
7.44 CORROSION OF STEEL
Ordinarily, steel corrodes in the presence of both oxygen and water, but corrosion
rarely takes place in the absence of either. For instance, steel does not corrode in
dry air, and corrosion is negligible when the relative humidity is below 70%, the
critical humidity at normal temperature. Likewise, steel does not corrode in water
that has been effectively deaerated. Therefore, the corrosion of structural steel is
not a serious problem, except where water and oxygen are in abundance and where
these primary prerequisites are supplemented with corrosive chemicals such as soluble
salts, acids, cleaning compounds, and welding fluxes.
In ideal dry atmosphere, a thin transparent film of iron oxide forms. This layer
of ferric oxide is actually beneficial, since it protects the steel from further oxidation.
When exposed to water and oxygen in generous amounts, steel corrodes at an
average rate of roughly 5 mils loss of surface metal per year. If the surface is
comparatively dry, the rate drops to about 1?2 mil per year after the first year, the
usual case in typical industrial atmospheres. Excessively high corrosion rates occur
only in the presence of electrolytes or corrosive chemicals. Usually, this condition
is found in localized areas of a building.
Mill scale, the thick layer of iron oxides that forms on steel during the rolling
operations, is beneficial as a protective coating, if it is intact and adheres firmly to
the steel. In the mild environments generally encountered in most buildings, mill
scale that adheres tightly after weathering and handling offers no difficulty. In buildings
exposed to high humidity and corrosive gases, broken mill scale may be detSTRUCTURAL
STEEL CONSTRUCTION 7.125
rimental to both the steel and the paint. Through electrochemical action, corrosion
sets in along the edges of the cracks in the mill scale and in time loosens the scale,
carrying away the paint.
Galvanic corrosion takes place when dissimilar metals are connected together.
Noble metals such as copper and nickel should not be connected to structural steel
with steel fasteners, since the galvanic action destroys the fasteners. On the other
hand, these metals may be used for the fasteners, because the galvanic action is
distributed over a large area and consequently little or no harm is done. When
dissimilar metals are to be in contact, the contacting surfaces should be insulated;
paint is usually satisfactory.
7.45 PAINTING STEEL STRUCTURES
Evidence obtained from dismantled old buildings and from frames exposed during
renovation indicates that corrosion does not occur when steel surfaces are protected
from the atmosphere. Where severe rusting was found and attributed to leakage of
water, presence or absence of shop paint had no significant influence. Consequently,
the AISC ‘‘Specifications for Structural Steel for Buildings’’ exempts from onecoat
shop paint, at one time mandatory, all steel framing that is concealed by interior
finishing materials—ceilings, fireproofing partitions, walls, and floors.
Structures may be grouped as follows: (1) those that need no paint, shop or field;
(2) those in which interior steelwork will be exposed, probably field painted; (3)
those fully exposed to the elements. Thus, shop paint is required only as a primer
coat before a required coat of field paint.
Group (1) could include such structures as apartment buildings, hotels, dormitories,
office buildings, stores, and schools, where the steelwork is enclosed by other
materials. The practice of omitting the shop and field paint for these structures,
however, may not be widely accepted because of tradition and the slowness of
building-code modernization. Furthermore, despite the economic benefit of paint
omission, clean, brightly painted steel during construction has some publicity value.
In group (2) are warehouses, industrial plants, parking decks, supermarkets, onestory
schools, inside swimming pools, rinks, and arenas, all structures shielded from
the elements but with steel exposed in the interior. Field paint may be required for
corrosion protection or appearance or both. The severity of the corrosion environment
depends on type of occupancy, exposure, and climatic conditions. The paint
system should be carefully selected for optimum effectiveness.
In group (3) are those structures exposed at all times to the weather: crane
runways, fire escapes, towers, exposed exterior columns, etc. When made of carbon
steel, the members will be painted after erection and therefore should be primed
with shop paint. The paint system selected should be the most durable one for the
atmospheric conditions at the site. For corrosion-resistant steels, such as those meeting
ASTM A242 and A588, field painting may be unnecessary. On exposure, these
steels acquire a relatively hard coat of oxide, which shields the surface from progressive
rusting. The color, russet brown, has architectural appeal.
7.46 PAINT SYSTEMS
The Steel Structures Painting Council has correlated surface preparations and primer,
intermediate, and finish coats of paints into systems, each designed for a
7.126 SECTION SEVEN
common service condition (‘‘Steel Structure Painting Manual’’). In addition, the
Council publishes specifications for each system and individual specifications for
surface preparations and paints. Methods for surface cleaning include solvent, handtool,
power-tool, pickling, flame, and several blast techniques.
Surface preparation is directly related to the type of paints. In general, a slowdrying
paint containing oil and rust-inhibitive pigments and one possessing good
wetting ability may be applied on steel nominally cleaned. On the other hand, a
fast-drying paint with poor wetting characteristics requires exceptionally good surface
cleaning, usually entailing complete removal of mill scale. Therefore, in specifying
a particular paint, the engineer should include the type of surface preparation,
to prevent an improper surface condition from reducing the effectiveness of an
expensive paint.
Paint selection and surface preparation are a matter of economics. For example,
while blast-cleaned surfaces are concealed to be the best paint foundation for lasting
results, the high cost is not always justified. Nevertheless, the Council specifies a
minimum surface preparation by a blast cleaning process for such paints as alkyd,
phenolic, vinyl, coal tar, epoxy, and zinc-rich.
As an aid for defining and evaluating the various surface preparations, taking
into account the initial condition of the surface, an international visual standard is
available and may be used. A booklet of realistic color photographs for this purpose
can be obtained from the Council or ASTM. The applicable standard and acceptance
criteria are given in ‘‘Quality Criteria and Inspection Standards,’’ American
Institute of Steel Construction.
The Council stresses the relationship between the prime coat (shop paint) and
the finish coats. A primer that is proper for a particular type of field paint could
be an unsatisfactory base for another type of field paint. Since there are numerous
paint formulations, refer to Council publications when faced with a painting condition
more demanding than ordinary.
In the absence of specific contract requirements for painting, the practice described
in the AISC ‘‘Specification for Structural Steel for Buildings’’ may be followed.
This method may be considered ‘‘nominal.’’ The steel is brushed, by hand
or power, to remove loose mill scale, loose rust, weld slag, flux deposit, dirt, and
foreign matter. Oil and grease spots are solvent cleaned. The shop coat is a commercial-
quality paint applied by brushing, dipping, roller coating, flow coating, or
spraying to a 2-mil thickness. It affords only short-time protection. Therefore, finished
steel that may be in ground storage for long periods or otherwise exposed to
excessively corrosive conditions may exhibit some paint failure by the time it is
erected, a condition beyond the control of the fabricator. Where such conditions
can be anticipated, as for example, an overseas shipment, the engineer should select
the most effective paint system.
7.47 FIELD-PAINTING STEEL
There is some question as to justification for protecting steelwork embedded in
masonry or in contact with exterior masonry walls built according to good workmanship
standards but not impervious to moisture. For example, in many instances,
the masonry backing for a 4-in brick wall is omitted to make way for column
flanges. Very definitely, a 4-in wall will not prevent penetration of water. In many
cases, also, though a gap is provided between a wall and steelwork, mortar dripSTRUCTURAL
STEEL CONSTRUCTION 7.127
pings fall into the space and form bridges over which water may pass, to attack
the steel. The net effect is premature failure of both wall and steel. Walls have been
shattered—sheared through the brick—by the powerful expansion of rust formations.
The preventatives are: (1) coating the steel with suitable paint and (2) good
wall construction.
A typical building code reads: ‘‘Special precautions shall be taken to protect the
outer surfaces of steel columns located in exterior walls against corrosion, by painting
such surfaces with waterproof paints, by the use of mastic, or by other methods
of waterproofing approved by the building inspector.’’
FIGURE 7.63 Flashing at spandrel and lintels.
In most structures an asphalt-type
paint is used for column-flange protection.
The proviso is sometimes extended
to include lintels and spandrels, since
the danger of corrosion is similar, depending
on the closeness and contact
with the wall. However, with the latter
members, it is often judicious to supplement
the paint with flashing, either metallic
or fabric. A typical illustration,
taken from an actual apartment-building
design, is shown in Fig. 7.63.
In general, building codes differ on
field paint; either paint is stipulated or
the code is silent. From a practical viewpoint,
the question of field painting cannot
be properly resolved with a single
broad rule. For an enclosed building in
which the structural members are enveloped,
for example, a field coat is sheer
wastage, except for exterior steel members
in contact with walls. On the other
hand, exposed steel subject to highhumidity
atmospheres and to exceptionally
corrosive gases and contaminants
may need two or three field coats.
Manufactured buildings should always
be closely scrutinized, bearing in
mind that original conditions are not always permanent. As manufacturing processes
change, so do the corrosive environments stimulated by new methods. It is well to
prepare for the most adverse eventuality.
Special attention should be given to steel surfaces that become inaccessible, e.g.,
tops of purlins in contact with roof surfaces. A three-coat job of particularly suitable
paint may pay off in the long run, even though it delays placement of the roof
covering.
7.48 STEEL IN CONTACT WITH CONCRETE
According to the ‘‘Steel Structures Painting Manual,’’ Vol. I, ‘‘Good Painting Practice’’
(Steel Structures Painting Council, 40 24th Street, Suite 600, Pittsburgh, PA
15213):
7.128 SECTION SEVEN
1. Steel that is embedded in concrete for reinforcing should not be painted.
Design considerations require strong bond between the reinforcing and the concrete
so that the stress is distributed. Painting of such steel does not supply sufficient
bond. If the concrete is properly made and of sufficient thickness over the metal,
the steel will not corrode.
2. Steel that is encased in exposed lightweight concrete that is porous should
be painted with at least one coat of good-quality rust-inhibitive primer. When conditions
are severe, or humidity is high, two or more coats of paint should be applied,
since the concrete may accelerate corrosion.
3. When steel is enclosed in concrete of high density or low porosity, and when
the concrete is at least 2 to 3 in thick, painting is not necessary, since the concrete
will protect the steel.
4. Steel in partial contact with concrete is generally not painted. This creates
an undesirable condition, for water may seep into the crack between the steel and
the concrete, causing corrosion. A sufficient volume of rust may be built up, spalling
the concrete. The only remedy is to chip or leave a groove in the concrete at the
edge next to the steel and seal the crack with an alkali-resistant calking compound
(such as bituminous cement).
5. Steel should not be encased in concrete that contains cinders, since the acidic
condition will cause corrosion of the steel.
FIRE PROTECTION FOR STRUCTURAL STEEL
Structural steel is a noncombustible material. It is therefore satisfactory for use
without protective coverage in many types of buildings where combustibility loading
is low, from the viewpoint of either building ordinances or owner’s preference.
When structural steel is used in this fashion, it is described as ‘‘exposed’’ or ‘‘unprotected.’’
Unprotected steel may be selected wherever building codes permit combustible
construction.
Exposed or unprotected structural steel is commonly used for industrial-type
buildings, hangars, auditoriums, stadiums, warehouses, parking garages, billboards,
towers, and low stores, schools, and hospitals. In most cases, these structures contain
little combustible material. In others, where the contents are highly combustible,
sprinkler systems may be incorporated to protect the steelwork.
Steel building frames and floor systems should be covered with fire-resistant
materials in certain buildings to reduce the chance of fire damage. These structures
may be tall buildings, such as offices, apartments, and hotels, or low-height buildings,
such as warehouses, where there is a large amount of combustible content.
The buildings may be located in congested areas, where the spread of fire is a
strong possibility. So for public safety, as well as to prevent property loss, building
codes regulate the amount of fire resistance that must be provided.
The following are some of the factors that enter into the determination of minimum
fire resistance for a specific structure: height, floor area, type of occupancy
(a measure of combustible contents), fire-fighting apparatus, sprinkler systems, and
location in a community (fire zone), which is a measure of hazard to adjoining
properties.
STRUCTURAL STEEL CONSTRUCTION 7.129
7.49 EFFECT OF HEAT ON STEEL
A moderate rise in temperature of structural steel, say up to 500F, is beneficial in
that the strength is about 10% greater than the normal value. Above 500F, strength
falls off, until at 700F it is nearly equal to the normal temperature strength. At a
temperature of 1000F, the compressive strength of steel is about the same as the
maximum allowable working stress in columns.
Unprotected steel members have a rating of about 15 min, based on fire tests of
columns with cross-sectional areas of about 10 in2. Heavier column, possessing
greater mass for dissipation of heat, afford greater resistance—20 min perhaps.
Columns with reentrant space between flanges filled with concrete, but otherwise
exposed, have likewise been tested. Where the total area of the solid cross section
approximates 36 in2, the resistance is 30 min, and where the area is 64 in2, the
resistance is 1 hr.
The average coefficient of expansion for structural steel between the temperatures
of 100 and 1200F is given by the formula
C  0.0000061  0.0000000019t (7.81)
in which C  coefficient of expansion per F and t  temperature, F.
Below 100F, the average coefficient of expansion is taken as 0.0000065.
The modulus of elasticity of structural steel, about 29,000 ksi at room temperature,
decreases linearly to 25,000 ksi at 900F. Then, it drops at an increasing rate
at higher temperatures.
7.50 FIRE PROTECTION OF EXTERIOR
Steel members, such as spandrel beams and columns, on the exterior of a building
may sometimes be left exposed or may be protected in an economical manner from
fire damage, whereas interior steel members of the same building may be required
to be protected with more expensive insulating materials, as discussed in Art. 7.51.
Standard fire tests for determining fire-endurance ratings of exterior steel members
are not available. But from many tests, data have been obtained that provide a basis
for analytical, thermodynamic methods for fire-safe design. (See for example, ‘‘Fire-
Safe Structural Steel—A Design Guide,’’ American Iron and Steel Institute, 1101
17th St., N.W., Washington, DC 20036.)
The tests indicate that an exterior steel spandrel beam with its interior side
protected by fire-resistant construction need only have its flanges fire protected.
This may be simply done by application of fireproofing, such as sprayed-on mineral
fibers, to the upper surface of the top flange and the under surface of the bottom
flange. In addition, incombustible flame-impingement shields should enclose the
flanges to deflect flames that may be emitted through windows. The shields, for
example, may be made of 1?4-in-thick weathering steel. This construction prevents
the temperature of the spandrel beam from reaching a critical level.
Exposed-steel columns on the outside of a building may be made fire safe by
placement at adequate distances from the windows. Such columns may also be
located closer to the building when placed on the side of windows at such distances
7.130 SECTION SEVEN
FIGURE 7.64 Fire protection of steel columns by encasement with (a) concrete, (b) plaster
on gypsum lath, (c) plaster on metal lath, (d ) furring and gypsumboard, (e) gypsumboard
without furring, and ( ?) gypsum block and plaster.
that the steel is protected by the building walls against flame impingement. Thermodynamic
analysis can indicate whether or not the chosen locations are fire safe.
7.51 MATERIALS FOR IMPROVING FIRE
RESISTANCE
Structured steel may be protected with any of many materials—brick, stone, concrete,
gypsumboard, gypsum block, sprayed-on mineral fibers, and various fireresistant
plasters.
Concrete insulation serves well for column protection, in that it gives additional
stability to the steel section. Also, it is useful where abrasion resistance is needed.
Concrete, however, is not an efficient insulating medium compared with fireresistant
plasters. Normally, it is placed completely around the columns, beams, or
girders, with all reentrant spaces filled solid (Fig. 7.64a). Although this procedure
contributes to the stability of columns and effects composite action in beams and
slabs, it has the disadvantage of imposing great weight on the steel frame and
foundations. For instance, full protection of a W12 column with stone concrete
weighs about 355 psf, whereas plaster protection weighs about 40 psf, and lightweight
concretes made with such aggregates as perlite, vermiculite, expanded shale,
expanded slag, pumice, pumicite and sintered flyash weigh less than 100 psf.
Considerable progress has been made in the use of lightweight plasters with
aggregates possessing good insulating properties. Two aggregates used extensively
are perlite and vermiculite. They replace sand in the sanded-gypsum plaster mix.
STRUCTURAL STEEL CONSTRUCTION 7.131
A 1-in thickness weighs about 4 psf, whereas the same thickness of sanded-gypsum
plaster weighs about 10 psf.
Typical details of lightweight plaster protection for columns are shown in Fig.
7.64b and c. Generally, vermiculite and perlite plastic thicknesses of 1 to 13?4 in
afford protection of 3 and 4 h, depending on construction details. Good alternatives
include gypsum board (Fig. 7.64d and e) or gypsum block (Fig. 7.64?).
For buildings where rough usage is expected, a hard, dense insulating material
such as concrete, brick, or tile would be the logical selection for fire protection.
For many buildings, finished ceilings are mandatory. It is therefore logical to
employ the ceiling for protecting roof and floor framing. All types of gypsum
plasters are used extensively for this dual purpose. Figure 7.65 illustrates typical
installations. For 2-h floors, ordinary sand-gypsum plaster 3?4 in thick is sufficient.
Three- and four-hour floors may be obtained with perlite gypsum and vermiculite
gypsum in the thickness range of 3?4 to 1 in.
Instead of plastered ceilings, use may be made of fire-rated dry ceilings, acoustic
tiles, or drop (lay-in) panels (Fig. 7.65d and e).
Another alternative is to spray the structural steel mechanically (where it is not
protected with concrete) with plasters of gypsum, perlite, or vermiculite, proprietary
cementitious mixtures, or mineral fibers not deemed a health hazard during spraying
(Fig. 7.66). In such cases, the fire-resistance rating of the structural system is independent
of the ceiling. Therefore, the ceiling need not be of fire-rated construction.
Drop panels, if used, need not be secured to their suspended supports.
Still another sprayed-on material is the intumescent fire-retardant coating, essentially
a paint. Tested in conformance with ASTM Specification E119, a 3?16-inthick
coat applied to a steel column has been rated 1 h, a 1?2-in-thick coating 2 h.
As applied, the coating has a hard, durable finish, but at high temperatures, it puffs
to many times its original thickness, thus forming an effective insulating blanket.
Thus, it serves the dual need for excellent appearance and fire protection.
Aside from dual functioning of ceiling materials, the partitions, walls, etc., being
of incombustible material, also protect the structural steel, often with no additional
assistance. Fireproofing costs, therefore, may be made a relatively minor expense
in the overall costs of a building through dual use of materials.
7.52 PIERCED CEILINGS AND FLOORS
Some buildings require recessed light fixtures and air-conditioning ducts, thus interrupting
the continuity of fire-resistive ceilings. A rule that evolved from early
standard fire tests permitted 100 in2 of openings for noncombustible pipes, ducts,
and electrical fixtures in each 100 ft2 of ceiling area.
It has since been demonstrated, with over 100 fire tests that included electrical
fixtures and ducts, that the fire-resistance integrity of ceilings is not impaired when,
in general:
Recessed light fixtures, 2 by 4 ft, set in protective boxes, occupy no more than
25% of the gross ceiling area.
Air-duct openings, 30 in maximum in any direction, are spaced so as not to
occupy more than 576 in2 of each 100 ft2 of gross ceiling area. They must be
protected with fusible-link dampers against spread of smoke and heat.
These conclusions are not always applicable. Reports of fire tests of specific
floor systems should be consulted.
7.132 SECTION SEVEN
FIGURE 7.65 Fire protection of floor framing with incombustible floor construction:
(a) section showing suspended plaster ceiling; (b) attachd plaster ceiling;
(c) furred plaster ceiling; (d ) suspended ceiling with lay-in, fire-rated acoustic
panels; (e) detail of panel support in (d ); ( ?) detail showing fire protection around
recessed lighting; (g) detail showing fire protection around air-conditioning duct
and grille.
STRUCTURAL STEEL CONSTRUCTION 7.133
FIGURE 7.66 Typical fire protection with sprayed material.
A serious infringement of the fire rating of a floor system could occur when
pipes, conduit, or other items pierce the floor slab, a practice called ‘‘poke-through.’’
Failure to calk the openings with insulating material results in a lowering of fire
ratings from hours to a few minutes.
7.53 FIRE-RESISTANCE RATINGS
Most standard fire tests on structural-steel members and assemblies have been conducted
at one of two places—the National Institute of Standards and Technology,
Washington, D.C., or the Underwriters Laboratories, Northbrook, Ill. Fire-testing
laboratories also are available at Ohio State University, Columbus, Ohio, and the
University of California, Berkeley, Calif. Laboratory test reports form the basis for
establishing ratings. Summaries of these tests, together with tabulation of recognized
ratings, are published by a number of organizations listed below. The trade
associations, for the most part, limit their ratings to those constructions employing
the material they represent.
The American Insurance Association (formerly The National Board of Fire Underwriters),
1130 Connecticut Ave., N.W., Suite 100, Washington, DC 20036
The National Institute of Standards and Technology, 100 Bureau Drive, Administration
Bldg. #101, Mailstop 4701, Gaithersburg, MD 20899
Gypsum Association, 810 First St., N.E., #510, Washington, DC 20002
Metal Lath/ Steel Framing Association, 600 Federal St., Chicago, IL 60605
Perlite Institute, 88 New Dorp Plaza, Staten Island, NY 10306-2994
American Iron and Steel Institute, 1000 16th St., N.W., Washington, DC 20036
7.134 SECTION SEVEN
American Institute of Steel Construction, One E. Wacker Dr., Chicago, IL
60601-2001
7.54 BIBLIOGRAPHY
Designing Fire Protection for Steel Columns; Designing Steel Protection for Steel Trusses;
Fire-Safe Structural Steel, American Iron and Steel Institute, 1101 17th Street, N.W., Washington,
DC 20036.
Design Guide—Iron and Steel Buildings, 1873–1952; Guide to Shop Painting of Structural
Steel; Structural Steel Detailing, American Institute of Steel Construction, OneWacker Drive,
Chicago, IL 60601.
Fundamentals of Welding; Structural Welding Code, D1.1; American Welding Society; 550
N.W. Le Jeune Rd., Miami, FL 33126.
E. H. Gaylord, Jr., et al., ‘‘Design of Steel Structures,’’ 3d ed.; E. H. Gaylord, Jr., and C. N.
Gaylord, ‘‘Structural Engineering Handbook,’’ 3d ed.; F. S. Merritt and R. L. Brockenbrough,
‘‘Structural Steel Designers Handbook,’’ 2d ed.; A. J. Rokach, ‘‘Structural Steel Design,
LRFD,’’ McGraw-Hill, Inc., New York.
T. V. Galambos, ‘‘Guide to Stability Design Criteria for Metal Structures,’’ John Wiley &
Sons, Inc., New York.
8.1
SECTION EIGHT
COLD-FORMED STEEL
CONSTRUCTION
Don S. Wolford
Consulting Engineer
Middletown, Ohio
Wei-Wen Yu
University of Missouri–Rolla
Rolla, Missouri
The term cold-formed steel construction, as used in this section, refers to structural
components that are made of flat-rolled steel. This section deals with fabricated
components made from basic forms of steel, such as bars, plates, sheet, and strip.
COLD-FORMED SHAPES
Cold-formed shapes usually imply relatively small, thin sections made by bending
sheet or strip steel in roll-forming machines, press brakes, or bending brakes. Because
of the relative ease and simplicity of the bending operation and the comparatively
low cost of forming rolls and dies, the cold-forming process lends itself
well to the manufacture of unique shapes for special purposes and makes it possible
to use thin material shaped for maximum stiffness.
The use of cold-formed shapes for ornamental and other non-load-carrying purposes
is commonplace. Door and window frames, metal-partition work, non-loadbearing
studs, facing, and all kinds of ornamental sheet-metal work employ such
shapes. The following deals with cold-formed shapes used for structural purposes
in the framing of buildings.
There is no standard series of cold-formed structural sections, such as those for
hot-rolled shapes, yet although groups of such sections have been designed (‘‘Coldformed
Steel Design Manual,’’ American Iron and Steel Institute, 1101 17th St.,
NW, Washington, DC 20036). For the most part, however, cold-formed structural
shapes are designed to serve a particular purpose. The general approach of the
designer is therefore similar to that involved in the design of built-up structural
sections.
8.2 SECTION EIGHT
Cold-formed shapes invariably cost more per pound than hot-rolled sections.
They will be found to be more economical under the following circumstances:
1. Where their use permits a substantial reduction in weight compared to hotrolled
sections. This occurs where relatively light loads are to be supported over
short spans, or where stiffness rather than strength is the controlling factor in the
design.
2. In special cases where a suitable combination of standard hot-rolled shapes
would be heavy and uneconomical.
3. Where quantities required are too small to justify the investment necessary
to produce a suitable hot-rolled section.
4. In dual-purpose panel work, where both strength and coverage are desired.
8.1 MATERIAL FOR COLD-FORMED
STEEL SHAPES
Cold-formed shapes are usually made from hot-rolled sheet or strip steel, which
costs less per pound than cold-rolled steel. The latter, which has been cold-rolled
to desired thickness, is used for thinner gages or where, for any reason, the surface
finish, mechanical properties, or closer tolerances that result from cold-reducing is
desired. Manufacture of cold-formed shapes from plates for use in building construction
is possible but is done infrequently.
8.1.1 Plate, Sheet, or Strip
The commercial distinction between steel plates, sheet, and strip is principally a
matter of thickness and width of material. In some sizes, however, classification
depends on whether the material is furnished in flat form or in coils, whether it is
carbon or alloy steel, and, particularly for cold-rolled material, on surface finish,
type of edge, temper or heat treatment, chemical composition, and method of production.
Although the manufacturers’ classification of flat-rolled steel products by
size is subject to change from time to time, that given in Table 8.1 for carbon steel
is representative.
Carbon steel is generally used. High-strength, low-alloy steel, however, may be
used where strength or corrosion resistance justify it, and stainless steel may be
used for exposed work.
8.1.2 Mechanical Properties
Material to be used for structural purposes generally conforms to one of the standard
specifications of ASTM. Table 8.2 lists the ASTM specifications for structuralquality
carbon and low-alloy sheet and strip, and their principal mechanical properties.
COLD-FORMED STEEL CONSTRUCTION 8.3
TABLE 8.1 Classification by Size of Flat-Rolled Carbon Steel
a. Holt-rolled
Width, in
Thickness, in
0.2300
and thicker 0.2299–0.2031 0.2030–0.1800 0.1799–0.0470
To 31?2 incl. Bar Bar Strip Stripa
Over 31?2 to 6 incl. Bar Bar Strip Stripb
Over 6 to 8 incl. Bar Strip Strip Strip
Over 8 to 12 incl. Platec Strip Strip Strip
Over 12 to 48 incl. Plated Sheet Sheet Sheet
Over 48 Plated Plated Plated Sheet
b. Cold-rolled
Width, in
Thicknesses, in
0.2500 and
thicker 0.2499–0.0142 0.0141 and thinner
To 12, incl. Bar Stripe,f Stripe
Over 12 to 2315?16, incl. Sheetg Sheetg Striph
Over 2315?16 Sheet Sheet Black platei
a 0.0255-in minimum thickness.
b 0.0344-in minimum thickness.
c Strip, up to and including 0.5000-in thickness, when ordered in coils.
d Sheet, up to and including 0.5000-in thickness, when ordered in coils.
e Except that when the width is greater than the thickness, with a maximum width of 1?2 in and a crosssectional
area not exceeding 0.05 in2, and the material has rolled or prepared edges, it is classified as flat
wire.
f Sheet, when slit from wider coils and supplied with cut edge (only) in thicknesses 0.0142 to 0.0821
and widths 2 to 12 in. inclusive, and carbon content 0.25% maximum by ladle analysis.
gMay be classified as strip when a special edge, a special finish, or single-strand rolling is specified or
required.
h Also classified as black platei, depending on detailed specifications for edge, finish, analysis, and other
features.
i Black plate is a cold-rolled, uncoated tin-mill product that is supplied in relatively thin gages.
8.1.3 Stainless-Steel Applications
Stainless-steel cold-formed shapes, although not ordinarily used in floor and roof
framing, are widely used in exposed components, such as stairs, railings, and balustrades;
doors and windows; mullions, fascias; curtain walls and panel work; and
other applications in which a maximum degree of corrosion resistance, retention of
appearance and luster, and compatibility with other materials are primary considerations.
Stainless-steel sheet and strip are available in several types and grades,
with different strength levels and different degrees of formability, and in a wide
range of finishes.
Information useful in design of stainless-steel cold-formed members can be obtained
from the ‘‘Specification for the Design of Cold-Formed Stainless Steel Structural
Members,’’ American Society of Civil Engineers (ASCE), 1801 Alexander
Bell Drive, Reston, VA 20191-4400. The specification is applicable to material
covered by ASTM A666, ‘‘Austenitic Stainless Steel, Sheet, Strip, Plate and Flat
8.4
TABLE 8-2 Principal Mechanical Properties of Structural Quality Sheet, Strip, and Plate Steel
ASTM
designation Material Grade
Minimum
yield
point, ksi
Minimum tensile
strength, ksi
Hot rolled Cold rolled
Minimum
elongation, %
in 2 in
Bend test,
180
, ratio
of inside
diameter
to
thickness
A570 Hot-rolled sheet and strip, carbon steel 30
36
40
45
50
30
36
40
45
50
49
53
55
60
65
?
?
?
?
?
1
11?2
2
21?2
3
A606 Hot-rolled and cold-rolled sheet and strip, high-strength,
low-alloy steel
Cut lengths
Coils
Annealed or
normalized
Cold rolled
50
45
45
45
70
65
65
65
22
22
22
22
1
1
1
1
HR§ CR§
A607 Hot-rolled and cold-rolled, high-strength, low-alloy columbium
or vanadium steels, sheet and strip, cut
lengths or coils
45
50
55
60
65
70
45
50
55
60
65
70
60
65
70
75
80
85
60
65
70
75
80
85
23 22
20 20
18 18
16 16
14 15
12 14
1
1
11?2
2
21?2
3
A611 Cold-rolled sheet, structural carbon-steel sheet, cut lengths
or coils
A
B
C
D
25
30
33
40
42
45
48
52
26
24
22
20
0
1
11?2
2
TABLE 8-2 Principal Mechanical Properties of Structural Quality Sheet, Strip, and Plate Steel
(Continued)
ASTM
designation Material Grade
Minimum
yield
point, ksi
Minimum tensile
strength, ksi
Holt
rolled Cold rolled
Minimum
elongation, %
in 2 in
Bend test,
180
, ratio
of inside
diameter
to
thickness
A572 High-strength, low-alloy columbium-vanadium
steels of structural quality (plates only)
42
50
60
65
42
50
60
65
60
65
75
80
24
21
18
17
‡
‡
‡
‡
A588 High-strength, low-alloy structural steel with 50
ksi minimum yield point to 4 in thick (plates
only)
A
B
C
D
E
F
G
H
J
50
50
50
50
50
50
50
50
50
70
70
70
70
70
70
70
70
70
21
21
21
21
21
21
21
21
21
‡
‡
‡
‡
‡
‡
‡
‡
‡
A715 High-strength, low-alloy hot-rolled steel with improved
formability 50
60
70
80
50
60
70
80
60
70
80
90
HR§ CR§
22 20
22 18
18 16
18 16
1
11?2
A792 Aluminum-zinc alloy coated steel sheet by the
hot-dip process, general requirements
33
37
40
50A
50B
80
33
37
40
50
50
80
45
52
65
82
20
18
16
12
12
12
11?2
2
21?2
—
—
*Varies, see specification. † Not specified or required. ‡ S14 bend test. §HR 
 hot rolled; CR 
 cold rolled.
8.5
A653 Galvanized sheet steel, zinc-coated by the hot-dip
process, structural quality
SQ 33
37
40
50 class 1
80
50 class 2
33
37
40
50
80
45
52
55
65
82
70
20
18
16
12
12
11?2
2
21?2
†
†
†
HSLA
50
60
70
80
50
60
70
80
60
70
80
90
TYP1 TYP2
20 22
16 18
12 14
10 12
A36 Structural steel (plates only) 36 58–80 23 ‡
A242 High-strength, low-alloy structural steel (plates 3?4
in and under)
50 70 † ‡
A283 Low and intermediate tensile strength carbon
steel plates
A
B
C
D
24
27
30
33
45–60
50–65
55–75
60–80
30
28
25
23
A500 Cold-formed welded and seamless carbon steel
structural tubing (round tubing)
A
B
C
D
33
42
46
36
45
58
62
58
25
23
21
23
Cold-formed welded and seamless carbon steel
structural tubing (shaped tubing)
A
B
C
D
39
46
50
36
45
58
62
58
25
23
21
23
A529 Structural steel with 42 ksi minimum yield point
(1?2 in maximum thickness) (plates only)
42
50
42
50
60–85
70–100
22
21
‡
8.6
TABLE 8-2 Principal Mechanical Properties of Structural Quality Sheet, Strip, and Plate Steel
(Continued)
ASTM
designation Material Grade
Minimum
yield
point, ksi
Minimum tensile
strength, ksi
Holt
rolled Cold rolled
Minimum
elongation, %
in 2 in
Bend test,
180
, ratio
of inside
diameter
to
thickness
A572 High-strength, low-alloy columbium-vanadium
steels of structural quality (plates only)
42
50
60
65
42
50
60
65
60
65
75
80
24
21
18
17
‡
‡
‡
‡
A588 High-strength, low-alloy structural steel with 50
ksi minimum yield point to 4 in thick (plates
only)
A
B
C
D
E
F
G
H
J
50
50
50
50
50
50
50
50
50
70
70
70
70
70
70
70
70
70
21
21
21
21
21
21
21
21
21
‡
‡
‡
‡
‡
‡
‡
‡
‡
A715 High-strength, low-alloy hot-rolled steel with improved
formability 50
60
70
80
50
60
70
80
60
70
80
90
HR§ CR§
22 20
22 18
18 16
18 16
1
11?2
A792 Aluminum-zinc alloy coated steel sheet by the
hot-dip process, general requirements
33
37
40
50A
50B
80
33
37
40
50
50
80
45
52
65
82
20
18
16
12
12
12
11?2
2
21?2
—
—
*Varies, see specification. † Not specified or required. ‡ S14 bend test. §HR 
 hot rolled; CR 
 cold rolled.
COLD-FORMED STEEL CONSTRUCTION 8.7
Bars for Structural Applications.’’ It contains requirements for 201, 202, 301, 302,
304, and 316 types of stainless steels. Further information on these steels as well
as steels covered by ASTM A176, A240, and A276 may be obtained from the
American Iron and Steel Institute (AISI).
8.1.4 Coatings
Material for cold-formed shapes may be either black (uncoated), galvanized, or
aluminized. Because of their higher costs, metal-coated steels are used only where
exposure conditions warrant paying more for the increased protection afforded
against corrosion.
Low-carbon sheets suitable for coating with vitreous enamel are frequently used
for facing purposes, but not as a rule to perform load-carrying functions in buildings.
8.1.5 Selection of Grade
The choice of a grade of material, within a given class or specification, usually
depends on the severity of the forming operation required to make the required
shape, strength desired, weldability requirements, and the economics involved.
Grade C of ASTM A611, with a specified minimum yield point of 33 ksi has long
been popular for structural use. Some manufacturers, however, use higher-strength
grades to good advantage.
8.1.6 Gage Numbers
Thickness of cold-formed shapes was formerly expressed as the manufacturers’
standard gage number of the material from which the shapes were formed. Use of
millimeters or decimal parts of an inch, instead of gage numbers, is now the standard
practice. However, for information, the relationships among gage number,
weight, and thickness for uncoated and galvanized sheets are given in Table 8.3 for
even gages.
8.2 UTILIZATION OF COLD WORK OF FORMING
When strength alone, particularly yield strength, is an all-important consideration
in selecting a material or grade for cold-formed shapes (Table 8.2), it is sometimes
possible to take advantage of the strength increase that results from cold working
of material during the forming operation and thus use a lower-strength, more workable,
and possible more economical grade than would otherwise be required. The
increase in cold-work strength is ordinarily most noticeable in relatively stocky,
compact sections produced in thicker steels. Cold-formed chord sections for openweb
steel joists are good examples (Fig. 8.22). Overall average yield strengths of
more than 150% of the minimum specified yield strength of the plain material have
been obtained in such sections.
The strengthening effect of the forming operation varies across the section but
is most pronounced at the bends and corners of a cold-formed section. Accordingly,
8.8 SECTION EIGHT
TABLE 8.3 Gages, Weights, and Thicknesses of Sheets
Steel
manufacturer’s
standard gage
No.
Weight,
psf
Equivalent
sheet
thickness, in*
Galvanized
sheet gage
No.
Weight,
psf
Thickness
equivalent, † in
4 9.3750 0.2242
6 8.1250 0.1943
8 6.8750 0.1644 8 7.03125 0.1681
10 5.6250 0.1345 10 5.78125 0.1382
12 4.3750 0.1046 12 4.53125 0.1084
14 3.1250 0.0747 14 3.28125 0.0785
16 2.5000 0.0598 16 2.65625 0.0635
18 2.0000 0.0478 18 2.15625 0.0516
20 1.5000 0.0359 20 1.65625 0.0396
22 1.2500 0.0299 22 1.40625 0.0336
24 1.0000 0.0239 24 1.15625 0.0276
26 0.7500 0.0179 26 0.90625 0.0217
28 0.6250 0.0149 28 0.78125 0.0187
30 0.5000 0.0120 30 0.65625 0.0157
32 0.40625 0.0097 32 0.56250 0.0134
34 0.34375 0.0082
36 0.28125 0.0067
38 0.25000 0.0060
* Thickness equivalents of steel are based on 0.023912 in / (lb-ft2) (reciprocal of 41.820 psf per inch of
thickness, although the density of steel is ordinarily taken as 489.6 lb / ft3, 0.2833 lb / in3, or 40.80 psf per
inch of thickness). The density is adjusted because sheet weights are calculated for specified widths and
lengths of sheets, with all shearing tolerances on the over side, and also because sheets are somewhate
thicker at the center than at the edges. The adjustment yields a close approximation of the relationship
between weight and thickness. (‘‘Steel Products Manual, Carbon Steel Sheets,’’ American Iron and Steel
Institute.)
†Total thickness, in, including zinc coating. To obtain base metal thickness, deduct 0.0015 in per ounce
coating class, or refer to ASTM A653.
for shapes in which bends and corners constitute a high percentage of the whole
section, cold working increases the overall strength more than for shapes having a
high proportion of thin, wide, flat elements that are not heavily worked in forming.
For the latter type of shapes, the strength of the plain, unformed sheet or strip may
be the controlling factor in the selection of a grade of material.
Full-section tests constitute a relatively simple, straightforward method of determining
as-formed strength. They are particularly applicable to sections that do
not contain any elements that may be subject to local buckling. However, each case
has to be considered individually in determining the extent to which cold forming
will produce an increase in utilizable strength. For further information, refer to the
AISI ‘‘Specification for the Design of Cold-Formed Steel Structural Members’’ and
its ‘‘Commentary,’’ 1996, American Iron and Steel Institute, 1101 17th St., NW,
Washington, DC 20036.
8.3 TYPES OF COLD-FORMED SHAPES
Many cold-formed shapes used for structural purposes are similar in their general
configurations to hot-rolled structural sections. Channels, angles, and zees can be
COLD-FORMED STEEL CONSTRUCTION 8.9
roll-formed in a single operation from one piece of material. I sections are usually
made by welding two channels back to back or by welding two angles to a channel.
All sections of this kind may be made with either plain flanges as in Fig. 8.1a to
d, j, and m or with flanges stiffened by means of lips at outer edges, as in Fig. 8.1e
to h, k, and n.
FIGURE 8.1 Typical cold-formed steel structural
sections
In addition to these sections, which
follow somewhat conventional lines and
have their counterparts in hot-rolled
structural sections, the flexibility of the
forming process makes it relatively easy
to obtain inverted U, or hat-shaped, sections
and open box sections (Fig. 8.1o
to q). These sections are very stiff in a
lateral direction and can be used without
lateral support where other more conventional
types of sections would fail
because of lateral instability.
Other special shapes are illustrated in
Fig. 8.2. Some of these are nonstructural
in nature; others are used for specialpurpose
structural members. Figure 8.3
shows a few cold-formed stainless steel
sections.
An important characteristic of coldformed
shapes is that the thickness of
section is substantially uniform. (A
slight reduction in thickness may occur
at bends, but that may be ignored for
computing weights and section properties.)
This means that, for a specified
thickness, the amount of flange material
in a section, such as a channel, is almost
entirely a function of the width of the
section, except for shapes where additional
flange area is obtained by doubling
the material back on itself.
Another distinguishing feature of
cold-formed sections is that the corners
are rounded on both the inside and the
outside of the bend, since the shapes are
formed by bending flat material.
Sharp corners, such as can be obtained
with hot-rolled structural channels,
angles, and zees, cannot be obtained
in cold-formed shapes by simple
bending, although they can be achieved
in a coining or upsetting operation. This,
however, is not customary in the manufacture of structural cold-formed sections;
and in proportioning such sections, the inside radius of bends should never be less,
and should preferably be 33 to 100% greater, than specified for the relatively narrow
ASTM bend-test specimens. Deck and panel sections, such as are used for floors,
roofs, and walls, are as a rule considerably wider, relative to their depth, than are
the structural framing members shown in Figs. 8.1 to 8.3.
8.10 SECTION EIGHT
FIGURE 8.2 Miscellaneous cold-formed shapes. (Bethlehem Steel Corp.)
DESIGN PRINCIPLES FOR COLD-FORMED
STEEL SHAPES
The structural behavior of cold-formed shapes follows the same laws of structural
mechanics as does that of conventional structural-steel shapes and plates. Thus,
design procedures commonly used in the selection of hot-rolled shapes are generally
applicable to cold-formed sections. Although only a portion of a section, in some
cases, may be considered structurally effective, computation of the structural properties
of the effective option follows conventional procedure.
8.4 SOME BASIC CONCEPTS OF COLD-FORMED
STEEL DESIGN
The uniform thickness of most cold-formed sections, and the fact that the widths
of the various elements composing such a section are usually large relative to the
COLD-FORMED STEEL CONSTRUCTION 8.11
FIGURE 8.3 Cold-formed stainless steel sections. (The
International Nickel Co., Inc.)
thickness, make it possible to consider, in computing structural properties (moment
of inertia, section modulus, etc.) that such properties vary directly as the first power
of the thickness. So, in most cases, section properties can be approximated by first
assuming that the section is made up of a series of line elements, omitting the
thickness dimension. Then, final values can be obtained by multiplying the lineelement
result by the thickness.
With this method, the final multiplier is always the first power of the thickness,
and first-power quantities such as radius of gyration and those locating the centroid
of the section do not involve the thickness dimension. The assumption that the area,
moment of inertia, and section modulus vary directly as the first power of the
thickness is particularly useful in determining the required thickness of a section
after the widths of the various elements composing the section have been fixed.
This method is sufficiently accurate for most practical purposes. It is advisable,
however, particularly when a section is fairly thick compared to the widths of the
elements, to check the final result through an exact method of computation.
Properties of thin elements are given in Table 8.4.
Various Failure Modes. One of the distinguishing characteristics of lightweight
cold-formed sections is that they are usually composed of elements that are relatively
wide and thin. As a result, attention must be given to certain modes of
structural behavior ordinarily neglected in dealing with heavier sections, such as
hot-rolled structural shapes.
TABLE 8.4 Properties of Area and Line Elements
COLD-FORMED STEEL CONSTRUCTION 8.13
When thin, wide elements are in axial compression, as in the case of a beam
flange or a part of a column, they tend to buckle elastically at stresses below the
yield point of the steel. This local buckling is not to be confused with the general
buckling that occurs in the failure of a long column or of a laterally unsupported
beam. Rather, local buckling represents failure of a single element of a section, and
conceivably may be relatively unrelated to buckling of the entire member. In addition,
there are other factors, such as shear lag, which gives rise to nonuniform
stress distribution; torsional instability, which may be more pronounced in thin
sections than in thicker ones and requires more attention to bracing; and other
related structural phenomena customarily ignored in conventional structural design
that sometimes must be considered with thin material. Means of taking care of
these factors in ordinary structural design are described in the ‘‘Specification for
the Design of Cold-Formed Steel Structural Members.’’
Design Bases. The allowable stress design method (ASD) is used currently in
structural design of cold-formed steel structural members and described in the rest
of this section. In addition, the load and resistance factor design method (LRFD)
can also be used for design. Both methods are included in the 1996 edition of the
AISI ‘‘Specification for the Design of Cold-Formed Steel Structural Members.’’
However, these two methods cannot be mixed in designing the various cold-formed
steel components of a structure.
In the allowable stress design method, the required strengths (bending moments,
shear forces, axial loads, etc.) in structural members are computed by structural
analysis for the working or service loads using the load combinations given in the
AISI Specification. These required strengths are not to exceed the allowable design
strengths as follows:
R  R / n
where R 
 required strength
Rn 
 nominal strength specified in the AISI Specification
 
 safety factor specified in the AISI Specification
Rn / 
 allowable design strength
Unlike the allowable stress design method, the LRFD method uses multiple load
factors and resistance factors to provide a refinement in the design that can account
for different degrees of the uncertainties and variabilities of analysis, design, loading,
material properties, and fabrication. In this method, the required strengths are
not to exceed the design strengths as follows:
R  R u n
where Ru 
 
 iQi 
 requires strength
Rn 
 nominal strength specified in the AISI Specification

 resistance factor specified in the AISI Specification
i 
 load factors
Qi 
 load effects
Rn 
 design strength
The load factors and load combinations are also provided in Chapter A of the AISI
Specification for the design of different types of cold-formed steel structural members
and connections. For design examples, see AISI ‘‘Cold-Formed Steel Design
Manual,’’ 1996 edition.
8.14 SECTION EIGHT
The Committee on Specifications of the American Iron and Steel Institute has
strived to put all formulas in the ‘‘Specification for the Design of Cold-Formed
Steel Structural Members’’ on nondimensional bases so that their use with English
or SI units is rigorous and convertible.
(AISI ‘‘Cold-Formed Steel Design Manual,’’ American Iron and Steel Institute,
1101 17th St., NW, Washington, DC 20036.)
8.5 STRUCTURAL BEHAVIOR OF FLAT
COMPRESSION ELEMENTS
In buckling of flat, thin compression elements in beams and columns, the flat-width
ratio w/ t is an important factor. It is the ratio of width w of a single flat element,
exclusive of any edge fillets, to the thickness t of the element (Fig. 8.4). Local
buckling of elements with large w/ t may be resisted with stiffeners or bracing.
FIGURE 8.4 Compression elements.
Flat compression elements of coldformed
structural members are accordingly
classified as stiffened or unstiffened.
Stiffened compression elements
have both edges of the element parallel
to the direction of stress stiffened by a
web, flange, or stiffening lip. If the sections
in Fig. 8.1a to n are used as compression
members, the webs are considered
as stiffened compression elements.
The wide, lipless flange elements and
the lips that stiffen the outer edges, however,
are unstiffened elements. Any section
can be broken down into a combination
of stiffened and unstiffened elements.
Only part of an element may be considered effective under compression in computation
of net section properties. The portion that may be treated as effective
depends on w/ t for the element.
The cold-formed structural cross sections shown in Fig. 8.5 indicate that the
effective portions b of the width of a stiffened compression element are considered
to be divided into two parts, located next to the two edge stiffeners of that element.
(A stiffener may be a web, another stiffened element, or a lip in beams. Lips in
these examples are presumed to be fully effective.) In computation of net section
properties, only the effective portions of stiffened compression elements are used
and the ineffective portions are disregarded. For beams, because flange elements
subjected to uniform compression may not be fully effective, reduced section properties,
such as moments of inertia and section moduli, must be used. For computation
of the effective widths of webs, see Art. 8.7. Effective areas of column cross
sections are based on full cross-sectional areas less all ineffective portions for use
in the formula for axially loaded columns, Eq. (8.22), in Art. 8.13.
The critical load, Pcr , kips, for elastic flexural buckling of a bar of uniform cross
section, concentrically end loaded as a column, is given by the Euler formula:
2 2 P 
  EI/L (8.1) cr
COLD-FORMED STEEL CONSTRUCTION 8.15
FIGURE 8.5 Effective width of stiffened compression elements with
stiffening lips assumed to be fully effective.
where E 
 modulus of elasticity, 29,500 ksi for steel
I 
 moment of inertia of bar cross section, in4
L 
 column length of bar, in
Bryan, in 1891, determined the critical buckling stress, ?cr , ksi, for a thin rectangular
plate compressed between two opposite edges with the other two edges
supported, to be given by
2 2 2 ? 
 k E(t /w) /12(1  	 ) (8.2) cr
where k 
 a coefficient depending on edge-support restraint
w 
 width of late, in
t 
 thickness of plate, in
	
 Poisson’s ratio
8.16 SECTION EIGHT
In 1932, von Karman gave the following formula for determining the effective
width-to-thickness ratio b/ t at yielding along the simply supported edges of a thin
rectangular plate subjected to compression between the other two opposite edges:
b/ t 
 1.9tE/? (8.3) y
where b 
 effective width for a plate of width w, in, and ?y 
 yield strength of
plate material, ksi.
After extensive tests of cold-formed steel structural sections, Winter, in 1947,
recommended that von Karman’s formula be modified to
0.475E/?max b/ t 
 1.9tE/? 1  (8.4)   max w/ t
where ? 
 maximum stress at simply supported edges, ksi. This formula for max
determining the effective widths of stiffened, thin, flat elements was first used in
the AISI ‘‘Light-Gage Steel Design Manual,’’ 1949. Subsequent studies showed that
the factor 0.475 was unnecessarily conservative and that 0.415 was more appropriate.
It was used in AISI specifications between 1968 and 1980 to evaluate postbuckling
strength of thin, flat elements.
Until 1986, all AISI specifications based strength of thin, flat elements stiffened
along one edge on buckling stress. In contrast, effective width was used for thin,
flat elements stiffened along both edges. This treatment changed after Pekoz in
1986 presented a unified approach using effective width as the basis of design for
both stiffened and unstiffened elements and even for web elements subjected to
stress gradients. Pekoz proposed the following three equations to generalize Eq.
(8.4) with a factor of 0.415:

 [1.052(w/ t)?/E] /k (8.5)
where k 
 4.00 for stiffened elements

 0.43 for unstiffened elements
? 
 stress in the compression elements of the section computed on the basis
of the design width, in
w 
 flat width of the element exclusive of radii, in
t 
 base thickness of element, in

 a slenderness factor
The effective width is computed from
b 
 w  0.673 (8.6a)
b 
 	w  0.673 (8.6b)
where 	 is a reduction factor to be computed from
1  0.22/ 
	
 (8.7)

These equations were adopted in the AISI ‘‘Specification for the Design of Cold-
Formed Steel Structural Members,’’ 1986 and are retained in the 1996 edition of
the AISI Specifications. See also Arts. 8.6 to 8.8.
COLD-FORMED STEEL CONSTRUCTION 8.17
8.6 UNSTIFFENED COLD-FORMED ELEMENTS
SUBJECT TO LOCAL BUCKLING
As indicated in Art. 8.5, the effective width of an unstiffened element in compression
may be computed from Eqs. (8.5) to (8.7). By definition, unstiffened elements
have only one edge in the direction of compression stress supported by a web or
stiffened element while the other edge has no auxiliary support (Fig. 8.6a). The
coefficient k in Eq. (8.5) is 0.43 for such an element. When the flat-width-tothickness
ratio does not exceed 72/ , where ? 
 compressive stress, ksi, an ?
unstiffened element is fully effective and b 
 w. Generally, however, Eq. (8.5)
becomes
1.052(w/ t)?/E

 
0.0093(w/ t)? (8.8)
0.43
where E 
 29,500 ksi for steel. Substitution of  in Eq. (8.7) yields b/w 
 	. Fig.
(8.7a) shows a nest of curves for the relationship of b/ t to w/ t for unstiffened
elements for w/ t between 0 and 60 with ? between 15 and 90 ksi.
In beam deflection determinations requiring use of the moment of inertia of the
cross section, the allowable stress ? is used to calculate the effective width of an
unstiffened element in a cold-formed steel member loaded as a beam. However, in
beam strength determinations requiring use of the section modulus of the cross
section, 1.67? is the stress to be used in Eq. (8.8) to calculate the effective width
of the unstiffened element and provide an adequate margin of safety.
In determination of safe loads for a cold-formed steel section used as a column,
the effective width for an unstiffened element should be determined for a nominal
buckling stress, Fn, to ensure an adequate margin of safety.
8.7 STIFFENED COLD-FORMED ELEMENTS
SUBJECT TO LOCAL BUCKLING
As indicted in 8.5, the effective width of a stiffened element in compression may
be computed from Eqs. (8.5) to (8.7). By definition, stiffened elements have one
edge in the direction of compression stress supported by a web or stiffened element
and the other edge also supported by a qualified stiffener (Fig. 8.6b). The coefficient
k in Eq. (8.5) is 4.00 for such an element. When the flat-width-to-thickness ratio
does not exceed 220/ , where ? 
 compressive stress, ksi, computed on the basis ?
of the effective section, a stiffened element is fully effective and b 
 w. Generally,
however, Eq. (8.5) becomes
1.052(w/ t)?/E

 
0.0031(w/ t)? (8.9)
4
where E 
 29,500 ksi for steel. Substitution of  in Eq. (8.7) yields b/w 
 	.
Moreover, when   0.673, b 
 w and when   0.673, b 
 	w. Figure 8.7b
shows a nest of curves for the relationship of b/ t to w/ t for stiffened elements for
w/ t between 0 and 500 with ? between 10 and 90 ksi.
In beam deflection determinations requiring use of the moment of inertia of the
cross section, the allowable stress ? is used to calculate the effective width of a
8.18
FIGURE 8.6 Schematic diagrams showing effective widths for unstiffened and stiffened elements, intermediate
stiffeners, beam webs, and edge stiffeners.
COLD-FORMED STEEL CONSTRUCTION 8.19
FIGURE 8.7 Curves relate effective-width ratio b / t to flat-width ratio w/ t at various stresses ?
for (a) unstiffened elements and (b) stiffened elements.
stiffened element in a cold-formed steel member loaded as a beam. However, in
beam strength determinations requiring use of the section modulus of the cross
section, 1.67? is the stress to be used in Eq. (8.9) to calculate the effective width
of the stiffened element and provide a margin of safety.
In determination of the safe loads for a cold-formed steel section used as a
column, effective width for a stiffened element must be determined for a nominal
buckling stress, Fn, to ensure an adequate margin of safety.
Since effective widths are proportional to , the effective width of a stiffened k
element is 
 3.05 times as large as that of an unstiffened element at 4.00/0.43
applicable combinations of ? and w/ t. Thus, stiffened elements offer greater
strength and economy.
Single Intermediate Stiffener. For uniformly compressed stiffened elements with
a single intermediate stiffener, as shown in Fig. 8.6c, calculations for required moment
of inertia Ia of the stiffener are based on a parameter S.
S 
 1.28E/? (8.10)
For Case I, S bo / t, where bo 
 flat width, in, including the stiffener. Ia 
 0
and no stiffener is required.
For Case II, S  bo / t  3S. The required moment of inertia is determined from
4 I / t 
 [50(b / t) /S]  50 (8.11a) a o
For Case III, bo / t 3S. The required moment of inertia is determined from
4 I / t 
 [128(b / t) /S]  285 (8.11b) a o
8.20 SECTION EIGHT
Webs Subjected to Stress Gradients. Effective widths also are applicable to stiffened
elements subject to stress gradients in compression, such as in the webs of
beams. Figure 8.6d illustrates the application. The effective widths b1 and b2 are
determined with the use of the following equations:
b 
 b / (3  
) (8.12) 1 e
where 

 ?2/?1
?1 
 stress, ksi, in compression flange (Fig. 8.6d)
?2 
 stress, ksi, in opposite flange (Fig. 8.6d)
be 
 effective width b determined from Eqs. (8.5) to (8.7) with ?1 substituted
for ? and with k calculated from Eq. (8.14)
Stress ?2 may be tensile (negative) or compressive (positive). When both ?1 and ?2
are compressive, ?1 ?2.
1 b 
 ?2b for 
 0.236 (8.13a) 2 e
where b1  b2 should not exceed the depth of the compression portion of the web
calculated for the effective cross section.
b 
 b  b for 
 0.236 (8.13b) 2 e 1
3 k 
 4  2(1  
)  2(1  
) (8.14)
Uniformly Compressed Elements with Edge Stiffener. While a slanted lip, as
depicted in Fig. 8.6e, may be used as an edge stiffener for a cold-formed steel
section, calculation of stresses for such a section is complex. (See AISI ‘‘Specifi-
cation for the Design of Cold-Formed Steel Structural Members.’’) Consequently,
the following is primarily applicable to 90
 lips.
Calculation of the required moment of inertia, Ia, falls into one of three cases:
For Case I, w/ t  S/3. b 
 w, where b is the effective width, and no edge
support is needed. S is defined by Eq. (8.10) and is the maximum w/ t for full
effectiveness of the flat width without auxiliary support.
For Case II, S/3  w/ t  S. The required moment of inertia of the lip is
determined from
4 3 I / t 
 399{[(w/ t) /S]  k /4} (8.15) a u
where ku 
 0.43. When S/3 is substituted for w/ t in Eq. (8.15), Ia 
 0 and no
support is needed at the edge for which a lip is being considered (see Case I).
When w/ t 
 S, a stiffening lip would be required to have a depth-thickness ratio
d/ t of 11.3. The maximum stress in a lip with this value of d/ t, however, could be
only 40.6 ksi, which corresponds to a maximum allowable stress of 24.3 ksi in
bending and 22.6 ksi in compression, with safety factors of 1.67 and 1.80, respectively.
For Case III, w/ t S. The required moment of inertia of the edge stiffener is
determined from
COLD-FORMED STEEL CONSTRUCTION 8.21
8.8 APPLICATION OF EFFECTIVE WIDTHS
The curves of Fig. 8.7 were plotted from values of Eqs. (8.8) and (8.9). They may
be used to determine b/ t for different values of w/ t and unit stresses ?. The effective
width b is dependent on the actual stress ?, which in turn is determined by reducedsection
properties that are a function of effective width. Employment of successive
approximations consequently may be necessary in using these equations and curves.
A direct solution for the correct value of b/ t can be obtained from the formulas,
however, when ? is known or is held to a specified maximum allowable value for
deflection determination (20 ksi for Fy 
 33 ksi, for example). This is true, though,
only when compression controls; for example, for symmetrical channels and Z and
I sections used as flexural members bending about their major axis (Fig. 8.1e, f, k
and n) or for unsymmetrical channels and Z and I sections with neutral axis closer
to the tension flange than to the compression flange. If w/ t of the compression
flange does not exceed about 60, little error will result in assuming that ? 
 0.60 
33 
 20 ksi for Fy 
 33 ksi. This is so even though the neutral axis is above the
geometric centerline. For wide, inverted, pan-shaped sections, such as deck and
panel sections, a somewhat more accurate determination using successive approximations
will prove necessary.
For computation of moment of inertia for deflection or stiffness calculations,
properties of the full unreduced section can be used without significant error when
w/ t of the compression elements does not exceed 60. For greater accuracy, use Eqs.
(8.8) and (8.9) to obtain appropriate effective widths.
Example. As an example of effective-width determination, consider the hat section
of Fig. 8.8. The section is to be made of steel with a specified minimum yield
strength Fy 
 33 ksi. It is to be used as a simply supported beam with the top
flange in compression, at a basic working stress of 20 ksi. Safe load-carrying ca-
FIGURE 8.8 Hat section.
pacity is to be computed; so ? 
 20  1.67 
 33 ksi
is used to obtain b/ t.
The top flange is a stiffened compression element
with 3-in flat width. If the thickness is 1?16 in, then the
flat-width-thickness ratio (w/ t) is 48 (greater than w/ t

 220/ 
 38), stiffening is required, and Eq. (8.9) 33
applies. For w/ t 
 48 and ? 
 33 ksi, Eq. (8.9) gives
b/ t 
 41. Thus, with b/w 
 41/ 48, only 85% of the
top-flange flat width can be considered effective. The
neutral axis will lie below the horizontal center line,
and compression will control. In this case, the assumption that ? 
 33 ksi, made
at the start, controls maximum stress, and b/ t can be determined directly from Eq.
(8.9) without successive approximations. However, for a wide hat section in which
the horizontal axis is nearer the compression than the tension flange, stress in the
tension flange controls, and successive approximations are required for the determination
of unit stress and effective width of the compression flange.
(‘‘Cold-Formed Steel Design Manual,’’ American Iron and Steel Institute, 1101
17th St., NW, Washington, DC 20036.)
8.22 SECTION EIGHT
8.9 MAXIMUM FLAT-WIDTH RATIOS OF
COLD-FORMED SHAPES
When the flat-width-thickness ratio (w/ t) exceeds about 30 for an unstiffened element
and about 250 for a stiffened element, noticeable buckling of the element
may develop at relatively low stresses. Present practice is to permit buckles to
develop in the sheet and to take advantage of what is known as post-buckling
strength of the section. The effective-width formulas, Eqs. (8.5) to (8.7), are based
on this practice. To avoid intolerable deformations, however, w/ t, disregarding intermediate
stiffeners and based on the actual thickness t of the element, should not
exceed the following:
Stiffened compression element having one longitudinal edge connected to 60
a web or flange, the other to a simple lip
Stiffened compression element with both longitudinal edges connected to 500
a web or flange element, such as in a hat, U, or box-type section
Unstiffened compression element 60
8.10 UNIT STRESSES FOR
COLD-FORMED STEEL
For sheet and strip of A611, Grade C steel with a specified minimum yield strength
Fy 
 33 ksi, use a basic allowable stress ? 
 20 ksi in tension and bending. For
other strengths of steels, ? is determined by taking 60% of the specified minimum
yield strength Fy. (This procedure implies a safety factor of 1.67.) However, an
increase of 331?3% in allowable stress is customary for combined wind or earthquake
forces with other loads. It should be noted that the 1996 AISI specification uses
‘‘strength’’ (moment, force, etc.) rather than unit stress.
8.11 LATERALLY UNSUPPORTED
COLD-FORMED BEAMS
If cold-formed steel sections are not laterally supported at frequent intervals, the
allowable unit stress must be reduced to avoid failure from lateral instability. The
amount of reduction depends on the shape and proportions of the section and the
spacing of lateral supports. (See AISI ‘‘Specification for the Design of Cold-Formed
Steel Structural Members.’’)
Because of the torsional flexibility of lightweight channel and Z sections, their
use as beams without close lateral support is not recommended. When a compression
flange is fully connected to a deck or sheathing material, the flange is considered
braced for its full length and bracing of the other flange may not be needed
to prevent buckling of the beam. This depends on the collateral material and its
connections, dimensions of the member, and the span.
When laterally unsupported beams must be used, or where lateral buckling of a
flexural member is likely to occur, consideration should be given to the use of
relatively bulky sections that have two webs, such as hat or box sections (Fig. 8.1o,
p, and q).
COLD-FORMED STEEL CONSTRUCTION 8.23
8.12 ALLOWABLE SHEAR STRENGTH IN WEBS
The shear V, kips, at any section should not exceed the allowable shear Va, kips,
calculated as follows:
For h/ t  0.96k E/F , v y
V 
 0.4F ht (8.17) a y
For 0.96  h/ t  1.415 k E/F k E/F , v y v y
2 V 
 0.38t k EF (8.18) a v y
For h/ t  1.415k E/F , v y
3 V 
 0.54k Et /h (8.19) a v
where t 
 web thickness, in
h 
 depth of the flat portion of the web measured along the plane of the
web, in
E 
 modulus of elasticity of the steel 
 29,500 ksi
k 
 v shear buckling coefficient 
 5.34 for unreinforced webs for which
(h/ t) does not exceed 200 max
Fy 
 specified yield stress of the steel, ksi
For design of reinforced webs, especially when h/ t exceeds 200, see AISI ‘‘Specification
for the Design of Cold-Formed Steel Structural Members.’’
For a web consisting of two or more sheets, each sheet should be considered as
a separate element carrying its share of the shear.
For beams with unreinforced webs, the moment M and shear V should satisfy
the following interaction equation:
2 2 (M/M )  (V/V )  1.0 (8.20) axo a
where M 
 axo allowable moment about the centroidal axis, in-kips, when bending
alone is present
Va 
 allowable shear, kips, when shear alone exists
M 
 applied bending moment, in-kips
V 
 actual shear, kips
In addition to above, web crippling should also be checked.
8.13 CONCENTRICALLY LOADED
COMPRESSION MEMBERS
The following formulas apply to members in which the resultant of all loads acting
on a member is an axial load passing through the centroid of the effective section
(calculated at the nominal buckling stress Fn, ksi). The axial load should not exceed
Pa, kips, calculated from
P 
 P / (8.21) a n c
8.24 SECTION EIGHT
FIGURE 8.9 Ratio of nominal column buckling stress to yield strength.
P 
 A F (8.22) n e n
where Pn 
 ultimate compression load, kips
c 
 factor of safety for axial compression, 1.80
Ae 
 effective area at stress Fn, in2
The magnitude of Fn is determined as follows, ksi:
For c  1.5,
2 c F 
 (0.658 ) F (8.23a) n y
For c  1.5,
0.877
F 
 F (8.23b)   n y 2 c
where c 

Fy 	Fe
Fy 
 yield stress of the steel, ksi
Fe 
 the least of the elastic flexural, torsional and torsional-flexural buckling
stress
Figure 8.9 shows the ratio between the column buckling stress Fn and the yield
strength Fy.
For elastic flexural behavior,
2  E
F 
 (8.24) e 2 (KL/ r)
COLD-FORMED STEEL CONSTRUCTION 8.25
where K 
 effective length factor
L 
 unbraced length of member, in
r 
 radius of gyration of full, unreduced cross section, in
E 
 modulus of elasticity of the steel, ksi
Moreover, angle sections should be designed for the applied axial load P acting
simultaneously with a moment equal to PL/1000 applied about the minor principal
axis and causing compression in the tips of the angle legs.
The slenderness ratio KL/ r of all compression members preferably should not
exceed 200, except that during construction only, KL/ r preferably should not exceed
300.
For treatment of sections that may be subject to torsional or torsional-flexural
buckling, refer to AISI ‘‘Specification for the Design of Cold-Formed Steel Structural
Members,’’ American Iron and Steel Institute, 1101 17th St., NW, Washington,
DC 20036.
8.14 COMBINED AXIAL AND
BENDING STRESSES
Combined axial and bending stresses in cold-formed sections can be handled the
same way as for structural steel. The interaction criterion to be used is given in the
AISI ‘‘Specification for the Design of Cold-Formed Structural Members.’’
JOINING OF COLD-FORMED STEEL
Cold-formed members may be assembled into desired shapes or spliced or joined
to other members with any of various types of fasteners. For the purpose, welds,
bolts, and screws are most frequently used, but other types, such as rivets, studs,
and metal stitching, can also be used.
8.15 WELDING OF COLD-FORMED STEEL
Electric currents are generally used in either of two ways to joint cold-formed steel
components, with electric-arc welding or resistance welding. The former method is
described in Art. 8.16 and the latter in Art. 8.17.
Welding offers important advantages to fabricators and erectors in joining steel
structural components. Welded joints make possible continuous structures, with
economy and speed in fabrication; 100% joint efficiencies are possible.
Conversion to welding of joints initially designed for mechanical fasteners is
poor practice. Joints should be specifically designed for welding, to take full advantage
of possible savings. Important considerations include the following: The
overall assembly should be weldable; welds should be located where notch effects
are minimal; the final appearance should not suffer from unsightly welds; and welding
should not be expected to correct poor fit-up.
Steels bearing protective coatings require special consideration. Surfaces precoated
with paint or plastic are damaged by welding. Coatings may adversely affect
8.26 SECTION EIGHT
FIGURE 8.10 Types of sheet-steel welds: (a) square-groove weld: (b) arc spot weld (round puddle
weld); (c) arc seam weld (oblong puddle weld); (d ) fillet welds; (e) flare bevel-groove weld; ( ? )
flare V-groove weld.
weld quality. Metal-coated steels, such as galvanized (zinc-coated), aluminized, and
terne-coated (lead-tin alloy), however may be successfully welded using procedures
tailored for the steel and its coating.
Generally, steel to be welded should be clean and free of contaminants such as
oil, grease, paints, and scale. Paint should be applied only after the welding process.
(See ‘‘Welding Handbook,’’ American Welding Society, 550 NW LeJeune Rd.,
Miami, FL 33126 and O. W. Blodgett, ‘‘Design of Weldments,’’ James F. Lincoln
Welding Foundation, Cleveland, OH 44117.)
8.16 ARC WELDING OF COLD-FORMED STEEL
Arc welding may be done in the shop or in the field. The basic sheet-steel weld
types are shown in Fig. 8.10. Factors favoring arc welding are portability and versatility
of equipment as well as freedom in joint design. Only one side of a joint
need be accessible, and overlap of parts is not required if joint fit-up is good.
8.16.1 Helpful Hints for Welding
Distortion may occur with lightweight steel weldments, but it can be minimized by
avoiding overwelding. Weld sizes should be matched with service requirements.
Always design welded joints to minimize shrinking, warping, and twisting. Jigs
and fixtures for holding lightweight work during welding should be used to control
distortion. Directions and amounts of distortion can be predicted and sometimes
counteracted by preangling the parts. Discrete selection of weld sequence can also
be used to control distortion.
Groove welds (made by butting sheet edges together, Fig. 8.10a) can be designed
for 100% joint efficiency. Calculation of design stress is usually unnecessary if the
weld penetrates 100% of the section.
COLD-FORMED STEEL CONSTRUCTION 8.27
Stresses in fillet welds should be considered as shear on the throat for any
direction of applied stress. The dimension of the throat is calculated as 0.707 times
the length of the shorter leg of the weld. For example, a 12-in-long, 1?4-in-fillet
weld has a leg dimension of 1?4 in, a throat of 0.177 in, and an equivalent area of
2.12 in2. For all grades of steel, fillet and plug welds should be proportioned according
to the AISI specification for the allowable stress design method; the safety
factor is 2.50, unless otherwise noted.
8.16.2 Types of Arc Welding
Shielded metal arc welding, also called manual stick electrode, is the most common
arc-welding process because of its versatility. The method, however, requires skilled
operators. The welds can be made in any position, but vertical and overhead welding
should be avoided when possible.
Gas metal arc welding uses special equipment to feed a continuous spool of
bare or flux-cored wire into the arc. A shielding gas such as argon or carbon dioxide
is used to protect the arc zone from the contaminating effects of the atmosphere.
The process is relatively fast, and close control can be maintained over the deposit.
The process is not applicable to materials 1?32 in thick but is extensively used for
thicker steels.
Gas tungsten arc welding operates by maintaining an arc between a nonconsumable
tungsten electrode and the work. Filler metal may or may not be added. Close
control over the weld can be maintained. This process is not widely used for highproduction
fabrication, except in specialized applications, because of higher cost.
One form of spot welding is an adaptation of gas metal arc welding wherein a
special welding torch and automatic timer are employed. The welding torch is
positioned on the work and a weld is deposited by burning through the top layer
of the lap joint. The filler wire provides sufficient metal to fill the hole, thereby
fusing together the two parts. Access to only one side of the joint is necessary.
Field welding by unskilled operators is feasible. This makes the process advantageous.
Another form of arc spot welding utilizes gas tungsten arc welding. The heat of
the arc melts a spot through one of the sheets and partly through the second. When
the arc is cut off, the pieces fuse. No filler metal is added.
Design of arc-welded joints of sheet steel is also treated in the AmericanWelding
Society ‘‘Specification for Welding Sheet Steel in Structures,’’ AWS D1.3.
8.16.3 Groove Welds in Butt Joints
The maximum load for a groove weld in a butt joint, welded from one or both
sides, should be determined on the basis of the lower-strength base steel in the
connection, provided that an effective throat equal to or greater than the thickness
of the material is consistently obtained.
8.16.4 Arc Spot Welds
Arc spot welds (Fig. 8.10b), also known as puddle welds, are permitted for welding
sheet steel to thicker supporting members in the flat position. Such welds, which
result when coalescence proceeds from the surface of one sheet into one or more
8.28 SECTION EIGHT
other sheets of a lapped joint without formation of a hole, should not be made on
steel where the thinnest connected part is more than 0.15 in thick, or through a
combination of steel sheets having a total thickness exceeding 0.15 in. Arc spot
welds are specified by minimum effective diameter of fused area, de. Minimum
effective allowable diameter is 3?8 in. The nominal shear load Pn, kips, on each arc
spot weld between sheet or between sheets and a supporting member should not
exceed the smaller of the values given by Eqs. (8.25) to (8.28).
2 P 
 0.589d F (8.25) n e xx
For da / t  0.815 E/F , u
P 
 2.20td F (8.26) n a u
For 0.815  da / t  1.397 E/F E/F , u u
5.59E/Fu P 
 0.280 1  td F (8.27)   n au d / t a
For da / t 1.397 , E/Fu
P 
 1.40td F (8.28) n a u
where da 
 average diameter, in, of the arc spot weld at midthickness of sheet

 d  t for a single sheet

 d  2t for multiple sheets (not more than four lapped sheets over a
supporting member)
d 
 visible diameter of outer surface of arc spot weld, in
de 
 effective diameter of fused area, in

 0.7d  1.5t  0.55d
t 
 total combined base steel thickness, in (exclusive of coatings) of sheets
involved in shear transfer
Fxx 
 stress-level designation in AWS electrode classification, ksi
Fu 
 tensile strength of the base steel as specified, ksi
The distance measured in the line of force from the centerline of a weld to the
nearest edge of an adjacent weld or to the end of the connected part toward which
the force is directed should be at least e , in, as given by min
e 
 e (8.29) min e
where e 
 P/ (Fu t)
e 
 factor of safety for sheet tearing

 2.0 when Fu /F 1.08 sy

 2.22 when Fu /Fsy  1.08
P 
 force transmitted by weld, kips
Fsy 
 yield strength of sheet steel, ksi, as specified
t 
 thickness of thinnest connected sheet, in
In addition, the distance from the centerline of any weld to the end or boundary
of the connected member should be at least 1.5d. In no case should the clear
distance between welds and the end of the member be less than d.
COLD-FORMED STEEL CONSTRUCTION 8.29
The nominal tension load Pn, kips, on an arc spot weld between a sheet and a
supporting member should be computed as the smaller of either:
2 P 
 0.785d F (8.30a) n e xx
or either:
For Fu /E  0.00187
P 
 [6.59  3150(F /E)]td F  1.46td F (8.30b) n u a u a u
For Fu /E 0.00187
P 
 0.70td F n a u
(8.30c)
The following limitations also apply: emin d, Fxx 60 ksi, Fu  82 ksi, and t 
0.028 in.
As for arc spot welds (Art. 8.16.4), if measurements indicate that a given weld
procedure will consistently give larger diameters da or de, as applicable, the larger
diameter may be used to calculate the maximum allowable load, if that procedure
will be used.
8.16.5 Arc Seam Welds
These are basically the same as arc spot welds but are made linearly without slots
in the sheets (Fig. 8.10c). Arc seam welds apply to the following types of joints:
1. Sheet to a thicker supporting member in the flat position
2. Sheet to sheet in the horizontal or flat position
The shear load Pn, kips, on an arc seam weld should not exceed the values given
by either Eq. (8.31) or (8.32).
2 de P
 Ld 0.75F (8.31)   n e xx 4
p 
 2.5tF (0.25L  0.96d ) (8.32) n u a
where da 
 average width, in, of arc seam weld

 d  t for a single sheet

 d  2t for a double sheet
d 
 width, in, of arc seam weld
L 
 length, in, of weld not including the circular ends (in computations, L
should not exceed 3d)
de 
 effective width, in, of weld at fused surfaces

 0.7d  1.5t
Fu and Fxx are defined as for arc spot welds (Art. 8.16.4). Minimum edge distances
also are defined as for arc spot welds.
If measurements indicate that a given weld procedure will consistently give a
larger effective width de or larger average diameter da, as applicable, these values
8.30 SECTION EIGHT
may be used to calculate the maximum allowable load on an arc seam weld, if that
welding procedure will actually be used.
8.16.6 Fillet Welds
These are made along the edges of sheets in lapped or T joints (Fig. 8.10d). The
fillet welds may be made in any position and either sheet to sheet or sheet to thicker
steel member.
The shear load Pn, kips, on a fillet weld in lapped or T joints should not exceed
the value of Pn computed from Eqs. (8.33) to (8.34).
For longitudinal loading along the weld:
P 
 (1  0.01L/ t)tLF L/ t  25 (8.33) n u
P 
 0.75tLF L/ t 25 (8.34) n u
where t 
 smaller thickness of sheets being welded, in
L 
 length, in, of the fillet weld
Fu 
 specified tensile strength of base steel, ksi
For loading transverse to the weld:
P 
 tLF (8.35) n u
For t  0.15 in,
P 
 0.75t LF (8.36) n w xx
where Fxx 
 stress-level designation in AWS electrode classification, ksi
tw 
 effective throat of weld, in

 0.707 times the smaller of the weld-leg lengths
8.16.7 Flare Groove Welds
These are made on the outsides of curved edges of bends in cold-formed shapes
(Fig. 8.10e and ?). The welds may be made in any position to join:
1. Sheet to sheet for flare V-groove welds
2. Sheet to sheet for flare bevel-groove welds
3. Sheet to thicker steel member for flare bevel-groove welds.
The shear load Pn, kips, on a weld is governed by the thickness t, in, of the
sheet adjacent to the weld. The load should not exceed the values of Pn given by
Eqs. (8.37) to (8.40).
For flare bevel-groove welds subject to transverse loading,
P 
 0.833tLF (8.37) n u
where L 
 length, in, of the weld and Fu 
 specified tensile strength, ksi, of the
base steel.
For flare V-groove welds, subject to longitudinal loading,
COLD-FORMED STEEL CONSTRUCTION 8.31
P 
 0.75tLF t  t  2t or h  L (8.38) n u w
where tw 
 effective throat of the weld, in and h 
 lip height, in
P 
 1.50tLF t 2t and h L (8.39) n u w
In addition, if t  0.15 in,
P 
 0.75t LF (8.40) n w xx
where Fxx 
 stress-level designation in AWS electrode designation, ksi.
8.17 RESISTANCE WELDING OF
COLD-FORMED STEEL
Resistance welding comprises a group of welding processes wherein coalescence
is produced by the heat obtained from resistance of the work to flow of electric
current in a circuit of which the work is part and by the application of pressure.
Because of the size of the equipment required, resistance welding is essentially a
shop process. Speed and low cost are factors favoring its selection.
Almost all resistance-welding processes require a lap-type joint. The amount of
contacting overlap varies from 3?8 to 1 in, depending on sheet thickness. Access to
both sides of the joint is normally required. Adequate clearance for electrodes and
welder arms must be provided.
8.17.1 Spot Welding
Spot welding is the most common resistance-welding process. The weld is formed
at the interface between the pieces being joined and consists of a cast-steel nugget.
The nugget has a diameter about equal to that of the electrode face and should
penetrate about 60 to 80% of each sheet thickness.
For structural design purposes, spot welds can be treated the same way as bolts,
except that no reduction in net section due to holes need be made. Table 8.5 gives
the essential information for design purposes for uncoated steel based on ‘‘Recommended
Practices for Resistance Welding.’’ American Welding Society, 1966.
The maximum allowable loads per weld for design purposes are based on shear
strengths of welds observed in tests after application of a safety factor of 2.5 bounds
of data. Note that the thickest steel for plain spot welding is 1?8 in. Thicker material
can be resistance welded by projection or by pulsation methods if high capacity
spot welders for material thicker than 1?8 in are not available.
8.17.2 Projection Welding
This is a form of spot welding in which the effects of current and pressure are
intensified by concentrating them in small areas of projections embossed in the
sheet to be welded. Thus, satisfactory resistance welds can be made on thicker steel
using spot welders ordinarily limited to thinner stocks.
8.32 SECTION EIGHT
TABLE 8.5 Design Data for Spot and Projection Welding of Low-Carbon Sheet Steel
Thickness
t of
thinnest
outside
piece, in
Min OD of
electrode,
D. ir.
Min
contacting
overlap,
in
Min
weld
spacing
c to c, in
Approx
dia of
fused zone,
in Min shear
strength
per weld
lb
Dia of
projection,
D, in
Spot welding
0.021 3?8 7?16 3?8 0.13 320
0.031 3?8 7?16 1?2 0.16 570
0.040 1?2 1?2 3?4 0.19 920
0.050 1?2 9?16 7?8 0.22 1,350
0.062 1?2 5?8 1 0.25 1,850
0.078 5?8 11?16 11?4 0.29 2,700
0.094 5?8 3?4 11?2 0.31 3,450
0.109 5?8 13?16 15?8 0.32 4,150
0.125 7?8 7?8 13?4 0.33 5,000
Projection welding
0.125 11?16 9?16 0.338 4,800 0.281
0.140 3?4 5?8 7?16 6,000 0.312
0.156 13?16 11?16 1?2 7,500 0.343
0.171 7?8 3?4 9?16 8,500 0.375
0.187 15?16 13?16 9?16 10,000 0.406
8.17.3 Pulsation Welding
Pulsation, or multiple-impulse, welding is the making of spot welds with more than
one impulse of current, a technique that makes some spot welders useful for thicker
materials. The tradeoffs influencing choice between projection welding and impulse
welding involve the work being produced, volume of output, and equipment available.
8.17.4 Recommended Practices for Spot Welding
The spot welding of higher-strength steels than those contemplated under Table 8.5
may require special welding conditions to develop the higher shear strengths of
which the higher-strength steels are capable.
All steels used for spot welding should be free of scale; therefore, either hotrolled
and pickled or cold-rolled steels are usually specified.
Steels containing more than 0.15% carbon are not as readily spot welded as
lower-carbon steels, unless special techniques are used to ensure ductile welds.
High-carbon steels such as ASTM A653, SQ Grade 50 (formerly, A446, Grade D),
which can have a carbon content as high as 0.40% by heat analysis, are not recommended
for resistance welding. Designers should resort to other means of joining
such steels.
COLD-FORMED STEEL CONSTRUCTION 8.33
TABLE 8.6 Nominal Shear Strength per Spot for Low-Carbon Sheet Steel
Thickness of
thinnest outside
sheet, in
Nominal shear
strength per
spot, kips
Thickness of
thinnest outside
sheet, in
Nominal shear
strength per
spot, kips
0.010 0.13 0.080 3.33
0.020 0.48 0.090 4.00
0.030 1.00 0.100 4.99
0.040 1.42 0.110 6.07
0.050 1.65 0.125 7.29
0.060 2.28 0.190 10.16
0.070 2.83 0.250 15.00
Maintenance of sufficient overlaps in detailing spot-welded joints is important
to ensure consistent weld strengths and minimum distortions at joints. Minimum
weld spacings specified in Table 8.5 should be observed, or shunting to previously
made adjacent welds may reduce the electric current to a level below that needed
for welds being made. Also, the joint design should provide sufficient clearance
between electrodes and work to prevent short-circuiting of current needed to make
satisfactory spot welds. For further information on spot welding of coated steels,
see ‘‘Recommended Practices for Resistance Welding of Coated Low-Carbon
Steel,’’ American Welding Society, 550 N.W. Lejeune Rd., Miami, FL 33126.
The nominal shear strength per spot, is a function of the thickness of the thinnest
outside sheet. Table 8.6 lists spot shear strengths for sheets with thicknesses from
0.010 to 0.250 in, as recommended for design by the American Iron and Steel
Institute.
8.18 BOLTING OF COLD-FORMED
STEEL MEMBERS
Bolting is convenient in cold-formed construction. Bolts, nuts, and washers should
generally conform to the requirements of the ASTM specifications listed in Table
8.7. The maximum sizes of bolt holes are given in Table 8.8. Standard holes should
be used in bolted connections when possible. If slotted holes are used, the length
of the holes should be normal to the direction of the shear load. Washers should
be installed atop oversized or slotted holes.
8.18.1 Spacing of Bolts
The distance e, in, measured in the direction of applied force, from the center of a
standard hole to the nearest edge of an adjacent hole or to the end of the connected
part toward which the force is directed should not be less than e . min
e 
 e (8.41) min e
e 
 P/F t (8.42) u
8.34 SECTION EIGHT
TABLE 8.7 ASTM Bolt, Nut, and Washer Steels
A194 Carbon and alloy steel nuts for high-pressure and high-temperature service
A307 Carbon steel bolts and studs
A325 High-strength bolts for structural steel joints
A354 Grade BD quenched and tempered alloy-steel bolts, studs, and other externally
threaded fasteners (for bolt diameter less than 1?2 in)
A449 Quenched and tempered steel bolts and studs (for bolt diameter less than 1?2 in)
A490 Heat-treated steel structural bolts
A563 Carbon and alloy steel nuts
F436 Hardened steel washers
F844 Washers, steel, plain (flat), unhardened for general use
F959 Compressible washer-type, direct-tension indicators for use with structural
fasteners
TABLE 8.8 Maximum Size of Bolt Holes, in.
Nominal
bolt
diameter,
in
Standard
hole
diameter
dh, in
Oversized
hole
diameter
dh, in
Short-slotted
hole, in
Long-slotted
hole, in
Less than 1?2 d  1?32 d  1?16 (d  1?32)
by (d  1?4)
(d  1?32)
by (21?2d)
1?2 or larger d  1?16 d  1?8 (d  1?16)
by (d  1?4)
(d  1?16)
by (21?2d)
where e 
 safety factor for sheet tearing

 2.00 when Fu /Fsy 1.08

 2.22 when Fu /Fsy  1.08
P 
 force, kips, transmitted by a bolt
t 
 thickness, in, of thinnest connected part
Fu 
 tensile strength, ksi, of connected part
Fsy 
 yield strength, ksi, of connected part
In addition, the minimum distance between centers of bolt holes should provide
sufficient clearance for bolt heads, nuts, washers, and wrench but be at least 3 times
the nominal diameter d, in. The distance from the center of any standard hole to
the end or boundary of the connecting member should be at least 11?2d.
8.18.2 Bolted Cold-Formed Members in Tension
Calculation of the allowable tension force on the net section of a bolted connection
depends on the thickness t, in, of the thinnest connected part. When t exceeds 3?16
in, design of the connection is governed by the AISC ‘‘Specification for Structural
Steel Buildings, Allowable Stress Design and Plastic Design,’’ American Institute
of Steel Construction, One East Wacker Drive, Chicago, IL 60601. When t does
not exceed 3?16 in and washers are provided under the bolt head and nut, the following
is applicable:
COLD-FORMED STEEL CONSTRUCTION 8.35
The tension force on the net section should not exceed Pa, kips, calculated from
Eq. (8.43).
P 
 P / (8.43) a n t
P 
 A F (8.44) n n t
where t 
 safety factor for tension on net section

 2.22 for single shear

 2.00 for double shear
An 
 area of net section of thinnest sheet, in2
The nominal limiting tension stress Ft , kips, is given by
F 
 (1  0.9r  3rd/ s)F  F (8.45) t u u
where s 
 bolt spacing, in, measured normal to line of stress

 width of sheet for a single bolt in the net section
Fu 
 tensile strength, ksi, of connected part
d 
 nominal diameter, in, of bolt
r 
 ratio of force transmitted by the bolts at the section to the tension force
in the member at that section (if r  0.2, it may be taken equal to zero)
When washers are not provided under the bolt head and nut, see AISI specifi-
cation.
8.18.3 Bearing Stresses and Bolt Tension
The bearing force should not exceed Pa, kips, calculated from Eq. (8.46).
P 
 P / (8.46) a n b
P 
 F dt (8.47) n p
where b 
 safety factor for bearing 
 2.22
Fp 
 nominal bearing stress, ksi, in connected part
d 
 nominal diameter of bolt, in
t 
 thickness, in, of thinnest connected part
Table 8.9 lists nominal bearing stresses for bolted connections.
Table 8.10 lists nominal shear and tension stresses for various grades of bolts.
The bolt force resulting in shear, tension, or combinations of shear and tension
should not exceed the allowable force Pa, kips, calculated from Eq. (8.48).
P 
 A F/ (8.48) a b
where Ab 
 gross cross-sectional area of bolt, in2
F 
 nominal stress, ksi, Fnv, Fnt, or F in Tables 8.10 and 8.11 nt
Safety factors given in Tables 8.10 and 8.11 may be used with Eq. (8.48) to compute
allowable loads on bolted joints.
Table 8.11 lists nominal tension stresses for bolts subjected to a combination of
shear and tension.
8.36 SECTION EIGHT
TABLE 8.9 Nominal Bearing Stresses for Bolted Connections of Cold-Formed Steel
Componentsa
Type of joint
Nominal bearing stress Fp, ksi
With washers under both
bolt head and nutb
Without washers under bolt
head and nut or with only
one washer c
Inside sheet of double-shear
connection
3.33Fu (Fu /Fsy 1.08)d
3.00Fu (Fu /Fsy  1.08)d
3.00Fu
e
Sheets in single shear and
outside sheets of doubleshear
connection
3.00Fu 2.22Fu
e
aFor joints with parts 3?16 in or more thick, see the ‘‘Specification for Structural Steel Buildings,’’
American Institute of Steel Construction.
bFor joints with parts 0.024 in or more thick.
cFor joints with parts 0.036 in or more thick.
dFu /Fsy is the ratio of the tensile strength of a connected part to its yield strength.
e For Fu /Fsy 1.08
8.18.4 Example—Tension Joints with Two Bolts
Assume that the bolted tension joints of Fig. 8.11 comprise two sheets of 3?16-inthick,
A611, Grade C steel. For this steel, Fsy 
 33 ksi and Fu 
 48 ksi. The sheets
in each joint are 4 in wide and are connected by two 5?8-in-diameter, A325 bolts,
with washers under both bolt head and nut.
Case 1 of Fig. 8.11 has the two bolts arranged in a single transverse row. A
force T/2 is applied to each bolt and the total force T has to be carried by the net
section of each sheet through the bolts. So, in Eq. (8.45), r 
 2(T/2) /T 
 1.
Spacing of the bolts s 
 2 in and d/ s 
 5?8/2 
 0.312. The tension stress in the
net section, computed from Eq. (8.45), is then
F 
 (1  0.9  1  3  1  0.312)F 
 1.04 F  F t u u u
Use Ft 
 Fu.
Substitution in Eq. (8.44) with Fu 
 48 ksi yields the nominal tension load on
the net section:
11 3 P 
 [4  (2  ?16)]  ?16  48 
 23.63 kips n
The allowable load is
P 
 P / 
 23.63/2.22 
 10.64 kips a n
This compares with the tensile strength of each sheet for tension member design:
11 3 P 
 A F 
 [4  (2  ?16)]  ?16  33 
 16.24 kips n n sy
The allowable load is
P 
 P / 
 16.24/1.67 
 9.72 kips a n
Use Pa 
 9.72 kips.
COLD-FORMED STEEL CONSTRUCTION 8.37
TABLE 8.10 Nominal Tensile and Shear Strength for Bolts
Description of bolts
Tensile strength
Factor of
safety

Nominal
stress
Fnt, ksi
Shear strength
Factor of
safety

Nominal
stress
Fnv, ksi
A307 bolts, Grade A
1?4 in  d  1?2 in
2.25 40.5 2.4 24.0
A307 bolts, Grade A
d 1?2 in
2.25 45.0 27.0
A325 bolt, when threads
are not excluded from
shear planes
2.0 90.0 54.0
A325 bolts, when threads
are excluded from
shear planes
90.0 72.0
A354 Grade BD bolts
1?4 in  d  1?2 in,
when threads are not
excluded from shear
planes
101.0 59.0
A354 Grade BD bolts
1?4 in  d  1?2 in,
when threads are
excluded from shear
planes
101.0 90.0
A449 bolts
1?4 in  d  1?2 in,
when threads are not
excluded from shear
planes
81.0 47.0
A449 bolts
1?4 in  d  1?2 in,
when threads are
excluded from shear
planes
81.0 72.0
A490 bolts, when threads
are not excluded from
shear planes
112.5 67.5
A490 bolts, when threads
are excluded from
shear planes
112.5 90.0
8.38 SECTION EIGHT
TABLE 8.11 Nominal Tension Stress, (ksi), for Bolts Subject to the Combination of Fnt
Shear and Tension
Description of bolts
Threads not excluded
from shear planes
Threads excluded
from shear planes
Factor
of safety 
A325 bolts 110  3.6?v  90 110  2.8?v  90 2.0
A354 Grade BD bolts 122  3.6?v  101 122  2.8?v  101
A449 bolts 100  3.6?v  81 100  2.8?v  81
A490 bolts 136  3.6?v  112.5 136  2.8?v  112.5
A307 bolts, Grade A
When 1?4 in  d  1?2 in
When d 1?2 in
52  4?v  40.5
58.5  4?v  45
2.25
The shear stress, ?v, shall also satisfy Table 8.10.
FIGURE 8.11 Bolted connections with two bolts.
Case 2 of Fig. 8.11 has the two bolts, with 4-in spacing, arranged in a single
line along the direction of applied force. For the top sheet (Fig. 8.11) at section 1-
1 then, r 
 (T/2) /T 
 1?2, and for this sheet at section 2-2, r 
 (T/2)/(T/2) 
 1.
For the top sheet at both sections, d/ s 
 5?8/4 
 0.156.
From Eq. (8.45), for the top sheet at section 1-1,
1 1 F 
 (1  0.9  ?2  3  ?2  0.156)F 
 0.784 F t u u
The maximum load for that sheet would then be
11 3 P 
 [4  ?16]  ?16  0.784  48 
 23.37 kips n
For section 2-2, top sheet,
F 
 (1  0.9  1  3  1  0.156)F 
 0.568F t u u
Maximum load for section 2-2, top sheet, would then be
COLD-FORMED STEEL CONSTRUCTION 8.39
11 3 P /2 
 (4  ?16)  ( ?16)  0.568  48 
 16.93 kips n
P 
 33.86 kips n
Compare sections 1-1 and 2-2, Pn 
 23.37 kips. The allowable load is:
P 
 P / 
 23.37/2.22 
 10.53 kips a n
This compares with the tensile strength of each sheet for tension member design:
11 3 P 
 A F 
 [4  ?16]( ?16)  33 
 20.50 kips n n sy
The allowable load is:
P 
 P / 
 20.50/1.67 
 12.28 kips a n
Use Pa 
 10.53 kips.
The minimum distance between a bolt center and adjacent bolt edge or sheet
edge is for Case 1:
3 e 
 P/F t 
 (9.72 /2) /(48  ?16) 
 0.54 in u
e 
 e 
 0.54  2 
 1.08 in min
For Case 2:
3 e 
 (10.53/2) /(48  ?16) 
 0.59 in
e 
 0.59  2 
 1.18 in min
The bearing strength Pn per bolt of the 3?16-in-thick steel sheet is:
5 3 P 
 F dt 
 (3  48)  ?8  ?16 
 16.88 kips n p
The allowable bearing load for two bolts:
P 
 2P / 
 2  16.88/2.22 
 15.21 kips  10.53 kips O.K. a n
Using the A325 bolts with threads not excluded from the shear plane, the
allowable shearing strength of each bolt is:
2 5 P 
 A F / 
 ( ?8)  0.7854  54/ 2.4 
 6.9 kips s b nv
For two bolts, the allowable load is:
P 
 2  6.9 
 13.8 kips  10.53 kips O.K. a
In summary, the allowable loads for Cases 1 and 2 are 9.72 kips and 10.53 kips,
respectively. The shear capacity of bolts should also be checked.
8.40 SECTION EIGHT
FIGURE 8.12 Tapping screws. NOTE: A blank space does not signify necessarily that the type of
screw cannot be used for this purpose; it denotes that the type of self-tapping screw will not
generally give the best results in this type of material. (Parker-Kalon Corp., Emhart Corp., Campbellsville,
Ky.)
8.19 SELF-TAPPING SCREWS FOR JOINING
SHEET STEEL COMPONENTS
Self-tapping screws that are hardened so that their threads form or cut mating
threads in one or both of the sheet steel parts being connected are frequently used
for making field joints. Such screws provide a rapid and efficient means of making
light-duty connections. The screws are especially useful for such purposes as fastening
sheet-metal siding, roofing, and decking to structural steel; making attachments
at joints, side laps, and closures in siding, roofing, and decking; fastening
collateral materials to steel framing; and fastening steel studs to sill plates or channel
tracks. The screws may also be used for fastening bridging to steel joists and
studs, fastening corrugated decking to steel joists, and similar connections to secondary
members.
Since 1996, the AISI specification included design rules for determining nominal
loads for shear and tension. The safety factor to be used for computing the allowable
load is 3.0.
Several types of tapping screws are shown in Fig. 8.12. Other types are available.
There are many different head styles—slotted, recessed, hexagonal, flat, round, etc.
Some types, called Sems, are supplied with preassembled washers under the heads.
Other types are supplied with neoprene washers for making watertight joints in
roofing.
All the types of screws shown in Fig. 8.12 require prepunched or predrilled
holes. Self-drilling screws, which have a twist drill point that drills the proper size
of hole just ahead of threading, are especially suited for field work, because they
eliminate separate punching or drilling operations. Another type of self-drilling
screw, capable of being used in relatively thin sheets of material in situations where
the parts being joined can be firmly clamped together, has a very sharp point that
pierces the material until the threads engage.
COLD-FORMED STEEL CONSTRUCTION 8.41
TABLE 8.12 Average Diameters of Self-Tapping Screws, in*
Number or size,
in
Types AB and B
Outside Root
Type F†
Outside
Type U
Outside
No. 4 0.112 0.084 0.110 0.114
No. 6 0.137 0.102 0.136 0.138
No. 8 0.164 0.119 0.161 0.165
No. 10 0.186 0.138 0.187 0.180
No. 12 0.212 0.161 0.213 0.209
No. 14‡ or 1?4 0.243 0.189 0.247 0.239‡
5?16 0.312 0.240 0.309 0.312
3?8§ 0.376 0.304 0.371 0.375
*Averages of standard maximum and minimum dimensions adopted
under ANSI B18.6.4-1966.
†Type F has threads of machine-screw type approximating the Unified
Thread Form (ANSI B1.101960). The figures shown are averages of those
for two different thread pitches for each size of screw.
‡ Size No. 14 for Type U.
§ Does not apply to Type AB.
Torsional-strength requirements for self-tapping screws have been standardized
under American National Standards Institute B18.6.4, ‘‘Slotted and Recessed Head
Tapping Screws and Metallic Drive Screws.’’ Safe loads in shear and tension on
such screws can vary considerably, depending on type of screw and head, tightening
torque, and details of the assembly. When screws are used for structural loadcarrying
purposes, the user should rely on experience with the particular application,
manufacturer’s recommendations, or actual tests of the type of assembly involved.
Essential body dimensions of some types of self-tapping screws are given in
Table 8.12. Complete details on these and other types, and recommended hole sizes,
may be found in ANSI B18.6.4 and in manufacturers’ publications.
8.20 SPECIAL FASTENERS FOR
COLD-FORMED STEEL
Special fasteners, such as tubular rivets, blind rivets (capable of being driven from
one side only), special bolts used for ‘‘blind insertion,’’ special studs, lock nuts,
and the like, and even metal stitching, which is an outgrowth of the common office
stapling device for paper, are used for special applications. When such a fastener
is required, refer to manufacturers’ catalogs for design information, and base any
structural strength attributed to the fastener on the results of carefully made tests
or the manufacturer’s recommendations.
COLD-FORMED STEEL FLOOR, ROOF, AND
WALL CONSTRUCTION
Steel roof deck consists of ribbed sheets with nesting or upstanding-seam joints
designed for the support of roof loads between purlins or frames. A typical roof8.42
SECTION EIGHT
FIGURE 8.13 Roof-deck assembly.
FIGURE 8.14 Typical cold-formed steel roof-deck sections. (a) Narrow rib: (b) intermediate rib;
(c) wide rib; (d ) intermediate rib in 36-in-wide sheets with nested side laps; (e) wide rib in 32-inwide
sheets with upstanding seams.
deck assembly is shown in Fig. 8.13. The Steel Deck Institute, P.O. Box 25, Fox
River Grove, IL 60021, has developed much useful information on steel roof deck.
8.21 STEEL ROOF DECK
Various types of steel roof deck are available and may be classified in accordance
with recommendations of the Steel Deck Institute (SDI). All types consist of long,
narrow sections with longitudinal ribs at least 11?2 in deep and spaced about 6 in
on centers (Fig. 8.14). Other rib dimensions are shown in Fig. 8.14a to c for some
standard styles.
COLD-FORMED STEEL CONSTRUCTION 8.43
8.21.1 Types of Steel Roof Deck
Steel roof deck is commonly available in 24- and 30-in covering widths, but sometimes
in 18- and 36-in widths, depending on the manufacturer. Thickness of steel
commonly used is 0.048 or 0.036 in, but most building codes permit 0.030-in-thick
steel to be used. Figure 8.14d and e shows full-width decking in cross section.
Usual spans, which may be simple, two-span continuous, or three-span continuous,
range from 4 to 10 ft. The SDI ‘‘Design Manual for Composite Decks, Form Decks,
Roof Decks and Cellular Deck Floor Systems with Electrical Distribution’’ gives
allowable total uniform loading (dead and live), lb / ft2, for various steel thicknesses,
spans, and rib widths.
Some manufacturers make special long-span roof-deck sections, such as the 3-
in-deep, Type N roof deck shown in Fig. 8.15, in 24- to 16-ga black and galvanized.
FIGURE 8.15 Cross sections of types NS and
NI roof deck for 9- to 15-ft spans.
The weight of the steel roof deck
shown in Fig. 8.14 depends on rib dimensions
and edge details. For structural
design purposes, weights of 2.8,
2.1, and 1.7 lb / ft2 can be used for the
usual design thicknesses of 0.048,
0.036, and 0.030 in, respectively, for
black steel in all rib widths, as commonly
supplied.
Steel roof deck is usually made of
structural-quality sheet or strip, either
black (ASTM A611, Grades C, D or E)
or galvanized (A653 SQ Grade 33 or
higher). Both steels have minimum yield strengths of 33 ksi. Black steel is given
a shop coat of priming paint by the roof deck manufacturer. Galvanized steel may
or may not be painted; if painted, it should first be bonderized to ensure paint
adherence. Aluminized steel is another metal-coated steel option.
SDI Design Manual includes ‘‘Recommendations for Site Storage and Erection’’
and standard details for accessories. See also SDI ‘‘Manual of Construction with
Steel Deck.’’
8.21.2 Load-Carrying Capacity of Steel Roof Deck
The Steel Deck Institute has adopted a set of basic design specifications, with limits
on rib dimensions, as shown in Fig. 8.14a to c, and publishes allowable uniform
loading tables for narrow-, intermediate-, and wide-rib steel roof deck (Table 8.13,
for example). These tables are based on section moduli and moments of inertia
computed with effective-width procedures stipulated in the AISI ‘‘Specification for
the Design of Cold-Formed Steel Structural Members’’ (Art. 8.8). SDI has banned
compression flange widths otherwise assumed to be effective. Moreover, SDI ‘‘Basic
Design Specifications’’ recommends the following:
Moment and Deflection Coefficients. Where steel roof decks are welded to supports,
a moment coefficient of 1?10 (applied to WL) should be used for three or more
spans. Deflection coefficients of 0.0054 and 0.0069 (applied to WL3 /EI) should be
used for two span and three span, respectively. All other steel roof-deck installations
should be designed as simple spans, with moment and deflection coefficients 1?8
and 5?384, respectively. (W 
 total uniform load, L 
 span, E 
 modulus of elasticity,
I 
 moment of inertia.)
8.44
TABLE 8.13 Allowable Total (Dead plus Live) Uniform Loads, psf, on Steel Roof Deck*
Deck
type
Span
condition
Design
thickness,
in
Span—c to c joists or purlins, ft-in
4-0 4-6 5-0 5-6 6-0 6-6 7-0 7-6 8-0 8-6 9-0
NR 22
NR 20
NR18
NR 22
NR 20
NR 18
NR 22
NR 20
NR 18
0.0295
0.0358
0.0474
0.0295
0.0358
0.0474
0.0295
0.0358
0.0474
73
91
125
80
97
128
100
121
160
58
72
99
63
76
101
79
96
126
47
58
80
51
62
82
64
77
102
48
66
42
51
68
53
64
85
40
55
43
57
44
54
71
47
48
46
61
42
52 45
4-0 4-6 5-0 5-6 6-0 6-6 7-0 7-6 8-0 8-6 9-0
IR 22
IR 20
IR 18
IR 22
IR 20
IR 18
IR 22
IR 20
IR 18
0.0295
0.0358
0.0474
0.0295
0.0358
0.0474
0.0295
0.0358
0.0474
84
104
142
90
110
145
113
137
181
66
82
112
71
87
114
89
108
143
54
67
91
58
70
93
72
88
116
44
55
75
48
58
77
60
72
96
46
63
40
49
64
50
61
81
54
41
55
43
52
69
46
47
45
59
40
41
52 45 40
TABLE 8.13 Allowable Total (Dead plus Live) Uniform Loads, psf, on Steel Roof Deck* (Continued)
Deck
type
Span
condition
Design
thickness,
in
Span—c to c joists or purlins, ft-in
8.45
5-0 5-6 6-0 6-6 7-0 7-6 8-0 8-6 9-0 9-6 10-0
WR 22
WR 20
WR 18
WR 22
WR 20
WR 18
WR 22
WR 20
WR 18
0.0295
0.0358
0.0474
0.0295
0.0358
0.0474
0.0295
0.0358
0.0474
90
113
159
96
123
164
119
153
204
70
88
122
79
102
136
99
127
169
56
70
96
67
86
114
83
107
142
46
57
77
57
73
98
71
91
121
48
64
49
63
84
61
79
105
40
54
43
55
73
53
68
91
46
48
64
47
58
79
40
43
57
41
50
67
51
36
43
58
46
51
41
* Load tables were calculated with sectional properties for minimum thicknesses of 0.028, 0.034, and 0.045 in,
corresponding respectively to design thickness of 0.0295, 0.0358, and 0.0474 in, exclusive of coating on base metal.
Loads shown in tables are uniformly distributed total (dead plus live) loads, psf. Loads in shaded areas are governed
by live-load deflection not in excess of 1?240  span. The dead load included is 10 psf. All other loads are governed by
the allowable flexural stress limit of 20 ksi for a 33-ksi minimum yield point.
Rib-width limitations shown are taken at the theoretical intersection points of flange.
Span length assumes c-to-c spacing of supports. Tabulated loads shall not be increased by assuming clear-span
dimensions.
Bending moment formulas used for flexural stress limitation are: for simply supported and two-span decking, M 

wl 2 / 8; for decking with three continuous spans or more, M 
 wl 2 / 10.
 Deflection formulas for deflection limitation are: For simply supported decking, 
 5wl 4 / 384El; for two- and
three-span decking, 
 0.0054 wl 4 / EI and 0.0069 wl 4 / EI, respectively.
Normal installations covered by these tables do not require midspan fasteners for spans of 5 ft or less.
From ‘‘Design Manual for Composite Decks, Form Decks, Roof Decks and Cellular Deck Floor Systems with Electrical
Distribution,’’ Steel Deck Institute.
8.46 SECTION EIGHT
Maximum Deflections. The deflection under live load should not exceed 1?240 of
the clear span, center to center of supports. (Suspended ceiling, lighting fixtures,
ducts or other utilities should not be supported by the roof deck.)
Anchorage. Steel roof deck should be anchored to the supporting framework to
resist the following uplifts:
45 lb / ft2 for eave overhang
30 lb / ft2 for all other roof areas
The dead load of the roof-deck construction may be deducted from the above uplife
forces.
8.21.3 Diaphragm Action of Decks
In addition to their normal function as roof panels under gravity loading, steel roof
deck assemblies can be used as shear diaphragms under lateral loads, such as wind
and seismic forces. When steel roof deck is used for these purposes, special attention
should be paid to connections between panels and attachments of panels to
building frames. For design purposes, see SDI ‘‘Diaphragm Design Manual.’’
8.21.4 Details and Accessories of Steel Roof Deck
In addition to the use of nesting or upstanding seams, most roof-deck sections are
designed so that ends can be lapped shingle fashion.
Special ridge, valley, eave, and cant strips are provided by roof-deck manufacturers
(Fig. 8.16).
Roof decks are commonly arc welded to structural steel supports with puddle
welds at least 1?4 in in diameter or with elongated welds of equal perimeter. Electrodes
should be selected for amperage adjusted to fuse all layers of steel roof
decking to supporting members without creating blowholes around the welds.Welding
washers are recommended for thicknesses less than 0.028 in.
Fillet welds at least 1 in long should be used to connect lapped edges of roof
deck.
Tapping screws are an alternative means of attaching steel roof deck to structural
support members, which should be at least 1?16 in thick. All edge ribs and a sufficient
number of interior ribs should be connected to supporting members at intervals not
exceeding 18 in. When standard steel roof deck spans 5 ft or more, adjacent sheets
should be fastened together at midspan with either welds or screws.
8.21.5 Roof Deck Insulation and Fire Resistance
Although insulation is not ordinarily supplied by the roof-deck manufacturer, it is
standard practice to install 3?4- or 1-in-thick mineral fiberboard between roof deck
and roofing. SDI further recommends that all steel decks be covered with a material
of sufficient insulating value to prevent condensation under normal occupancy conditions.
Insulation should be adequately attached to the steel deck by means of
adhesives or mechanical fasteners. Insulation materials should be protected from
the elements at all times during storage and installation.
COLD-FORMED STEEL CONSTRUCTION 8.47
FIGURE 8.16 Roof-deck details.
The UL ‘‘Fire Resistance Directory,’’ Underwriter’s Laboratories, Inc., 333
Pfingsten Rd., Northbrook, IL 60062, lists fire-resistance ratings for steel roof-deck
construction. Some systems with fire ratings up to 2 h are listed in Table 8.14.
8.22 CELLULAR STEEL FLOOR AND ROOF
PANELS*
Several different designs of cellular steel panels and fluted steel panels for floor
and roof construction are available. Sections of some of these panels are illustrated
in Fig. 8.17.
8.22.1 Cellular-Steel-Floor Raceway System
One form of cellular steel floor assembly with a distribution system for electrical
wiring, telephone cables, and data cables is described below and is illustrated in
Fig. 8.18. This system is used in many kinds of structures, including massive highrise
buildings for institutional, business, and mercantile occupancies.
The cellular-steel-floor raceway system is basically a profiled steel deck containing
wiring raceways and having structural concrete on top. The cellular deck
* Courtesy of R. E. Albrecht, Engineer, H. H. Robertson Company, Ambridge, Pa.
8.48 SECTION EIGHT
TABLE 8.14 Fire Resistance Ratings for Steel Floor and Roof Assemblies*
Roof construction Insulation
Underside
protection Authority
2-h rating†
Min. 11?2-in-deep
steel deck on steel
joists or steel
beams
Min. 13?4-in-thick
listed mineral
fiberboard
Min. 13?4-in-thick,
direct-applied,
sprayed
vermiculite plaster,
UL listed
UL design P711†
Min. 11?2-in-deep
steel deck on steel
joists or steel
beams
Min. 11?16-in-thick
listed mineral
fiberboard
Min. 19?16-in-thick,
direct-applied,
sprayed fiber
protection, UL
listed
UL design P818†
Floor construction Concrete
Underside
protection Authority
2-h rating‡
11?2-, 2-, or 3-in-deep
steel floor units on
steel beams
21?2-in-thick normalweight
or
lightweight
concrete
Min. 3?8-in-thick,
direct-applied,
sprayed
vermiculite plaster,
UL listed
UL design D739‡
11?2-, 2, or 3-in-deep
steel floor units on
steel beams
21?2-in-thick normalweight
or
lightweight
concrete
Min. 3?8-in-thick,
direct-applied,
sprayed fiber
protection, UL
listed
UL design D858†
* Based on ‘‘Fire Resistance Directory,’’ 1990, Underwriters Laboratories, Inc., 333 Pfingsten Rd., Northbrook,
IL 60062.
†11?2-h and 1-h ratings are also available.
‡ 1-h, 21?2-h, 3-h, and 4-h ratings are also available.
consists of closely spaced cellular raceways. These are connected to a main trench
header duct with removable cover plate for lay-in wiring. Set on a repetitive module,
the cellular raceways are assigned to electrical power, telephone, and data wiring.
At prescribed intervals, as close as 2 ft longitudinally and 2 ft transversely over the
floor, preset inserts may be provided for access to the wiring and activation workstations.
When an insert is activated at a workstation, connections for electrical
power, telephone, and data are provided at one outlet. Insert fittings may be flush
with the top floor surface or project above it.
This system provides the required fire-resistive barrier between stories of a building.
The cellular metal floor units also serve the structural purposes of acting as
working platforms and concrete forms during construction and as tensile reinforcement
for the concrete floor slab after the building is occupied.
Cellular steel floor raceways have many desirable features including moderately
low cost, good flexibility, which contributes to lower life-cycle cost, and minimal
COLD-FORMED STEEL CONSTRUCTION 8.49
FIGURE 8.17 Composite cellular and fluted steel floor sections. (Courtesy H. H.
Robertson Co., Ambridge, Pa.)
FIGURE 8.18 Composite cellular and fluted steel floor sections. (Courtesy H. H. Robertson
Co., Ambridge, Pa.)
limitations on placement of outlets. Little or no increase over floor depth required
for strictly structural purposes is necessary to accommodate the system.
Wiring may penetrate the floor surface only at outlet fittings. Therefore, if carpet
is used, it will have to be cut and a flap peeled back to provide access to the fittings.
Use of carpet tiles rather than sheet carpet facilitates access to the preset inserts.
Where service outlets are not required to be as close as 2 ft on centers, a blend
of fluted and cellular floor sections may be used. As an example, alternating 3-ftwide
fluted floor deck with 2-ft-wide cellular floor panels results in a module for
8.50 SECTION EIGHT
service outlets of 5 ft in the transverse direction and as close as 2 ft in the longitudinal
direction. Other modules and spacings are available.
8.22.2 Steels Used for Cellular and Fluted Decking
Cellular and fluted floor and roof sections (decking) usually are made of steel 0.030
in or more thick complying with the requirements of ASTM A611, Grades C, D,
or E, for uncoated steel or ASTM A653 structural quality, for galvanized steel, with
a minimum yield points of 33 ksi. The steel may be either galvanized or painted.
8.22.3 Structural Design of Steel Floor and Roof Panels
Design is usually based on the ‘‘Specification for the Design of Cold-Formed Steel
Structural Members,’’ American Iron and Steel Institute, 1101 17th St., NW, Washington,
DC 20036. Structural design of composite floor slabs incorporating sheetsteel
floor and roof panels is usually based on ‘‘Standard for the Structural Design
of Composite Slabs,’’ ANSI/ASCE 3-91 and ‘‘Standard Practice for Construction
and Inspection of Composite Slabs,’’ ANSI/ASCE 9-91, American Society of Civil
Engineers, 1801 Alexander Bell Drive, Reston, VA 20191-44001.
Details of design and installation vary with types of panels and manufacturers.
In any particular instance, refer to the manufacturer’s recommendations.
8.22.4 Fire Resistance of Cellular and Fluted Steel Decking
Any desired degree of fire protection for cellular and fluted steel floor and roof
assemblies can be obtained with concrete toppings and plaster ceilings or directapplication
compounds (sprayed-on fireproofing). Fire-resistance ratings for a considerable
number of assemblies are available. (See ‘‘Fire-Resistant Steel-Frame
Construction,’’ American Institute of Steel Construction,’’ and ‘‘Fire Resistance Directory,’’
Underwriters Laboratories).
8.23 CORRUGATED SHEETS FOR ROOFING,
SIDING, AND DECKING
Although the use of corrugated sheets of thin steel for roofing and siding leaves
something to be desired for weathertightness and appearance, they are used for
barns and similar buildings for some protection against weather elements. They are
cheap, easy to install on a wood frame, and last for many years if galvanized.
(Corrugated steel sheets are the oldest type of cold-formed steel structural members.
They have been used since 1784, when Henry Cort introduced sheet rolling in
England.)
The commonest form of corrugated sheet, the arc-and-tangent type, has the basic
cross section shown in Fig. 8.19a. Its section properties are readily calculated with
factors taken from Fig. 8.19b to f and substituted in the following formulas.
The area, in2, of the corrugated sheet may be determined from
COLD-FORMED STEEL CONSTRUCTION 8.51
FIGURE 8.19 Factors for determining section properties of the arc-and-tangent type of corrugated
steel sheet shown in (a).
A 
 bt (8.49)
where b 
 width of sheet, in
t 
 sheet thickness, in

 (See Fig. 8.19d)
(2 /K  ) sin  (1  2 /K) cos  1
1  cos 
8.52 SECTION EIGHT
K 
 pitch-depth ratio of a corrugation 
 p/d
p 
 pitch, in, of corrugation
d 
 depth, in, of corrugation

 tangent angle, radians, or angle of web with respect to the neutral axis
of the sheet cross section
The moment of inertia, in4, of the corrugated sheet may be obtained from
3 2 I 
 C bt  C bd t (8.50) 5 6
where C5 
 (See Fig. 8.19b)
q(6  sin 2  8 sin )  4 sin  K cos 
12K
C6 

1 4 3 3 2 q 6  sin 2  8 sin  tan  sin     K 3
 q2(4 sin  K tan3  sin  4 )
 q (See Fig. 8.19c)
3 2 1 K tan  2 3  K tan      4 48 cos 
q 
 (See Fig. 8.19e)
r Ktan  2


d 4(sec  1)
The section modulus of the corrugated sheet may be computed from
2I
S 
 (8.51)
d  t
The radius of gyration, in, is given by
I
	
 (8.52) 	A
and the tangent length-depth ratio is
m sin  K

  (8.53)
d 1  cos  2
(See Fig. 8.19f.)
Example—Corrugated Sheet Properties. Consider a corrugated sheet with a
6-in pitch, 2-in depth, inside radius R of 11?8 in, and thickness t of 0.135 in. The
mean radius r is then 1.125  0.135/2 
 1.192 in; q 
 r /d 
 1.192/2 
 0.596
in, and K 
 p/d 
 6?2 
 3. From Fig. 8.19e, angle  is found to be nearly 45
.
For p/d 
 3 and  
 45
, Fig. 8.19b, c, d, and f indicate that C5 
 0.14, C6 

0.145 
 1.24, and m/d 
 0.93. Section properties per inch of corrugated width
are then computed as follows:
From Eq. (8.49),
2 A 
 1.24  1  0.135 
 0.167 in
From Eq. (8.50),
COLD-FORMED STEEL CONSTRUCTION 8.53
3 2 4 I 
 0.14  1(0.135)  0.145  1(2) 0.135 
 0.0786 in
From Eq. (8.51),
2  0.0786 3 S
 
0.0736 in
2  0.135
From Eq. (8.52),
0.0786
	
 
0.686 in 	 0.167
and from Eq. (8.53),
m 
 0.93  2 
 1.86 in
I, S, and A for corrugated sheets with widths b are obtained by multiplying the
per-inch values by b.
Unit Stresses. The allowable unit bending stress Fr , ksi, at extreme fibers of
corrugated sections of carbon or low-alloy steel may be taken as 0.6Fy, if r / t does
not exceed 1650/Fy . For 1650/Fy  r / t  6500/Fy ,
F 
 331t / r  0.399F (8.54) r y
where Fy 
 specified minimum yield point of the steel, ksi.
Section properties of corrugated sheets with cross sections composed of flat
elements may be computed with the linear method given in Art. 8.4, by combining
properties of the various elements as given in Table 8.4. (See also ‘‘Sectional Properties
of Corrugated Sheets Determined by Formula,’’ Civil Engineering, February
1954.)
8.24 LIGHTWEIGHT STEEL METRIC SHEETING
Metric sheeting, the cross section of which is shown in Fig. 8.20, has a corrugationlike
conformation with locking side edges. It has a laying width of 500 mm or 0.5
m (192?3 in), and is available in thicknesses of 5, 7, 8, 10, and 12 ga. Sheets are
installed vertically in soil with edges of successive units interlocking. For additional
corrosion protection, metric sheeting may be ordered galvanized after continuous
cold forming in lengths of 4 to 40 ft.
FIGURE 8.20 Steel metric sheeting.
Applications include checkdams,
core walls, wingwalls, trench walls, excavations,
low retaining walls, ditch
checks, jetties and lagoon baffles. The
sheeting often can be put into soft
ground with the aid of a backhoe, although
for harder subgrades, conventional
drop, vibratory, or diesel hammers applied to a light driving head make
emplacement easier. The tight metal-to-metal interlock at the edges of metric sheeting
contains soil and controls water movement. Table 8.15 lists its structural properties.
8.54 SECTION EIGHT
TABLE 8.15 Physical Properties of Metric Sheeting*
Thickness
Gage in
Weight
lb / lin ft
of pile
lb/ft2
of
wall
Section properties
Section modulus,
in3
Per section Per ft
Moment of inertia,
in4
Per section Per ft
5 0.2092 19.1 11.6 5.50 3.36 9.40 5.73
7 0.1793 16.4 10.0 4.71 2.87 7.80 4.76
8 0.1644 15.2 9.3 4.35 2.65 7.36 4.49
10 0.1345 12.5 7.6 3.60 2.20 6.01 3.67
12 0.1046 9.9 6.0 2.80 1.71 4.68 2.85
* Based on ‘‘CONTECH Metric Sheeting,’’ 1990, CONTECH Construction Products Inc., Middletown,
Ohio.
Metric sheeting should not be confused with steel sheetpiling, which is a heavier
hot-rolled steel product used for major construction projects, including breakwaters,
bulkheads, cofferdams, and docks. Metric sheeting is nevertheless an economical
product suitable for many less-demanding applications for both temporary and permanent
uses. An advantage for contractors is that it can be withdrawn and reused
on another job.
More information on lightweight steel construction is available from CONTECH
Construction Products, 1001 Grove Street, Middletown, OH 45044
8.25 STAINLESS STEEL STRUCTURAL DESIGN
Cold-formed, stainless-steel structural members require different design approaches
from those presented in Arts. 8.1 through 8.13 for cold-formed structural members
of carbon and low-alloy steels. An exception is the stainless steels of the ferritic
type that are largely alloyed with chromium and exhibit a sharp-yielding stressstrain
curve. The austenitic types of stainless steel, incorporating substantial
amounts of nickel as well as chromium, have stress-strain curves that are rounded,
do not show sharp yield points, and exhibit proportional limits that are quite low.
Because of excellent corrosion resistance, stainless steels are suitable for exterior
wall panels and exterior members of buildings as well as for other applications
subject to corrosive environments.
The ‘‘Specification for the Design of Cold-Formed Stainless Steel Structural
Members,’’ ANSI-ASCE 8-90, American Society of Civil Engineers, 1801 Alexander
Bell Drive, Reston, VA 20191-4400, presents treatments paralleling those of
Arts. 8.1 through 8.13, except the primary emphasis is on the load resistance factor
design (LRFD) method. The allowable strength design (ASD) method, however, is
also mentioned. For detailed information on austenitic grades of stainless steel, see
ASTM A666, ‘‘Austenitic Stainless Steel, Sheet, Strip, Plate and Flat Bar for Structural
Applications.’’
(W. W. Yu, ‘‘Cold-Formed Steel Design,’’ 3rd ed., John Wiley and Sons, Inc.,
New York.)
COLD-FORMED STEEL CONSTRUCTION 8.55
FIGURE 8.21 Principal framing systems for preengineered steel buildings.
PREENGINEERED STEEL BUILDINGS
Preengineered steel buildings may be selected from catalogs. They are fully designed
by a manufacturer, who supplies them with all structural and covering material,
and all fasteners.
8.26 CHARACTERISTICS OF PREENGINEERED
STEEL BUILDINGS
These structures eliminate the need for engineers and architects to design and detail
both the structures and the required accessories and openings, as would be done
for conventional buildings with components from many individual suppliers. Available
with floor areas of up to 1 million ft2, preengineered buildings readily meet
requirements for single-story structures, especially for industrial plants and commercial
buildings (Fig. 8.21).
Preengineered buildings may be provided with custom architectural accents.
Also, standard insulating techniques may be used with thermal accessories incorporated
to provide energy efficiency. Exterior wall panels are available with durable
factory-applied colors.
8.56 SECTION EIGHT
Many preengineered steel building suppliers are also able to modify their standard
designs, within certain limits, while still retaining the efficiencies of predesign
and automated volume fabrication. Examples of such modifications include the
addition of cranes; mezzanines; heating, ventilating, and air-conditioning equipment;
sprinklers; lighting; and ceiling loads with special building dimensions.
Preengineered buildings make extensive use of cold-formed steel structural
members. These lend themselves to mass production, and their designs can be more
accurately fitted to the specific structural requirements. For instance, a roof purlin
can be designed with the depth, moment of inertia, section modulus, and thickness
required to carry the load, as opposed to picking the next higher size of standard
hot-rolled shape, with more weight than required. Also, because this purlin is used
on many buildings, the quantity justifies investment in automated equipment for
forming and punching. This equipment is nevertheless flexible enough to permit a
change of thickness or depth of section to produce similar purlins for other buildings.
The engineers designing a line of preengineered buildings can, because of the
repeated use of the design, justify spending additional design time refining and
optimizing the design. Most preengineered buildings are designed with the aid of
computers. Their programs are specifically tailored to produce systems of such
buildings. A rerun of a design to eliminate a few pounds of steel is justified, since
the design will be used many times during the life of that building model.
8.27 STRUCTURAL DESIGN OF
PREENGINEERED BUILDINGS
The buildings are designed for loading criteria in such a way that they may be
specified to meet the geographical requirements of any location. Combinations of
dead load, snow load, live load, and wind conform with requirements of several
model building codes.
Standards in ‘‘Metal Building Systems,’’ Metal Building Manufacturers Association,
1300 Sumner Ave., Cleveland, OH 44115 discuss methods of load application
and maximum loading, for use where load requirements are not established
by local building codes. Other appropriate design specifications include:
Structural Steel. ‘‘Specification for Structural Steel Buildings,’’ American Institute
of Steel Construction, One East Wacker Dr., Chicago, IL 60601.
Cold-Formed Steel. ‘‘Specification for the Design of Cold-Formed Steel Structural
Members,’’ American Iron and Steel Institute, 1101 17th St., NW, Washington,
DC 20036.
Welding. ‘‘Structural Welding Code,’’ D1.3 and ‘‘Specification for Welding Sheet
Steel in Structures,’’ D1.3, American Welding Society, 550 NW LeJeune Rd., Miami,
FL 33152.
The Systems Building Association promotes marketing of metal buildings and
is located at 28 Lowery Dr., P.O. Box 117, West Milton, OH 45383.
COLD-FORMED STEEL CONSTRUCTION 8.57
FIGURE 8.22 Some examples of open-web steel joists.
OPEN-WEB STEEL JOISTS
The first steel joist was produced in 1923 and consisted of solid round bars for top
and bottom chords and a web formed from a single continuous bent bar, thus
simulating a Warren truss. The Steel Joist Institute (SJI) was organized to promote
sales of such joists in 1925 and has sponsored further research and development
since then.
8.28 DESIGN OF OPEN-WEB STEEL JOISTS
Currently, open-web steel joists are still relatively small, parallel-chord trusses, but
hot-rolled steel shapes usually make up the components. (For a time, cold-formed
steel shapes were preferred for chords to utilize higher working stresses available
in cold-formed sections of ordinary carbon-steel grades. Unfavorable fabrication
costs, however, led to a change to the hot-rolled steel chords.)
Joists are suitable for direct support of floors and roofs of buildings, when designed
according to SJI ‘‘Standard Specifications, Load Tables and Weight Tables
for Steel Joists and Joist Girders,’’ Steel Joist Institute, 3127 10th Ave., North Ext.,
Myrtle Beach, SC 29577. Moreover, since 1972, the American Institute of Steel
8.58 SECTION EIGHT
FIGURE 8.23 Some examples of open-web steel-joist floor construction.
Construction (AISC) has cooperated with SJI in producing an industry standard for
steel joist design. However, exact forms of chords and webs, and their methods of
manufacture, then as now, have continued to be in the provenance of SJI members.
Figure 8.22 shows a number of proprietary steel joists designs.
Joists are designed primarily for use under uniform distributed loading with
substantially uniform spacing of joists, as depicted in Fig. 8.23. They can carry
concentrated loads, however, especially of loads are applied at joist panel points.
Partitions running crosswise to joists usually can be considered as being distributed
by the concrete floor slabs, thus avoiding local bending of joist top chords. Even
so, joists must always be size-selected to resist the bending moments, shears, and
reactions of all loads, uniform or otherwise. So joist loadings given in tables for
uniform loading should be used with caution and modified when necessary.
One cardinal rule is that the clear span of a joist should never exceed 24 times
its depth. Another rule is that deflections should not exceed 1?360 of the joist span
for floors and roofs to which plaster ceilings are attached or 1?240 of the span for
all other cases.
SJI publishes loading tables for K-series (short span). LH-series (long span), and
DLH-series (deep long span) joist girders. The K-series joists are available in depths
COLD-FORMED STEEL CONSTRUCTION 8.59
FIGURE 8.24 Open-web steel joist with (a) ceiling extension. (b) extended end. (Courtesy of
Steel Joist Institute.)
of 8 to 30 in and spans of 8 to 60 ft in 13 different chord weights to sustain uniform
loads along the span as high as 550 lb / ft. LH-series joists are available in depths
from 18 to 48 in and spans of 25 to 96 ft in six different chord weights capable of
supporting total loads of 12,000 to 57,600 lb. DLH-series joists are available in
depths of 52 to 72 in and spans from 89 to 144 ft in 17 different chord weights
with total-load capacities of 26,700 to 80,200 lb. Load capacities in the foregoing
were based on a maximum allowable tensile strength of 30 ksi, which calls for
high-strength, low-alloy steel having a specified minimum yield strength of 50 ksi
or cold-formed steel having the same yield strength.
Fire resistance ratings of 1, 11?2, 2, and 3 hours are possible using concrete floors
above decks as thin as 2 in and as thick as 31?2 in with various types of ceiling
protection systems. The Steel Joist Institute identifies such ceiling protection systems
as exposed grids, concealed grids, gypsum board, cementitious, or sprayed
fiber.
8.29 CONSTRUCTION DETAILS FOR OPEN-WEB
STEEL JOISTS
It is essential that bridging be installed between joists as soon as possible after the
joists are placed and before application of any construction loads. The most commonly
used type of bridging is continuous horizontal bracing composed of steel
rods fastened perpendicular to the top and bottom chords of the joists. Diagonal
bridging, however, is also permitted. The attachment of the floor or roof is expected
to provide additional support of the joists against lateral buckling.
It is important that masonry anchors be used on wall-bearing joists. Where the
joists rest on steel beams, they should be welded, or clipped to the beams.
Plastered ceilings attached directly to regular open-web steel joists are usually
supported at underslung ends by means of ceiling extensions, as shown in Fig.
8.24a. Extended ends, as shown in Fig. 8.24b, allow floor and roof treatments
beyond outer supporting stringers.
Relatively small openings between joists may usually be framed with angle,
channel, and Z-shaped headers supported on adjacent joists. Larger openings should
be framed in structural steel. Headers should preferably be located so that they are
supported at trimmer-joist panel points.
9.1
SECTION NINE
CONCRETE CONSTRUCTION
Edward S. Hoffman
President, Edward S. Hoffman, Ltd.,
Structural Engineers, Chicago
David P. Gustafson
Vice President of Engineering
Concrete Reinforcing Steel Institute, Schaumburg, Illinois
Economical, durable construction with concrete requires a thorough knowledge of
its properties and behavior in service, of approved design procedures, and of recommended
field practices. Not only is such knowledge necessary to avoid disappointing
results, especially when concrete is manufactured and formed on the building
site, but also to obtain maximum benefits from its unique properties.
To provide the needed information, several organizations promulgate standards,
specifications, recommended practices, guides, and reports. Reference is made to
these where appropriate throughout this section. Information provided herein is
based on the latest available editions of the documents. Inasmuch as they are revised
frequently, the latest editions should be used for current design and construction.
CONCRETE AND ITS INGREDIENTS
The American Concrete Institute ‘‘Building Code Requirements for Structural Concrete,’’
ACI 318, contains the following basic definitions:
Concrete is a mixture of portland cement or any other hydraulic cement, fine
aggregate, coarse aggregate, and water, with or without admixtures.
Admixture is a material other than hydraulic cement, aggregate, or water, used
as an ingredient of concrete and added to concrete before or during its mixing to
modify its properties.
In this section, unless indicated otherwise, these definitions apply to the terms
concrete and admixture.
9.1 CEMENTITIOUS MATERIALS
The ACI 318 Building Code defines cementitious materials as those that have cementitious
value when used in concrete either by themselves, such as portland
9.2 SECTION NINE
cement, blended hydraulic cements, or expansive cement, or in combination with
fly ash (ASTM specification C618), raw or calcined natural pozzolans (ASTM
C618), ground granulated blast-furnace slag (ASTM C989), or silica fume (ASTM
C1240). Addition to a concrete mix of fly ash, silica fume, or slag decreases permeability,
protects reinforcement, and increases strength. Concrete made with polymers,
plastics with long-chain molecules, can have many qualities much superior
to those of ordinary concrete. See also Sec. 4.
9.2 CEMENTS
The ACI 318 Building Code requires cement to conform to ASTM C150, ‘‘Standard
Specification for Portland Cement;’’ or ASTM C595, ‘‘Standard Specification for
Blended Hydraulic Cements;’’ or ASTM C845, ‘‘Standard Specification for Expansive
Hydraulic Cement.’’ Portland cements meeting the requirements of ASTM
C150 are available in Types I to V and air-entraining Types IA to IIIA for use
under different service conditions. The ACI 318 Building Code prohibits the use
of slag cement, Types A and SA (ASTM C595), because these types are not intended
as principal cementing constituents of structural concrete.
Although all the preceding cements can be used for concrete, they are not interchangeable.
Note that both tensile and compressive strengths vary considerably,
at early ages in particular, even for the five types of basic portland cement. Consequently,
although project specifications for concrete strength are usually based ?
c
on a standard 28-day age for the concrete, the proportions of ingredients required
differ for each type. For concrete strengths up to 19,000 psi for columns in highrise
buildings, specified compressive strengths are usually required at 56 days after
initial set of the concrete. For the usual building project, where the load-strength
relationship is likely to be critical at a point in strength gain equivalent to 7-day
standard curing (Fig. 9.1), substitution of a different type (sometimes brand) of
cement without reproportioning the mix may be dangerous.
The accepted specifications (ASTM) for cements do not regulate cement temperature
nor color. Nevertheless, in hot-weather concreting, the temperature of the
fresh concrete and therefore of its constituents must be controlled. Cement temperatures
above 170F are not recommended (‘‘Hot Weathering Concreting,’’ ACI
305R).
For exposed architectural concrete, not intended to be painted, control of color
is desirable. For uniform color, the water-cement ratio and cement content must be
kept constant, because they have significant effects on concrete color. Bear in mind
that because of variations in the proportions of natural materials used, cements from
different sources differ markedly in color. A change in brand of cement therefore
can cause a change in color. Color differences also provoke a convenient check for
substitution of types (or brands) of cement different from those used in trial batches
made to establish proportions to be employed for a building.
9.3 AGGREGATES
Only material conforming to specifications for normal-weight aggregate (ASTM
C33) or lightweight aggregate for structural concrete (ASTM C330) is accepted
CONCRETE CONSTRUCTION 9.3
FIGURE 9.1 Typical strength-gain rate with standard curing
of non-air-entrained concrete having a ratio of water to cementitious
materials of 0.50.
under the ACI 318 Building Code without special tests. When an aggregate for
which no experience record is available is considered for use, the modulus of elasticity
and shrinkage as well as the compressive strength should be determined from
trial batches of concrete made with the aggregate. In some localities, aggregates
acceptable under C33 or C330 may impart abnormally low ratios of modulus of
elasticity of strength or high shrinkage to concrete. Such aggregates should (E /?
) c c
not be used.
9.4 PROPORTIONING CONCRETE MIXES
Principles for proportioning concrete to achieve a prescribed compressive strength
after a given age under standard curing are simple.
1. The strength of a hardened concrete mix depends on the water-cementitious
materials ratio (ratio of water to cementitious materials, by weight). The water and
cementitious materials form a paste. If the paste is made with more water, it becomes
weaker (Fig. 9.2).
2. The ideal minimum amount of paste is that which will coat all aggregate
particles and fill all voids.
3. For practical purposes, fresh concrete must possess workability sufficient for
the placement conditions. For a given strength and with given materials, the cost
of the mix increases as the workability increases. Additional workability is provided
by more fine aggregate and more water, but more cementitious materials must also
be added to keep the same water-cementitious materials ratio.
9.4 SECTION NINE
FIGURE 9.2 Curves show variation of 28-day
compressive strength of normal-weight concrete
with water-cementitious materials ratio. Solid
lines indicate average results of tests. Dashed
lines indicate relationship given in the ACI 318
Building Code for maximum permissible watercementitious
materials ratio and specified 28-day
strengths.
Because of the variations in material constituents, temperature, and workability
required at jobsites, theoretical approaches for determining ideal mix proportions
usually do not give satisfactory results on the jobsite. Most concrete therefore is
proportioned empirically, in accordance with results from trial batches made with
the materials to be used on the jobsite. Small adjustments in the initial basic mix
may be made as a project progresses; the frequency of such adjustments usually
depends on the degree of quality control.
When new materials or exceptional quality control will be employed, the trialbatch
method is the most reliable and efficient procedure for establishing proportions.
In determination of a concrete mix, past field experience or a series of trial
batches is used to establish a curve relating the water-cementitious materials ratio
to the strength and ingredient proportions of concrete, including admixtures if specified,
for the range of desired strengths and workability (slump). Each point on the
curve should represent the average test results on at least three specimens, and the
curve should be determined by at least three points. Depending on anticipated
quality control, a demonstrated or expected coefficient of variation or standard
deviation is assumed for determination of minimum average strength of test specimens
(Art. 9.10). Mix proportions are selected from the curve to produce this
average strength.
For any large project, significant savings can be made through use of quality
control to reduce the overdesign otherwise required by a building code (law). When
CONCRETE CONSTRUCTION 9.5
FIGURE 9.3 Curves show variation of 28-day
compressive strength of non-air-entrained concrete
with type of aggregate and watercementitious
materials ratio, except that strengths
exceeding 7000 psi were determined at 56 days.
All mixes contained a water-reducing agent and
100 lb / yd3 of fly ash. Calculation of watercementitious
materials ratio included two-thirds
of the fly-ash weight in the cement content.
the owner’s project specifications include a minimum content of cementitious materials,
however, much of the economic incentive for the use of quality control is
lost. See Fig. 9.3 for typical water-cementitious materials ratios.
Note that separate procedures are required for selecting proportions when lightweight
aggregates are used, because their water-absorption properties differ from
those of normal-weight aggregates.
(‘‘Building Code Requirements for Structural Concrete,’’ ACI 318 ‘‘Standard
Specifications for Structural Concrete,’’ ACI 301; ‘‘Standard Practice for Selecting
Proportions for Normal, Heavyweight, and Mass Concrete,’’ ACI 211.1; ‘‘Standard
Practice for Selecting Proportions for Structural Lightweight Concrete,’’ ACI 211.2;
‘‘Recommended Practice for Evaluation of Strength Test Results of Concrete,’’ ACI
214, American Concrete Institute, P.O. Box 9094, Farmington Hills, MI 48333,
‘‘Design and Control of Concrete Mixtures,’’ EB001TC, Portland Cement Association,
5420 Old Orchard Road, Skokie, IL 60077.)
9.6 SECTION NINE
9.5 YIELD CALCULATION
Questions often arise between concrete suppliers and buyers regarding ‘‘yield,’’ or
volume of concrete supplied. A major reason for this is that often the actual yield
may be less than the yield calculated from the volumes of ingredients. For example,
if the mix temperature varies, less air may be entrained; or if the sand becomes
drier and no corrections in batch weights are made, the yield will be under that
calculated.
If the specific gravity (sp. gr.) and absorption (abs.) of the aggregates have been
determined in advance, accurate, yield calculations can be performed as often as
necessary to adjust the yield for control of the concrete.
Example
Yield of Non-Air-Entrained Concrete. The following material properties were
recorded for materials used in trial batches: fine aggregate (sand) sp. gr. 
 2.65,
abs. 
 1%; coarse aggregate (gravel) sp. gr. 
 2.70, abs. 
 0.5%; and cement, sp.
gr. 
 3.15 (typical). These properties are not expected to change significantly as
long as the aggregates used are from the same source. The basic mix proportions
for 1 yd3 of concrete, selected from the trial batches are
Cement: 564 lb (6 bags)
Surface-dry sand: 1170 lb
Surface-dry gravel: 2000 lb
Free water: 300 lb /yd3 (36 gal /yd3)
Check the yield:
564 3 Cement volume
 
2.87 ft
3.15  62.4
3 Water volume 
 300/62.4 
 4.81 ft
1170 3 Sand volume
 
7.08 ft
2.65  62.4
2000 3 Gravel volume
 
11.87 ft
2.70  62.4
3 Total volume of solid constituents 
 26.63 ft
Volume of entrapped air 
 27  26.63 
 0.37 ft3 (1.4%)
Total weight, lb /yd3 
 564  300  1170  2000 
 4034
Total weight, lb / ft3 
 4034/27 
 149.4
Weight of standard 6  12 in cylinder (0.1963 ft3) 
 29.3 lb
These results indicate that some rapid field checks should be made. Total weight,
lb, divided by the total volume, yd3, reported on the trip tickets for truck mixers
should be about 4000 on this project, unless a different slump was ordered and the
CONCRETE CONSTRUCTION 9.7
proportions adjusted accordingly. If the specified slump for the basic mix was to
be reduced, weight, lb /yd3, should be increased, because less water and cement
would be used and the cement paste (water plus cement) weighs 864/7.68 
 113
lb/ft3  149.4 lb / ft3. If the same batch weights are used for all deliveries, and the
slump varies erratically, the yield also will vary. For the same batch weights, a
lower slump is associated with underyield, a higher slump with overyield. With a
higher slump, overyield batches are likely to be understrength, because some of the
aggregate has been replaced by water.
The basic mix proportions in terms of weights may be based on surface-dry
aggregates or on oven-dry aggregates. The surface-dry proportions are somewhat
more convenient, since absorption then need not be considered in calculation of
free water. Damp sand and gravel carry about 5 and 1% free water, respectively.
The total weight of this free water should be deducted from the basic mix weight
of water (300 lb /yd3 in the example) to obtain the weight of water to be added to
the cement and aggregates. The weight of water in the damp aggregates also should
be added to the weights of the sand and gravel to obtain actual batch weights, as
reported on truck-mixer delivery tickets.
9.6 PROPERTIES AND TESTS OF FRESH
(PLASTIC) CONCRETE
About 21?2 gal of water can be chemically combined with each 94-lb sack of cement
for full hydration and maximum strength. Water in excess of this amount will be
required, however, to provide necessary workability.
Workability. Although concrete technologists define and measure workability and
consistency separately and in various ways, the practical user specifies only one—
slump (technically a measure of consistency). The practical user regards workability
requirements simply as provision of sufficient water to permit concrete to be placed
and consolidated without honeycomb or excessive water rise; to make concrete
‘‘pumpable’’ if it is to be placed by pumps; and for slabs, to provide a surface that
can be finished properly. These workability requirements vary with the project and
the placing, vibration, and finishing equipment used.
Slump is tested in the field very quickly. An open-ended, 12-in-high, truncated
metal cone is filled in three equal-volume increments and each increment is consolidated
separately, all according to a strict standard procedure (ASTM C143,
‘‘Slump of Hydraulic-Cement Concrete’’). Slump is the sag of the concrete, in,
after the cone is removed. The slump should be measured to the nearest 1?4 in which
is about the limit of accuracy reproducible by expert inspectors.
Unless the test is performed exactly in accordance with the standard procedure,
the results are not comparable and therefore are useless.
The slump test is invalidated if: the operator fails to anchor the cone down by
standing on the base wings; the test is performed on a wobbly base, such as formwork
carrying traffic or a piece of metal on loose pebbles; the cone is not filled by
inserting material in small amounts all around the perimeter, or filled and tamped
in three equal increments; the top two layers are tamped deeper than their depth
plus about 1 in; the top is pressed down to level it; the sample has been transported
and permitted to segregate without remixing; unspecified operations, such as tap9.8
SECTION NINE
ping the cone, occur; the cone is not lifted up smoothly in one movement; the cone
tips over because of filling from one side or pulling the cone to one side; or if the
measurement of slump is not made to the center vertical axis of the cone.
Various penetration tests are quicker and more suitable for untrained personnel
than the standard slump test. In each case, the penetration of an object into a flat
surface of fresh concrete is measured and related to slump. These tests include use
of the patented ‘‘Kelley ball’’ (ASTM C360, ‘‘Ball Penetration in Freshly Mixed
Hydraulic Cement Concrete’’) and a simple, standard tamping rod with a bullet
nose marked with equivalent inches of slump.
Air Content. A field test frequently required measures the air entrapped and entrained
in fresh concrete. Various devices (air meters) that are available give quick,
convenient results. In the basic methods, the volume of a sample is measured, then
the air content is removed or reduced under pressure, and finally the remaining
volume is measured. The difference between initial and final volume is the air
content. (See ASTM C138, C173, and C231.)
Cement Content. Tests on fresh concrete sometimes are employed to determine
the amount of cement present in a batch. Although performed more easily than
tests on hardened concrete, tests on fresh concrete nevertheless are too difficult for
routine use and usually require mobile laboratory equipment.
9.7 PROPERTIES AND TESTS OF HARDENED
CONCRETE
The principal properties of concrete with which designers are concerned and symbols
commonly used for some of these properties are:

 ?
c specified compressive strength, psi, determined in accordance with ASTM
C39 from standard 6-  12-in cylinders under standard laboratory curing;
unless otherwise specified, is based on tests on cylinders 28 days old ?
c
Ec 
 modulus of elasticity, psi, determined in accordance with ASTM C469; usually
assumed as Ec 
 w1.5 , or for normal-weight concrete (about 145 (33)
?
c
lb/ft3), Ec 
 57,000
?
c
w 
 weight, lb / ft3, determined in accordance with ASTM C138 or C567
?t 
 direct tensile strength, psi
?ct 
 average splitting tensile strength, psi, of lightweight-aggregate concretes determined
by the split cylinder test (ASTM C496)
?r 
 modulus of rupture, psi, the tensile strength at the extreme fiber in bending
(commonly used for pavement design) determined in accordance with ASTM
C78
Other properties, frequently important for particular conditions are: durability to
resist freezing and thawing when wet and with deicers, color, surface hardness,
impact hardness, abrasion resistance, shrinkage, behavior at high temperatures
(about 500F), insulation value at ordinary ambient temperatures, insulation at the
high temperatures of a standard fire test, fatigue resistance, and for arctic construction,
behavior at cold temperatures (60 to 75F). For most of the research on
these properties, specially devised tests were employed, usually to duplicate or
simulate the conditions of service anticipated. (See ‘‘Index to Proceedings of the
American Concrete Institute.’’)
CONCRETE CONSTRUCTION 9.9
In addition to the formal testing procedures specified by ASTM and the special
procedures described in the research references, some practical auxiliary tests, precautions
in evaluating tests, and observations that may aid the user in practical
applications follow.
Compressive Strength, . The standard test (ASTM C39) is used to establish the ?
c
quality of concrete, as delivered, for conformance to specifications. Tests of companion
field-cured cylinders measure the effectiveness of the curing (Art. 9.14).
Core tests (ASTM C42) of the hardened concrete in place, if they give strengths
higher than the specified or an agreed-on percentage of (often 85%), can be ?
 ?
 c c
used for acceptance of material, placing, consolidation, and curing. If the cores
taken for these tests show unsatisfactory strength but companion cores given accelerated
additional curing show strengths above the specified , these tests estab- ?
c
lish acceptance of the material, placing, and consolidation, and indicate the remedy,
more curing, for the low in-place strengths.
For high-strength concretes, say above 5000 psi, care should be taken that the
capping material is also high strength. Better still, the ends of the cylinders should
be ground to plane.
Indirect testing for compressive strength includes surface-hardness tests (impact
hammer). Properly calibrated, these tests can be employed to evaluate field curing.
(See also Art. 9.14.)
Modulus of Elasticity Ec. This property is used in all design, but it is seldom
determined by test, and almost never as a regular routine test. For important projects,
it is best to secure this information at least once, during the tests on the trial
batches at the various curing ages. An accurate value will be useful in prescribing
camber or avoiding unusual deflections. An exact value of Ec is invaluable for longspan,
thin-shell construction, where deflections can be large and must be predicted
accurately for proper construction and timing removal of forms.
Tensile Strength. The standard splitting test is a measure of almost pure uniform
tension ?ct. The beam test (Fig. 9.4a) measures bending tension ?r on extreme
surfaces (Fig. 9.4b), calculated for an assumed perfectly elastic, triangular stress
distribution.
The split-cylinder test (Fig. 9.4c) is used for structural design. It is not sensitive
to minor flaws or the surface condition of the specimen. The most important application
of the splitting test is in establishment of design values for reinforcingsteel
development length, shear in concrete, and deflection of structural lightweight
aggregate concretes.
The values of ?ct (Fig. 9.4d) and ?r bear some relationship to each other, but are
not interchangeable. The beam test is very sensitive, especially to flaws on the
surface of maximum tension and to the effect of drying-shrinkage differentials, even
between the first and last of a group of specimens tested on the same day. The
value ?r is widely used in pavement design, where all testing is performed in the
same laboratory and results are then comparable.
Special Properties. Frequently, concrete may be used for some special purpose
for which special properties are more important than those commonly considered.
Sometimes, it may be of great importance to enhance one of the ordinary properties.
These special applications often become apparent as new developments using new
materials or as improvements using the basic materials. The partial list of special
properties is constantly expanding—abrasion and impact resistance (heavy-duty
floor surfacings), heat resistance (chimney stacks and jet engine dynamometer
9.10 SECTION NINE
FIGURE 9.4 Test methods for tensile strength of concrete: (a) beam test
determines modulus of rupture ?r; (b) stress distribution assumed for calculation
of ?r; (c) split-cylinder test measures internal tension ?ct; (d ) stress
distribution assumed for ?ct.
cells), light weight (concrete canoes), super-high-compressive strength, over ksi
(high-rise columns), waterproof concrete, resistance to chemical attack (bridge
decks, chemical industry floors, etc.), increased tensile strength (highway resurfacing,
precast products, etc.), shrinkage-compensating concrete (grouting under base
plates), etc. Some of these special properties are achieved with admixtures (see Art.
9.9). Some utilize special cements (high-alumina cement for heat resistance or expansive
cement for shrinkage-compensating concrete). Some utilize special aggregates
(lightweight aggregate, steel fiber, plastic fiber, glass fiber, and special heavy
aggregate). (See ‘‘State-of-the-Art Report on Fiber Reinforced Concrete,’’ ACI
544.1R). Some special properties—increased compressive and tensile strength, waterproofing,
and improved chemical resistance are achieved with polymers, either
as admixtures or surface treatment of hardened concrete. (See ‘‘Guide for the Use
of Polymers in Concrete,’’ ACI 548.1R.)
9.8 MEASURING AND MIXING
CONCRETE INGREDIENTS
Methods of measuring the quantities and mixing the ingredients for concrete, and
the equipment available, vary greatly. For very small projects where mixing is
performed on the site, the materials are usually batched by volume. Under these
conditions, accurate proportioning is very difficult. To achieve a reasonable minimum
quality of concrete, it is usually less expensive to prescribe an excess of
cement than to employ quality control. The same conditions make use of airCONCRETE
CONSTRUCTION 9.11
entraining cement preferable to separate admixtures. This practical approach is preferable
also for very small projects to be supplied with ready-mixed concrete. Economy
with excess cement will be achieved whenever volume is so small that the
cost of an additional sack of cement per cubic yard is less than the cost of a single
compression test.
For engineered construction, some measure of quality control is always employed.
In general, all measurements of materials including the cement and water
should be by weight. The ACI 318 Building Code provides a sliding scale of
overdesign for concrete mixes that is inversely proportional to the degree of quality
control provided. In the sense used here, such overdesign is the difference between
the specified and the actual average strength as measured by tests. ?
c
Mixing and delivery of structural concrete may be performed by a wide variety
of equipment and procedures:
Site mixed, for delivery by chute, pump, truck, conveyor, or rail dump cars.
(Mixing procedure for normal-aggregate concretes and lightweight-aggregate
concretes to be pumped are usually different, because the greater absorption of
some lightweight aggregates must be satisfied before pumping.)
Central-plant mixed, for delivery in either open dump trucks or mixer trucks.
Central-plant batching (weighing and measuring), for mixing and delivery by
truck (‘‘dry-batched’’ ready mix).
Complete portable mixing plants are available and are commonly used for large
building or paving projects distant from established sources of supply.
Generally, drum mixers are used. For special purposes, various other types of
mixers are required. These special types include countercurrent mixers, in which
the blades revolve opposite to the turning of the drum, usually about a vertical axis,
for mixing very dry, harsh, nonplastic mixes. Such mixes are required for concrete
masonry or heavy-duty floor toppings. Dry-batch mixers are used for dry shotcrete
(sprayed concrete), where water and the dry-mixed cement and aggregate are
blended between the nozzle of the gun and impact at the point of placing.
(‘‘Guide for Measuring, Mixing, Transporting, and Placing Concrete,’’ ACI
304R.)
9.9 ADMIXTURES
The ACI 318 Building Code requires prior approval by the engineer of admixtures
to be used in concrete.
Air Entrainment. Air-entraining admixtures (ASTM C260) may be interground
as additives with the cement at the mill or added separately at the concrete mixing
plant, or both. Where quality control is provided, it is preferable to add such admixtures
at the concrete plant so that the resulting air content can be controlled for
changes in temperature, sand, or project requirements.
Use of entrained air is recommended for all concrete exposed to weathering or
deterioration from aggressive chemicals. The ACI 318 Building Code requires air
entrainment for all concrete subject to freezing temperatures while wet. Detailed
recommendations for air content are available in ‘‘Standard Practice for Selecting
9.12 SECTION NINE
Proportions for Normal, Heavyweight, and Mass Concrete,’’ ACI 211.1, and ‘‘Standard
Practice for Selecting Proportions for Structural Lightweight Concrete,’’ ACI
211.2.
One common misconception relative to air entrainment is the fear that it has a
deleterious effect on concrete strength. Air entrainment, however, improves workability.
This will usually permit some reduction in water content. For lean, lowstrength
mixes, the improved workability permits a relatively large reduction in
water content, sand content, and water-cementitious materials ratio, which tends to
increase concrete strength. The resulting strength gain offsets the strength-reducing
effect of the air itself, and a net increase in concrete strength is achieved. For rich,
high-strength mixes, the relative reduction in the ratio of water to cementitious
materials, water-cementitious materials ratio, is lower and a small net decrease in
strength results, about on the same order of the air content (4 to 7%). The improved
durability and reduction of segregation in handling, because of the entrained air,
usually make air entrainment desirable, however, in all concrete except extremely
high-strength mixtures, such as for lower-story interior columns or heavy-duty interior
floor toppings for industrial wear.
Accelerators. Calcium chloride for accelerating the rate of strength gain in concrete
(ASTM D98) is perhaps the oldest application of admixtures. Old specifications
for winter concreting or masonry work commonly required use of a maximum
of 1 to 3% CaCl2 by weight of cement for all concrete. Proprietary admixtures now
available may include accelerators, but not necessarily CaCl2. The usual objective
for use of an accelerator is to reduce curing time by developing 28-day strengths
in about 7 days (ASTM C494).
In spite of users’ familiarity with CaCl2, a number of misconceptions about its
effect persist. It has been sold (sometimes under proprietary names) as an accelerator,
a cement replacement, an ‘‘antifreeze,’’ a ‘‘waterproofer,’’ and a ‘‘hardener.’’
It is simply an accelerator; any improvement in other respects is pure serendipity.
Experience, however, indicates corrosion damage from indiscriminate use of chloride-
containing material in concrete exposed to stray currents, containing dissimilar
metals, containing prestressing steel subject to stress corrosion, or exposed to severe
wet freezing or salt water. The ACI 318 Building Code prohibits the use of calcium
chloride or admixtures containing chloride from other than impurities from admixture
ingredients in prestressed concrete, in concrete containing embedded aluminum,
or in concrete cast against stay-in-place galvanized forms. The Code also
prohibits the use of calcium chloride as an admixture in concrete that will be
exposed to severe or very severe sulfate-containing solutions. For further information,
see ‘‘Chemical Admixtures for Concrete,’’ ACI 212.3R.
Retarders. Unless proper precautions are taken, hot-weather concreting may cause
‘‘flash set,’’ plastic shrinkage, ‘‘cold joints,’’ or strength loss. Admixtures that provide
controlled delay in the set of a concrete mix without reducing the rate of
strength gain during subsequent curing offer inexpensive prevention of many hotweather
concreting problems. These (proprietary) admixtures are usually combined
with water-reducing admixtures that more than offset the loss in curing time due
to delayed set (ASTM C494). See ‘‘Hot Weathering Concreting,’’ ACI 305R, for
further details on retarders, methods of cooling concrete materials, and limiting
temperatures for hot-weathering concreting.
Superplasticizers. These admixtures, which are technically known as ‘‘high-range
water reducers,’’ produce a high-slump concrete without an increase in mixing water.
Slumps of up to 10 in. for a period of up to 90 min can be obtained. This
CONCRETE CONSTRUCTION 9.13
greatly facilitates placing concrete around heavy, closely spaced reinforcing steel,
or in complicated forms, or both, and reduces the need for vibrating the concrete.
It is important that the slump of the concrete be verified at the jobsite prior to the
addition of the superplasticizer. This ensures that the specified water-cementitious
materials ratio required for watertight impermeable concrete is in fact being
achieved. The superplasticizer is then added to increase the slump to the approved
level.
Waterproofing. A number of substances, such as stearates and oils, have been
used as masonry-mortar and concrete admixtures for ‘‘waterproofing.’’ Indiscriminate
use of such materials in concrete without extremely good quality control usually
results in disappointment. The various water-repellent admixtures are intended
to prevent capillarity, but most severe leakage in concrete occurs at honeycombs,
cold joints, cracks, and other noncapillary defects. Concrete containing waterrepellent
admixtures also requires extremely careful continuous curing, since it will
be difficult to rewet after initial drying.
Waterproof concrete can be achieved by use of high-strength concrete with a
low water-cementitious materials ratio to reduce segregation and an air-entraining
agent to minimize crack width. Also, good quality control and inspection is essential
during the mixing, placing, and curing operations. Surface coatings can be used to
improve resistance to water penetration of vertical or horizontal surfaces. For detailed
information on surface treatments, see ‘‘Guide to Durable Concrete,’’ ACI
201.2R.
Cement Replacement. The term ‘‘cement replacement’’ is frequently misused in
reference to chemical admixtures intended as accelerators or water reducers.
Strictly, a cement replacement is a finely ground material, usually weakly cementitious
(Art. 9.1), which combines into a cementlike paste replacing some of the
cement paste to fill voids between the aggregates. The most common applications
of these admixtures are for low-heat, low-strength mass concrete or for concrete
masonry. In the former, they fill voids and reduce the heat of hydration; in the latter,
they fill voids and help to develop the proper consistency to be self-standing as the
machine head is lifted in the forming process. Materials commonly used are fly
ash, silica fume, ground granulated blast-furnace slag, hydraulic lime, natural cement,
and pozzolans.
Special-Purpose Admixtures. The list of materials used from earliest times as
admixtures for various purposes includes almost everything from human blood to
synthetic coloring agents.
Admixtures for coloring concrete are available in all colors. The oldest and
cheapest is perhaps carbon black.
Admixtures causing expansion for use in sealing cracks or under machine bases,
etc., include powdered aluminum and finely ground iron.
Special admixtures are available for use where the natural aggregate is alkali
reactive, to neutralize this reaction.
Proprietary admixtures are available that increase the tensile strength or bond
strength of concrete. They are useful for making repairs to concrete surfaces.
For special problems requiring concrete with unusual properties, detailed recommendations
of ‘‘Chemical Admixtures for Concrete,’’ ACI 212.3R, and references
it contains, may be helpful.
For all these special purposes, a thorough investigation of admixtures proposed
is recommended. Tests should be made on samples containing various proportions
for colored concrete. Strength and durability tests should be made on concrete to
9.14 SECTION NINE
be exposed to sunlight, freezing, salt, or any other job condition expected, and
special tests should be made for any special properties required, as a minimum
precaution.
QUALITY CONTROL
9.10 MIX DESIGN
Concrete mixes are designed with the aid of test records obtained from field experience
with the materials to be used. When field test results are not available,
other means of mix proportioning can be used as described in this article. In any
case, the proportions of ingredients must be selected to produce, so that for any
three test specimens, the average strength equals or exceeds the specified compressive
strength and no individual strength test (average of two specimens) falls ?
c
below by more than 500 psi. ?
c
The required average strength, depends on the standard deviation s expected. ?
cr
Strength data for determining the standard deviation can be considered suitable if
they represent either a group of at least 30 consecutive tests representing materials
and conditions of control similar to those expected or the statistical average for two
groups totaling 30 or more tests. The tests used to establish standard deviation
should represent concrete produced to meet a specified strength within 1000 psi of
that specified for the work proposed. For a single group of consecutive test results,
the standard deviation is calculated
2 2 2 2 (x  x)  (x  x)  (x  x)  


  (x  x) 1 2 3 n s 
 (9.1)  n  1
where x1, x2, . . . , xn 
 strength, psi, obtained in test of first, second, . . . , nth
sample, respectively
n 
 number of tests

 x average strength, psi of n cylinders
For two groups of consecutive test results combined, the standard deviation is calculated
2 2 (n  1)(s )  (n  1)(s ) 1 1 2 2 s 
 (9.2)  (n  n  2) 1 2
where s1, s2 
 standard deviation calculated from two test records, 1 and 2, respectively
n1, n2 
 number of tests in each test record, respectively
(‘‘Recommended Practice for Evaluation of Strength Test Results of Concrete,’’ACI
214.)
The strength used as a basis for selecting proportions of a mix should exceed
the required by at least the amount indicated in Table 9.1. ?
c
CONCRETE CONSTRUCTION 9.15
TABLE 9.1 Recommended Average
Strengths of Test Cylinders for Selecting
Proportions for Concrete Mixes
Range of standard
deviation s, psi
Average strength ?
cr
psi
Under 300  400 ?
c
300–400  550 ?
c
400–500  700 ?
c
500–600  900 ?
c
Over 600  1200 ?
c
TABLE 9.2 Required Average Compressive Strength When
Data Are Not Available to Establish a Standard Deviation
Specified compressive
strength, , psi ?
c
Required average compressive
strength, , psi ?
cr
Less than 3000  1000 ?
c
3000 to 5000  1200 ?
c
5000 to 10,000*  1400 ?
c
Over 10,000 to 15,000*  1800 ?
c
*From ACI 301 ‘‘Standard Specifications for Structural Concrete.’’
The values for in Table 9.1 are the larger of the values calculated from Eqs. ?
cr
(9.3) and (9.4).
?
 
 ?
  1.34 ks (9.3) cr c
?
 
 ?
  2.23 ks  500 (9.4) cr c
where k 
 1.00 for 30 tests, 1.03 for 25,
1.08 for 20, and 1.16 for 15.
For an established supplier of concrete, it is very important to be able to document
the value of s. This value is based on a statistical analysis in which Eq. (9.1)
is applied to at least 30 consecutive tests, and Eq. (9.2) is applied to two groups
of consecutive tests totaling at least 30 tests. These tests must represent similar
materials and conditions of control not stricter than those to be applied to the
proposed project. The lower the value of s obtained from the tests, the closer the
average strength is permitted to be to the specified strength. A supplier is thus
furnished an economic incentive, lower cementitious materials content, to develop
a record of good control (low s). A supplier who does maintain such a record can,
in addition, avoid the expenses of trial batches.
When no such production record exists, the required average strength can ?
 , cr
be determined from Table 9.2. Documentation of the required average strength must
be established. The documentation should consist of field strength records or trial
mixtures confirming that the proposed concrete proportions will produce an average
compressive strength equal to or greater than Alternatively, when an acceptable ?
 . cr
9.16 SECTION NINE
TABLE 9.3 Required Air Entrainment in
Concrete Exposed to Freezing and Thawing
Nominal maximum
size of coarse
aggregate, in.
Total air content,
% by volume
Severe
exposure
Moderate
exposure
3?8 71?2 6
1?2 7 51?2
3?4 6 5
1 6 41?2
11?2 51?2 41?2
2 5 4
3 41?2 31?2
*From ACI 318-99, Table 4.2.1. for  5000 psi, ?
c
air content may be reduced 1%. ‘‘Severe exposure’’ is
where concrete in a cold climate may be in almost
continuous contact with moisture prior to freezing, or
where deicing salts are used. ‘‘Moderate exposure’’ is
where concrete in a cold climate will only be exposed
to moisture prior to freezing and where no deicing salts
are used.
record of field test results is not available, the ACI 318 Building Code, with several
restrictions, permits the use of trial batches as a basis for selecting initial proportions.
This condition is likely to occur when new sources of cement or aggregate
are supplied to an established plant, to a new facility, such as a portable plant on
the site, or for the first attempt at a specified strength more than 1000 psi above ?
c
previous specified strengths.
The ACI 318 Building Code includes provisions for proportioning concrete
mixes based on other experience or information, if approved by the Engineer. This
alternative procedure is restricted to proportioning concrete with a specified  ?
c
4000 psi. The required average compressive strength must be at least 1200 psi ?
cr
greater than Concrete proportioned by this procedure must also conform to the ?
. c
Code’s durability requirements. These provisions are intended to allow the construction
work to continue when there is an unexpected interruption in concrete supply
and time does not permit tests and evaluation. These provisions are also aimed at
small projects where the cost of trial batches is not justified.
The initially established proportions can be used during progress of a project
only as long as the strength-test results justify them. The process of quality control
of concrete for a project requires maintenance of a running average of strength-test
results and changes in the proportions whenever the actual degree of control (standard
deviation s) varies from that assumed for the initial proportioning. Equations
(9.3) and (9.4) are applied for this analysis. With project specifications based on
the ACI 318 Building Code, no minimum cementitious-materials content is required;
so good control during a long-time project is rewarded by permission to
use a lower cementitious-materials content than would be permitted with inferior
control.
Regardless of the method used for proportioning the basic initial proportions
should be based on mixes with both air content and slump at the maximum permitted
by the project specifications.
CONCRETE CONSTRUCTION 9.17
Other ACI 318 Building Code requirements for mix design are:
1. Concrete exposed to freezing and thawing or to deicing chemicals while wet
should have air entrained within the limits in Table 9.3, and the water-cementitious
materials ratio by weight should not exceed 0.45. If lightweight aggregate is used,
should be at least 4500 psi. ?
c
2. For watertight, normal-weight concrete, maximum water-cementitious materials
ratios by weight are 0.50 for exposure to fresh water and 0.40 for seawater or
deicing chemicals. With lightweight aggregate, minimum is 4000 psi for concrete ?
c
exposed to fresh water and is 5000 psi for seawater or deicing chemicals. ?
c
Although the Code does not distinguish between a ‘‘concrete production facility’’
with in-house control and an independent concrete laboratory control service, the
distinction is important. Very large suppliers have in-house professional quality
control. Most smaller suppliers do not. Where the records of one of the latter might
indicate a large standard deviation, but an independent quality-control service is
utilized, the standard deviation used to select should be based on the proven ?
cr
record of the control agency. Ideally, the overdesign should be based, in these cases,
on the record of the control agency operating in the concrete plant used.
9.11 CHECK TESTS OF MATERIALS
Without follow-up field control, all the statistical theory involved in mixed proportioning
becomes an academic exercise.
The complete description of initial proportions should include: cement analysis
and source; specific gravity, absorption, proportions of each standard sieve size;
fineness modulus; and organic tests for fine and coarse aggregates used, as well as
their weights and maximum nominal sizes.
If the source of any aggregate is changed, new trial batches should be made. A
cement analysis should be obtained for each new shipment of cement.
The aggregate gradings and organic content should be checked at least daily, or
for each 150 yd3. The moisture content (or slump) should be checked continuously
for all aggregates, and suitable adjustments should be made in batch weights. When
the limits of ASTM C33 or C330 for grading or organic content are exceeded,
proper materials should be secured and new mix proportions developed, or until
these measurements can be effected, concrete production may continue on an emergency
basis but with a penalty of additional cement.
9.12 AT THE MIXING PLANT—
YIELD ADJUSTMENTS
Well-equipped concrete producers have continuous measuring devices to record
changes in moisture carried in the aggregates or changes in total free water in the
contents of the mixer. The same measurements, however, may be easily made manually
by quality-control personnel.
To illustrate: for the example in Art. 9.5, the surface-dry basic mix is cement,
564 lb; water, 300 lb; sand, 1170 lb; and gravel, 2000 lb. Absorption is 1% for the
9.18 SECTION NINE
sand and 0.5% for the gravel. If the sand carries 5.5% and the gravel 1.0% total
water by weight, the added free water becomes:
Sand: 1170 (0.055  0.01) 
 53 lb
Gravel: 2000 (0.010  0.005) 
 10 lb
Batch weights adjusted for yield become:
Cement: 564 lb
Water: 300  53  10 
 237 lb
Sand: 1170  53 
 1223 lb
Gravel: 2000  10 
 2010 lb
Note that the corrective adjustment includes adding to aggregate weights as well
as deducting water weight. Otherwise, the yield will be low, and slump (slightly)
increased. The yield would be low by about
53  10 3 3 
 0.381 ft /yd 
 1.4%
2.65  62.4
9.13 AT THE PLACING POINT—
SLUMP ADJUSTMENTS
With good quality control, no water is permitted on the mixing truck. If the slump
is too low (or too high) on arrival at the site, additional cement must be added. If
the slump is too low (the usual complaint), additional water and cement in the
prescribed water-cementitious materials ratio can also be added. After such additions,
the contents must be thoroughly mixed, 2 to 3 min at high speed. Because
placing-point adjustments are inconvenient and costly, telephone or radio communication
with the supply plant is desirable so that most such adjustments may be
made conveniently at the plant.
Commonly, a lesser degree of control is accepted in which the truck carries
water, the driver is on the honor system not to add water without written authorization
from a responsible agent at the site, and the authorization as well as the
amounts added are recorded on the record (trip ticket) of batch weights.
Note: If site adjustments are made, test samples for strength-test specimens
should be taken only after all site adjustments. For concrete in critical areas, such
as lower-floor columns in high-rise buildings, strictest quality control is recommended.
9.14 STRENGTH TESTS
Generally, concrete quality is measured by the specified compressive strength of ?
c
6-  12-in cylinders after 28 days of laboratory curing.
CONCRETE CONSTRUCTION 9.19
Conventional Tests. The strength tests performed after various periods of field
curing are typically specified to determine curing adequacy. For lightweightaggregate
concretes only, the same type of laboratory-cured test specimen is tested
for tensile splitting strength ?ct to establish design values for deflection, development
of reinforcing steel, and shear. Applicable ASTM specifications for these tests
are
C31, ‘‘Making and Curing Concrete Test Specimens in the Field.’’
C39, ‘‘Test for Compressive Strength of Cylindrical Concrete Specimens.’’
C496, ‘‘Test for Splitting Tensile Strength of Cylindrical Concrete Specimens.’’
The specifications for standard methods and procedures of testing give general
directions within which the field procedures can be adjusted to jobsite conditions.
One difficulty arises when the specimens are made in the field from samples taken
at the jobsite. During the first 48 h after molding, the specimens are very sensitive
to damage and variations from standard laboratory curing conditions, which can
significantly reduce the strength-test results. Yet, jobsite conditions may preclude
sampling, molding, and field storage on the same spot.
If the fresh-concrete sample must be transported more than about 100 ft to the
point of molding cylinders, some segregation occurs. Consequently, the concrete
sample should be remixed to restore its original condition. After the molds for test
cylinders have been filled, if the specimens are moved, high-slump specimens segregate
in the molds; low-slump specimens in the usual paper or plastic mold are
often squeezed out of shape or separated into starting cracks. Such accidental damage
varies with slump, temperature, time of set and molding, and degree of carelessness.
If the specimen cylinders are left on the jobsite, they must be protected against
drying and accidental impact from construction traffic. If a worker stumbles over a
specimen less than 3 days old, it should be inspected for damage. The best practice
is to provide a small, insulated, dampproofed, locked box on the site in which
specimens can be cast, covered, and provided with 60 to 80F temperature and
100% humidity for 24 to 72 h. Then, they can be transported and subjected to
standard laboratory curing conditions at the testing laboratory. When transported,
the cylinders should be packed and handled like fresh eggs, since loose rattling will
have about an equivalent effect in starting incipient cracks.
Similarly, conditions for field-cured cylinders must be created as nearly like
those of the concrete in place as possible. Also, absolute protection against impact
or other damage must be provided. Because most concrete in place will be in much
larger elements than a test cylinder, most of the in-place concrete will benefit more
from retained heat of hydration (Fig. 9.5). This effect decreases rapidly, because
the rate of heat development is greatest initially. To ensure similar curing conditions,
field-cured test cylinders should be stored for the first 24 h in the field curing box
with the companion cylinders for laboratory curing. After this initial curing, the
field-cured cylinders should be stored near the concrete they represent and cured
under the same conditions.
Exceptions to this initial curing practice arise when the elements cast are of
dimensions comparable to those of the cylinders, or the elements cast are not protected
from drying or low temperatures, including freezing, or test cylinders are
cured inside the elements they represent (patented system).
These simple, seemingly overmeticulous precautions will eliminate most of the
unnecessary, expensive, project-delaying controversies over low tests. Both con9.20
SECTION NINE
FIGURE 9.5 Effect of curing temperature on strength-gain rate of concrete,
with 28-day strength as basis.
tractor and owner are justifiably annoyed when costly later tests on hardened concrete,
after an even more costly project delay, indicate that the original freshconcrete
test specimens were defective and not the building concrete.
Special Tests. Many other strength tests or tests for special qualities are occasionally
employed for special purposes. Those most often encountered in concrete
building construction are strength tests on drilled cores and sawed beams (ASTM
C42); impact tests (ASTM C805), e.g., Schmidt hammer; pullout tests (ASTM
C900); penetration tests (ASTM C803); determination of modulus of elasticity during
the standard compression test; and deflection measurements on a finished building
element under load (Chap. 20, ACI 318-99). (See also ‘‘Commentary on ACI
318-99’’ and the ‘‘Manual of Concrete Inspection,’’ (ACI SP-2.)
Newer methods for evaluating in-situ strength of concrete include the following:
Methods, such as the one in which test cylinders are field-cured inside the in-situ
concrete, measure compressive strength directly, refined even to measuring it in a
desired direction. Others actually measure other properties, such as penetration,
impact, or pullout, which are indirect measures of compressive strength, but may
be employed because the property they measure is itself important. For example,
in cantilevered form construction where forms for each new lift are bolted into the
previous lift, pullout results may be more meaningful than standard compression
tests. (See ‘‘Testing Hardened Concrete,’’ ACI Monograph No. 9, 1976.) Most of
the in-situ tests may also be classified as accelerated tests, although not all accelerated
tests are performed in situ.
Because construction time is continually becoming a more important factor in
overall construction economy, the standard 28-day strength becomes less significant.
CONCRETE CONSTRUCTION 9.21
For example, the final strength at completion of a high-rise project requiring highstrength
concrete in lower-story columns is often specified 90-days. At the other
extreme, a floor system may be loaded by the forms and concrete for the floor
above in as little as 2 days. These conditions demand accelerated testing. (See
‘‘Standard Specifications for Structural Concrete,’’ ACI 301; and ASTM C684,
‘‘Standard Test Method for Making, Accelerated Curing, and Testing Concrete
Compression Test Specimens.’’)
9.15 TEST EVALUATION
On small projects, the results of tests on concrete after the conventional 28 days of
curing may be valuable only as a record. In these cases, the evaluation is limited
to three options: (1) accept results, (2) remove and replace faulty concrete, or (3)
conduct further tests to confirm option (1) or (2) or for limited acceptance at a
lower-quality rating. The same comment can be applied to a specific element of a
large project. If the element supports 28 days’ additional construction above, the
consequences of these decisions are expensive.
Samples sufficient for at least five strength tests of each class of concrete should
be taken at least once each day, or once for each 150 yd3 of concrete or each 5000
ft2 of surface area placed. Each strength test should be the average for two cylinders
from the same sample. The strength level of the concrete can be considered satisfactory
if the averages of all sets of three consecutive strength-test results equal or
exceed the specified strength and no individual strength-test result falls below ?
c
by more than 500 psi. ?
c
If individual tests of laboratory-cured specimens produce strengths more than
500 psi below , steps should be taken to assure that the load-carrying capacity ?
c
of the structure is not jeopardized. Three cores should be taken for each case of a
cylinder test more than 500 psi below . If the concrete in the structure will be ?
c
dry under service conditions, the cores should be air-dried (temperature 60 to 80F,
relative humidity less than 60%) for 7 days before the tests and should be tested
dry. If the concrete in the structure will be more than superficially wet under service
conditions, the cores should be immersed in water for at least 48 h and tested wet.
Regardless of the age on which specified design strength is based, large ?
c
projects of the long duration offer the opportunity for adjustment of mix proportions
during the project. If a running average of test results and deviations from the
average is maintained, then, with good control, the standard deviation achieved may
be reduced significantly below the usually conservative, initially assumed standard
deviation. In that case, a saving in cement may be realized from an adjustment
corresponding to the improved standard deviation. If control is poor, the owner
must be protected by an increase in cement. Project specifications that rule out
either adjustment are likely to result in less attention to quality control.
FORMWORK
For a recommended overall basis for project specifications and procedures, see
‘‘Guide to Formwork for Concrete,’’ ACI 347R. For materials, details, etc., for
builders, see ‘‘Formwork for Concrete,’’ ACI SP-4. For requirements in project
specifications, see ‘‘Standard Specifications for Structural Concrete, ACI 301.
9.22 SECTION NINE
9.16 RESPONSIBILITY FOR FORMWORK
The exact legal determination of responsibilities for formwork failures among
owner, architect, engineer, general contractor, subcontractors, or suppliers can be
determined only by a court decision based on the complete contractual arrangements
undertaken for a specific project.
Generally accepted practice makes the following rough division of responsibilities:
Safety. The general contractor is responsible for the design, construction, and
safety of formwork. Subcontractors or material suppliers may subsequently be held
responsible to the general contractor. The term ‘‘safety’’ here includes prevention
of any type of formwork failure. The damage caused by a failure always includes
the expense of the formwork itself, and may also include personal injury or damage
to the completed portions of a structure. Safety also includes protection of all personnel
on the site from personal injury during construction. Only the supervisor of
the work can control the workmanship in assembly and the rate of casting on which
formwork safety ultimately depends.
Structural Adequacy of the Finished Concrete. The structural engineer is responsible
for the design of the reinforced concrete structure. The reason for project
specifications requiring that the architect or engineer approve the order and time of
form removal, shoring, and reshoring is to ensure proper structural behavior during
such removal and to prevent overloading of recently constructed concrete below or
damage to the concrete from which forms are removed prematurely. The architect
or engineer should require approval for locations of construction joints not shown
on project drawings or project specifications to ensure proper transfer of shear and
other forces through these joints. Project specifications should also require that
debris be cleaned from form material and the bottom of vertical element forms,
and that form-release agents used be compatible with appearance requirements and
future finishes to be applied. None of these considerations, however, involves the
safety of the formwork per se.
9.17 MATERIALS AND ACCESSORIES
FOR FORMS
When a particular design or desired finish imposes special requirements, and only
then, the engineer’s project specifications should incorporate these requirements and
preferably require sample panels for approval of finish and texture. Under competitive
bidding, best bids are secured when the bidders are free to use ingenuity and
their available materials (‘‘Formwork for Concrete,’’ ACI SP-4).
9.18 LOADS ON FORMWORK
Formwork should be capable of supporting safely all vertical and lateral loads that
might be applied to it until such loads can be supported by the ground, the concrete
structure, or other construction with adequate strength and stability. Dead loads on
CONCRETE CONSTRUCTION 9.23
formwork consist of the weight of the forms and the weight of and pressures from
freshly placed concrete. Live loads include weights of workers, equipment, material
storage, and runways, and accelerating and braking forces from buggies and other
placement equipment. Impact from concrete placement also should be considered
in formwork design.
Horizontal or slightly inclined forms often are supported on vertical or inclined
support members, called shores, which must be left in place until the concrete
placed in the forms has gained sufficient strength to be self-supporting. The shores
may be removed temporarily to permit the forms to be stripped for reuse elsewhere,
if the concrete has sufficient strength to support dead loads, but the concrete should
then be reshored immediately. Loads assumed for design of shoring and reshoring
of multistory construction should include all loads transmitted from the stories
above as construction proceeds.
9.18.1 Pressure of Fresh Concrete on Vertical Forms
This pressure may be estimated from
R
p 
 150  9000 (9.5)
T
where p 
 lateral pressure, psf
R 
 rate of filling, ft /h
T 
 temperature of concrete, F
See Fig. 9.6a.
For columns, the maximum pressure pmax is 3000 psf or 150h, whichever is less,
where h 
 height, ft, of fresh concrete above the point of pressure. For walls where
R does not exceed 7 ft /h, pmax 
 2000 psf or 150h, whichever is less.
For walls with rate of placement R  7,
43,400 R
p 
 150 2800 (9.6)
T T
where pmax 
 2000 psf or 150h, whichever is less. See Fig. 9.6b.
The calculated form pressures should be increased if concrete unit weight exceeds
150 pcf, cements are used that are slower setting than standard portland
cement, slump is more than 4 in. with use of superplasticizers, retarders are used
to slow set, the concrete is revibrated full depth, or forms are externally vibrated.
Under these conditions, a safe design assumes that the concrete is a fluid with
weight w and pmax 
 wh for the full height of placement.
9.18.2 Design Vertical Loads for Horizontal Forms
Best practice is to consider all known vertical loads, including the formwork itself,
plus concrete, and to add an allowance for live load. This allowance, including
workers, runways, and equipment, should be at least 50 psf. When concrete will
be distributed from overhead by a bucket or by powered buggies, an additional
allowance of at least 25 psf for impact load should be added. Note that the weight
of a loaded power buggy dropping off a runway, or an entire bucket full of concrete
9.24 SECTION NINE
FIGURE 9.6 Internal pressures exerted by concrete on formwork: (a)
column forms; (b) wall forms.
CONCRETE CONSTRUCTION 9.25
dropped at one spot, is not considered and might exceed designs based on 50- or
75-psf live load. Formwork should be designed alternatively, with continuity, to
accept such spot overloads and distribute them to various unloaded areas, or with
independently braced units to restrict a spot overload to a spot failure. The first
alternative is preferable.
9.18.3 Lateral Loads for Shoring
Most failures of large formwork are ‘‘progressive,’’ vertically through several floors,
or horizontally, as each successive line of shoring collapses like a house of cards.
To eliminate all possibility of a large costly failure, the overall formwork shoring
system should be reviewed before construction to avoid the usual ‘‘house-of-cards’’
design for vertical loads only. Although it is not always possible to foresee exact
sources or magnitudes of lateral forces, shoring for a floor system should be braced
to resist at least 100 lb / lin ft acting horizontally upon any of the edges, or a total
lateral force on any edge equal to 2% of the total dead loads on the floor, whichever
is larger.
Wall forms should be braced to resist local building-code wind pressures, plus
at least 100 lb / lin ft at the top in either direction. The recommendation applies to
basement wall forms even though wind may be less, because of the high risk of
personal injury in the usual restricted areas for form watchers and other workers.
9.19 FORM REMOVAL AND RESHORING
Much friction between contractors’ and owners’ representatives is created because
of misunderstanding of the requirements for form removal and reshoring. The contractor
is concerned with a fast turnover of form reuse for economy (with safety),
whereas the owner wants quality, continued curing for maximum in-place strength,
and an adequate strength and modulus of elasticity to minimize initial deflection
and cracking. Both want a satisfactory surface.
Satisfactory solutions for all concerned consist of the use of high-early-strength
concrete or accelerated curing, or substitution of a means of curing protection other
than formwork. The use of field-cured cylinders (Arts. 9.7 and 9.14) in conjunction
with appropriate nondestructive in-place strength tests (Art. 9.14) enables owner
and contractor representatives to measure the rate of curing to determine the earliest
time for safe form removal.
Reshoring or ingenious formwork design that keeps shores separate from surface
forms, such as ‘‘flying forms’’ that are attached to the concrete columns, permits
early stripping without premature stress on the concrete. Properly performed, reshoring
is ideal from the contractors’ viewpoint. But the design of reshores several
stories in depth becomes very complex. The loads delivered to supporting floors
are very difficult to predict and often require a higher order of structural analysis
than that of the original design of the finished structure. To evaluate these loads,
knowledge is required of the modulus of elasticity Ec of each floor (different),
properties of the shores (complicated in some systems by splices), and the initial
stress in the shores, where is dependent on how hard the wedges are driven or the
number of turns of screw jacks, etc. (‘‘Formwork for Concrete,’’ ACI SP-4). When
stay-in-place shores are used, reshoring is simpler (because variations in initial
9.26 SECTION NINE
stress, which depend on workmanship, are eliminated), and a vertically progressive
failure can be averted.
One indirect measure is to read deflections of successive floors at each stage.
With accurate measurements of Ec, load per floor can then be estimated by structural
theory. A more direct measure (seldom used) is strain measurement on the shores,
usable with metal shores only. On large projects, where formwork cost and cost of
failure justify such expense, both types of measurement can be employed.
9.20 SPECIAL FORMS
Special formwork may be required for uncommon structures, such as folded plates,
shells, arches, and posttensioned-in-place designs, or for special methods of construction,
such as slip forming with the form rising on the finished concrete or with
the finished concrete descending as excavation progresses, permanent forms of any
type, preplaced-grouted-aggregate concreting, underwater concreting, and combinations
of precast and cast-in-place concreting.
9.21 INSPECTION OF FORMWORK
Inspection of formwork for a building is a service usually performed by the architect,
engineer, or both, for the owner and, occasionally, directly by employees of
the owner. Formwork should be inspected before the reinforcing steel is in place
to ensure that the dimensions and location of the concrete conform to design drawings
(Art. 9.16). This inspection would, however, be negligent if deficiencies in the
areas of contractor responsibility were not noted also.
(See ‘‘Guide to Formwork for Concrete,’’ ACI 347R, and ‘‘Formwork for Concrete,’’
ACI SP-4, for construction check lists, and ‘‘Manual of Concrete Inspection,’’
ACI SP-2.)
REINFORCEMENT
9.22 REINFORCING BARS
The term deformed steel bars for concrete reinforcement is commonly shortened
to rebars. The short form will be used in this section.
Standard rebars are produced in 11 sizes, designated on design drawings and in
project specifications by a size number. Since the late 1990’s, bar producers have
been manufacturing soft-metric rebars for use in both metric and inch-pound construction
projects. Soft metric rebars have the same physical features as the corresponding
inch-pound bars, i.e., the same nominal diameters and weight per foot
(Table 9.4). Soft metric bars are marked with the metric size number and the metric
grade of steel.
CONCRETE CONSTRUCTION 9.27
TABLE 9.4 ASTM Standard Rebars
Bar
size no.a
Nominal dimensionsb
Diameter
mm [in.]
Cross-sectional
area, mm2
[in.2]
Weight
kg/m [lbs / ft]
10 [3] 9.5 [0.375] 71 [0.11] 0.560 [0.376]
13 [4] 12.7 [0.500] 129 [0.20] 0.994 [0.668]
16 [5] 15.9 [0.625] 199 [0.31] 1.552 [1.043]
19 [6] 19.1 [0.750] 284 [0.44] 2.235 [1.502]
22 [7] 22.2 [0.875] 387 [0.60] 3.042 [2.044]
25 [8] 25.4 [1.000] 510 [0.79] 3.973 [2.670]
29 [9] 28.7 [1.128] 645 [1.00] 5.060 [3.400]
32 [10] 32.3 [1.270] 819 [1.27] 6.404 [4.303]
36 [11] 35.8 [1.410] 1006 [1.56] 7.907 [5.313]
43 [14] 43.0 [1.693] 1452 [2.25] 11.38 [7.65]
57 [18] 57.3 [2.257] 2581 [4.00] 20.24 [13.60]
a Equivalent inch-pound bar sizes are the designations enclosed within brackets.
b The equivalent nominal dimensions of inch-pound bars are the values enclosed within brackets.
TABLE 9.5 Rebar Sizes and Grades Conforming to ASTM
Specifications
Type of steel
and ASTM
specification Bar size numbers Grade*
Billet steel
A615/A615M
10–19 [3–6]
10–36, 43, 57 [3–11, 14, 18]
19–36, 43, 57 [6–11, 14, 18]
300 [40]
420 [60]
520 [75]
Low-alloy steel
A706/A706M
10–36, 43, 57 [3–11, 14, 18] 420 [60]
*Minimum yield strength.
Table 9.5 shows the bar sizes and strength grades covered by ASTM Specifi-
cations A615/A615M and A706/A706M.* The grade number indicates minimum
yield strength, MPa [ksi] of the steel. Grade 420 [60] billet-steel rebars, conforming
to ASTM A615/A615M, are currently the most widely used type.
Low-alloy steel rebars conforming to the ASTM A706/A706M Specification are
intended for applications where controlled tensile properties are essential, for ex-
*Many of the ASTM specifications for steel reinforcement are in a dual units format—metric units and
inch-pound units. The designations of such specifications are also in a dual format, e.g., A615/A615M. The
metric units in the specification apply when ‘‘A615M’’ is specified. Similarly, inch-pound units apply under
‘‘A615.’’
Since rail-steel and axle steel reinforcing bars (ASTM A996/A996M) are not generally available except
in a few areas of the country, these types of bars are not discussed herein. Should the need arise to evaluate
or specify rail-steel or axle-steel bars, ASTM Specification A996/A996M should be reviewed.
9.28 SECTION NINE
ample, in earthquake-resistant design and construction. The A706/A706M Speci-
fication also includes requirements to enhance ductility and bendability. Rebars
conforming to A706/A706M are also intended for welding. Weldability is accomplished
by the specification’s limits or controls on the chemical composition of the
steel. Welding of rebars should conform to the requirements of ‘‘StructuralWelding
Code–Reinforcing Steel,’’ ANSI/AWS D1.4.
Billet-steel rebars conforming to ASTM A615/A615M are not produced to meet
weldability requirements. They may be welded, however, by complying with the
requirements in ANSI/AWS D1.4.
Coated rebars, either epoxy-coated or zinc-coated (galvanized), are used where
corrosion protection is desired in reinforced concrete structures. The ACI 318 Building
Code requires epoxy-coated rebars to conform to ASTM Specifications A775/
A775M or A934/A934M. Zinc-coated (galvanized) rebars are required to conform
to ASTM A767/A767M.
ASTM Specification A955M for stainless steel rebars was published in 1996.
Stainless steel rebars are intended for use in highly-corrosive environments, or in
buildings which require non-magnetic steel reinforcement.
In 1997, ASTM issued Specification A970/A970M for headed reinforcing bars.
A headed rebar consists of a head fastened or connected to one or both ends of a
rebar. The head, which can be a rectangular or round steel plate, is connected to
the rebar by welding or threading. Another type of headed rebar has an integrallyforged
head. The purpose of the head is to provide end anchorage of the rebar in
concrete. Headed rebars can be used advantageously in lieu of bars with standard
end hooks thereby relieving congestion of reinforcement and enhancing constructability.
9.23 WELDED-WIRE FABRIC (WWF)
Welded-wire fabric is an orthogonal grid made with two kinds of cold-drawn wire:
plain or deformed. The wires can be spaced in each direction of the grid as desired,
but for buildings, usually at 12 in maximum. Sizes of wires available in each type,
with standard and former designations, are shown in Table 9.6.
Welded-wire fabric usually is designated WWF on drawings. Sizes of WWF are
designated by spacing followed by wire sizes; for example, WWF 6  12, W12/
W8, which indicates plain wires, size W12, spaced at 6 in, and size W8, spaced at
12 in. WWF 6  12, D-12/D-8 indicated deformed wires of the same nominal size
and spacing.
All WWF can be designed for Grade 60 material. Wire and welded-wire fabric
are produced to conform with the following ASTM standard specifications:
ASTM A82, Plain Wire
ASTM A496, Deformed Wire
ASTM A185, Plain Wire, WWF
ASTM A497, Deformed Wire, WWF
Epoxy-coated wire and welded wire fabric are covered by the ASTM specifi-
cation A884/A884M. Applications of epoxy-coated wire and WWF include use as
corrosion-protection systems in reinforced concrete structures and reinforcement in
reinforced-earth construction, such as mechanically-stabilized embankments.
CONCRETE CONSTRUCTION 9.29
TABLE 9.6 Standard Wire Sizes for Reinforcement
Size of
deformed
wire
(A496)
Size of
plain
wire
(A82)
Nominal
dia,
in.
Nominal
area,
in.2
Size of
deformed
wire
(A496)
Size of
plain
wire
(A82)
Nominal
dia,
in.
Nominal
area,
in.2
D-45 W45 0.757 0.450
D-31 W31 0.628 0.310 D-12 W12 0.390 0.120
D-30 W30 0.618 0.300 D-11 0.374 0.110
D-29 0.608 0.290 D-10 W10 0.356 0.100
D-28 W28 0.597 0.280 D-9 0.338 0.090
D-27 0.586 0.270 D-8 W8 0.319 0.080
D-26 W26 0.575 0.260 D-7 0.298 0.070
D-25 0.564 0.250 D-6 W6 0.276 0.060
D-24 W24 0.553 0.240 W5.5 0.265 0.055
D-23 0.541 0.230 D-5 W5 0.252 0.050
D-22 W22 0.529 0.220 W4.5 0.239 0.045
D-21 0.517 0.210 D-4 W4 0.225 0.040
D-20 W20 0.504 0.200 W3.5 0.211 0.035
D-19 0.491 0.190 D-3 0.195 0.030
D-18 W18 0.478 0.180 W2.9 0.192 0.029
D-17 0.465 0.170 W2.5 0.178 0.025
D-16 W16 0.451 0.160 D2 W2 0.159 0.020
D-15 0.437 0.150 W1.4 0.134 0.014
D-14 W14 0.422 0.140 W1.2 0.124 0.012
D-13 0.406 0.130 D-1 0.113 0.010
W0.5 0.080 0.005
9.24 PRESTRESSING STEEL
Cold-drawn high-strength wires, singly or stranded, with ultimate tensile strengths
up to 270 ksi, and high-strength, alloy-steel bars, with ultimate tensile strengths up
to 160 ksi, are used in prestressing. The applicable specifications are:
ASTM A416/A416M, Uncoated Seven-Wire Stress-Relieved Strand
ASTM A421/A421M, Uncoated Stress-Relieved Wire
ASTM A722/A722M, Uncoated High-Strength Bar
Single strands are used for plant-made pretensioned, prestressed members. Posttensioned
prestressing may be performed with the member in place, on a site fabricating
area, or in a plant. Posttensioned tendons usually consist of strands or bars.
Single wires, grouped into parallel-wire tendons, may also be used in posttensioned
applications.
9.25 FABRICATION AND PLACING OF REBARS
Fabrication of rebars consists of cutting to length and required bending. The preparation
of field placing drawings and bar lists is termed detailing. Ordinarily, the
9.30 SECTION NINE
TABLE 9.7 Standard Hooks*
Recommended end hooks—all grades of steel, in or ft-in
Bar
size no.
180 hooks
D† A orG J
90
hooks
A or G
3 21?4 5 3 6
4 3 6 4 8
5 33?4 7 5 10
6 41?2 8 6 1–0
7 51?4 10 7 1–2
8 6 11 8 1–4
9 91?2 1–3 113?4 1–7
10 103?4 1–5 1–11?4 1–10
11 12 1–7 1–23?4 2–0
14 181?4 2–3 1–93?4 2–7
18 24 3–0 2–41?2 3–5
†D 
 finished inside bend diameter, in.
Seismic
Stirrup /Tie
rebar supplier details, fabricates, and delivers to the site, as required. In the farwestern
states, the rebar supplier also ordinarily places the bars, In the New York
City area, fabrication is performed on the site by the same (union) workers who
place the reinforcement. (See ‘‘Details and Detailing of Concrete Reinforcement,’’
ACI 315).
Standard Hooks. The geometry and dimensions of standard hooks that conform
to the ACI 318 Building Code and industry practice are shown in Table 9.7.
Fabrication Tolerances. These are covered in ‘‘Standard Specifications for Tolerances
for Concrete Construction and Materials,’’ ACI 117.
Shipping Limitations. Shipping widths or loading limits for a single bent bar and
an L-shaped bar are shown in Fig. 9.7. Bundles of bars occupy greater space. The
limit of 7 ft 4 in has been established as an industry practice to limit the bundle
size to an 8-ft maximum load width. (‘‘Manual of Standard Practice,’’ Concrete
Reinforcing Steel Institute.)
CONCRETE CONSTRUCTION 9.31
TABLE 9.7 Standard Hooks* (Continued )
Stirrup and tie hook dimensions, in or ft-in—all
grades of steel
Bar
size
no. D
90
hook
Hook
A or G
135 hook
Hook
A or G
H,
approx.
135 seismic stirrup / tie hook
dimensions (ties similar) in.—all
grades of steel
Bar
size no. D
135 hook
Hook
A or G
H,
approx.
3 11?2 4 4 21?2 3 11?2 41?4 3
4 2 41?2 41?2 3 4 2 41?2 3
5 21?2 6 51?2 33?4 5 21?2 51?2 33?4
6 41?2 1–0 8 41?2 6 41?2 8 41?2
7 51?4 1–2 9 51?4 7 51?4 9 51?4
8 6 1–4 101?2 6 8 6 101?2 6
* All specific sizes recommended by CRSI in this table meet minimum requirements of the ACI 318
Building Code.
Courtesy of the Concrete Reinforcing Steel Institute.
FIGURE 9.7 Shipping limitations: (a) height limit; (b) length and height
limits.
Erection. For construction on small sites, such as high-rise buildings in metropolitan
areas, delivery of materials is a major problem. Reinforcement required for
each area to be concreted at one time is usually delivered separately. Usually, the
only available space for storage of this reinforcing steel is the formwork in place.
Under such conditions, unloading time becomes important.
The bars for each detail length, bar size, or mark number are wired into bundles
for delivery. A lift may consist of one or more bundles grouped together for loading
or unloading. The maximum weight of a single lift for unloading is set by the
jobsite crane capacity. The maximum weight of a shop lift for loading is usually
far larger, and so shop lifts may consist of several separately bundled field lifts.
Regional practices and site conditions establish the maximum weight of bundles
and lifts. Where site storage is provided, the most economical unloading without
an immediately available crane is by dumping or rolling bundles off the side. Unloading
arrangements should be agreed on in advance, so that loading can be carried
out in the proper order and bars bundled appropriately. Care must be exercised
during the unloading and handling of epoxy-coated rebars to minimize damage to
the coating. (‘‘Placing Reinforcing Bars,’’ CRSI.)
Placement Tolerances. The ACI 318 Building Code prescribes rebar placement
tolerances applicable simultaneously to effective depth d and to concrete cover in
all flexural members, walls, and columns as follows:
9.32 SECTION NINE
Where d in 8 in or less, 3?8 in; more than 8 in 1?2 in. The tolerance for the
clear distance to formed soffits is 1?4 in. These tolerances may not reduce cover
more than one-third of that specified. For additional information on tolerances, see
‘‘Standard Specifications for Tolerances for Concrete Construction and Materials,’’
ACI 117.
Bundling. Rebars may be placed in concrete members singly or in bundles (up
to four No. 11 or smaller bars per bundle). This practice reduces rebar congestion
or the need for several layers of single, parallel bars in girders. For columns, it
eliminates many interior ties and permits use of No. 11 or smaller bars where small
quantities of No. 14 or No. 18 bars are not readily available.
Only straight bars should be bundled ordinarily. Exceptions are bars with end
hooks, usually at staggered locations, so that the bars are not bent as a bundle
(‘‘Placing Reinforcing Bars,’’ CRSI).
A bundle is assembled by wiring the separate bars tightly in contact. If they are
preassembled, placement in forms of long bundles requires a crane. Because cutoffs
or splices of bars within a bundle must be staggered, it will often be necessary to
form the bundle in place.
Bending and Welding Limitations. The ACI 318 Building Code contains the following
restrictions:
All bars must be bent without heating, except as permitted by the engineer.
Bars partly embedded in hardened concrete may not be bent without permission
of the engineer.
No welding of crossing bars (tack welding) is permitted without the approval of
the engineer.
For unusual bends, heating may be permitted because bars bend more easily
when heated. If not embedded in thin sections of concrete, heating the bars to a
maximum temperature of 1500F facilitates bending, usually without damage to the
bars or splitting of the concrete. If partly embedded bars are to be bent, heating
controlled within these limits, plus the provision of a round fulcrum for the bend
to avoid a sharp kink in the bar, are essential.
Tack welding creates a metallurgical notch effect, seriously weakening the bars.
If different size bars are tacked together, the notch effect is aggravated in the larger
bar. Tack welding therefore should never be permitted at a point where bars are to
be fully stressed, and never for the assembly of ties or spirals to column verticals
or stirrups to main beam bars.
When large, preassembled reinforcement units are desired, the engineer can plan
the tack welding necessary as a supplement to wire ties at points of low stress or
to added bars not required in the design.
9.26 BAR SUPPORTS
Bar supports are commercially available in three general types of material: wire,
precast concrete, and all-plastic. Descriptions of the various types of bar supports,
CONCRETE CONSTRUCTION 9.33
as well as recommended maximum spacings and details for use, are given in the
CRSI ‘‘Manual for Standard Practice.’’
Wire bar supports are generally available in the United States in three classes
of rust prevention: plastic-protected, stainless-steel-protected, and no protection
(plain). Precast-concrete bar supports are normally supplied in three styles; plain
block, block with embedded wires, and block with a hole for the leg of a vertical
bar for top- and bottom-bar support.
Various types and sizes of all-plastic bar supports and sideform spacers are
available. Consideration should be given to the effects of thermal changes, inasmuch
as the coefficient of thermal expansion of the plastic can differ significantly from
that of concrete. Investigation of this property is advisable before use of all-plastic
supports in concrete that will be exposed to high variations in temperature.
Bar supports for use with epoxy-coated rebars should be made of dielectric
material. Alternatively, wire bar supports should be coated with dielectric material,
such as plastic or epoxy.
9.27 INSPECTION OF REINFORCEMENT
This involves approval of rebar material for conformance to the physical properties
required, such as ASTM specifications for the strength grade specified; approval of
the bar details and placing drawings; approval of fabrication to meet the approved
details within the prescribed tolerances; and approval of rebar placing.
Approvals of rebar material may be made on the basis of mill tests performed
by the manufacturer for each heat from which the bars used originated. If samples
are to be taken for independent strength tests, measurements of deformations, bending
tests, and minimum weight, the routine samples may be best secured at the mill
or the fabrication shop before fabrication. Occasionally, samples for check tests are
taken in the field; but in this case, provision should be made for extra lengths of
bars to be shipped and for schedules for the completion of such tests before the
material is required for placing. Sampling at the point of fabrication, before fabrication,
is recommended.
Inspection of fabrication and placement is usually most conveniently performed
in the field, where gross errors would require correction in any event.
Under the ACI 318 Building Code, the bars should be free of oil, paint, form
coatings, and mud when placed. Rust or mill scale sufficiently loose to damage the
bond is normally dislodged in handling.
If heavily rusted bars (which may result from improper storage for a long time
exposed to rusting conditions) are discovered at the time of placing, a quick field
test of suitability requires only scales, a wire brush, and calipers. In this test, a
measured length of the bar is wire-brushed manually and weighed. If less than 94%
of the nominal weight remains, or if the height of the deformations is deficient, the
rust is deemed excessive. In either case, the material may then be rejected or penalized
as structurally inadequate. Where space permits placing additional bars to
make up the structural deficiency (in anchorage capacity or weight), as in walls
and slabs, this solution is preferred, because construction delay then is avoided.
Where project specifications impose requirements on rust more severe than the
structural requirements of the ACI 318 Building Code, for example, for decorative
surfaces exposed to weather, the inspection should employ the special criteria required.
9.34 SECTION NINE
CONCRETE PLACEMENT
9.28 GOOD PRACTICE
The principles governing proper placement of concrete are:
Segregation must be avoided during all operations between the mixer and the
point of placement, including final consolidation and finishing.
The concrete must be thoroughly consolidated, worked solidly around all embedded
items, and should fill all angles and corners of the forms.
Where fresh concrete is placed against or on hardened concrete, a good bond
must be developed.
Unconfined concrete must not be placed under water.
The temperature of fresh concrete must be controlled from the time of mixing
through final placement, and protected after placement.
(‘‘Guide for Measuring, Mixing, Transporting, and Placing Concrete,’’ ACI
304R; ‘‘Standard Specifications for Structural Concrete,’’ACI 301; ‘‘Guide for Concrete
Floor and Slab Construction,’’ ACI 302.1R.)
9.29 METHODS OF PLACING
Concrete may be conveyed from a mixer to point of placement by any of a variety
of methods and equipment, if properly transported to avoid segregation. Selection
of the most appropriate technique for economy depends on jobsite conditions, especially
project size, equipment, and the contractor’s experience. In building construction,
concrete usually is placed with hand- or power-operated buggies; dropbottom
buckets with a crane; inclined chutes; flexible and rigid pipe by pumping;
shotcrete, in which either dry materials and water are sprayed separately or mixed
concrete is shot against the forms; and for underwater placing, tremie chutes (closed
flexible tubes). For mass-concrete construction, side-dump cars on narrow-gage
track or belt conveyers may be used. For pavement, concrete may be placed by
bucket from the swinging boom of a paving mixer, directly by dump truck or mixer
truck, or indirectly by trucks into a spreader.
A special method of placing concrete suitable for a number of unusual conditions
consists of grout-filling preplaced coarse aggregate. This method is particularly
useful for underwater concreting, because grout, introduced into the aggregate
through a vertical pipe gradually lifted, displaces the water, which is lighter than
the grout. Because of bearing contact of the aggregate, less than usual overall
shrinkage is also achieved.
9.30 EXCESS WATER
Even within the specified limits on slump and water-cementitious materials ratio,
excess water must be avoided. In this context, excess water is present for the conCONCRETE
CONSTRUCTION 9.35
ditions of placing if evidence of water rise (vertical segregation) or water flow
(horizontal segregation) occurs. Excess water also tends to aggravate surface defects
by increased leakage through form openings. The result may be honeycomb, sandstreaks,
variations in color, or soft spots at the surface.
In vertical formwork, water rise causes weak planes between each layer deposited.
In addition to the deleterious structural effect, such planes, when hardened,
contain voids through which water may pass.
In horizontal elements, such as floor slabs, excess water rises and causes a weak
laitance layer at the top. This layer suffers from low strength, low abrasion resistance,
high shrinkage, and generally poor quality.
9.31 CONSOLIDATION
The purpose of consolidation is to eliminate voids of entrapped air and to ensure
intimate complete contact of the concrete with the surfaces of the forms and the
reinforcement. Intense vibration, however, may also reduce the volume of desirable
entrained air; but this reduction can be compensated by adjustment of the mix
proportions.
Powered internal vibrators are usually used to achieve consolidation. For thin
slabs, however, high-quality, low-slump concrete can be effectively consolidated,
without excess water, by mechanical surface vibrators. For precast elements in rigid,
watertight forms, external vibration (of the form itself) is highly effective. External
vibration is also effective with in-place forms, but should not be used unless the
formwork is specially designed for the temporary increase in internal pressures to
full fluid head plus the impact of the vibrator (‘‘Guide to Formwork for Concrete,’’
ACI 347R).
Except in certain paving operations, vibration of the reinforcement should be
avoided. Although it is effective, the necessary control to prevent overvibration is
difficult. Also, when concrete is placed in several lifts of layers, vibration of vertical
rebars passing into partly set concrete below may be harmful. Note, however, that
revibration of concrete before the final set, under controlled conditions, can improve
concrete strength markedly and reduce surface voids (bugholes). This technique is
too difficult to control for general use on field-cast vertical elements, but it is very
effective in finishing slabs with powered vibrating equipment.
Manual spading is most efficient for removal of entrapped air at form surfaces.
This method is particularly effective where smooth impermeable form material is
used and the surface is upward sloping.
On the usual building project, different conditions of placement are usually encountered
that make it desirable to provide for various combinations of the techniques
described. One precaution generally applicable is that the vibrators not be
used to move the concrete laterally.
(‘‘Guide for Consolidation of Concrete,’’ ACI 309R.)
9.32 CONCRETING VERTICAL ELEMENTS
The interior of columns is usually congested; it contains a large volume of reinforcing
steel compared with the volume of concrete, and has a large height com9.36
SECTION NINE
pared with its cross-sectional dimensions. Therefore, though columns should be
continuously cast, the concrete should be placed in 2- to 4-ft-deep increments and
consolidated with internal vibrators. These should be lifted after each increment
has been vibrated. If delay occurs in concrete supply before a column has been
completed, every effort should be made to avoid a cold joint. When the remainder
of the column is cast, the first increment should be small, and should be vibrated
to penetrate the previous portion slightly.
In all columns and reinforced narrow walls, concrete placing should begin with
2 to 4 in of grout. Otherwise, loose stone will collect at the bottom, resulting in
the formation of honeycomb. This grout should be proportioned for about the same
slump as the concrete or slightly more, but at the same or lower water-cementitious
material ratio. (Some engineers prefer to start vertical placement with a mix having
the same proportions of water, cement, and fine aggregate, but with one-half the
quantity of coarse aggregate, as in the design mix, and to place a starting layer 6
to 12 in deep.)
When concrete is placed for walls, the only practicable means to avoid segregation
is to place no more than a 24-in layer in one pass. Each layer should be
vibrated separately and kept nearly level.
For walls deeper than 4 ft, concrete should be placed through vertical, flexible
trunks or chutes located about 8 ft apart. The trunks may be flexible or rigid, and
come in sections so that they can be lifted as the level of concrete in place rises.
The concrete should not fall free, from the end of the trunk, more than 4 ft or
segregation will occur, with the coarse aggregate ricocheting off the forms to lodge
on one side. Successive layers after the initial layer should be penetrated by internal
vibrators for a depth of about 4 to 6 in to ensure complete integration at the surface
of each layer. Deeper penetration can be beneficial (revibration), but control under
variable jobsite conditions is too uncertain for recommendation of this practice for
general use.
The results of poor placement in walls are frequently observed: sloping layer
lines; honeycombs, leaking, if water is present; and, if cores are taken at successive
heights, up to a 50% reduction in strength from bottom to top. Some precautions
necessary to avoid these ill effects are:
Place concrete in level layers through closely spaced trunks or chutes.
Do not place concrete full depth at each placing point.
Do not move concrete laterally with vibrators.
For deep, long walls, reduce the slump for upper layers 2 to 3 in below the
slump for the starting layer.
On any delay between placing of layers, vibrate the concrete thoroughly at the
interface.
If concreting must be suspended between planned horizontal construction joints,
level off the layer cast, remove any laitance and excess water, and make a
straight, level construction joint, if possible, with a small cleat attached to the
form on the exposed face (see also Art. 9.39).
9.33 CONCRETING HORIZONTAL ELEMENTS
Concrete placement in horizontal elements follows the same general principles outlined
in Art. 9.32. Where the surface will be covered and protected against abrasion
and weather, few special precautions are needed.
CONCRETE CONSTRUCTION 9.37
For concrete slabs, careless placing methods result in horizontal segregation,
with desired properties in the wrong location, the top consisting of excess water
and fines with low abrasion and weather resistance, and high shrinkage. For a good
surface in a one-course slab, low-slump concrete and a minimum of vibration and
finishing are desirable. Immediate screeding with a power-vibrated screed is helpful
in distributing low-slump, high-quality concrete. No further finishing should be
undertaken until free water, if any, disappears. A powered, rotary tamping float can
smooth very-low-slump concrete at this stage. Final troweling should be delayed,
if necessary, until the surface can support the weight of the finisher.
When concrete is placed for deep beams that are monolithic with a slab, the
beam should be filled first. Then, a short delay for settlement should ensue before
slab concrete is cast. Vibration through the top slab should penetrate the beam
concrete sufficiently to ensure thorough consolidation.
When a slab is cast, successive batches of concrete should be placed on the
edge of previous batches, to maintain progressive filling without segregation. For
slabs with sloping surfaces, concrete placing should usually begin at the lower edge.
For thin shells in steeply sloping areas, placing should proceed downslope.
Slump should be adjusted and finishing coordinated to prevent restraint by horizontal
reinforcing bars from causing plastic cracking in the fresh concrete.
9.34 BONDING TO HARDENED CONCRETE
The surface of hardened concrete should be rough and clean where it is to be
bonded with fresh concrete.
Vertical surfaces of planned joints may be prepared easily by wire brushing
them, before complete curing, to expose the coarse aggregate. (The timing can be
extended, if desired, by using a surface retarder on the bulkhead form.) For surfaces
fully cured without earlier preparation, sandblasting, bush hammering, or acid
washes (thoroughly rinsed off) are effective means of preparation for bonding new
concrete. (See also Art. 9.33.)
Horizontal surfaces of previously cast concrete, for example, of walls, are similarly
prepared. Care should be taken to remove all laitance and to expose sound
concrete and coarse aggregate. (See also Art. 9.32. For two-course floors, see Art.
9.35.)
9.35 HEAVY-DUTY FLOOR FINISHES
Floor surfaces highly resistant to abrasion and impact are required for many industrial
and commercial uses. Such surfaces are usually built as two-course construction,
with a base or structural slab topped by a wearing surface. The two
courses may be cast integrally or with the heavy-duty surface applied as a separate
topping.
In the first process, which is less costly, ordinary structural concrete is placed
and screeded to nearly the full depth of the floor. The wearing surface concrete,
made with special abrasion-resistant aggregate, emery, iron fillings, etc., then is
mixed, spread to the desired depth, and troweled before final set of the concrete
below.
9.38 SECTION NINE
The second method requires surface preparation of the base slab, by stiff brooming
before final set to roughen the surface and thorough washing before the separate
heavy-duty topping is cast. For the second method, the topping is a very dry (zeroslump)
concrete, made with 3?8-in maximum-size special aggregate. This topping
should be designed for a minimum strength, 
 6000 psi. It must be tamped into ?
c
place with powered tampers or rotary floats. (Note: If test cylinders are to be made
from this topping, standard methods of consolidation will not produce a proper test;
tamping similar in effect to that applied to the floor itself is necessary.) One precaution
vital to the separate topping method is that the temperatures of topping and
base slab must be kept compatible.
(‘‘Guide for Concrete Floor and Slab Construction,’’ ACI 302.1R.)
9.36 CONCRETING IN COLD WEATHER
Frozen materials should never be used. Concrete should not be cast on a frozen
subgrade, and ice must be removed from forms before concreting. Concrete allowed
to freeze wet, before or during early curing, may be seriously damaged. Furthermore,
temperatures should be kept above 40F for any appreciable curing (strength
gain).
Concrete suppliers are equipped to heat materials and to deliver concrete at
controlled temperatures in cold weather. These services should be utilized.
In very cold weather, for thin sections used in buildings, the freshly cast concrete
must be enclosed and provided with temporary heat. For more massive sections or
in moderately cold weather, it is usually less expensive to provide insulated forms
or insulated coverings to retain the initial heat and subsequent heat of hydration
generated in the concrete during initial curing.
The curing time required depends on the temperature maintained and whether
regular or high-early-strength concrete is used. High-early-strength concrete may
be achieved with accelerating admixtures (Art. 9.9) or with high-early-strength cement
(Types III or IIIA) or by a lower water-cementitious materials ratio, to produce
the required 28-day strength in about 7 days.
An important precaution in using heated enclosures is to supply heat without
drying the concrete or releasing carbon dioxide fumes. Exposure of fresh concrete
to drying or fumes results in chalky surfaces. Another precaution is to avoid rapid
temperature changes of the concrete surfaces when heating is discontinued. The
heat supply should be reduced gradually, and the enclosure left in place to permit
cooling to ambient temperatures gradually, usually over a period of at least 24 h.
(‘‘Cold Weather Concreting,’’ ACI 306R; ‘‘Standard Specification for Cold
Weather Concreting,’’ ACI 306.1; and ‘‘Standard Specifications for Structural Concrete,’’
ACI 301.)
9.37 CONCRETING IN HOT WEATHER
Mixing and placing concrete at a high temperature may cause flash set in the mixer,
during placing, or before finishing can be completed. Also, loss of strength can
result from casting hot concrete.
CONCRETE CONSTRUCTION 9.39
In practice, most concrete is cast at about 70  20F. Research on the effects
of casting temperature shows highest strengths for concrete cast at 40F and significant
but practically unimportant increasing loss of strength from 40F to 90F.
For higher temperatures, the loss of strength becomes important. So does increased
shrinkage. The increased shrinkage is attributable not only to the high temperature,
but also to the increased water content required for a desired slump as temperature
increases. See Fig. 9.5.
For ordinary building applications, concrete suppliers control temperatures of
concrete by cooling the aggregates and, when necessary, by supplying part of the
mixing water as crushed ice. In very hot weather, these precautions plus sectional
casting, to permit escape of the heat of hydration, may be required for massive
foundation mats. Retarding admixtures are also used with good effect to reduce
slump loss during placing and finishing.
(‘‘Hot Weather Concreting,’’ ACI 305R; and ‘‘Standard Specifications for Structural
Concrete,’’ ACI 301.)
9.38 CURING CONCRETE
Curing of concrete consists of the processes, natural and artificially created, that
affect the extent and rate of hydration of the cement.
Many concrete structures are cured without artificial protection of any kind. They
are allowed to harden while exposed to sun, wind, and rain. This type of curing is
unreliable, because water may evaporate from the surface.
Various means are used to cure concrete by controlling its moisture content or
its temperature. In practice, curing consists of conserving the moisture within newly
placed concrete by furnishing additional moisture to replenish water lost by evaporation.
Usually, little attention is paid to temperature, except in winter curing and
steam curing.
Most effective curing is beneficial in that it makes the concrete more watertight
and increases the strength.
Methods for curing may be classified as:
1. Those that supply water throughout the early hydration process and tend to
maintain a uniform temperature. These methods include ponding, sprinkling, and
application of wet burlap or cotton mats, wet earth, sawdust, hay, or straw.
2. Those designed to prevent loss of water but having little influence on maintaining
a uniform temperature. These methods include waterproof paper and impermeable
membranes. The latter is usually a clear or bituminous compound
sprayed on the concrete to fill the pores and thus prevent evaporation. A fugitive
dye in the colorless compound aids the spraying and inspection.
A white pigment that gives infrared reflectance can be used in a curing compound
to keep concrete surfaces cooler when exposed to the sun.
The criterion for judging the adequacy of field curing provided in the ACI 318
Building Code is that the field-cured test cylinders produce 85% of the strengths
developed by companion laboratory-cured cylinders at the age for which strength
is specified.
(‘‘Standard Practice for Curing Concrete,’’ ACI 308; ‘‘Standard Specification for
Curing Concrete,’’ ACI 308.1; and ‘‘Standard Specifications for Structural Concrete,’’
ACI 301.)
9.40 SECTION NINE
FIGURE 9.8 Control joints for restraining temperature and shrinkage cracks: (a) vertical section
through a slab on grade; (b) horizontal section through a wall.
9.39 JOINTS IN CONCRETE
Several types of joints may occur or be formed in concrete structures:
Construction joints are formed when fresh concrete is placed against hardened
concrete.
Expansion joints are provided in long components to relieve compressive
stresses that would otherwise result from a temperature rise.
Contraction joints (control joints) are provided to permit concrete to contract
during a drop in temperature and to permit drying shrinkage without resulting
uncontrolled random cracking.
Contraction joints should be located at places where concrete is likely to crack
because of temperature changes or shrinkage. The joints should be inserted where
there are thickness changes and offsets. Ordinarily, joints should be spaced 30 ft
on center or less in exposed structures, such as retaining walls.
To avoid unsightly cracks due to shrinkage, a dummy-type contraction joint is
frequently used (Fig. 9.8). When contraction takes place, a crack occurs at this
deliberately made plane of weakness. In this way, the crack is made to occur in a
straight line easily sealed.
Control joints may also consist of a 2- or 3-ft gap left in a long wall or slab,
with the reinforcement from both ends lapped in the gap. Several weeks after the
wall or slab has been concreted, the gap is filled with concrete. By that time, most
of the shrinkage has taken place.
In expansion joints, a filler is usually provided to separate the two parts of the
structure. This filler should be a compressive substance, such as corkboard or premolded
mastic. The filler should have properties such that it will not be squeezed
out of the joint, will not slump when heated by the sun, and will not stain the
surface of the concrete.
To be waterproof, a joint must be sealed. For this purpose, copper flashing may
be used. It is usually embedded in the concrete on both sides of the joint, and
folded into the joint so that the joint may open without rupturing the metal. The
flashing must be strong enough to hold its position when the concrete is cast.
Proprietary flexible water stops and polysulfide calking compounds may also be
used as sealers.
Open expansion joints are sometimes used for interior locations where the opening
is not objectionable. When exposed to water from above, as in parking decks,
open joints may be provided with a gutter below to drain away water.
CONCRETE CONSTRUCTION 9.41
The engineer should show all necessary vertical and horizontal joints on design
drawings. All pertinent details affecting reinforcement, water stops, and sealers
should also be shown.
Construction joints should be designed and located if possible at sections of
minimum shear. These sections will usually be at the center of beams and slabs,
where the bending moment is highest. They should be located where it is most
convenient to stop work. The construction joint is often keyed for shearing strength.
If it is not possible to concrete an entire floor in one operation, vertical joints
preferably should be located in the center of a span. Horizontal joints are usually
provided between columns and floor; columns are concreted first, then the entire
floor system.
FIGURE 9.9 Types of construction joints.
Circled numbers indicate order of casting.
Various types of construction joints
are shown in Fig. 9.9. The numbers on
each section refer to the sequence of
placing concrete.
If the joint is horizontal as in Fig.
9.9a, water may be trapped in the key
of the joint. If the joint is vertical, the
key is easily formed by nailing a wood
strip to the inside of the forms. A raised
key, as in Fig. 9.9b, makes formwork
difficult for horizontal joints.
In the horizontal joint in Fig. 9.9c,
the key is made by setting precastconcrete
blocks into the concrete at intermittent
intervals. The key in Fig. 9.9d
is good if the shear acts in the directions
shown.
The V-shaped key in Fig. 9.9e can be
made manually in the wet concrete for
horizontal joints.
The key is eliminated in Fig. 9.9?,
reliance being placed on friction on the roughened surface. This method may be
used if the shear forces are small, or if there are large compressive forces or suf-
ficient reinforcement across the joint.
See also Arts. 9.32 to 9.34.
9.40 INSPECTION OF CONCRETE PLACEMENT
Concrete should be inspected for the owner before, during, and after casting. Before
concrete is placed, the formwork must be free of ice and debris and properly coated
with bond-breaker oil. The rebars must be in place, properly supported to bear any
traffic they will receive during concrete placing. Conduit, inserts, and other items
to be embedded must be in position, fixed against displacement. Construction personnel
should be available, usually carpenters, bar placers and other trades, if piping
or electrical conduit is to be embedded, to act as form watchers and to reset any
rebars, conduit, or piping displaced.
As concrete is cast, the slump of the concrete must be observed and regulated
within prescribed limits, or the specified strengths based on the expected slump
may be reduced. An inspector of placing who is also responsible for sampling and
9.42 SECTION NINE
making cylinders, should test slump, entrained air, temperatures, and unit weights,
during concreting and should control any field adjustment of slump and added water
and cement. The inspector should also ascertain that handling, placing, and finishing
procedures that have been agreed on in advance are properly followed, to avoid
segregated concrete. In addition, the inspector should ensure that any emergency
construction joints made necessary by stoppage of concrete supply, rain, or other
delays are properly located and made in accordance with procedures specified or
approved by the engineer.
Inspection is complete only when concrete is cast, finished, protected for curing,
and attains full strength.
(‘‘Manual of Concrete Inspection,’’ ACI SP2.)
STRUCTURAL ANALYSIS OF REINFORCED
CONCRETE STRUCTURES
Under the ACI 318 Building Code, reinforced concrete structures generally may be
analyzed by elastic theory. When specific limiting conditions are met, certain approximate
methods are permitted. For some cases, the Code recommends an empirical
method.
9.41 ANALYSES OF ONE-WAY FLOOR AND
ROOF SYSTEMS
The ACI 318 Building Code permits an approximate analysis for continuous systems
in ordinary building if:
Components are not prestressed.
Beams and one-way slabs are continuous over two or more spans.
In successive spans, the ratio of the larger span to the smaller does not exceed
1.20.
The spans carry only uniform loads.
The ratio of live to dead service load(s) (not factored) does not exceed 3.
Members are prismatic.
This analysis determines the maximum moments and shears at faces of supports
and the midspan moments representing envelope values for the respective loading
combinations. In this method, factored moments are computed from
2 M 
 Cw L (9.7) u u n
where C 
 coefficient, given in Fig. 9.10
wu 
 uniform factored load
Ln 
 clear span for positive factored moment or factored shear and the average
of adjacent clear spans for negative factored moment
For an elastic (‘‘exact’’) analysis, the spans L of members that are not built
CONCRETE CONSTRUCTION 9.43
FIGURE 9.10 Coefficients C for calculation of factored bending moments from Mu 
 Cwu
in approximate analysis of beams and one-way slabs with uniform load wu. For factored 2 Ln
shears, Vu 
 0.5wuLn. (a) More than two spans. (b) Two-span beam or slab. (c) Slabs—all
spans, Lu  10 ft.
integrally with their supports should be taken as the clear span plus the depth of
slab or beam but need not exceed the distance between centers of supports. For
spans of continuous frames, spans should be taken as the distance between centers
of supports. For solid or ribbed slabs with clear spans not exceeding 10 ft, if built
integrally with their supports, spans may be taken as the clear distance between
supports.
If an elastic analysis is performed for continuous flexural members for each
loading combination expected, calculated factored moments may be redistributed if
the ratio  of tension-reinforcement area to effective concrete area or ratio of 

, where 
 is the compression-reinforcement ratio, to the balanced-reinforcement
ratio b, lie within the limits given in the ACI 318 Building Code. Positive factored
moments should be increased by a percentage  and negative factored moments
decreased by  to reflect the moment redistribution property of underreinforced
concrete in flexure. When  or   
 is not more than 0.5 b, the percentage is
given by
 


 20 1  (9.8)   b
For example, suppose a 20-ft interior span of a continuous slab with equal spans
is made of concrete with a strength of 4 ksi and reinforced with bars having a ?
c
yield strength ?y of 60 ksi. Factored dead and live loads are both 0.100 ksf. The
factored moments are determined as follows:
Maximum negative factored moments occur at the supports of the interior span
when this span adjacent spans carry both dead and live loads. Call this loading
Case 1. For Case 1 then, maximum negative factored moment equals
2 M 
 (0.100  0.100)(20) /11 
 7.27 ft-kips / ft u
The corresponding positive factored moment at midspan is 2.73 ft-kips / ft.
Maximum positive factored moment in the interior span occurs when it carries
full load but adjacent spans support only dead loads. Call this loading Case 2. For
9.44 SECTION NINE
FIGURE 9.11 Factored bending moments in an interior 20-ft span of a continuous oneway
slab: (a) factored moments for Case 1 (this and adjacent spans fully loaded) and Case
II (this span fully loaded but adjacent spans with only dead load); (b) Case I factored
moments after redistribution.
Case 2, then, the negative factored moment is (10.00  5.00) 
 5.00 ft-kips /
ft, and the maximum positive factored moment is 5.00 ft-kips / ft. Figure 9.11a
shows the maximum factored moments.
For the concrete and reinforcement properties given, the balanced-reinforcement
ratio computed from Eq. (9.27) is b 
 0.0285. Assume now that reinforcement
ratios for the top reinforcement and bottom reinforcement are 0.00267 and 0.002,
respectively. If alternate bottom bars extend into the supports, 
 
 0.001. Substitution
in Eq. (9.8) gives for the redistribution percentage
0.00267  0.001

 20 1 
18.8%   0.0285
The negative factored moment (Case 1) therefore can be decreased to Mu 

7.27(1  0.188) 
 5.90 ft-kips / ft. The corresponding positive factored moment
at midspan is 10  5.90 
 4.10 kips / ft (Fig. 9.11b).
For Case 2 loading, if the negative factored moment is increased 18.8%, it
becomes 5.94  5.90 ft-kips / ft. Therefore, the slab should be designed for the
factored moments shown in Fig. 9.11b.
9.42 TWO-WAY SLAB FRAMES
For two-way slab systems, the ACI 318 Building Code permits a three-dimensional
(space-frame) analysis in which the ‘‘equivalent frame’’ combines the flexibility
(reciprocal of stiffness) of the real column and the torsional flexibility of the slabs
or beams attached to the column at right angles to the direction of the bending
moment under consideration. This method, applicable for all ratios of successive
spans and of dead to live load, is an elastic (‘‘exact’’) analysis called the ‘‘equivalent
frame method.’’
An approximate procedure, the ‘‘direct design method,’’ is also permitted (within
limits of load and span). This method constitutes the direct solution of a one-cycle
moment distribution. (See also Art. 9.59.)
(E. S. Hoffman, et al., ‘‘Structural Design Guide to the ACI Building Code,’’
4th ed., Kluwer Academic Publishers, Boston/Dordrecht/London.)
CONCRETE CONSTRUCTION 9.45
9.43 SPECIAL ANALYSES
Space limitations preclude more than a brief listing of some of the special analyses
required for various special types of reinforced concrete construction and selected
basic references for detailed information. Further references to applicable research
are available in each of the basic references.
Seismic-loading-resistant ductile frames: ACI 318; ACI Detailing Manual.
High-rise construction, frames, shear walls, frames plus shear walls, and tube
concept: ‘‘Planning and Design of Tall Buildings,’’ Vols. SC, CL, and CB, American
Society of Civil Engineers.
Environmental engineering structures: ‘‘Environmental Engineering Concrete
Structures,’’ ACI 350R.
Bridges: ‘‘Analysis and Design of Reinforced Concrete Bridge Structures,’’ ACI
343R.
Nuclear structures: ASME-ACI Code for Concrete Reactor Vessels and Containments
Structures, ACI 359, also ACI 349 and 349R.
It should be noted that the ACI 318 Building Code specifically provides for the
acceptance of analyses by computer or model testing to supplement the manual
calculations when required by building officials.
STRUCTURAL DESIGN OF FLEXURAL MEMBERS
9.44 STRENGTH DESIGN WITH FACTORED
LOADS
Safe, economical strength design of reinforced concrete structures requires that their
ultimate-load-carrying capacity be predictable or known. The safe, or service-loadcarrying
capacity can then be determined by dividing the ultimate-load-carrying
capacity by a factor of safety.
The ACI 318 Building Code provides for strength design of reinforced concrete
members by use of factored loads (actual and specified loads multiplied by load
factors). Factored axial forces, shears, and moments in members are determined as
if the structure were elastic. Strength-design theory is then used to design critical
sections for these axial forces, shears, and moments.
Strength design of reinforced concrete flexural members (Art. 9.46) may be
based on the following assumptions and applicable conditions of equilibrium and
compatibility of strains:
1. Strains in the reinforcing steel and the concrete is directly proportional to the
distance from the neutral axis (Fig. 9.12) except for deep flexural members with a
span-depth ratio less than 1.25 of the clear span for simple spans and 2.5 for
continuous spans. See also Art. 9.88.
2. The maximum usable strain at the extreme concrete compression surface
equals 0.003 in / in
9.46 SECTION NINE
FIGURE 9.12 Stresses and strains in a rectangular reinforcedconcrete
beam, reinforced for tension only, at ultimate load: (a) crosssection
of beam; (b) strain distribution; (c) two types of stress distribution.
3. When the strain, in. / in. in reinforcing steel is less than ?y /Es, where ?y 

yield strength of the steel and Es 
 its modulus of elasticity (29,000,000 psi), the
steel stress, psi, equals 29,000,000 times the steel strain. After the steel yield
strength has been reached, the stress remains constant at ?y, though the strain increases.
4. Except for prestressed concrete (Art. 9.104) or plain concrete, the tensile
strength of the concrete is negligible in flexure.
5. The shape of the concrete compressive distribution may be assumed to be a
rectangle, trapezoid, parabola, or any other shape in substantial agreement with
comprehensive strength tests.
6. For a rectangular stress block, the compressive stress in the concrete should
be taken as . This stress may be assumed constant from the surface of max- 0.85?
c
imum compressive strain to a depth of a 
 1c, where c is the distance to the
neutral axis (Fig. 9.12). For 
 4000 psi, 1 
 0.85. For greater concrete ?
c
strengths, 1 should be reduced 0.05 for each 1000 psi in excess of 4000, but 1
should not be taken less than 0.65.
(See also Art. 9.8.2 for columns).
9.44.1 Strength-Reduction Factors
The ACI Code requires that the strength of a member based on strength design
theory include strength-reduction factors 	to provide for small adverse variations
in materials, workmanship, and dimensions individually within acceptable tolerances.
The degree of ductility, importance of the member, and the accuracy with
which the member’s strength can be predicted were considered in considered in
assigning values to 	:
	 should be taken as 0.90 for flexure and axial tension; 0.85 for shear and
torsion; 0.70 for bearing on concrete; for axial compression combined with bending,
0.75 for members with spiral reinforcement, and 0.70 for other members; and 0.65
for flexure, compression, shear, and bearing in structural plain concrete.
CONCRETE CONSTRUCTION 9.47
9.44.2 Load Factors
For combinations of loads, a structure and its members should have the following
strength U, computed by adding factored loads and multiplying by a factor based
on probability of occurrence of the load combination:
Dead load D and live load L, plus their internal moments and forces:
U 
 1.4D  1.7L (9.9)
Wind load W:
U 
 0.75(1.4D  1.7L  1.7W) (9.10)
When D and L reduce the effects of W:
U 
 0.9D  1.3W (9.11)
Earthquake forces E:
U 
 0.75(1.4D  1.7L  1.87E) (9.12)
When D and L reduce the effects of E:
U 
 0.9D  1.43E (9.13)
Lateral earth pressure H:
U 
 1.4D  1.7L  1.7H (9.14)
When D and L reduce the effects of H:
U 
 0.9D  1.7H (9.15)
Lateral pressure F from liquids (for well-defined fluid pressures):
U 
 1.4D  1.7L  1.4F (9.16)
Impact effects, if any, should be included with the live load L.
Where the structural effects T of differential settlement, creep, shrinkage, or
temperature change can be significant, they should be included with the dead load
D, and the strength should not be less than 1.4D  1.4T, or
U 
 0.75(1.4D  1.4T  1.7L) (9.17)
9.45 ALLOWABLE-STRESS DESIGN AT SERVICE
LOADS (ALTERNATIVE DESIGN METHOD)
Nonprestressed, reinforced-concrete flexural members (Art. 9.63) may be designed
for flexure by the alternative design method of the ACI 318 Building Code (working-
stress design). In this method, members are designed to carry service loads
(load factors and 	 are taken as unity) under the straight-line (elastic) theory of
9.48 SECTION NINE
stress and strain. (Because of creep in the concrete, only stresses due to short-time
loading can be predicted with reasonable accuracy by this method.)
Working-stress design is based on the following assumptions:
1. A section plane before bending remains plane after bending. Strains therefore
vary with distance from the neutral axis (Fig. 9.13c).
FIGURE 9.13 Stresses and strains in a beam
with compression reinforcement, as assumed for
working-stress design: (a) rectangular crosssection
of beam; (b) transformed section with
twice the reinforcing steel area, to allow for effects
of creep of concrete; (c) assumed strains;
(d) assumed distribution of stresses in the concrete.
2. The stress-strain relation for concrete
plots as a straight line under service
loads within the allowable working
stresses (Fig. 9.13c and d), except for
deep beams.
3. Reinforcing steel resists all the
tension due to flexure (Fig. 9.13a and
b).
4. The modular ratio, n 
 Es /Ec,
where Es and Ec are the moduli of elasticity
of reinforcing steel and concrete,
respectively, may be taken as the nearest
whole number, but not less than 6 (Fig.
9.13b).
5. Except in calculations for deflection,
n lightweight concrete should be
assumed the same as for normal-weight concrete of the same strength.
6. The compressive stress in the extreme surface of the concrete must not exceed
is the 29-day compressive strength of the concrete. 0.45?
, where ?
 c c
7. The following tensile stress in the reinforcement must not be greater than the
following:
Grades 40 and 50 20 ksi
Grade 60 or greater 24 ksi
For 3?8-in. or smaller-diameter reinforcement in one-way slabs with spans not
exceeding 12 ft, the allowable stress may be increased to 50% of the yield strength
but not to more than 30 ksi.
8. For doubly-reinforced flexural members, including slabs with compression
reinforcement, an effective modular ratio of 2Es /Ec should be used to transform the
compression-reinforcement area for stress computations to an equivalent concrete
area (Fig. 9.13b). (This recognizes the effects of creep.) The allowable stress in the
compression reinforcement may not exceed the allowable tension stress.
Because the strains in the reinforcing steel and the adjoining concrete are equal,
the stress in the tension steel ?s is n times the stress in the concrete ?c. The total
force acting on the tension steel then equals nAs?c. The steel area As, therefore can
be replaced in stress calculations by a concrete area n times as large.
The transformed section of a reinforced concrete beam is a cross section normal
to the neutral surface with the reinforcement replaced by an equivalent area of
concrete (Fig. 9.13b). (In doubly-reinforced beams and slabs, an effective modular
ratio of 2n should be used to transform the compression reinforcement and account
for creep and nonlinearity of the stress-strain diagram for concrete.) Stress and
strain are assumed to vary with the distance from the neutral axis of the transformed
CONCRETE CONSTRUCTION 9.49
section; that is, conventional elastic theory for homogeneous beams may be applied
to the transformed section. Section properties, such as location of neutral axis,
moment of inertia, and section modulus S, may be computed in the usual way for
homogeneous beams, and stresses may be calculated from the flexure formula,
? 
 M/S, where M is the bending moment at the section. This method is recommended
particularly for T-beams and doubly-reinforced beams.
From the assumptions the following formulas can be derived for a rectangular
section with tension reinforcement only.
n? k c 
 (9.18)
? 1 k s
2 k 
 
2n  (n )  n  (9.19)
k
j 
 1  (9.20)
3
where  
 As /bd and b is the width and d the effective depth of the section (Fig.
9.13).
Compression capacity:
2 2 1 M 
 ?2? kjbd 
 K bd (9.21a) c c c
where Kc 
 1?2?c kj.
Tension capacity:
2 2 M 
 ? A jd 
 ? jbd 
 K bd (9.21b) s s s s s
where ks 
 ?s j.
Design of flexural members for shear, torsion, and bearing, and of other types
of members, follows the strength design provisions of the ACI 318 Building Code,
because allowable capacity by the alternative design method is an arbitrarily specified
percentage of the strength.
9.46 STRENGTH DESIGN FOR FLEXURE
Article 9.44 summarizes the basic assumptions for strength design of flexural members.
The following formulas are derived from those assumptions.
The area As of tension reinforcement in a reinforced-concrete flexural member
can be expressed as the ratio
As 
 (9.22)
bd
where b 
 beam width and d 
 effective beam depth 
 distance from the extreme
compression surface to centroid of tension reinforcement. At nominal (ultimate)
strength of a critical section, the stress in this steel will be equal to its yield strength
?y, psi, if the concrete does not first fail in compression. (See also Arts. 9.47 to
9.50 for additional reinforcement requirements.)
9.50 SECTION NINE
9.46.1 Singly-Reinforced Rectangular Beams
For a rectangular beam, reinforced with only tension steel (Fig. 9.12), the total
tension force in the steel at nominal (ultimate) strength is
T 
 A ? 
 ? bd (9.23) s y y
It is opposed by an equal compressive force
C 
 0.85?
b  c (9.24) c 1
where 
 ?
c specified compressive strength of the concrete, psi
c 
 distance from extreme compression surface to neutral axis
1 
 a constant (given in Art. 9.44)
Equating the compression and tension forces at the critical section gives:
?y c 
 d (9.25)
0.85  ?
 1 c
The criterion for compression failure is that the maximum strain in the concrete
equals 0.003 in / in. In that case:
0.003
c 
 d (9.26)
? /E  0.003 s s
where ?s is the steel stress, ksi, and Es 
 29,000,000 psi is the steel modulus of
elasticity.
Tension-Steel Limitations. Under balanced conditions, the concrete will reach its
maximum strain of 0.003 in/in when the tension steel reaches its yield strength ?y.
Then, c as given by Eq. (9.26) will equal c as given by Eq. (9.25). Also, the
reinforcement ratio for balanced conditions in a rectangular beam with tension steel
only becomes:
0.85  ?
 87,000 1 c
 
 (9.27) b ? 87,000  ? y y
All structures should be designed to avoid sudden collapse. Therefore, reinforcement
should yield before the concrete crushes. Gradual yielding will occur if the
quantity of tensile reinforcement is less than the balanced percentage determined
by strength design theory. To avoid compression failures, the ACI 318 Building
Code, therefore limits the reinforcement ratio  to a maximum of 0.75 b.
The Code also requires that  for positive-moment and negative-moment reinforcement
be at least and not less than 200/?y to prevent sudden collapse 3
?
/? c y
when the design moment strength is equal to or less than the cracking moment.
This requirement does not apply, however, if the reinforcement area at every section
of the member is at least one-third greater than that required by the factored moment.
The ratio, 200/?y, will govern, except when  4400 psi. For a statically ?
c
determinate T-section with the flange in tension,  should be at least with 6
?
/? c y
the flange width used for determining .
For flexural members of any cross-sectional shape, without compression reinforcement,
the tension reinforcement is limited by the ACI 318 Building Code so
CONCRETE CONSTRUCTION 9.51
that As?y does not exceed 0.75 times the total compressive force at balanced conditions.
The total compressive force may be taken as the area of a rectangular stress
block of a rectangular member; the strength of overhanging flanges or compression
reinforcement, or both, may be included. For members with compression reinforcement,
the portion of tensile reinforcement equalized by compression reinforcement
need not be reduced by the 0.75 factor.
Flexural Design Strength: Tension Steel Only. For underreinforced rectangular
beams with tension reinforcement only (Fig. 9.12) and a rectangular stress block
with depth a (  0.75 b), the flexural design strength may be determined from:
0.59 ?y 2 	M 
 0.90bd ? 1 (9.28a)   n y ?
c
a

 0.90A ? d  (9.28b)   s y 2

 0.90A ? jd (9.28c) s y
where a 
 and jd 
 d  a/2. A ? /0.85?
b s y c
9.46.2 Doubly-Reinforced Rectangular Beams
For a rectangular beam with compression-steel area and tension-steel area As, A
s
the compression-reinforcement ratio is
A
s

 
 (9.29)
bd
and the tension-reinforcement ratio is
As

 (9.30)
bd
where b 
 width of beam and d 
 effective depth of beam. For design,  should
not exceed
?
 ?
 s s 0.75   
  
 (9.31a)   b ? ? y y
for
0.85?
  ?
 87,000 c 1 s

 
 (9.31b) b ? 87,000 ? ? y y y
where 
 stress in the compression steel, psi, and other symbols are the same as ?
s
those defined for singly-reinforced beams (Art. 9.46.1). The compression force on
the concrete alone in a cross-section (Fig. 9.14) is
C 
 0.85?
ba (9.32) 1b c
where a 
 1c is the depth of the stress block and the compression reinforcement
9.52 SECTION NINE
FIGURE 9.14 Stresses and strains, at ultimate load in a rectangular
beam with compression reinforcement: (a) beam cross-section;
(b) strain distribution; (c) two types of stress distribution; (d) compression
stress in reinforcement.
resists . Forces equal in magnitude to these but opposite in direction stress the A
?
 s s
tension reinforcement. The depth to the neutral axis c can be found from the maximum
compressive strain of 0.003 in / in or by equating the compression and tension
forces on the section. (See also Art. 9.64.)
9.46.3 T-Beams
When a T form is used to provide needed compression area for an isolated beam,
flange thickness should be at least one-half the web width, and flange width should
not exceed 4 times the web width.
When a T is formed by a beam cast integrally with a slab, only a portion of the
slab is effective. For a symmetrical T-beam, the effective flange width should not
exceed one-fourth the beam span, nor should the width of the overhang exceed 8
times the slab thickness nor one-half the clear distance to the next beam. For a
beam having a flange on one side only, the effective flange width should not exceed
one-twelfth the span, 6 times the slab thickness, nor one-half the clear distance to
the next beam.
The overhang of a T-beam should be designed to act as a cantilever. Spacing of
the cantilever reinforcement should not exceed 18 in or 5 times the flange thickness.
In computing the moment capacity of a T-beam, it may be treated as a singlyreinforced
beam with overhanging concrete flanges (Fig. 9.15). The compression
force on the web (rectangular beam) is
C 
 0.85?
b a (9.33) w cw
where bw 
 width of web. The compression force on the overhangs is
C 
 0.85?
(b  b )h (9.34) ? c w ?
where h? 
 flange thickness and b 
 effective flange width of the T-beam. Forces
equal in magnitude to these but opposite in direction stress the tension steel:
T 
 A ? (9.35) w swy
T 
 A ? (9.36) ? s? y
where Asw 
 area of reinforcing steel required to develop compression strength of
CONCRETE CONSTRUCTION 9.53
FIGURE 9.15 Stresses and strains in a T-beam at ultimate load: (a) beam crosssection;
(b) strain distribution; (c stress distributions in web; (d ) block distribution
of flange compression stresses.
web and As? 
 area of reinforcing steel required to develop compression strength
of overhanging flanges. The reinforcement ratio for balanced conditions is given
by
0.85?
  A b 87,000 c 1 s? w 
  (9.37)  	 b b ? 87,000  ? b d y y w
The depth to the neutral axis c can be found in the same way as for rectangular
beams (Arts. 9.46.1 and 9.46.2).
9.47 SHEAR IN FLEXURAL MEMBERS
Design at a section of a reinforced-concrete flexural member with factored shear
force Vu is based on
V  	V 
 	(V  V ) (9.38) u n c s
where 	
 strength-reduction factor (given in Art. 9.44.1)
Vu 
 factored shear force at a section
Vc 
 nominal shear strength of concrete
Vs 
 nominal shear strength provided by reinforcement
Except for brackets, deep beams, and other short cantilevers, the section for maximum
shear may be taken at a distance d from the face of the support when the
reaction in the direction of the shear introduces compression into the end region of
the member.
For shear in two-way slabs, see Art. 9.59.
For nonprestressed flexural members of normal-weight concrete without torsion,
the nominal shear strength Vc provided by the concrete is limited to a maximum
of bwd, where bw is the width of the beam web, d 
 depth to centroid of 2
?
c
reinforcement, and is the specified concrete compressive strength, unless a more ?
c
detailed analysis is made. In such an analysis, Vc should be obtained from
2,500  V d w u V 
 1.9
?
  b d  3.5 
?
 b d (9.39)   c c w c w Mu
9.54 SECTION NINE
where Mu 
 factored bending moment occurring simultaneously with Vu at the section
considered, but Vud/Mu must not exceed 1.0
w 
 As /bwd
As 
 area of nonprestressed tension reinforcement
For one-way joist construction, the ACI 318 Building Code allows these values of
Vc to be increased 10%.
For lightweight concrete, Vc should be modified by substituting ?ct / 6.7 for
where ?ct is the average splitting tensile strength of lightweight concrete, but 
?
, c
not more than 6.7 When ?ct is not specified, values of affecting Vc should 
?
. 
?
 c c
be multiplied by 0.85 for sand-lightweight concrete and 0.75 for all-lightweight
concrete.
Shear Reinforcement. When Vu exceeds 	Vc, shear reinforcement must be provided
to resist the excess factored shear. The shear reinforcement may consist of
stirrups making an angle of 45 to 90 with the longitudinal reinforcement, longitudinal
bars bent at an angle of 30 or more, or a combination of stirrups and bent
bars. The nominal shear strength provided by the shear reinforcement Vs must not
exceed 8 
?
b d. c w
Spacing of required shear reinforcement placed perpendicular to the longitudinal
reinforcement should not exceed 0.5d for nonprestressed concrete, 75% of the overall
depth for prestressed concrete, or 24 in. Inclined stirrups and bent bars should
be spaced so that at least one intersects every 45 line extending toward the supports
from middepth of the member to the tension reinforcement. When Vs is greater
than 4 the maximum spacing of shear reinforcement should be reduced 
?
b d, c w
by one-half. (See Art. 9.109 for shear-strength design for prestressed concrete members.)
The area required in the legs of a vertical stirrup, in2, is
V s s A 
 (9.40a) v ? d y
where s 
 spacing of stirrups, in and ?y 
 yield strength of stirrup steel, psi. For
inclined stirrups, the leg area should be at least
V s s A 
 (9.40b) v (sin  cos )? d y
where 
 angle of inclination with longitudinal axis of member.
For a single bent bar or a single group of parallel bars all bent at an angle 
with the longitudinal axis at the same distance from the support, the required area
is
Vs A 
 (9.41) v ? sin  y
in which Vs should not exceed 3 
?
b d. c w
A minimum area of shear reinforcement is required in all members, except slabs,
footings, and joists or where Vu is less than 0.5	Vc. The minimum area of shear
reinforcement is given by Av 
 50bws/?y.
See also Art. 9.65.
CONCRETE CONSTRUCTION 9.55
9.48 TORSION IN REINFORCED
CONCRETE MEMBERS
Under twisting or torsional moments, a member develops normal (warping) and
shear stresses. The ACI 318 Building Code assumes that no torsion is resisted by
concrete and the entire nominal torsional strength is provided by reinforcement.
The reinforcement required for torsion must be added to that required for shear,
moment, and axial force.
Torsional design may be based on
T  	 T (9.42) u s
where Tu 
 factored torsional moment
	
 strength-reduction factor, 
 0.85
Ts 
 nominal torsional moment strength provided by torsion reinforcement
For non-prestressed members, torsion can be neglected when
2 T  	
?
(A ) /p (9.43) u c cp cp
where Acp 
 area enclosed by outside perimeter of concrete cross-section, in.2
pcp 
 outside perimeter of the concrete cross-section, in.
For prestressed members, torsion effects can be neglected when
2 T  	
?
 [(A ) /p ] 
1  ? /4
?
 (9.44) u c cp cp pc c
where ?pc 
 compressive stress in concrete (after allowance for all prestress losses)
at centroid of cross section resisting externally applied loads or at junction of web
and flange when the centroid lies within the flange, psi. (In a composite member,
?pc is resultant compressive stress at centroid of composite section, or at junction
of web and flange when centroid lies within the flange, due to both prestress and
moments resisted by precast members acting alone.)
For T-beam construction, where stirrup reinforcement is required for torsion, it
may be more practical to neglect the area and perimeter of the overhanging flanges
than to provide reinforcement for them.
In statically indeterminate prestressed and non-prestressed structures, where the
torsional moment, Tu, in a member is not required to maintain equilibrium, design
may be based upon reduced torsional cracking moments equal to four times the
values given in Eqs. (9.43) and (9.44). When taking advantage of redistribution of
torsional moments, the end moments of continuous members may be reduced likewise
and the positive moments increased.
To reduce unsightly cracking and prevent crushing of surface concrete, the size
of a solid cross-section is limited such that
2 22 
(V /b d)  (T p / 1.7 A )  	 (V /b d  8
?
) (9.45) u w u h oh c w c
and the size of a hollow cross section is limited such that
2 (V /b d)  (T p / 1.7 A )  	 (V /b d  8
?
) (9.46) u w u h oh c w c
9.56 SECTION NINE
where Aoh 
 area enclosed by centerline of the outermost closed transverse torsion
reinforcement, in2
ph 
 perimeter of the centerline of the outermost closed transverse torsion
reinforcement, in
The reinforcement for torsion requires that
	 T 	 T (9.47) n u
where Tn 
 nominal torsional moment strength which 
 Ts, the nominal torsional
moment strength provided by torsion reinforcement
Stirrups. The transverse reinforcement required for torsion is calculated from
T 
 (2A A ? cot ) /s (9.48) n o t yv
where s 
 spacing of torsion reinforcement in direction parallel to longitudinal
reinforcement, in
Ao 
 0.85 Aoh
At 
 area of one leg of a closed stirrup within a distance s, in2
?yv 
 yield strength of closed transverse torsion reinforcement, psi

 angle of concrete compression diagonals in truss analogy for torsion,
which must not be taken smaller than 30 nor larger than 60 for nonprestressed
members but may be taken as 45 for non-prestressed members
and as 37.5 for prestressed members with an effective prestress
force not less than 40% of the tensile strength of the longitudinal reinforcement
For design, Eq. (9.48) can be re-arranged to calculate
A / s 
 T / (	 2 A ? cot ) (9.48a) t n o yv
where 	
 strength-reduction factor, 
 0.85
Since At is defined as the area of one leg of a closed stirrup, it must be taken into
account when the stirrup requirements for shear and torsion are added to provide
the total amount of transverse reinforcement required. Stirrup area for shear, Av, is
based on all the legs of a stirrup. If the required stirrup area for shear is Av / s, and
that for torsion is At / s, the total amount of transverse reinforcement required to
resist shear and torsion is calculated
A A 2A vt v t Total 
  (9.49)   s s s
Longitudinal Reinforcement. The additional longitudinal reinforcement, A
, required
for torsion is calculated from
2 A 	 (A / s)p (? /? )cot (9.50) l t h yv y

where At / s 
 amount calculated from Eq. (9.48a)
?y
 
 yield strength of longitudinal torsion reinforcement
The amount of longitudinal torsion reinforcement in the flexural compression
zone may be reduced by an amount equal to Mu / (0.9 d ?y
), where Mu is the factored
moment acting at the section in combination with Tu.
CONCRETE CONSTRUCTION 9.57
FIGURE 9.16 Cross-section properties and reinforcement details of a typical spandrel beam
subjected to bending, shear and torsion.
Where torsion reinforcement is required, the minimum area of transverse torsion
reinforcement, At, must also conform to
A 	 [(50b s/? )  A ] /2 (9.51) t w yv v
and the minimum area of longitudinal torsion reinforcement, A
, must conform to
A 	 5 
?
 A /?  (A / s)(? /? )p (9.52) 
 c cp y
 t yv y
 h
where At / s must be taken 	 25 bw/?yv.
The spacing of transverse torsion reinforcement should not exceed the smaller
of ph /8 or 12 in. The longitudinal reinforcement required for torsion must be placed
inside closed stirrups with a maximum spacing of 12 in and distributed around
their perimeter with one bar or tendon in each corner. Bars must have a diameter
	 s /24 but not less than a #3 size.
Refer to Fig. 9.16 for an example of cross-section properties and reinforcement
details of a typical spandrel beam subjected to bending, shear and torsion.
See also Art. 9.66.
9.58 SECTION NINE
9.49 DEVELOPMENT, ANCHORAGE, AND
SPLICES OF REINFORCEMENT
Steel reinforcement must be bonded to the concrete sufficiently so that the steel
will yield before it is freed from the concrete. Despite assumptions made in the
past to the contrary, bond stress between concrete and reinforcing bars is not uniform
over a given length, not directly related to the perimeter of the bars, not equal
in tension and compression, and may be affected by lateral confinement. The ACI
318 Building Code requirements therefore reflect the significance of average bond
resistance over a length of bar or wire sufficient to develop its strength (development
length).
The calculated tension or compression force in each reinforcing bar at any section
[Eqs. (9.53) to (9.61) and (9.64)] must be developed on each side of that section
by a development length Ld, or by end anchorage, or both. Hooks can be used to
assist in the development of tension bars only.
The critical sections for development of reinforcement in flexural members are
located at the points of maximum stress and where the reinforcement terminates or
is bent.
The following requirements of the ACI 318 Building Code for the development
of reinforcement were proposed to help provide for shifts in the location of maximum
moment and for peak stresses that exist in regions of tension in the remaining
bars wherever adjacent bars are cut off or bent. In addition, these requirements help
minimize any loss of shear capacity or ductility resulting from flexural cracks that
tend to open early whenever reinforcement is terminated in a tension zone.
9.49.1 Development for All Flexural Reinforcement
Reinforcement should extend a distance of d of 12db, whichever is larger, beyond
the point where the steel is no longer required to resist tensile stress, where d is
the effective depth of the member and db is the nominal diameter of the reinforcement.
This requirement, however, does not apply at supports of simple spans and
at the free end of cantilevers.
Continuing reinforcement should extend at least the development length Ld beyond
the point where terminated or bent reinforcement is no longer required to
resist tension.
Reinforcement should not be terminated in a tension zone unless one of the
following conditions is satisfied:
1. Shear at the cutoff point does not exceed two-thirds of the design shear
strength, 	Vn.
2. Stirrup area Av not less than 60bws/?y and exceeding that required for shear
and torsion is provided along each terminated bar over a distance from the termination
point equal to 0.75d. (Av 
 cross-sectional area of stirrup leg, bw 
 width
of member, and ?y 
 yield strength of stirrup steel, psi.) The spacing should not
exceed d/8 b, where b is the ratio of the area of the bars cut off to the total area
of bars at the cutoff section.
3. For No. 11 bars and smaller, continuing bars provide double the area required
for flexure at the cutoff point, and the factored shear does not exceed three-fourths
of the design shear strength, 	Vn.
CONCRETE CONSTRUCTION 9.59
9.49.2 Development for Positive-Moment Reinforcement
A minimum of one-third the required positive-moment reinforcement for simple
beams should extend along the same face of the member into the support, and in
beams, for a distance of not less than 6 in.
A minimum of one-fourth the required positive-moment reinforcement for continuous
members should extend along the same face of the member into the support,
and in beams, for a distance of at least 6 in.
For lateral-load-resisting members, the positive-moment reinforcement to be extended
into the support in accordance with the preceding two requirements should
be able to develop between the face of the support and the end of the bars the yield
strength ?y of the bars.
Positive-moment tension reinforcement at simple supports and at points of in-
flection should be limited to a diameter such that the development length, in computed
for ?y with Eqs. (9.54) to (9.58) and (9.61) does not exceed
Mn L   L (9.53) d a Vu
where Mn 
 nominal moment strength at the section, in-lb, assuming all reinforcement
at the section stressed to ?y 
 As?y(d  a/2)
Vu 
 factored shear at the section, lb
La 
 embedment length, in beyond center of support; at a point of inflection,
La is limited to d or 12db, whichever is greater
d 
 effective depth, in of member
db 
 nominal bar diameter, in
As 
 area of tensile reinforcement, in2
a 
 depth, in of rectangular stress block (Art. 9.46.1)
The value of Mn /Vu can be increased by 30% when the ends of the reinforcement
are confined by a compressive reaction. It is not necessary to satisfy Eq. (9.53) for
reinforcing bars that terminate beyond the center of simple supports with a standard
hook, or terminate with a mechanical anchorage equivalent to a standard hook.
9.49.3 Development for Negative-Moment Reinforcement
Negative-moment reinforcement in continuous, restrained, or cantilever members
should be developed in or through the supporting member.
Negative-moment reinforcement should have sufficient distance between the face
of the support and the end of each bar to develop its full yield strength.
A minimum of one-third of the required negative-moment reinforcement at the
face of the support should extend beyond the point of inflection the greatest of d,
12db, or one-sixteenth of the clear span.
9.49.4 Computation of Development Length
Tension development length, Ld, is the length of deformed bar or deformed wire
required to develop, or to transfer to the concrete, the full tensile capacity of the
bar or wire. The tension development length of an uncoated bar or wire in normal
weight concrete is expressed as a function of yield strength of the bar; ?y; the square
9.60 SECTION NINE
root of the compressive strength of the concrete, the diameter of the bar, db; 
?
; c
depth of concrete below horizontal bars; bar spacings; concrete cover; and lateral
confinement reinforcement such as stirrups or ties. The ACI 318 Building Code
reinforcements also contain provisions to account for epoxy-coated bars and embedment
of bars in lightweight aggregate concrete. Tension development length can
also be reduced when more flexural reinforcement is provided than the amount
required by analysis.
The ACI 318-99 Building Code provides the designer with a choice of methods
for determining tension development length, Ld—a direct short-cut method; or a
more rigorous method which is applicable to all conditions of bar spacing, concrete
cover and transverse reinforcement. A third method is provided by the commentary
to ACI 318-99, which sanctions use of the provisions in the 1989 Code.
Using the direct short-cut method for determining the tension development
length of deformed bars or deformed wire in tension—with a clear spacing not less
than db, concrete cover not less than db, and stirrups and ties throughout Ld not less
than code minimum; or clear spacing not less than 2db and concrete cover not less
than db—the equations for calculating Ld are:
for #6 and smaller bars and wire
L 
 (0.04? 
/
?
)d 	 12 in. (9.54) d y c b
for #7 and larger bars and wire
L 
 (0.05? 
/
?
)d 	 12 in. (9.55) d y c b
The direct short-cut method’s equations for determining the tension development
deformed bars and deformed wire for all other cases are:
for #6 and smaller bars and wire
L 
 (0.06? 
/
?
)d 	 12 in. (9.56) d y c b
for #7 and larger bars and wire
L 
 (0.075? 
/
?
)d 	 12 in. (9.57) d y c b
In Eqs. (9.54) through (9.57):

 1.3 for top bars and 1.0 for other bars; ‘‘top bars’’ are horizontal bars with
more than 12 in. of concrete cast below them

 1.0 for uncoated bars

 1.5 for epoxy-coated bars with cover 3db; or clear spacing 6db

 1.2 for other concrete cover and clear spacing conditions of epoxy-coated bars
The product of  need not be taken more than 1.7


 factor for lightweight aggregate concrete 
 1.3


 6.7 	 1.0 when the splitting tensile strength, ?ct, of lightweight ag- 
?
/? c ct
gregate concrete is specified.
Under the more rigorous method, tension development length is calculated:
0.075? 
 d y b L 
 (9.58) d 
?
[(c  K ) /d ] c tr b
CONCRETE CONSTRUCTION 9.61
where 
 0.8 for bar sizes #3–#6

 1.0 for bar sizes #7–#18
The term (c  Ktr) /db is limited to a value of 2.5
c 
 the smaller of: (1) one-half of the center-to-center spacing of the bars; or (2)
the concrete cover to the center of the bar, in
Ktr 
 Atr?yt /(1500 sn)
Atr 
 total area of all transverse reinforcement within the spacing s, which crosses
the potential plane of splitting through the bars being developed in2
?yt 
 specified yield strength of transverse reinforcement, psi
s 
 maximum center-to-center spacing of transverse reinforcement within Ld, in
n 
 number of bars being developed along the plane of splitting.
Increased Ld is required for bundled bars: in 3-bar bundles, 20%; in 4-bar bundles,
33%. For determining the appropriate modifying factors for use with bundled
bars, a unit of bundled bars should be treated as a single bar with a diameter derived
from the equivalent total area.
Application of all the various interdependent tension development length requirements
to each structural element in design would be extremely difficult and a
waste of design time. The authors recommend that the designer check the actual
dimensions available for tension development in the connection (or from a cutoff
point established as a fraction of the span on typical design drawing details), compare
to a table of development lengths required for each bar size, and select the
bar size allowable. Table 9.8, which is based on the direct short-cut method, presents
values of tension Ld for each size bar for normal-weight concrete with compressive
strengths of 3000, 4000 and 5000 psi. Note that separate values are tabulated
for ‘‘top bars’’ and ‘‘other bars.’’
9.49.5 Anchorage with Hooks
For rebars in tension, standard 90 and 180 end hooks can be used as part of the
length required for development or anchorage of the bars. Table 9.9 gives the minimum
tension embedment length Ldh required with standard end hooks (Fig. 9.17
and Table 9.9) and Grade 60 bars to develop the specified yield strength of the
bars.
9.49.6 Development for Welded-Wire Fabric in Tension
For deformed welded-wire fabric (WWF) with at least one cross wire within the
development length not less than 2 in. from the point of critical section (Fig. 9.18),
the tension development length is the length calculated from Eqs. (9.54) and (9.56)
using the direct short-cut method or from Eq. (9.58) using the more rigorous
method and then multiplied by a wire fabric factor. The wire fabric factor is the
larger of
(?  35,000)/?  1.0 (9.59) y y
or
5 d / s  1.0 (9.60) b w
9.62
TABLE 9.8 Tension Development Lengths, Ld, for Grade 60 Uncoated Bars (Inches)
Bar
size no.

 3,000 psi ?
c
Top bars
Case 1 Case 2
Other bars
Case 1 Case 2

 4,000 psi ?
c
Top bars
Case 1 Case 2
Other bars
Case 1 Case 2

 5,000 psi ?
c
Top bars
Case 1 Case 2
Other bars
Case 1 Case 2
3 22 32 17 25 19 28 15 22 17 25 13 19
4 29 43 22 33 25 37 19 29 22 33 17 26
5 36 54 28 41 31 47 24 36 28 42 22 32
6 43 64 33 50 37 56 29 43 33 50 26 38
7 63 94 48 72 54 81 42 63 49 73 37 56
8 72 107 55 82 62* 93 48 71 55 83 43 64
9 81 121 62 93 70 105 54 81 63 94 48 72
10 91 136 70 105 79 118 61 91 70 105 54 81
11 101 151 78 116 87 131 67 101 78 117 60 90
14 121 181 93 139 105 157 81 121 94 140 72 108
18 161 241 124 186 139 209 107 161 125 187 96 144
NOTES:
1. Values are based on Section 12.2.2 in ACI 318-99 Building Code.
2. Case 1 and Case 2 are defined:
Case
Structural element
Beams and columns Other elements
1 Concrete cover 	db, c.-c. bar
spacing 	2 db and with stirrups
or ties throughout Ld not less than
Code minimum
Concrete over 	db, c.-c. bar
spacing 	3 db
2 Concrete cover db or c.-c. bar
spacing 2 db
Concrete cover db or c.-c.
bar spacing 3 db
3. Values are for normal-weight concrete.
4. Standard 90 or 180 end hooks may be used to replace part of the required development length. See Table 9.9.
* Sample Calculation: For Case 1, bar size no. 8; using Eq. (9.55), Ld 
 (0.05?y

/ where ?y 
 60,000 
?
)d c b
psi;


 1.3 for ‘‘top’’ bars;


 1.0 for uncoated bars;



 1.0 for normal-weight concrete; 
 4,000 psi; and db 
 ?
c
1.0 in. Thus, Ld 
 or 62 in. (0.05  60,000  1.3  1.0  1.0 /
4,000)(1.0) 
 61.7
CONCRETE CONSTRUCTION 9.63
TABLE 9.9 Minimum Embedment Lengths for Hooks on Steel Reinforcement in Tension
a. Embedment lengths Ldh, in for standard end hooks on Grade 60 bars
in normal-weight concrete*
Bar
size
no.
Concrete compressive strength , psi ?
c
3000 4000 5000 6000 7000 8000
3 6 6 6 6 6 6
4 8 7 6† 6† 6† 6†
5 10 9 8 7 7 6†
6 12 10 9 8 8 7†
7 14 12 11 10 9 9
8 16 14 12 11 10 10
9 18 15 14 13 12 11
10 20 17 15 14 13 12†
11 22 29 17 16 14 14†
14 37 32 29 27 25 23
18 50 43 39 35 33 31
b. Embedment lengths, in to provide 2-in. concrete cover over tail
of standard 180 end hooks
No. 3 No. 4 No. 5 No. 6 No. 7 No. 8 No. 9 No. 10 No. 11 No. 14 No. 18
6 7 7 8 9 10 12 14 15 20 25
* Embedment length for 90 and 180 standard hooks is illustrated in Fig. 9.17. Details of standard
hooks are given in Table 9.7. Side cover required is a minimum of 21?2 in. End cover required for 90 hooks
is a minimum of 2 in. To obtain embedment lengths for grades of steel different from Grade 60, multiply
Ldh given in Table 9.9 by ?y / 60,000. If reinforcement exceeds that required, multiply Ldh by the ratio of
area required to that provided.
†For 180 hooks at right angles to exposed surfaces, obtain Ldh from Table 9.9b to provide 2-in. minimum
cover to tail (Fig. 9.17a).
FIGURE 9.17 Embedment lengths for 90 and 180 standard hooks.
9.64 SECTION NINE
FIGURE 9.18 Minimum development length for
deformed welded-wire fabric.
where db 
 nominal diameter of the wire, in
sw 
 spacing of the wires being developed, in
The resulting development length should be at least 8 in except for determining lap
splice lengths. When using Eqs. (9.54), (9.56) or (9.58), an epoxy-coated welded
wire fabric factor of 1.0 can be taken for . For deformed WWF with no cross
wires within the development length or with a single cross wire less than 2 in from
the point of the critical section, the wire fabric factor should also be taken as 1.0.
FIGURE 9.19 Minimum development length
for plain welded-wire fabric.
Plain welded-wire fabric is considered
to be developed by embedment of
two cross wires. The closer cross wire
should be located not less than 2 in from
the point of critical section (Fig. 9.19).
The ACI 318 Building Code also requires
the development length Ld, measured
from the point of critical section
to the outermost cross wire, to be at
least
0.27A ? 
 w y L 
 	 6 in. (9.61) d s 
?
 w c
where 
is the factor for lightweight-aggregate concrete, as indicated in Art. 9.49.4.
If excess tension reinforcement is provided, Ld may be reduced by the ratio of area
of steel required to the area of steel provided. The development length should be
at least 6 in. except in calculation of lap splices.
9.49.7 Tension Lap Splices
Bar sizes No. 11 or less and deformed wire may be spliced by lapping. Tension
lap splices are classified in two classes, A and B, depending on the stress in the
bars to be spliced. The minimum lap length Ls is expressed as a multiple of the
tension development length Ld of the bar or deformed wire (Art. 9.49.4).
Class A tension lap splices include splices at sections where the tensile stress
due to factored loads does not exceed 0.5?y and not more than one-half the bars at
these sections are spliced within one Class A splice length of the section. For Class
A splices,
L 
 L 	 12 in. (9.62) s d
Class B tension lap splices include splices at sections where the tensile stress
CONCRETE CONSTRUCTION 9.65
exceeds 0.5?y and where more than 50% of the bars at the section are spliced. For
Class B splices,
L 
 1.3L 	 12 in (9.63) s d
Laps for tension splices for uncoated Grade 60 rebars in normal-weight concrete
with are given in Table 9.10. ?
 
 3000, 4000 and 5000 psi c
The tension lap-splice lengths for welded-wire fabric are indicated in Figs. 9.20
and 9.21.
9.49.8 Development for Compression Reinforcement
Basic development length Ldb, in., for deformed bars in compression may be computed
from
0.02d ? b y L 
 	 0.0003d ? 	 8 in (9.64) db b y 
?
c
Compression development length Ld is calculated by multiplying Ldb by optional
modification factors. When bars are enclosed by a spiral at least 1?4 in in diameter
and with not more than a 4-in pitch, or by ties at least size No. 4 with a spacing
not more than 4 in., a modification factor of 0.75 may be used but the lap should
be at least 8 in. It excess reinforcement is provided, Ldb may be reduced by the
ratio of the area of steel required to area of steel provided. For general practice,
with concrete compressive strength psi, use 22db for compression em- ?
 	 3000 c
bedment of dowels (Table 9.11).
For bundled bars in compression, the development length of each bar within the
bundle should be increased by 20% for a three-bar bundle and 33% for a four-bar
bundle.
9.49.9 Compression Lap Splices
Minimum lap-splice lengths of rebars in compression Ls vary with nominal bar
diameter db and yield strength ?y of the bars. For bar sizes No. 11 or less, the
compression lap-splice length is the largest of 12 in or the values computed from
Eqs. (9.65a) and (9.65b):
L 
 0.0005? d ?  60,000 psi (9.65a) s yb y
L 
 (0.0009?  24)d ?  60,000 psi (9.65b) s y b y
When is less than 3000 psi, the length of lap should be one-third greater than ?
c
the values computed from the preceding equations.
When the bars are enclosed by a spiral, the lap length may be reduced by 25%.
For general practice, use 30 bar diameters for compression lap splices (Table 9.11).
Spiral should conform to requirements of the ACI 318 Building Code: Spirals
should extend from top of footing or slab in any story to the level of the lowest
horizontal reinforcement in members supported above. The ratio of volume of spiral
reinforcement to the total volume of the concrete core (out-to-out of spirals) should
be at least that given in Art. 9.83. Minimum spiral diameter in cast-in-place con9.66
TABLE 9.10 Tension Lap Splice Lengths for Grade 60 Uncoated Bars (Inches)
Bar
size no.
Lap
class

 3,000 psi ?
c
Top bars
Case 1 Case 2
Other bars
Case 1 Case 2

 4,000 psi ?
c
Top bars
Case 1 Case 2
Other bars
Case 1 Case 2

 5,000 psi ?
c
Top bars
Case 1 Case 2
Other bars
Case 1 Case 2
3 A 22 32 17 25 19 28 15 22 17 25 13 19
B 28 42 22 32 24 36 19 28 22 33 17 25
4 A 29 43 22 33 25 37 19 29 22 33 17 26
B 37 56 29 43 32 48 25 37 29 32 22 33
5 A 36 54 28 41 31 47 24 36 28 42 22 32
B 47 70 36 54 40 60 31 47 36 54 28 42
6 A 43 64 33 50 37 56 29 43 33 50 26 38
B 56 84 43 64 48 72 37 56 43 65 33 50
7 A 63 94 48 72 54 81 42 63 49 73 37 56
B 81 122 63 94 70 106 54 81 63 94 49 73
8 A 72 107 55 82 62 93 48 71 55 83 43 64
B 93 139 72 107 80* 121 62 93 72 108 55 83
9 A 81 121 62 93 70 105 54 81 63 94 48 72
B 105 157 81 121 91 136 70 105 81 122 63 94
10 A 91 136 70 105 79 118 61 91 70 105 54 81
B 118 177 91 136 102 153 79 118 91 137 70 105
11 A 101 151 78 116 87 131 67 101 78 117 60 90
B 131 196 101 151 113 170 87 131 101 152 78 117
NOTES:
1. Values are based on Sections 12.2.2 and 12.15 in ACI 318-99 Building Code.
2. See notes under Table 9.8 for definitions of Case 1 and Case 2.
3. Values are for normal-weight concrete.
* Sample Calculation:
From Sample Calculation under Table 9.8; for Case 1, bar size no. 8, top bars, Ld 
 61.7 in.
For Class B tension lap splice,
Lap length 
 1.3 Ld

 1.3 (61.7)

 80.2 or 80 in.
CONCRETE CONSTRUCTION 9.67
FIGURE 9.20 (a) Minimum lap splice length for deformed welded-wire fabric.
(b) Slab reinforced with deformed welded-wire fabric.
FIGURE 9.21 Minimum lap splice length for plain welded-wire fabric. Use the
larger of the values shown in (a) and (b). In calculation of splice length, the computed
value of development length Ld, not the minimum required value, should be
used. (a) Splice length when steel area used is less than twice the required area. (b)
Splice length when steel area used is two or more times the required area. (c) Slab
reinforced with plain welded-wire fabric providing twice the required reinforcement
area.
9.68 SECTION NINE
TABLE 9.11 Compression Dowel Embedment and
Compression Lap Splices, in for Grade 60 Bars and
All Concrete with 	 3000 psi ?
c
Bar
size
no.
Recommended
dowel
embedment
22db
Minimum lap length
Standard
lap
30db
With column
spirals*
22.5db
3 9 12 12
4 11 15 12
5 14 19 14
6 17 23 17
7 20 27 20
8 22 30 23
9 25 34 25
10 28 38 29
11 31 43 32
14 37 
 
 
** 
 
 
**
18 50 
 
 
** 
 
 
**
*For use in spirally-reinforced columns with spirals conforming
to requirements in Art. 9.49.9.
** Not permitted.
TABLE 9.12 Lap Splice Lengths of Spiral Reinforcement
Spiral reinforcement
Lap splice
length
Deformed uncoated bar or wire 48db
Plain uncoated bar or wire 72db
Epoxy-coated deformed bar or wire 72db
Plain uncoated bar or wire with a standard stirrup or tie hook at ends of lapped
spiral reinforcement*
48db
Epoxy-coated deformed bar or wire with a standard stirrup or tie hook at ends
of lapped spiral reinforcement*
48db
* The hooks must be embedded within the core confined by the spiral reinforcement.
struction is 3?8 in. Clear spacing between spirals should be limited to 1 to 3 in.
Spirals should be anchored by 11?2 extra turns of spiral bar or wire at each end of
a spiral unit. Lap splices, or full mechanical or welded splices can be used to splice
spiral reinforcement. Lap splice lengths should comply with Table 9.12, but not be
less than 12 in.
The ACI 318 Building Code contains provisions for lap splicing bars of different
sizes in compression. Length of lap should be the larger of the compression development
length required for the larger size bar or the compression lap-splice
CONCRETE CONSTRUCTION 9.69
length required for the smaller bar. It is permissible to lap-splice the large bar sizes,
Nos. 14 and 18, to No. 11 and smaller bars.
9.49.10 Mechanical and Welded Splices
As an alternative to lap splicing, mechanical splices or welded splices may be used.
When traditional lap splices satisfy all requirements, they are generally the most
economical. There are conditions, however, where they are not suitable: The ACI
318 Building Code does not permit lap splices of the large-size bars (Nos. 14 and
18) except in compression to No. 11 and smaller bars. Lap splices cause congestion
at the splice locations and their use then may be impracticable. Under certain conditions,
the required length of tension lap splices for No. 11 and similar-size bars
can be excessive and make the splices uneconomical. For these reasons, mechanical
splices or welded splices may be suitable alternatives.
Mechanical splices are made with proprietary devices. The ACI 318 Building
Code requires a full mechanical splice to have a capacity, in tension or compression,
equal to at least 125% of the specified ?y of the bar. End-bearing mechanical splices
may be used where the bar stress due to all conditions of factored loads is compressive.
For these types of compression-only splices, the ACI 318 Building Code
prescribes requirements for the squareness of the bars ends. Descriptions of the
commercially-available proprietary mechanical splice devices are given in ‘‘Mechanical
Connections of Reinforcing Bars,’’ ACI 439.3R, and ‘‘Reinforcement Anchorages,
and Splices,’’ Concrete Reinforcing Steel Institute.
For a full-welded splice, the ACI 318 Building Code requires the butt-welded
bars to have a tensile capacity of at least 125% of the specified ?y of the bar.
Welding should conform to ‘‘Structural Welding Code—Reinforcing Steel’’ (ANSI/
AWS D1.4), American Welding Society.
9.49.11 Anchorage of Web Reinforcement
Stirrups are reinforcement used to resist shear and torsion. They are generally bars,
wire or welded-wire fabric, either single leg or bent into L, U, or rectangular shapes.
Stirrups should be designed and detailed to be installed as close as possible to
the compression and tension surfaces of a flexural member as concrete cover requirements
and the proximity of other reinforcing steel will permit. They should
be installed perpendicular or inclined with respect to flexural reinforcement and
spaced closely enough to cross the line of every potential crack. Ends of singleleg,
simple U stirrups, or transverse multiple U stirrups should be anchored by one
of the following means:
1. A standard stirrup hook around a longitudinal bar for stirrups fabricated from
No. 5 bars or D31 wire or smaller sizes. Stirrups fabricated from bar sizes Nos. 6,
7, and 8 in Grade 40 can be anchored similarly.
2. For stirrups fabricated from bar sizes Nos. 6, 7, and 8 in Grade 60, a standard
stirrup hook around a longitudinal bar plus a minimum embedment of
between midheight of the member and the outside end of the hook. 0.014d ? /
?
 b y c
Each leg of simple U stirrups made of plain welded-wire fabric should be anchored
by one of the following means:
9.70 SECTION NINE
TABLE 9.13 Minimum Shrinkage and Temperature Reinforcement
In slabs where Grade 40 or 50 deformed bars are used 0.0020
In slabs where Grade 60 deformed bars or welded-wire fabric, deformed or plain,
are used (Table 9.18) 0.0018
In slabs reinforced with steel having a yield strength ?y exceeding 60,000 psi
measured at a strain of 0.0035 in / in 108/?y
This reinforcement should not be placed farther apart than 5 times the slab thickness or
more than 18 in.
1. Two longitudinal wires located at the top of the U and spaced at 2 in.
2. One longitudinal wire located at a distance of d/4 or less from the compression
face and a second wire closer to the compression face and spaced at least 2
in from the first wire. (d 
 distance, in from compression surface to centroid of
tension reinforcement.) The second wire can be located on the stirrup leg beyond
a bend, or on a bend with an inside diameter of at least 8db.
Each end of a single-leg stirrup, fabricated from plain or deformed welded-wire
fabric, should be anchored by two longitudinal wires spaced at 2 in minimum. The
inner wire of the two longitudinal wires should be located at least the larger of
d/4 or 2 in from the middepth of the member d/2. The outer longitudinal wire at
the tension face of the member should be located not farther from the face than
the portion of primary flexural reinforcement closest to the face.
Between anchored ends, each bend in the continuous portion of a simple U or
multiple U stirrup should enclose a longitudinal bar.
9.49.12 Stirrup Splices
Pairs of U stirrups or ties placed to form a closed unit may be considered properly
spliced when the legs are lapped over a minimum distance of 1.3Ld. In members
at least 18 in deep, such splices may be considered adequate for No. 3 bars of
Grade 60 and Nos. 3 and 4 bars of Grade 40 if the legs extend the full available
depth of the member.
9.50 CRACK CONTROL
Because of the effectiveness of reinforcement in limiting crack widths, the ACI 318
Building Code requires minimum areas of steel and limits reinforcement spacing,
to control cracking.
Beams and One-Way Slabs. If, in a structural floor or roof slab, principal reinforcement
extends in one direction only, shrinkage and temperature reinforcement
should be provided normal to the principal reinforcement, to prevent excessive
cracking. The additional reinforcement should provide at least the ratios of reinforcement
area to gross concrete area of slab given in Table 9.13, but not less than
0.0014.
To control flexural cracking, tension reinforcement in beams and one-way slabs
should be well distributed in zones of maximum concrete tension when the design
CONCRETE CONSTRUCTION 9.71
yield strength of the steel ?y is greater than 40,000 psi. Spacing of principal reinforcement
in slabs should not exceed 18 in or 3 times the slab thickness, except in
concrete-joist construction.
Where slab flanges of beams are in tension, a part of the main reinforcement of
the beam should be distributed over the effective flange width or a width equal to
one-tenth the span, whichever is smaller. When the effective flange width exceeds
one-tenth the span, some longitudinal reinforcement should be provided in the outer
portions of the flange. Also, reinforcement for one-way joist construction should
be uniformly distributed throughout the flange.
To control concrete cracking in beams and one-way slabs, the spacing, s, of
flexural reinforcement adjacent to a concrete surface in tension should not be greater
than
s  540/?  2.5 c (9.66) s c
where the calculated service load stress, ?s, can be taken as 60% of specified yield
strength and cc is the clear concrete cover. This change in ACI 318-99 replaces the
z factor of ACI 318-95 and previous code editions and directly specifies the maximum
bar spacing for crack control without reference to interior or exterior exposure.
For beams with Grade 60 reinforcement and tension bars with 2 in clear concrete
cover, the maximum bar spacing s 
 540/36  2.5(2) 
 15  5 
 10 in.
Two-Way Slabs. Flexural cracking in two-way slabs is significantly different from
that in one-way slabs. For control of flexural cracking in two-way slabs, such as
solid flat plates and flat slabs with drop panels, the ACI 318 Building Code restricts
the maximum spacing of tension bars to twice the overall thickness h of the slab
but not more than 18 in. In waffle slabs or over cellular spaces, however, reinforcement
should be the same as that for shrinkage and temperature in one-way slabs
(see Table 9.13).
9.51 DEFLECTION OF REINFORCED-CONCRETE
BEAMS AND SLABS
Reinforced-concrete flexural members must have adequate stiffness to limit deflection
to an amount that will not adversely affect the serviceability of the structure
under service loads.
Beam and One-Way Slabs. Unless computations show that deflections will be
small (Table 9.14), the ACI 318 Building Code requires that the depth h of nonprestressed,
one-way solids slabs, one-way ribbed slabs, and beams of normalweight
concrete—with Grade 60 reinforcement—be at least the fraction of the span
L given in Table 9.15.
When it is necessary to compute deflections, calculation of short-term deflection
may be based on elastic theory, but with an effective moment of inertia Ie.
For normal-weight concrete,
3 3 M M cr cr I 
 I  1  I  I (9.67)     	 e g cr g M M a a
9.72 SECTION NINE
TABLE 9.14 Maximum Ratios of Computed Deflection to Span L for Beams and Slabs
Type of member
Deflection to be considered
Deflection
limitation
Flat roofs not supporting or attached
to nonstructural elements likely to
be damaged by large deflections
Immediate deflection due to the live
load
L/180*
Floors not supporting or attached to
nonstructural elements likely to
be damaged by large deflections
Immediate deflection due to the live
load
L/360
Roof or floor construction
supporting or attached to
nonstructural elements likely to
be damaged by large deflections
Roof or floor construction
supporting or attached to
nonstructural elements not likely
to be damaged by large
deflections
That part of the total deflection that
occurs after attachment of the
nonstructural elements (the sum
of the long-term deflection due
to all sustained loads and the
immediate deflection due to any
additional live load)†
L/480‡
L/240§
* This limit is not intended to safeguard against ponding. Ponding should be checked by suitable calculations
of deflection, including the added deflections due to ponded water, and considering long-term
effects of all sustained loads, camber, construction, tolerances and reliability of provisions for drainage.
† The long-term deflection may be reduced by the amount of deflection that occurs before attachment
of the nonstructural elements.
‡ This limit may be exceeded if adequate measures are taken to prevent damage to supported or attached
elements.
§ But not greater than the tolerance provided for the nonstructural elements. This limit may be exceeded
if camber is provided so that the total deflection minus the camber does not exceed the limitation.
TABLE 9.15 Minimum Depths h of Reinforced-Concrete
Beams and One-Way Slabs*
One-way solid
slabs
Beams and oneway
ribbed slabs
Cantilever L/10 
 0.1000L L/8 
 0.1250L
Simple span L/20 
 0.0500L L/16 
 0.0625L
Continuous:
End span L/24 
 0.0417L L/ 18.5 
 0.0540L
Interior span L/28 
 0.0357L L/21 
 0.0476L
*For members with span L (Art. 9.41) not supporting or attached
to partitions or other construction likely to be damaged by large de-
flections. Thinner members may be used if justified by deflection computations.
For structural lightweight concrete of unit weight w, lb / ft3,
multiply tabulated values by 1.65  0.005w 	 1.09, for 90  w 
120. For reinforcement with yield strength ?y  60,000 psi, multiply
tabulated values by 0.4  ?y / 100,000.
CONCRETE CONSTRUCTION 9.73
FIGURE 9.22 Chart for determination of moment of inertia Icr
of transformed (cracked) section of one-way solid slab, given the
moment of inertia of the gross section, Ig 
 bh3 / 12, reinforcement
ratio  
 As /bd, unit weight w of concrete, pcf, and ratio
d /h of effective depth to thickness, for ?
 
 4 ksi. c
where Mcr 
 cracking moment 
 ?rIg /yt
Ma 
 service-load moments for which deflections are being compared
Ig 
 gross moment of inertia of concrete section
Icr 
 moment of inertia of cracked section transformed to concrete (for
solid slabs, see Fig. 9.22)
?r 
 modulus of rupture of concrete, psi 
 7.5 
?
c

 ?
c specified concrete compressive strength, psi
yt 
 distance from centroidal axis of gross section, neglecting the reinforcement,
to the extreme surface in tension.
When structural lightweight concrete is used, ?r in the computation of Mcr should
be taken as 1.12?ct  7.5 , where ?ct 
 average splitting tensile strength, psi, 
?
c
of the concrete. When ?ct is not specified, ?r should be taken as 5.6 for all 
?
c
lightweight concrete and as 6.4 for sand-lightweight concrete. 
?
c
For deflection calculations for continuous spans, Ie may be taken as the average
of the values obtained from Eq. (9.67) for the critical positive and negative moments.
Additional long-term deflection for both normal-weight and lightweight concrete
flexural members can be estimated by multiplying the immediate deflection due to
the sustained load by / (1  50 
), where  
 time-dependent factor (2.0 for 5
9.74 SECTION NINE
TABLE 9.16 Minimum Thickness h of Two-Way Slabs without Interior Beams (Grade 60
Reinforcement)
Without drop panels
Exterior panels
Without
edge
beams
With
edge
beams*
Interior
panels
With drop panels
Exterior panels
Without
edge
beams
With
edge
beams*
Interior
panels
Ln
30
Ln
33
Ln
33
Ln
33
Ln
36
Ln
36
*Beams between columns along exterior edges; 	 0.8 for the edge beam.
years or more, 1.4 for 12 months, 1.2 for 6 months, and 1.0 for 3 months, and 


 compression-steel ratio, the area of the compression reinforcement in.2, di- A
, s
vided by the concrete area bd, in2.
The sum of the short-term and long-term deflections should not exceed the limits
given in Table 9.14.
Two-Way Slabs. Unless computations show that deflections will not exceed the
limits listed in Table 9.14, the ACI 318 Building Code prescribes a minimum thickness
for non-prestressed two-way slabs. For two-way slabs without interior beams,
with a ratio of long to short span not exceeding 2, and with Grade 60 reinforcement,
the Code requires that the thickness h be at least the fraction of the clear span
given in Table 9.16. The thickness based on Table 9.16 cannot be less than 5 in.
for slabs without drop panels nor less than 4 in. for slabs with drop panels.
For two-way slabs having beams on all four edges, with m  0.2, the minimum
thickness h should be based on the preceding criteria for two-way slabs without
interior beams. For 0.2  m  2.0, the minimum thickness should not be less than
L (0.8  ? /200,000) n y h 
 (9.68)
36  5 (   2) m
and not less than 5 in.
For n  2.0, the thickness should not be less than
L (0.8  ? /200,000) n y h 
 (9.69)
36  9 
and not less than 3.5 in.
where Ln 
 clear span in long direction, in.
m 
 average value of  for all beams along panel edges

 ratio of flexural stiffness of beam section to flexural stiffness of a width
of slab bounded laterally by the centerline of the adjacent panel, if any,
on each side of the beam

 ratio of clear span in long direction to clear span in short direction
The computed deflections of prestressed-concrete construction should not exceed
the values listed in Table 9.14.
CONCRETE CONSTRUCTION 9.75
ONE-WAY REINFORCED-CONCRETE SLABS
A one-way reinforced-concrete slab is a flexural member that spans in one direction
between supports and is reinforced for flexure only in one direction (Art. 9.52). If
a slab is supported by beams or walls on four sides, but the span in the long
direction is more than twice that in the short direction, most of the load will be
carried in the short direction; hence, the slab can be designed as a one-way slab.
One-way slabs may be solid, ribbed, or hollow. (For one-way ribbed slabs, see
Arts. 9.54 to 9.58.) Hollow one-way slabs are usually precast (Art. 9.100). Castin-
place, hollow one-way slabs can be constructed with fiber or cardboard-cylinder
forms, inflatable forms that can be reused, or precast hollow boxes or blocks. Oneway
slabs can be haunched at the supports for flexure or for shear strength.
9.52 ANALYSIS AND DESIGN OF
ONE-WAY SLABS
Structural strength, fire resistance, crack control, and deflections of one-way slabs
must be satisfactory under service loads.
Strength and Deflections. Approximate methods of frame analysis can be used
with uniform loads and spans that conform to ACI 318 Building Code requirements
(see Art. 9.41). Deflections can be computed as indicated in Art. 9.51, or in lieu
of calculations the minimum slab thicknesses listed in Table 9.15 may be used. In
Fig. 9.22 is a plot of ratios of moments of inertia of cracked to gross concrete
section for one-way slabs. These curves can be used to simplify deflection calculations.
Strength depends on slab thickness and reinforcement and properties of materials
used. Slab thickness required for strength can be computed by treating a 1-ft width
of slab as a beam (Arts. 9.45 and 9.46).
Fire Resistance. One-way reinforced concrete slabs, if not protected by a fireresistant
ceiling, must have a thickness that conforms to the fire-resistant rating
required by the statutory building code. Table 9.17 gives minimum slab thickness
for various fire-resistance ratings for normal-weight and structural-lightweightconcrete
construction. Providing a minimum 3?4-in. concrete cover for reinforcement
in restrained construction is adequate under the Uniform Building Code and Standard
Building Code for fire-resistance ratings up to 4 hours.
Reinforcement. Requirements for minimum reinforcement for crack control are
summarized in Art. 9.50. Table 9.18 lists minimum reinforcement when Grade 60
bars are used. Reinforcement required for flexural strength can be computed by
treating a 1-ft width of slab as a beam (Arts. 9.44 to 9.46).
Rebar weights, lb / ft2 of slab area, can be estimated From Fig. 9.24a for oneway,
continuous, interior spans of floor or roof slabs made of normal-weight concrete.
One-way reinforced concrete slabs with spans less than 10 ft long can be reinforced
with a single layer of draped welded-wire fabric for both positive and negative
factored moments. These factored moments can be taken equal to wuL2 / 12,
where wu is the total factored uniform load and L is the span, defined in Art. 9.41,
9.76 SECTION NINE
TABLE 9.17 Minimum Slab Thickness, in, for Various Fire-Resistive Ratings
Type of concrete
Fire-resistive rating
1 hour 2 hours 3 hours
Normal weight concrete
Top slab thickness*
Siliceous aggregate 3.5 5.0 6.2
Carbonate aggregate 3.2 4.6 5.7
Structural lightweight concrete
Top slab thickness*
Sand-lightweight 2.7 3.8 4.6
Lightweight 2.5 3.6 4.4
*From Table 7-7-C-C in Uniform Building Code Std. 7-7 or Table 709.2.2.1 in Standard Building Code.
TABLE 9.18 Minimum and Maximum Reinforcement for One-Way Concrete Slabs
Slab
thickness
h, in
Minimum reinforcement*
Area As
in2 / ft
Bar size and
spacing, in
Weight‡
psf
Maximum reinforcement†
Area As
in2 / ft
Bar size and
spacing, in
Weight‡
psf
4 0.086 No. 3 @ 12 0.38 0.552 No. 6 @ 91?2 1.90
41?2 0.097 No. 3 @ 131?2 0.33 0.648 No. 6 @ 8 2.25
5 0.108 No. 3 @ 12 0.38 0.744 No. 6 @ 7 2.58
51?2 0.119 No. 3 @ 11 0.41 0.840 No. 6 @ 6 3.00
6 0.130 No. 4 @ 18 0.45 0.924 No. 7 @ 71?2 3.27
61?2 0.140 No. 4 @ 17 0.49 1.020 No. 7 @ 7 3.50
7 0.151 No. 4 @ 151?2 0.52 1.104 No. 8 @ 81?2 3.77
71?2 0.162 No. 4 @ 141?2 0.55 1.200 No. 8 @ 71?2 4.27
8 0.173 No. 4 @ 131?2 0.59 1.284 No. 9 @ 9 4.53
81?2 0.184 No. 4 @ 13 0.62 1.380 No. 9 @ 81?2 4.80
9 0.194 No. 4 @ 12 0.67 1.476 No. 9 @ 8 5.10
*For Grade 60 reinforcement. Minimum area As 	 0.0018bh, where b 
 slab width and h 
 slab
thickness.
†For 
 3000 psi; no compression reinforcement; 0.75 b 
 0.016; and 3?4 in concrete cover (not ?
c
exposed to weather). Maximum area As 
 0.016bd, where d 
 effective depth of slab.
‡Weight is based on the bar size and spacing for a 1-ft wide by 1-ft length of slab. No transverse
reinforcement is included in the weight.
This spacing for a 4-in slab is the maximum spacing for flexure but can be increased to 18 in for
temperature and shrinkage reinforcement.
if the slab meets ACI 318 Building Code requirements for approximate frame analysis
with uniform loads.
For development (bond) of reinforcement, see Art. 9.49.
Shear. Shear strength is usually not critical in one-way slabs carrying uniform
loads, but the ACI 318 Building Code requires that it be investigated (see Art.
9.47).
CONCRETE CONSTRUCTION 9.77
FIGURE 9.23 Typical one-way reinforced-concrete joist
construction.
9.53 EMBEDDED PIPES IN ONE-WAY SLABS
Generally, embedded pipes or conduit, other than those merely passing through,
should not be larger in outside dimension than one-third the slab thickness and
should be spaced at least three diameters or widths on centers. Piping in solid oneway
slabs is required to be placed between the top and bottom reinforcement unless
it is for radiant heating or snow melting.
ONE-WAY CONCRETE-JOIST CONSTRUCTION
One-way concrete-joist construction consists of a monolithic combination of castin-
place, uniformly spaced ribs (joists) and top slab (Fig. 9.23). (See also Art. 9.52).
The ribs are formed by placing rows of permanent or removable fillers in what
would otherwise be a solid slab.
9.78 SECTION NINE
FIGURE 9.24 For use in preliminary estimates, weights of reinforcing steel for an interior
span of a continuous slab: (a) for a one-way solid slab of 3000-psi concrete carrying 100-psf
service live load (170-psf factored live load); (b) for flat-plate, flat-slab, and one-way joist construction.
See also Fig. 9.31.
CONCRETE CONSTRUCTION 9.79
One-way joist construction was developed to reduce dead load. For long spans,
the utility of solid-slab construction is offset by the increase in dead load of the
slab. One-way concrete-joist construction provides adequate depth with less dead
load than for solid slabs, and results in smaller concrete and reinforcement quantities
per square foot of floor area.
Uniform-depth floor and roof construction can be obtained by casting the joists
integral with wide, supporting band beams of the same total depth as the joists.
This design eliminates the need for interior beam forms.
9.54 STANDARD SIZES OF JOISTS
One-way concrete-joist construction that exceeds the dimensional limitations of the
ACI 318 Building Code must be designed as slabs and beams. These dimensional
limitations are:
Maximum clear spacing between ribs—30 in
Maximum rib depth—3.5 times rib width
Minimum rib width—4 in
Minimum top-slab thickness with removable forms—2 in but not less than onetwelfth
the clear spacing of ribs
Minimum top-slab thickness with permanent forms—11?2 in but not less than
one-twelfth the clear spacing of ribs
Removable form fillers can be standard steel pans or hardboard, corrugated cardboard,
fiberboard, or glass-reinforced plastic. Standard removable steel pans that
conform to ‘‘Types and Sizes of Forms for One-Way Concrete-Joist Construction,’’
(ANSI/CRSI A48.1-1986), American National Standards Institute, include 20- and
30-in widths and depths of 8, 10, 12, 14, 16, and 20 in. Standard steel square-end
pans are available in 36-in lengths. Widths of 10, 15, and 20 in and tapered end
fillers are available as special items. For forms 20 and 30 in wide, tapered end
forms slope to 16 and 25 in, respectively, in a distance of 3 ft.
9.55 DESIGN OF ONE-WAY
CONCRETE-JOIST CONSTRUCTION
One-way concrete joists must have adequate structural strength, and crack control
and deflection must be satisfactory under service loads. Approximate methods of
frame analysis can be used with uniform loads and spans that conform to requirements
of the ACI 318 Building Code (see Art. 9.41). Table 9.15 lists minimum
depths of joists to limit deflection, unless deflection computations justify shallower
construction (Table 9.14). Load tables in the Concrete Reinforcing Steel Institute’s
‘‘CRSI Design Handbook’’ indicate when deflections under service live loads exceed
specified limits.
Economy can be obtained by designing joists and slabs so that the same-size
forms can be used throughout a project. It will usually be advantageous to use
square-end forms for interior spans and tapered ends for end spans, when required
with a uniform depth.
9.80 SECTION NINE
TABLE 9.19 Temperature and Shrinkage Reinforcement for One-Way Joist Construction
Top-slab
thickness,
in
Required area
of temperature
and shrinkage
reinforcement,
in2 Reinforcement
Reinforcement
weight, psf
2 0.043 WWF 4  12, W1.5/W1 0.19
21?2 0.054 WWF 4  12, W2/W1 0.24
3 0.065 WWF 4  12, W2.5/W1 0.29
31?2 0.076 No. 3 bars @ 171?2 in 0.26
4 0.086 No. 3 bars @ 15 in 0.30
41?2 0.097 No. 3 bars @ 131?2 in 0.33
5 0.108 No. 3 bars @ 12 in 0.38
51?2 0.119 No. 3 bars @ 11 in 0.41
Fire Resistance. Table 9.17 gives minimum top-slab thickness for fire resistance
when a fire-resistant ceiling is not used.
Temperature and Shrinkage Reinforcement. This reinforcement must be provided
perpendicular to the ribs and spaced not farther apart than 5 times the slab
thickness, or 18 in. The required area of Grade 60 reinforcement for temperature
and shrinkage is 0.0018 times the concrete area (Table 9.19). For flexural reinforcement,
see Art. 9.56. For shear reinforcement, see Art. 9.57.
Embedded Pipes. Top slabs containing horizontal conduit or pipes that are allowed
by the ACI 318 Building Code (Art. 9.53) must have a thickness of at least
1 in plus the depth of the conduit or pipe.
Bridging. Distribution ribs are constructed normal to the main ribs to distribute
concentrated loads to more than one joist and to equalize deflections. These ribs
are usually made 4 to 5 in wide and reinforced top and bottom with one No. 4 or
one No. 5 continuous rebar. One distribution rib is usually used at the center of
spans of up to 30 ft, and two distribution ribs are usually placed at the third points
of spans longer than 30 ft.
Openings. These can be provided in the top slab of one-way concrete joist construction
between ribs without significant loss in flexural strength. Header joists
must be provided along openings that interrupt one or more joists.
9.56 REINFORCEMENT OF JOISTS
FOR FLEXURE
Reinforcement required for strength can be determined as indicated in Art. 9.46,
by treating as a beam a section symmetrical about a rib and as wide as the spacing
of ribs on centers.
CONCRETE CONSTRUCTION 9.81
Minimum Reinforcement. For not greater than 4400 psi, reinforcement (both ?
c
positive and negative) with a yield strength ?y should have an area equal to or
greater than 200/?y times the concrete area of the rib bwd, where bw is the rib width
and d 
 rib depth. For exceeding 4400 psi, the area of reinforcement should be ?
c
at least equal to Less reinforcement can be used, however, if the areas y 3
?
b d/? . c w
of both the positive and negative reinforcement at every section are one-third greater
than the amount required by analysis. (See also Art. 9.55.)
Maximum Reinforcement. Positive- and negative-moment reinforcement ratios
must not be greater than three-quarters of the ratio that produces balanced conditions
(Art. 9.46). The positive-moment reinforcement ratio is based on the width
of the top flange, and the negative-moment reinforcement ratio is based on the
width of the rib bw.
Reinforcement for one-way concrete-joist construction consists of straight top
and bottom bars, cut off as required for moment.
For top-slab reinforcement, straight top- and bottom-bar arrangements provide
more flexibility in attaining uniform distribution of top bars to control cracking in
the slab than straight and bent bars.
Requirements for structural integrity included in the ACI 318 Building Code
affect detailing of the bottom bars in the ribs. Over supports, at least one bottom
bar should be continuous or lap spliced to a bottom bar in the adjacent span with
a Class A tension lap splice (Art. 9.49.7). At exterior supports, one bottom bar
should be terminated with a standard hook.
For development (bond) of reinforcement, see Art. 9.49.
Figure 9.24b shows rebar quantities, lb / ft2 of floor or roof area, for continuous
interior spans of one-way concrete-joist construction made with normal-weight concrete
for superimposed factored live load of 170 psf, for preliminary estimates.
9.57 SHEAR IN JOISTS
The factored shear force Vu at a section without shear reinforcement should not
exceed
V 
 	V 
 	(2.2
?
b d) (9.70) u c c w
where Vc 
 nominal shear strength of the concrete
	
 strength-reduction factor (Art. 9.44) 
 0.85
d 
 distance, in from extreme compression surface to centroid of tension
steel
bw 
 rib width, in.
Based on satisfactory performance of joist construction, the ACI 318 Building Code
allows the nominal shear strength Vc for concrete in joists to be taken 10% greater
than for beams or slabs. The width bw can be taken as the average of the width of
joist at the compression face and the width at the tension reinforcement. The slope
of the vertical taper of ribs formed with removable steel pans can safely be assumed
as 1 in 12. For permanent concrete block fillers, the shell of the block can be
included as part of bw, if the compressive strength of the masonry is equal to or
greater than that of the concrete.
9.82 SECTION NINE
FIGURE 9.25 Stirrups for concrete joist construction.
FIGURE 9.26 General arrangement of standard reusable forms for wide-module joist systems.
If shear controls the design of one-way concrete-joist construction, tapered ends
can be used to increase the shear capacity. The Concrete Reinforcing Steel Institute’s
‘‘CRSI Design Handbook’’ has comprehensive load tables for one-way concrete-
joist construction that indicate where shear controls and when tapered ends
are required for simple, end, and interior spans.
For joists supporting uniform loads, the critical section for shear strength at
tapered ends is the narrow end of the tapered section. Shear need not be checked
within the taper.
Reinforcement for shear must be provided when the factored shear force Vu
exceeds the shear strength of the concrete 	Vc. The use of single-prong No. 3
stirrups spaced at half depth, such as that shown in Fig. 9.25, is practical in narrow
joists; they can be placed between two bottom bars.
9.58 WIDE-MODULE JOIST CONSTRUCTION
Wide-module joist construction, which is also referred to as ‘‘skip-joist’’ construction,
is an approach to reduce form costs and develop longer spans than standard
one-way joist systems (Art. 9.54). Where statutory building codes require thickness
of top slabs at or about 4.5 in for fire ratings, the flexural capacity of the slab is
under-utilized within limitations of standard joist dimensions with maximum clear
spacing between joists of 30 in. The wide-module joist concept utilizes standard
reusable joist forms with alternate ribs blocked off. See Fig. 9.26. Deeper-size forms
with ribs depths 16 in or 20 in below the slab are usually used in wide-module
construction. Rib spacings may be 6 ft or more depending upon depth of rib, or
module established by architectural reasons.
The alternate name ‘‘skip-joist’’ is accurate only in that a potential rib is indeed
omitted or ‘‘skipped’’ The ribs are designed as beams. Minimum concrete cover on
CONCRETE CONSTRUCTION 9.83
FIGURE 9.27 Various arrangements of shear reinforcement.
reinforcement is 1.5 in., instead of 0.75 in. as in standard joists. Minimum shear
reinforcement is required. Shear carried by the concrete is 10% less than that allowed
for standard joists. Draped two-way reinforcement in the top slab is permitted.
The principal practical problem is providing shear reinforcement in the amounts
required in the ribs—detailed for practicable placing in narrow sections. Vertical
U-stirrups are acceptable, although practicable bending limitations may require that
they be set at an angle to the longitudinal reinforcement. See Fig. 9.27. Single leg
stirrups with alternating direction of the hooked ends have been considered. The
ACI 318 Building Code also permits single leg, deformed or plain welded wire
fabric (WWF) meeting special requirements. Figure 9.27 shows several possible
details. Minimum shear reinforcement requirements will control in most cases, either
throughout the span or at a short distance from supports.
TWO-WAY SLAB CONSTRUCTION
A two-way slab is a concrete panel reinforced for flexure in more than one direction.
(See also Art.. 9.63.) Many variations of this type of construction have been used
for floors and roofs, including flat plates, solid flat slabs, and waffle flat slabs.
Generally, the columns that support such construction are arranged so that their
9.84 SECTION NINE
centerlines divide the slab into square or nearly square panels, but if desired, rectangular,
triangular, or even irregular panels may be used.
9.59 ANALYSIS AND DESIGN OF FLAT PLATES
The flat plate is the simplest form of two-way slab—simplest for analysis, design,
detailing, bar fabrication and placing, and formwork. A flat plate is defined as a
two-way slab of uniform thickness supported by any combination of columns and
walls, with or without edge beams, and without drop panels, column capitals, and
brackets.
Shear and deflection limit economical flat-plate spans to under about 30 ft for
light loading and about 20 to 25 ft for heavy loading. While use of reinforcingsteel
or structural-steel shear heads for resisting shear at columns will extend these
limits somewhat, their main application is to permit use of smaller columns. A
number of other variations, however, can be used to extend economical load and
span limits (Arts. 9.60 and 9.61).
The ACI 318 Building Code permits two methods of analysis for two-way construction:
direct design, within limitations of span and load, and equivalent frame
(Art. 9.42). Limitations on use of direct design are:
A minimum of three spans continuous in each direction
Rectangular panels with a ratio of longer to shorter span, center-to-center of
supports within a panel, not greater than 2
Successive span ratios, center-to-center of supports in each direction, not to
exceed 2:3
Columns offset from centerlines of successive columns not more than 0.10 span
in either direction
Specified ratio of live load to dead load (unfactored) does not exceed 2
All loads are due to gravity only and uniformly distributed over the entire panel
9.59.1 Design Procedures for Flat Plates
The procedure for either method of design begins with selection of preliminary
dimensions for review, and continues with six basic steps.
Step 1. Select a plate thickness expected to be suitable for the given conditions
of load and span. This thickness, unless deflection computations justify thinner
plates, should not be less than h determined from Table 9.16. With Grade 60 reinforcement,
minimum thickness is, from Table 9.16, for an interior panel
Ln h 
 	 5 in (9.71)
33
where Ln 
 clear span in the direction moments are being determined. Also, as
indicated in Table 9.16, for discontinuous panels, the minimum h 
 Ln/30 	 5 in
if no edge beam is present.
CONCRETE CONSTRUCTION 9.85
TABLE 9.20 Distribution of Mo for the End
Span of a Flat Slab
Without
edge
beam
With
edge
beam
Negative factored
moment at
edge column
0.26 0.30
Positive factored
moment
0.52 0.50
Negative factored
moment at first
interior column
0.70 0.70
Step 2. Determine for each panel the total static factored moment
2 M 
 0.125w L L (9.72) o u2 n
where L2 
 panel width (center-to-center spans transverse to direction in which
moment is being determined)
wu 
 total factored load, psf 
 1.4D  1.7L, typically
D 
 dead load, psf
L 
 live load, psf
Step 3. Apportion Mo to positive and negative bending moments. In the directdesign
method:
For interior spans, the negative factored bending moment is
M 
 0.65M (9.73) u o
and the positive factored bending moment is
M 
 0.35M (9.74) u o
For end spans (edge panels), Mo is distributed as indicated in Table 9.20.
Step 4. Distribute panel moments Mu to column and middle strips.
Column strip is a design strip with a width of 0.25L2  0.25L1 on each side of
the column centerline, where L1 is the center-to-center span in the direction in which
moments are being determined (Fig. 9.28).
Middle strip is the design strip between two column strips (Fig. 9.28).
For flat plates without beams, the distribution of Mu becomes:
For positive moment, column strip 60%, middle strip 40%
For negative moment at the edge column, column strip 100%
For interior negative moments, column strip 75%, middle strip 25%
A factored moment may be modified up to 10% so long as the sum of the
positive and negative moments in the panel in the direction being considered is at
least that given by Eq. (9.72).
9.86 SECTION NINE
FIGURE 9.28 Division of flat plate into column and middle strips.
Step 5. Check for shear. Shear strength of slabs in the vicinity of columns or other
concentrated loads has to be checked for two conditions: when the slab acts as a
wide beam and when the load tends to punch through the slab. In the first case, a
diagonal crack might extend in a plane across the entire width of the slab. Design
for this condition is described in Art. 9.47. For the two-way action of the second
condition, diagonal cracking might occur along the surface of a truncated cone or
pyramid in the slab around the column.
The critical section for two-way action, therefore, should be taken perpendicular
to the plane of the slab at a distance d/2 from the periphery of the column, where
d is effective depth of slab. Unless adequate shear reinforcement is provided, the
factored shear force Vu for punching action must not exceed 	Vc; i.e., Vu  	Vc,
CONCRETE CONSTRUCTION 9.87
where 	 
 strength-reduction factor 
 0.85 and Vc is the nominal shear strength
of the concrete. Vc is the smallest of the values computed from Eqs. (9.75) to (9.77).
4
V 
 2  
?
b d (9.75)   c co c
d s V
 2 
?
b d (9.76)  	 c co bo
V 
 4
?
b d (9.77) c c o
where c 
 ratio of long side to short side of the column
bo 
 perimeter of critical section, in.
d 
 distance from extreme compression surface to centroid of tension reinforcement,
in.
s 
 40 for interior columns; 30 for edge columns; and 20 for corner columns

 ?
c specified compressive strength of the concrete, psi
When shear reinforcement is provided (Art. 9.47), Vu  	Vn, where Vn is the
nominal shear strength of the reinforced section and equals the sum of Vc and the
shear strength added by the reinforcement. Vn should not exceed With 6
?
b d. c o
shearhead reinforcement (steel shapes fabricated by welding with a full-penetration
weld into identical perpendicular arms) at interior columns, Vn may be as large as
7
?
b d. c o
Determine the maximum shear at each column for two cases: all panels loaded,
and live load on alternate panels for maximum unbalanced moment to the columns.
Combine shears due to transfer of vertical load to the column with shear resulting
from the transfer of part of the unbalanced moment to the column by eccentricity
of shear (Art. 9.59.3). At this point, if the combined shear is excessive, steps 1
through 5 must be repeated with a large column, thicker slab, or higher-strength
concrete in the slab; or shear reinforcement must be provided where Vu  	Vc (Art.
9.47).
Step 6. When steps 1 through 5 are satisfactory, select flexural reinforcement.
9.59.2 Stiffnesses in Two-Way Construction
The ‘‘Commentary’’ to the ACI 318 Building Code contains references for a sophisticated
procedure for computation of stiffnesses of slabs and equivalent columns
to determine moments and shears by an elastic analysis. Variations in cross sections
of slab and columns, drop panels, capitals, and brackets are taken into account.
Columns can be treated as infinitely stiff within the joint with the slab. The slab
can be considered to be stiffened somewhat within the depth of the column.
In the direct-design method, certain simplifications are permissible in computation
of stiffnesses (see ‘‘Commentary’’ on ACI 318-89).
9.59.3 Transfer of Unbalanced Moments
Design requirements for the transfer of unbalance moment between the slab and
columns are included in the ACI 318 Building Code. Consider an exterior-edge
9.88 SECTION NINE
column of a flat plate system where the unbalanced moment, Mu, resulting from
gravity loads on the slab, must be transferred to the column. The unbalanced moment
is transferred by flexure and by eccentricity of shear.
Part of the unbalanced moment, ?Mu, must be transferred by flexure within an
effective slab width equal to the column width plus 1.5h on side of the column,
i.e., a width of (c2  1.5h) where c2 is the edge-column width transverse to the
direction in which moments are being determined and h is the overall thickness of
the slab. The remaining part of the unbalanced moment, ?Mu, must be transferred
by eccentricity of shear about the centroid of the critical section which is located
at distance of d/2 from the column where d is the effective depth of the slab. (As
noted in the following discussion, the code supersedes the requirement of designing
for vMu by prescribing the magnitude of the gravity load moment to be transferred
by eccentricity of shear.) The fractions ? and v are calculated
1
 
 (9.78) ? 1  (2/3) 
b /b 1 2
 
 (1   ) (9.79) v ?
where b1 
 width of critical section measured in the direction in which moments
are being determined
b2 
 width of critical section measured in the direction perpendicular to b1
For a square edge column and square panels, approximately 60% of the unbalanced
moment will be transferred by flexure within the slab width (c2  3h) centered
on the column centerline. The result is that about 60% of the total top reinforcement
required in the column strip must be concentrated within the slab width
(c2  3h) at the edge column. The designer must ensure that the top reinforcing
bars selected can be physically fitted into the width (c2  3h) within allowable bar
spacings, and clearly show the bar spacings and details on the design drawings.
For transfer of gravity load moment from the slab to the edge column by eccentricity
of shear, the Code prescribes v(0.3 Mo) as the magnitude of the moment
to be transferred, rather than vMu, where Mo is calculated by Eq. (9.72).
For preliminary design, with square columns flush at edges of the flat plate, a
rapid estimate of the shear capacity to allow for effects of combined shear due to
gravity loads and to moment transfer can be made by using uniform vertical load
wu only, with nominal strength for factored load as follows:
For edge column, total shear Vu 
 0.5wuL2L1 and shear strength Vc 
 2 bod 
?
c
For first interior column, Vu 
 1.15wuL2L1 and shear strength Vc 
 bod 4
?
c
where 
 specified concrete compressive strength, psi. ?
c
Use of this calculation in establishing a preliminary design is a short cut, which
will often avoid the need for repeating steps 1 through 5 in Art. 9.59.1, because it
gives a close approximation for final design.
The minimum cantilever edge span of a flat plate so that all columns can be
considered interior columns and the direct-design method can be used without tedious
stiffness calculations is 4?15 of the length of the interior span (Fig. 9.29). This
result is obtained by equating the minimum cantilever moment at the exterior column
to the minimum negative-factored moment at the interior column.
CONCRETE CONSTRUCTION 9.89
FIGURE 9.29 Length of cantilever (at left) determines
whether the exterior column may be treated as an interior
column.
FIGURE 9.30 Reinforcing bar details for column and middle strips of flat plates.
9.59.4 Bar Lengths and Details for Flat Plates
The minimum lengths of reinforcing bars for flat plates shown in Fig. 9.30, prescribed
by the ACI 318 Building Code, save development (bond) computations.
The size of all top bars must be selected so that the tension development length Ld
required for the bar size, concrete strength, and grade of the bar is not greater than
the length available for development (see Table 9.8).
The size of top bars at the exterior edge must be small enough that the hook
plus straight extension to the face of the column is larger than that required for full
embedment (Table 9.9).
Column-strip bottom bars in Fig. 9.30 are shown extended into interior columns
so that they lap, and one line of bar supports may be used. This anchorage, which
9.90 SECTION NINE
exceeds ACI 318 Building Code minimum requirements, usually ensures ample
development length and helps prevent temperature and shrinkage cracks at the centerline.
Figure 9.24b shows weights of steel and concrete for flat plates of normal-weight
concrete carrying a superimposed factored load of 170 psf, for preliminary estimates.
Provisions for structural integrity for two-ways slabs specified in he ACI 318
Building Code require all column-strip bottom bars in each direction to be made
continuous or spliced with Class A tension lap splices. At least two of the columnstrip
bottom bars must pass within the column core. The bars must be anchored at
exterior supports. In slabs with shearheads, at least two of the bottom bars in each
direction must pass through the shearhead as close to the column as possible and
be continuous or spliced with a Class A tension lap splice. At exterior columns,
the bars must be anchored at the shearhead.
Crack Control. The ACI 318 Building Code’s requirements (Art. 9.50) apply only
to one-way reinforced elements. For two-way slabs, bar spacing at critical sections
should not exceed twice the slab thickness, except in the top slab of cellular or
ribbed (waffle) construction, where requirements for temperature and shrinkage reinforcement
govern.
9.60 FLAT SLABS
A flat slab is a two-way slab generally of uniform thickness, but it may be thickened
or otherwise strengthened in the region of columns by a drop panel, while the top
of the column below the slab may be enlarged by a capital (round) or bracket
(prismatic). If a drop panel is used to increase depth for negative reinforcement,
the minimum side dimensions of this panel are L3 /3 and L2 /3, where L1 and L2 are
the center-to-center spans in perpendicular directions. Minimum depth of a drop
panel is 1.25h, where h is the slab thickness elsewhere.
A waffle flat slab or waffle flat plate consists of a thin, two-way top slab and
a grid of joists in perpendicular directions, cast on square dome forms. For strengthening
around columns, the domes are omitted in the drop panel areas, to form a
solid head, which also may be made deeper than the joists. Other variations of
waffle patterns include various arrangements with solid beams on column centerlines
both ways. Standard sizes of two-way joist forms are given in Table 9.21.
The drop panel increases shear capacity. Hence, a solid flat slab can ordinarily
be designed for concrete for lower strength than for a flat plate. Also, deflection of
a flat slab is reduced by the added stiffness that drop panels provide.
The depth of drop panels can be increased beyond 1.25h to reduce negativemoment
reinforcement and to increase shear capacity when smaller columns are
desired. If this adjustment is made, shear in the slab at the edge of the drop panel
may become critical. In that case, shear capacity can be increased by making the
drop panel larger, up to about 40% of the span. See Fig. 9.31 for bar details (column
strip).
Waffle flat plates behave like solid flat slabs with drop panels. Somewhat higherstrength
concrete, to avoid the need of stirrups in the joists immediately around the
solid head, is usually desirable. If required, however, such stirrups can be made in
one piece as a longitudinal assembly, to extend the width of one dome between the
9.91 TABLE 9.21 Commonly Used Sizes of Two-Way Joist Forms†
Depth,
in
Volume,
ft3
per
dome
Weight
of displaced
concrete,
lb per
dome
3-in top slab
Equiv.
slab
thickness,
in
Weight*
psf
41?2-in top slab
Equiv.
slab
thickness,
in
Weight*
psf
30-in-wide domes
8 3.85 578 5.8 73 7.3 92
10 4.78 717 6.7 83 8.2 102
12 5.53 830 7.4 95 9.1 114
14 6.54 980 8.3 106 9.9 120
16 7.44 1116 9.1 114 10.6 133
20 9.16 1375 10.8 135 12.3 154
19-in wide domes
3-in top slab 41/2-in top slab
8 1.41 211 6.8 85 8.3 103
10 1.90 285 7.3 91 8.8 111
12 2.14 321 8.6 107 10.1 126
† ‘‘Types and Sizes of Forms for Two-Way Concrete-Joist Construction’’
(ANSI /CRSI A48.2-1986).
* Basis: unit weight of concrete, w 
 150 pcf.
9.92 SECTION NINE
FIGURE 9.31 Reinforcing bar details for column strips of flat slabs. Details of middle strips
are the same as for middle strips of flat plates (Fig. 9.30).
FIGURE 9.32 Reinforcing details for column strips of two-way waffle flat plates. B 
 24 bar
diameters or 12 in minimum. Details for middle strips are the same as for middle strips of flat
plates (Fig. 9.30).
drop head and the first transverse joist. For exceptional cases, such stirrups can be
used between the second row of domes also. See Fig. 9.32 for reinforcement details.
9.61 TWO-WAY SLABS ON BEAMS
The ACI 318 Building Code provides for use of beams on the sides of panels, on
column centerlines. (A system of slabs and beams supported by girders, however,
usually forms rectangular panels. In that case, the slabs are designed as one-way
slabs.)
Use of beams on all sides of a panel permits use of thinner two-way slabs, down
to a minimum thickness h 
 31?2 in. A beam may be assumed to resist as much as
85% of the column-strip moment, depending on its stiffness relative to the slab (see
the ACI 318 Building Code). A secondary benefit, in addition to the direct advantages
of longer spans, thinner slabs, and beam stirrups for shear, is that many local
codes allow reduced service live loads for design of the beams. These reductions
are based on the area supported and the ratio of dead to live load. For service live
loads up to 100 psf, such reductions are usually permitted to a maximum of 60%.
Where such reductions are allowed, the reduced total panel moment Mo (Art. 9.59.1)
CONCRETE CONSTRUCTION 9.93
FIGURE 9.33 For estimating purposes, weight of reinforcing steel in square interior
panels of flat plates, flat slabs, and waffle flat slabs of 4000-psi concrete, with rebars of
60-ksi yield strength, carrying a superimposed factored load of 200 lb / ft2. See also Fig.
9.24.
and the increased effective depth to reinforcing steel in the beams offer savings in
reinforcement to offset partly the added cost of formwork for the beams.
9.62 ESTIMATING GUIDE FOR TWO-WAY
CONSTRUCTION
Figure 9.33 can be used to estimate quantities of reinforcing steel, concrete, and
formwork for flat slabs, as affected by load and span. It also affords a guide to
preliminary selection of dimensions for analysis, and can be used as an aid in
selecting the structural system most appropriate for particular project requirements.
BEAMS
Most requirements of the ACI 318 Building Code for design of beams and girders
refer to flexural members. When slabs and joists are not intended, the Code refers
specifically to beams and occasionally to beams and girders, and provisions apply
equally to beams and girders. So the single term, beams, will be used in the following.
9.94 SECTION NINE
9.63 DEFINITIONS OF FLEXURAL MEMBERS
The following definitions apply for purposes of this section:
Slab. A flexural member of uniform depth supporting area loads over its surface.
A slab may be reinforced for flexure in one or two directions.
Joist-slab. A ribbed slab with ribs in one or two directions. Dimensions of
such a slab must be within the ACI 318 Building Code limitations (see Art.
9.54).
Beam. A flexural member designed to carry uniform or concentrated line
loads. A beam may act as a primary member in beam-column frames, or may
be used to support slabs or joist-slabs.
Girder. A flexural member used to support beams and designed to span between
columns, walls, or other girders. A girder is always a primary member.
9.64 FLEXURAL REINFORCEMENT
Nonprestressed beams should be designed for flexure as explained in Arts. 9.44 to
9.46. If beam capacity is inadequate with tension reinforcement only and the capacity
must be increased without increasing beam size, additional capacity may be
provided by addition of compression bars and more tension-bar area to match the
compression forces developable in the compression bars (Fig. 9.14). (Shear, torsion,
development, crack control, and deflection requirements must also be met to complete
the design. See Arts. 9.47 to 9.51 and 9.65 to 9.67.) Deflection need not be
calculated for ACI 318 Building Code purposes if the total depth h of the beam,
including top and bottom concrete cover, is at least the fraction of the span L given
in Table 9.15.
A number of interdependent complex requirements (Art. 9.49) regulate the permissible
cutoff points of bars within a span, based on various formulas and rules
for development (bond). An additional set of requirements applies if the bars are
cut off in a tensile area. These requirements can be satisfied for cases of uniform
gravity load and nearly equal spans for the top bars by extending at least 50% of
the top reinforcement to a point in the span 0.30Ln beyond the face of the support,
and the remainder to a point 0.20Ln, where Ln 
 clear span. For the bottom bars,
all requirements are satisfied by extending at least 40% of the total reinforcement
into the supports 6 in past the face, and cutting off the remainder at a distance
0.125Ln from the supports. Note that this arrangement does not cut off bottom bars
in a tensile zone. Figure 9.34 shows a typical reinforcement layout for a continuous
beam, singly-reinforced.
The structural detailing of reinforcement in beams is also affected by ACI 318
Building Code requirements for structural integrity. Beams are categorized as either
perimeter beams or nonperimeter beams. (A spandrel beam would be a perimeter
beam.) In perimeter beams, at least one-sixth of the tension-reinforcement area
required for negative moment (As /6) at the face of supports, and one-quarter of
the tension-reinforcement area required for positive moment (As /4) at midspan
have to be made continuous around the perimeter of the structure. Closed stirrups
are also required in perimeter beams. It is not necessary to place closed stirrups
within the joints. It is permissible to provide continuity of the top and bottom bars
CONCRETE CONSTRUCTION 9.95
FIGURE 9.34 Reinforcing bar details for uniformly loaded continuous beams.
At columns, embed alternate bottom bars (at least 50% of the tension-steel area)
a minimum of 6 in., to avoid calculation of development length at 0.125Ln.
FIGURE 9.35 Reinforcement required to ensure structural integrity of
beams. At least one-sixth of the negative-moment rebars and one-fourth of
the positive-moment rebars should be continuous around the perimeter of
the structure (a), with closed stirrups throughout, except at joints. Class A
tension lap splices may be made at midspan. For nonperimeter beams (b),
one-fourth the positive-moment rebars should be continuous. For clarity,
other rebars are not shown in (a) or (b).
by splicing the top bars at midspan and the bottom bars at or near the supports.
Splicing the bars with Class A tension lap splices (Art. 9.49.7) is acceptable. (See
Fig. 9.35a.)
For nonperimeter beams, the designer has two choices to satisfy the structural
integrity requirements: (1) provide closed stirrups or (2) make at least one-quarter
of the tension-reinforcement area required for positive moment (As /4) at midspan
continuous. Splicing the prescribed number of bottom bars over the supports with
Class A tension lap splices is acceptable. At discontinuous ends, the bottom bars
must be anchored with standard hooks. (see Fig. 9.35b.)
9.96 SECTION NINE
FIGURE 9.36 Stresses and strains in a T-beam reinforced for compression: (a) beam
cross section; (b) strain distribution; (c) block distribution of compression stresses; (d)
balanced strains.
The limit in the ACI 318 Building Code on tension-reinforcement ratio  that
it not exceed 0.75 times the ratio for balanced conditions applies to beams (Art.
9.46). Balanced conditions in a beam reinforced only for tension exist when the
tension steel reaches its yield strength ?y simultaneously with the maximum compressive
strain in the concrete at the same section becoming 0.003 in / in. Balanced
conditions occur similarly for rectangular beams, and for T-beams with negative
moment, that are provided with compression steel, or doubly-reinforced. Such sections
are under balanced conditions when the tension steel, with area As, yields just
as the outer concrete surface crushes, and the total tensile-force capacity As?y equals
the total compressive-force capacity of the concrete plus compression steel, with
area Note that the capacity of the compression steel cannot always be taken as A
. s
because the straight-line strain distribution from the fixed points of the outer A
? , s y
concrete surface and centroid of the tension steel may limit the compression-steel
stress to less than yield strength (Fig. 9.14).
For design of doubly-reinforced beams, the force As?y in the tension steel is
limited to three-fourths the compression force in the concrete plus the compression
in the compression steel at balanced conditions. For a beam meeting these conditions
in which the compression steel has not yielded, the design moment strength
is best determined by trial and error:
1. Assume the location of the neutral axis.
2. Determine the strain in the compression steel.
3. See if the total compressive force on the concrete and compression steel equals
As?y (Fig. 9.36).
Example. Design a T-beam to resist a negative factored moment of 225 ft-kips.
The dimensions of the beam are shown in Fig. 9.36. Concrete strength ?
 
 c
the reinforcing steel has a yield strength ?y 
 60 ksi, and strength-reduction 4 ksi,
factor 	
 0.90.
CONCRETE CONSTRUCTION 9.97
Need for Compression Steel. To determine whether compression reinforcement
is required, first check the strength of the section when it is reinforced only with
tension steel. For this purpose, compute the reinforcement ratio b for balanced
conditions from Eq. (9.27) with 1 
 0.85:
0.85  4000  0.85 87,000

  
 0.0285 b 60,000 87,000  60,000
The maximum reinforcement ratio permitted by the ACI 318 Building Code is
 
 0.75  
 0.75  0.0285 
 0.0214 max b
and the corresponding steel area is
2 A 
 0.0214  12.5  15 
 4.01 in s
As noted in Art. 9.46.1, depth of the stress block is
A ? 4.01  60,000 s y a
 
 
 5.66 in
0.85?
b 0.85  4000  12.5 c
From Eq. (9.28b), the maximum design moment strength with tension reinforcement
only is
	M 
 0.90  4.01  60,000(12.5  5.66/2)/12 
 174,500 ft-lb n(max)
The required strength, 225,000 ft-lb, is larger. Hence, compression reinforcement
is needed.
Compression on Concrete. (Trial-and-error solution.) Assume that the distance
c from the neutral axis to the extreme compression surface is 5.1 in. The depth a
then may be taken as 0.85c 
 4.33 in (Art. 9.46). For a rectangular stress distribution
over the concrete, the compression force on the concrete is
0.85?
b a 
 0.85  4  15  4.33 
 221 kips c w
Selection of Tension Steel. To estimate the tension steel required, assume a
moment arm jd 
 d  a/2 
 12.5  4.33/2 
 10.33 in. By Eq. (9.28c), the
tension-steel force therefore should be about
M 225  12 u A ? 
 60A
 
 
290 kips s y s 	jd 0.9  10.33
from which As 
 4.84 in2. Select five No. 9 bars, supplying As 
 5 in2 and providing
a tensile-steel ratio
5

 
0.0267
15  12.5
The bars can exert a tension force As?y 
 5  60 
 300 kips.
Stress in Compression Steel. For a linear strain distribution, the strain in the 
s
steel 21?2 in from the extreme compression surface can be found by proportion from
the maximum strain of 0.003 in / in at that surface. Since the distance c 
 a/ 1 

4.33/0.85 
 5.1 in,
9.98 SECTION NINE
5.1  2.5


 0.003 
 0.0015 in / in s 5.1
With modulus of elasticity Es taken as 29,000 ksi, the stress in the compression
steel is
?
 
 0.0015  29,000 
 43.5 ksi s
Selection of Compression Steel. The total compression force equals the 221-
kip force on the concrete previously computed plus the force on the compression
steel. If the total compression force is to equal to total tension force, the compression
steel must resist a force
A
?
 
 A
(43.5  3.4) 
 300  221 
 79 kips s s s
from which the compression-steel area (In the above calculation, the 2 A
 
 2 in . s
force on the steel is reduced by the force on the concrete, 	?
A
 
 0.85  c s
replaced by the steel.) 4A
 
 3.4A
, s s
Check the Balance of Forces (Fc 
 Ft). For an assumed position of the
neutral axis at 5.10 in with five No. 9 tension bars and two No. 9 compression
bars, the total compression force C is
Concrete: 0.85  4  4.33  15 
 221 kips
Steel: 2(43.5  3.4) 
 80 kips
C 
 301 kips
This compression force for practical purposes is equal to the total tension force: 5
 60  1 
 300 kips. The assumed position of the neutral axis results in a balance
of forces within 1% accuracy.
Nominal Flexural Strength. For determination of the nominal flexural strength
of the beam, moments about the centroid of the tension steel are added:
a
M 
 0.85?
ba d A
?
(d  d
) (9.80)   n c s s 2
Substitution of numerical values gives:
M 
 0.85  4  15  4.33(12.5  4.33/2)  2(43.5  3.4)(12.5  2.5) n

 221  10.33  80  10 
 257 ft-kips
Check Design Moment Strength (	Mn)
	M 
 0.90  257 
 231 ft-kips  M 
 225 ft-kips) OK n u
9.65 REINFORCEMENT FOR SHEAR
AND FLEXURE
Determination of the shear capacity of a beam is discussed in Art. 9.47. Minimum
shear reinforcement is required in all beams with total depth greater than 10 in, or
21?2 times flange (slab) thickness, or half the web thickness, except where the facCONCRETE
CONSTRUCTION 9.99
FIGURE 9.37 Required shear reinforcement in three zones of a beam
between supports and midspan is determined by cross-hatched areas.
tored shear force Vu is less than half the design shear strength 	Vc of the concrete
alone. Torsion should be combined with shear when the factored loads cause a
torsional moment Tu larger than for nonprestressed beams (see Art.
2 Acp
	
?
  c pcp
9.48).
Shear strength should be computed at critical sections in a beam from Eq. (9.38).
Open or closed stirrups may be used as reinforcement for shear in beams; but closed
stirrups are required for torsion. The minimum area for open or closed stirrups for
vertical shear only, to be used where 0.5	Vc  Vu  	Vc and the factored torsional
moment Tu can be neglected, should be calculated from
50b s w A 
 (9.81) v ?y
where Av 
 area of all vertical legs in the spacing s, in parallel to flexural reinforcement,
in2
bw 
 thickness of beam web, in2
?y 
 yield strength of reinforcing steel, psi
Note that this minimum area provides a capacity for 50-psi shear on the cross
section bws.
Where Vu exceeds Vc, the cross-sectional area Av of the legs of open or closed
vertical stirrups at each spacing s should be calculated from Eq. (9.40a). Av is the
total area of vertical legs, two legs for a common open U stirrup or the total of all
legs for a transverse multiple U. Note that there are three zones in which the
required Av may be supplied by various combinations of size and spacing of stirrups
(Fig. 9.37):
1. Beginning 1 or 2 in from the face of supports and extending over a distance
d from each support, where d is the depth from extreme compression surface to
centroid of tension steel (Av is based on Vu at d from support).
2. Between distance d from each support and the point where 	Vs 
 Vu  	Vc

 50bws (required Av decreases from maximum to minimum).
3. Distance over which minimum reinforcement is required (minimum Av extends
from the point where 	Vs 
 50bws to the point where Vu 
 0.5	Vc).
9.100 SECTION NINE
9.66 REINFORCEMENT FOR TORSION
AND SHEAR
Any beam that supports unbalanced loads that are transverse to the direction in
which it is subjected to bending moments transmits an unbalanced moment to the
supports and must be investigated for torsion. Generally, this requirement affects
all spandrel and other edge beams, and interior beams supporting uneven spans or
unbalanced live loads on opposite sides. The total unbalanced moment from a floor
system with one-way slabs in one direction and beams in the perpendicular direction
can often be considered to be transferred to the columns by beam flexure in one
direction, neglecting torsion in the slab. The total unbalanced moment in the other
direction, from the one-way slabs, can be considered to be transferred by torsional
shear from the beams to the columns.
Under the ACI 318 Building Code, factored torsional moment, Tu, is resisted by
reinforcement (Art. 9.48). No torsion is assumed to be resisted by concrete. When
Tu exceeds the value computed by Eq. (9.43) for non-prestressed members, the
effects of torsion must be considered.
The required area At of each leg of a closed stirrup for torsion should be computed
from Eq. (9.48). Stirrup spacing should not exceed ph /8 or 12 in, where ph
is the perimeter of the centerline of the outermost closed stirrup.
Torsion reinforcement also includes the longitudinal bars shown in each corner
of the closed stirrups in Fig. 9.16 and the longitudinal bars spaced elsewhere inside
the perimeter of the closed stirrups at not more than 12 in. At least one longitudinal
bar in each corner is required. [For required areas of these bars, see Eqs. (9.50)
and (9.52).] If a beam is fully loaded for maximum flexure and torsion simultaneously,
as in a spandrel beam, the area of torsion-resisting longitudinal bars At
should be provided in addition to flexural bars.
For interior beams, maximum torsion usually occurs with live load only on a
slab on one side of the beam. Maximum torsion and maximum flexure cannot occur
simultaneously. Hence, the same bars can serve for both.
The closed stirrups required for torsion should be provided in addition to the
stirrups required for shear, which may be the open type. Because the size of stirrups
must be at least No. 3 and maximum spacings are established in the ACI 318
Building Code for both shear and torsion stirrups, a closed-stirrup size-spacing
combination can usually be selected for combined shear and torsion. Where maximum
shear and torsion cannot occur under the same loading, the closed stirrups
can be proportioned for the maximum combination of forces or the maximum single
force; whichever is larger.
9.67 CRACK CONTROL IN BEAMS
The ACI 318 Building Code contains requirements limiting flexural reinforcement
spacing to regulate crack widths when the yield strength ?y of the reinforcement
exceeds 40,000 psi (Art. 9.50). Crack width is proportional to steel stress. The
tensile area of concrete tributary to and concentric with each bar, and thickness of
the concrete cover are important to crack control. The minimum concrete cover
requirements of the ACI 318 Building Code for reinforcement in beams and girders
are given in Table 9.22.
CONCRETE CONSTRUCTION 9.101
TABLE 9.22 Minimum Concrete Cover, in., for Beams and Girders
Bar size No.
Exposed to Earth or weather
Castin-
place
concrete
Precast
concrete
Prestressed
concrete
Not exposed to weather or in
contact with ground
Castin-
place
concrete
Precast
concrete
Prestressed
concrete
3, 4, and 5 11?2 11?4 11?2 11?2 5?8 11?2
6 through 11 2 11?2 11?2 11?2 db* 11?2
14 and 18 2 2 11?2 11?2 11?2 11?2
Stirrups Same as above for each size 3?8 1
* db 
 nominal bar diameter, in.
WALLS
Generally, any vertical member whose length and height are both much larger than
the thickness may be treated as a wall. Walls subjected to vertical loads are called
bearing walls. Walls subjected to no loads other than their own weight, such as
panel or enclosure walls, are called nonbearing walls. Walls with a primary function
of resisting lateral loads are called shear walls. They also may serve as bearing
walls. See Art. 9.89.
9.68 BEARING WALLS
Reinforced concrete bearing walls may be designed as eccentrically loaded columns
or by an empirical method given in the ACI 318 Building Code. The empirical
method may be used when the resultant of the applied load falls within the middle
third of the wall thickness. This method gives the capacity of the walls as
2 kLc P  	P 
 0.55	?
A 1  (9.82)   	 u nw c g 32h
where 
 ?
c specified concrete compressive strength
	
 strength-reduction factor 
 0.70
Ag 
 gross area of horizontal cross-section of wall
h 
 wall thickness
Lc 
 vertical distance between supports
k 
 effective length factor
When the wall is braced against lateral translation at top and bottom:
k 
 0.8 for restraint against rotation at one or both ends
k 
 1.0 for both ends unrestrained against rotation
When the wall is not braced against lateral translation, k 
 2.0 (cantilever walls).
9.102 SECTION NINE
The allowable average compressive stress ?c for a wall is obtained by dividing
Pu in Eq. (9.82) by Ag.
Length. The effective length of wall for concentrated loads may be taken as the
center-to-center distance between loads, but not more than the width of bearing
plus 4 times the wall thickness.
Thickness. The minimum thickness of bearing walls for which Eq. (9.82) is applicable
is one-twenty-fifth of the least distance between supports at the sides or
top, but not less than 4 in. Exterior basement walls and foundation walls should be
at least 71?2 in thick. Minimum thickness and reinforcement requirements may be
waived, however, if justified by structural analysis.
Reinforcement. The area of horizontal steel reinforcement should be at least
A 
 0.0025A (9.83) h wv
where Awv 
 gross area of the vertical cross-section of wall.
Area of vertical reinforcement should be at least
A 
 0.0015A (9.84) v wh
where Awh 
 gross area of the horizontal cross-section of wall. For Grade 60 bars,
No. 5 or smaller, or for welded-wire fabric, these steel areas may be reduced to
0.0020Awv and 0.0012Awh, respectively.
Walls 10 in or less thick may be reinforced with only one rectangular grid of
rebars. Thicker walls require two grids. The grid nearest the exterior wall surface
should contain between one-half and two-thirds the total steel area required for the
wall. It should have a concrete cover of at least 2 in but not more than one-third
the wall thickness. A grid near the interior wall surface should have a concrete
cover of at least 3?4 in but not more than one-third the wall thickness. Minimum
size of bars, if used, is No. 3. Maximum bar spacing is 18 in. (These requirements
do not apply to basement walls, however. If such walls are cast against and permanently
exposed to earth, minimum cover is 3 in. Otherwise, the cover should be
at least 2 in for bar sizes No. 6 and larger, and 11?2 in for No. 5 bars or 5?8-in wire
and smaller.)
At least two No. 5 bars should be placed around all window and door openings.
The bars should extend at least 24 in beyond the corners of openings.
Design for Eccentric Loads. Bearing walls with bending moments sufficient to
cause tensile stress must be designed as columns for combined flexure and axial
load, including slenderness effects if applicable. Minimum reinforcement areas and
maximum bar spacings are the same as for walls designed by the empirical method.
Lateral ties, as for columns, are required for compression reinforcement and where
the vertical bar area exceeds 0.01 times the gross horizontal concrete area of the
wall. (For column capacity, see Art. 9.82.)
Under the preceding provisions, a thin, wall-like (rectangular) column with a
steel ratio less than 0.01 will have a greater carrying capacity if the bars are detailed
as for walls. The reasons for this are: The effective depth is increased by omission
of ties outside the vertical bars and by the smaller cover (as small as 3?4 in) permitted
for vertical bars in walls. Furthermore, if the moment is low (eccentricity less than
one-sixth the wall thickness), so that the wall capacity is determined by Eq. (9.82),
the capacity will be larger than that computed for a column, except where the
column is part of a frame braced against sidesway.
CONCRETE CONSTRUCTION 9.103
If slenderness effects need to be considered, slender walls must comply with the
slenderness requirements for columns (Art. 9.86). For slender precast concrete wall
panels, where the panels are restrained at the top, an alternative design procedure
can be used. The alternative approach was introduced into Chapter 14 of the ACI
318-99 Building Code. Complying with the provisions in the alternative procedure
is deemed to satisfy the Code’s slenderness requirements for columns.
9.69 NONBEARING WALLS
Nonbearing reinforced-concrete walls, frequently classified as panels, partitions, or
cross walls, may be precast or cast in place. Panels serving merely as exterior
cladding, when precast, are usually attached to the columns or floors of a frame,
supported on grade beams, or supported by and spanning between footings, serving
as both grade beams and walls. Cast-in-place cross walls are most common in
substructures. Less often, cast-in-place panels may be supported on grade beams
and attached to the frame.
In most of these applications for nonbearing walls, stresses are low and alternative
materials, such as unreinforced masonry, when supported by beams above
grade, or panels of other materials, can be used. Consequently, unless esthetic requirements
dictate reinforced concrete, low-stressed panels of reinforced concrete
must be designed for maximum economy. Minimum thickness, minimum reinforcement,
full benefits of standardization for mass-production techniques, and design
for double function as both wall and deep beam must be achieved.
Thickness of nonbearing walls of reinforced concrete should be at least onethirtieth
the distance between supports, but not less than 4 in.
The ACI 318 Building Code, however, permits waiving all minimum arbitrary
requirements for thickness and reinforcement where structural analysis indicates
adequate strength and stability.
Where support is provided, as for a panel above grade on a grade beam, connections
to columns may be detailed to permit shrinkage. Friction between base of
panel and the beam can be reduced by an asphalt coating and omission of dowels.
These provisions will permit elimination or reduction of horizontal shrinkage reinforcement.
Vertical reinforcement is seldom required, except as needed for spacing
the horizontal bars.
If a nonbearing wall is cast in place, reinforcement can be nearly eliminated
except at edges. If the wall is precast, handling stresses will often control. Multiple
pickup points with rigid-beam pickups will reduce such stresses. Vacuum pad pickups
can eliminate nearly all lifting stresses.
Where deep-beam behavior or wind loads cause stresses exceeding those permitted
on plain concrete, the ACI 318 Building Code permits reduction of minimum
tension-reinforcement [As 
 200bd/?y (Art. 9.46)] if reinforcement furnished is onethird
greater than that required by analysis. (For deep-beam design, see Art. 9.88.)
9.70 CANTILEVER RETAINING WALLS
Under the ACI 318 Building Code, cantilever retaining walls are designed as slabs.
Specific Code requirements are not given for cantilever walls, but when axial load
becomes near zero, the Code requirements for flexure apply.
9.104 SECTION NINE
FIGURE 9.38 Factored loads and critical sections for design of cantilever retaining
walls.
Minimum clear cover for bars in walls cast against and permanently exposed to
earth is 3 in. Otherwise, minimum cover is 2 in. for bar sizes No. 6 and larger, and
11?2 for No. 5 bars or 5?8-in wire and smaller.
Two points requiring special consideration are analysis for load factors of 1.7
times lateral earth pressure and 1.4 times dead loads and fluid pressures, and provision
of splices at the base of the stem, which is a point of maximum moment.
The footing and stem are usually cast separately, and dowels left projecting from
the footing are spliced to the stem reinforcement.
A straightforward way of applying Code requirements for strength design is
illustrated in Fig. 9.38. Soil reaction pressure p and stability against overturning
are determined for actual weights of concrete D and soil W and assumed lateral
pressure of the soil H. The total cantilever bending moment for design of stem
reinforcement is then based upon 1.7H. The toe pressure used to determine the
footing bottom bars is 1.7p. And the top load for design of the top bars in the
footing heel is 1.4(W  Dh), where Dh is the weight of the heel. The Code requires
application of a factor of 0.9 to vertical loading that reduces the moment caused
by H.
Where the horizontal component of backfill pressure includes groundwater above
the top of the heel, use of two factors, 1.7 for the transverse soil pressure and 1.4
for the transverse liquid pressure, would not be appropriate. Because the probability
of overload is about the same for soil pressure and water pressure, use
FIGURE 9.39 Loads for simplified strength
design for toe of wall.
of a single factor, 1.7, is logical, as recommended
in the Commentary to the
ACI 318 Building Code. For environmental
engineering structures where
these conditions are common, ACI
Committee 350 had recommended use
of 1.7 for both soil and liquid pressure
(see ‘‘Environmental Engineering Concrete
Structures,’’ ACI 350R). Committee
350 also favored a more conservative
approach for design of the toe. It is more
convenient and conservative to consider
1.7 times the entire vertical reaction uniformly
distributed across the toe as well
as more nearly representing the actual
end-point condition (Fig. 9.39).
The top bars in the heel can be selected
for the unbalanced moment between the factored forces on the toe and the
stem, but need not be larger than for the moment of the top loads on the footing
CONCRETE CONSTRUCTION 9.105
FIGURE 9.40 Splice details for cantilever retaining walls: (a) for low walls;
(b) for high walls with Class B lap for dowels; (c) alternative details for high
walls, with Class A lap for dowels.
(earth and weight of heel). For a footing proportioned so that the actual soil pressure
approaches zero at the end of the heel, the unbalanced moment and the maximum
moment in the heel caused by the top loads will be nearly equal.
The possibility of an overall sliding failure, involving the soil and the structure
together, must be considered, and may require a vertical lug extending beneath the
footing, tie backs, or other provisions.
The base of the stem is a point of maximum bending moment and yet also the
most convenient location for splicing the vertical bars and footing dowels. The ACI
318 Building Code advises avoiding such points for the location of lap splices. But
for cantilever walls, splices can be avoided entirely at the base of the stem only for
low walls (8 to 10 ft high), in which L-shaped bars from the base of the toe can
be extended full height of the stem. For high retaining walls (over 10 ft high), if
all the bars are spliced at the base of the stem, a Class B tension lap splice is
required (Art. 9.49.7). If alternate dowel bars are extended one Class A tension lapsplice
length and the remaining dowel bars are extended at least twice this distance
before cutoff, Class A tension lap splices may be used. This arrangement requires
that dowel-bar sizes and vertical-bar sizes be selected so that the longer dowel bars
provide at least 50% of the steel area required at the base of the stem and the
vertical bars provide the total required steel at the cutoff point of the longer dowels
(Fig. 9.40).
9.71 COUNTERFORT RETAINING WALLS
In this type of retaining wall, counterforts (cantilevers) are provided on the earth
side between wall and footing to support the wall, which essentially spans as a
continuous one-way slab horizontally. Counterfort walls seldom find application in
building construction. A temporary condition in which basement walls may be
required to behave as counterfort retaining walls occurs though, if outside fill is
placed before the floors are constructed. Under this condition of loading, each
interior cross wall and end basement wall can be regarded as a counterfort. It is
usually preferable, however, to delay the fill operation rather than to design and
provide reinforcement for this temporary condition.
9.106 SECTION NINE
The advantages of counterfort walls are the large effective depth for the cantilever
reinforcement and concrete efficiently concentrated in the counterfort. For
very tall walls, where an alternative cantilever wall would require greater thickness
and larger quantities of reinforcing steel and concrete, the savings in material will
exceed the additional cost of forming the counterforts. Accurate design is necessary
for economy in important projects involving large quantities of material and requires
refinement of the simple assumptions in the definition of counterfort walls. The
analysis becomes complex for determination of the division of the load between
one-way horizontal slab and vertical cantilever action.
See also Art. 6.7 (F. S. Merritt, ‘‘Standard Handbook for Civil Engineers,’’
McGraw-Hill Publishing Company, New York.)
9.72 RETAINING WALLS SUPPORTED ON FOUR
SIDES
For walls more than 10 in thick, the ACI 318 Building Code requires two-way
layers of bars in each face. Two-way slab design of this reinforcement is required
for economy in basement walls or subsurface tank walls supported as vertical spans
by the floor above and the footing below, and as horizontal spans by stiff pilasters,
interior cross walls, or end walls.
This type of two-way slab is outside the scope of the specific provisions in the
Code. Without an ‘‘exact’’ analysis, which is seldom justified because of the uncertainties
involved in the assumptions for stiffnesses and loads, a realistic design
can be based on the simple two-way slab design method of Appendix A, Method
2, of the 1963 ACI 318 Building Code.
FOUNDATIONS
Building foundations should distribute wall and column loads to the underlying soil
and rock within acceptable limits on resulting soil pressure and total and differential
settlement. Wall and column loads consist of live load, reduced in accordance with
the applicable general building code, and dead load, combined, when required, with
lateral loads of wind, earthquake, earth pressure, or liquid pressure. These loads
can be distributed to the soil near grade by concrete spread footings, or to the soil
at lower levels by concrete piles or drilled piers.
9.73 TYPES OF FOUNDATIONS
A wide variety of concrete foundations are used for buildings. Some of the most
common types are illustrated in Fig. 9.41.
Spread wall footings consist of a plain or reinforced slab wider than the wall,
extending the length of the wall (Fig. 9.41a). Plain- or reinforced-concrete individual-
concrete spread footings consist of simple, stepped, or sloped two-way concrete
slabs, square or rectangular in plan (Fig. 9.41b to d). For two columns close
together, or an exterior column close to the property line so that individual spread
or pile-cap footings cannot be placed concentrically, a reinforced-concrete, spread
CONCRETE CONSTRUCTION 9.107
FIGURE 9.41 Common types of foundations for buildings.
combined footing (Fig. 9.41e) or a strap footing (Fig.. 9.41?) can be used to
obtain a nearly uniform distribution of soil pressure or pile loads. The strap footing
becomes more economical than a combined footing when the spacing between the
columns becomes larger, causing large bending moments in the combined footing.
For small soil pressures or where loads are heavy relative to the soil capacity,
a reinforced-concrete mat, or raft foundation (Fig. 9.41g) may prove economical.
A mat consists of a two-way slab under the entire structure. Concrete cross walls
or inverted beams can be utilized with a mat to obtain greater stiffness and economy.
Where sufficient soil strength is available only at lower levels, pile foundations
(Fig. 9.41h) or drilled-pier foundations (Fig. 9.41i) can be used.
9.74 GENERAL DESIGN PRINCIPLES
FOR FOUNDATIONS
The area of spread footings, the number of piles, or the number of drilled piers are
selected by a designer to support actual unfactored building loads without exceeding
settlement limitations, a safe soil pressure qa, or a safe pile or drilled-pier load. A
factor of safety from 2 to 3, based on the ultimate strength of the soil and its
settlement characteristics, is usually used to determine the safe soil pressure or safe
pile or drilled-pier load. See Art. 6.8.
Soil Pressures. After the area of the spread footing or the number and spacing
of piles or drilled piers has been determined, the spread footing, pile-cap footing,
or drilled pier can be designed. The strength-design method of the ACI 318 Build9.108
SECTION NINE
FIGURE 9.42 Spread footing subjected to
moment pressures.
ing Code (Art. 9.44) uses factored loads of gravity, wind, earthquake, earth pressure,
and fluid pressure to determine factored soil pressure qs, and factored pile or pier
load. The factored loadings are used in strength design to determine factored moments
and shears at critical sections.
For concentrically loaded footings, qs is usually assumed as uniformly distributed
over the footing area. This pressure is determined by dividing the concentric wall
or column factored load Pu by the area of the footing. The weight of the footing
can also be neglected in determining qs because the weight does not induce factored
moments and shears. The factored pile load for concentrically loaded pile-cap footings
is determined in a similar manner.
When individual or wall spread footings are subjected to overturning moment
about one axis, in addition to vertical load, as with a spread footing for a retaining
wall, the pressure distribution under the footing is trapezoidal if the eccentricity ex,
of the resultant vertical load Pu is within the kern of the footing, or triangular if
beyond the kern, as shown in Fig. 9.42. Thus, when ex  L/6, where L is the
footing length in the direction of eccentricity ex, the pressure distribution is trapezoidal
(Fig. 9.42a) with a maximum
P 6e u x q 
 1  (9.85)   s1 BL L
and a minimum
P 6e u x q 
 1  (9.86)   s2 BL L
where B 
 footing width. When ex 
 L/6, the pressure distribution becomes triangular
over the length L, with a maximum
2Pu q 
 (9.87) s BL
When ex  L/6, the length of the triangular distribution decreases to 1.5L  3ex
(Fig. 9.42b) and the maximum pressure rises to
CONCRETE CONSTRUCTION 9.109
FIGURE 9.43 Bearing stresses on column and pressure
against bottom of footing.
2Pu q 
 (9.88) s 1.5B(L  2e ) x
Reinforcement for Bearing. The bearing stress on the interface between a column
and a spread footing, pile cap, or drilled pier should not exceed the allowable stress
?b given by Eq. (9.89), unless vertical reinforcement is provided for the excess.
A A 2 2 ? 
 0.85	?
 ;  4 (9.89) b cA A 1 1
where 	
 strength-reduction factor 
 0.70

 ?
c specified concrete compressive strength
A1 
 loaded area of the column or base plate
A2 
 supporting area of footing, pile cap, or drilled pier that is the lower
base of the largest frustrum of a right pyramid or cone contained
wholly within the footing, with A1 the upper face, and with side slopes
not exceeding 2 horizontal to 1 vertical (Fig. 9.43).
If the bearing stress on the loaded area exceeds ?b, reinforcement must be provided
by extending the longitudinal column bars into the spread footing, pile cap, or
drilled pier or by dowels. If so, the column bars or dowels required must have a
minimum area of 0.005 times the loaded area of the column.
Provisions in the ACI 318 Building Code assure that every column will have a
minimum tensile capacity. Compression lap splices, which are permitted when the
column bars are always in compression for all loading conditions, are considered
to have sufficient tensile capacity so that no special requirements are needed. Similarly,
the required dowel embedment in the footing for full compression development
will provide a minimum tensile capacity.
Required compression-dowel embedment length cannot be reduced by end
hooks. Compression dowels can be smaller than column reinforcement. They cannot
be larger than No. 11 bars.
If the bearing stress on the loaded area of a column does not exceed , 0.85	?
c
column compression bars or dowels do not need to be extended into the footing,
pile cap, or pier, if they can be developed within 3 times the column dimension
(pedestal height) above the footing (Art. 9.49.8). It is desirable, however, that a
minimum of one No. 5 dowel be provided in each corner of a column.
9.110 SECTION NINE
FIGURE 9.44 Critical sections for factored shear and
moment in wall footings.
Footing Thickness. The minimum thickness allowed by the ACI 318 Building
Code for footing is 8 in for plain concrete footings on soil, 6 in above the bottom
reinforcement for reinforced-concrete footings on soil, and 12 in above the bottom
reinforcement for reinforced-concrete footings on piles. Plain-concrete pile-cap
footings are not permitted.
Concrete Cover. The minimum concrete cover required by the ACI 318 Building
Code for reinforcement cast against and permanently exposed to earth is 3 in.
9.75 SPREAD FOOTINGS FOR WALLS
The critical sections for shear and moment for spread footings supporting concrete
or masonry walls are shown in Fig. 9.44a and b. Under the soil pressure, the
projection of footing on either side of a wall acts as a one-way cantilever slab.
Unreinforced Footings. Requirements for design of unreinforced concrete footings
are included in the ACI 318 Building Code. For plain-concrete spread footings,
the maximum permissible flexural tension stress, psi, in the concrete is limited to
where 	 
 strength-reduction factor 
 0.65 and 
 specified concrete 5	
?
, ?
 c c
compressive strength, psi. For constant-depth, concentrically loaded footings with
uniform factored soil pressure qs and neglecting the weight of the projection of the
footing, the thickness h, in, can be calculated from
qs h 
 0.08X (9.90) 
?
c
where X 
 projection of footing, in and qs 
 net factored soil pressure, psf.
Shear is not critical for plain-concrete wall footings. The maximum tensile
stress, due to flexure controls the thickness. 	5
?
, c
Reinforced Footings. Because it is usually not economical or practical to provide
shear reinforcement in reinforced-concrete spread footings for walls, Vu is usually
limited to the maximum value that can be carried by the concrete, 	V 
 c
	2
?
b d. c w
Area of flexural reinforcement can be determined from As 
 Mu / 	?y jd as inCONCRETE
CONSTRUCTION 9.111
dicated in Art. 9.46. Sufficient length of reinforcement must be provided to develop
the full yield strength of straight tension reinforcement. The critical development
length is the shorter dimension Ld shown in Fig. 9.44a and b. The minimum lengths
required to develop various bar sizes are tabulated in Table 9.8 (Art. 9.49.4). Reinforcement
at right angles to the flexural reinforcement is usually provided as
shrinkage and temperature reinforcement and to support and hold the flexural bars
in position.
9.76 SPREAD FOOTINGS FOR
INDIVIDUAL COLUMNS
Footings supporting columns are usually made considerably larger than the columns
to keep pressure and settlement within reasonable limits. Generally, each column
is also placed over the centroid of its footing to obtain uniform pressure distribution
under concentric loading. In plan, the footings are usually square, but they can be
made rectangular to satisfy space restrictions or to support rectangular columns or
pedestals.
FIGURE 9.45 Critical sections for shear and
moment in column footings.
Under soil pressure, the projection on
each side of a column acts as a cantilever
slab in two perpendicular directions.
The effective depth of footing d is
the distance from the extreme compression
surface of the footing to the
centroid of the tension reinforcement.
Bending Stresses. Critical sections
for moment are at the faces of square
and rectangular concrete columns or
pedestals (Fig. 9.45a). For round and
regular polygon columns or pedestals,
the face may be taken as the side of a
square having an area equal to the area
enclosed within the perimeter of the column
or pedestal. For structural steel columns
with steel base plates, the critical
section for moment may be taken halfway
between the face of the column and
the edges of the plate.
For plain-concrete spread footings,
the flexural tensile stress must be limited to a maximum of where 	 
 5	
?
, c
strength-reduction factor 
 0.65 and 
 specified concrete compressive strength 
?
c
psi. Thickness of such footings can be calculated with Eq. (9.90). Shear is not
critical for plain-concrete footings.
Shear. For reinforced-concrete spread footings, shear is critical on two different
sections.
Two-way or punching shear (Fig. 9.45b) is critical on the periphery of the surfaces
at distance d/2 from the column, where d 
 effective footing depth.
One-way shear, as a measure of diagonal tension, is critical at distance d from
the column (Fig. 9.45b), and must be checked in each direction.
9.112 SECTION NINE
It is usually not economical or practical to provide shear reinforcement in column
footings. So the shear 	Vc that can be carried by the concrete controls the
thickness required.
For one-way shear for plain or reinforced concrete sections,
V 
 2
?
b d (9.91) c c w
where bw 
 width of section
d 
 effective depth of section
but Eq. (9.39) may be used as an alternative for reinforced concrete.
For two-way shear, Vc is the smallest of the values computed from Eqs. (9.75)
to (9.77).
Flexural Reinforcement. In square spread footings, reinforcing steel should be
uniformly spaced throughout, in perpendicular directions. In rectangular spread
footings, the ACI 318 Building Code requires the reinforcement in the long direction
to be uniformly spaced over the footing width. Also, reinforcement with an
area 2/ (   1) times the area of total reinforcement in the short direction should
be uniformly spaced in a width that is centered on the column and equal to the
short footing dimension, where  is the ratio of the long to the short side of the
footing. The remainder of the reinforcement in the short direction should be uniformly
spaced in the outer portions of the footing. To maintain a uniform spacing
for the bars in the short direction for simplified placing, the theoretical number of
bars required for flexure must be increased by about 15%. The maximum increase
occurs when  is about 2.5.
The required area of flexural reinforcement can be determined as indicated in
Art. 9.46. Maximum-size bars are usually selected to develop the yield strength by
straight tension embedment without end hooks. The critical length is the shorter
dimension Ld shown for wall footings in Figs. 9.44a and b.
9.77 COMBINED SPREAD FOOTINGS
A combined spread footing under two columns should have a shape and location
such that the center of gravity of the column loads coincides with the centroid of
the footing area. It can be square, rectangular, or trapezoidal, as shown in Fig. 9.46.
Net design soil-pressure distribution can be assumed to vary linearly for most
(rigid) combined footings. For the pressure distribution for flexible combined footings,
see the report, ‘‘Suggested Analysis and Design Procedures for Combined
Footings and Mats,’’ ACI 336.2R, American Concrete Institute.
If the center of gravity of the unfactored column loads coincides with the centroid
of the footing area, the net soil pressure qa will be uniform.
R
q 
 (9.92) a A?
where R 
 applied vertical load
A? 
 area of footing
The factored loads on the columns, however, may change the location of the
center of gravity of the loads. If the resultant is within the kern for footings with
CONCRETE CONSTRUCTION 9.113
FIGURE 9.46 Design conditions for combined spread footing of trapezoidal shape.
moment about one axis, the factored soil pressure qs can be assumed to have a
linear distribution (Fig. 9.46b) with a maximum at the more heavily loaded edge:
P Pec u u q 
  (9.93) s1 A I ? ?
and a minimum at the opposite edge:
P Pec u u q 
  (9.94) s2 A I ? ?
where Pu 
 factored vertical load
e 
 eccentricity of load
c 
 distance from center of gravity to section for which pressure is being
computed
I? 
 moment of inertia of footing area
If the resultant falls outside the kern of the footing, the net factored pressure qs can
be assumed to have a linear distribution with a maximum value at the more heavily
loaded edge and a lengthwise distribution of 3 times the distance between the
resultant and the pressed edge. The balance of the footing will have no net factored
pressure.
With the net factored soil-pressure distribution known, the factored shears and
moments can be determined (Fig. 9.46d and e). Critical sections for shear and
moment are shown in Fig. 9.46a. The critical section for two-way shear is at a
distance d/2 from the columns, where d is the effective depth of footing. The
critical section for one-way shear in both the longitudinal and transverse direction
is at a distance d from the column face.
9.114 SECTION NINE
FIGURE 9.47 Design conditions for a strap
footing.
Maximum negative factored moment, causing tension in the top of the footing,
will occur between the columns. The maximum positive factored moment, with
tension in the bottom of the footing, will occur at the face of the columns in both
the longitudinal and transverse direction.
Flexural reinforcement can be selected as shown in Art. 9.46. For economy,
combined footings should be made deep enough to avoid the use of stirrups for
shear reinforcement. In the transverse direction, the bottom reinforcement is placed
uniformly in bands having an arbitrary width, which can be taken as the width of
the column plus 2d. The amount at each column is proportional to the column load.
Size and length of reinforcing bars must be selected to develop the full yield
strength of the steel between the critical section, or point of maximum tension, and
the end of the bar (Art. 9.49.4).
9.78 STRAP FOOTINGS
When the distance between the two columns to be supported on a combined footing
becomes large, cost increases rapidly, and a strap footing, or cantilever-type footing,
may be more economical. This type of footing, in effect, consists of two footings,
one under each column, connected by a strap beam (Fig. 9.47). This beam distributes
the column loads to each footing to make the net soil pressure with unfactored
CONCRETE CONSTRUCTION 9.115
loads uniform and equal at each footing, and with factored loads uniform but not
necessarily equal. The center of gravity of the actual column loads should coincide
with the centroid of the combined footing areas.
The strap beam is usually designed and constructed so that it does not bear on
the soil (Fig. 9.47b). The concrete for the beam is cast on compressible material.
If the concrete for the strap beam were placed on compacted soil, the resulting soil
pressure would have to be considered in design of the footing.
The strap beam, in effect, cantilevers over the exterior column footing, and the
bending will cause tension at the top. The beam therefore requires top flexural
reinforcement throughout its entire length. Nominal flexural reinforcement should
be provided in the bottom of the beam to provide for any tension that could result
from differential settlement.
The top bars at the exterior column must have sufficient embedment length to
develop their full yield strength. If the distance between the interior face of the
exterior column and the property-line end of the horizontal portion of the top bar
is less than the required straight bar tension development length, the top bars should
have standard end hooks to provide proper anchorage (Art. 9.49.5).
Strength-design shear reinforcement [Eq. (9.40a)] will be required when Vu 
	Vc, and requirements for minimum shear reinforcement [Eq. (9.81)] must be observed
when Vu  	Vc /2, where Vc 
 shear carried by the concrete (Art. 9.47).
For the strap footing shown in Fig. 9.47, the exterior column footing can be
designed as a wall spread footing, and the interior column footing as an individualcolumn
spread footing (Arts. 9.75 and 9.76).
9.79 MAT FOUNDATIONS
A mat or raft foundation is a single combined footing for an entire building unit.
It is economical when building loads are relatively heavy and the safe soil pressure
is small (See also Arts. 9.73 and 9.74.)
Weight of soil excavated for the foundation decreases the pressure on the soil
under the mat. If excavated soil weighs more than the building, there is a net
decrease in pressure at mat level from that prior to excavation.
When the mat is rigid, a uniform distribution of soil pressure can be assumed
and the design can be based on a statically determinate structure, as shown in Fig.
9.48. (See ‘‘Suggested Analysis and Design Procedures for Combined Footings and
Mats,’’ ACI 336.2R, American Concrete Institute.)
If the centroid of the factored loads does not coincide with the centroid of the
mat area, the resulting nonuniform soil pressure should be used in the strength
design of the mat.
Strength-design provisions for flexure, one-way and two-way shear, development
length, and serviceability should conform to ACI 318 Building Code requirements
(Art. 9.59).
9.80 PILE FOUNDATIONS
Building loads can be transferred to piles by a thick reinforced-concrete slab, called
a pile-cap footing. The piles are usually embedded in the pile cap 4 to 6 in. They
9.116 SECTION NINE
FIGURE 9.48 Design conditions for a rigid mat footing.
should be cut to required elevation after driving and prior to casting the footing.
Reinforcement should be placed a minimum of 3 in. clear above the top of the
piles. The pile cap is required by the ACI 318 Building Code to have a minimum
thickness of 12 in. above the reinforcement. (See also Art. 9.74.)
Piles should be located so that the centroid of the pile cluster coincides with the
center of gravity of the column load. As a practical matter, piles cannot be driven
exactly to the theoretical design location. A construction survey should be made to
determine if the actual locations require modification of the original pile-cap design.
Pile-cap footings are designed like spread footings (Art. 9.76), but for concentrated
pile loads. Critical sections for shear and moment are the same. Reaction
from any pile with center dp /2 or more inside the critical section, where dp is the
pile diameter at footing base, should be assumed to produce no shear on the section.
The ACI 318 Building Code requires that the portion of the reaction of a pile with
center within dp /2 of the section be assumed as producing shear on the section
based on a straightline interpolation between full value for center of piles located
dp /2 outside the section and zero at dp /2 inside the section. For design of pile caps
for high-capacity piles, see ‘‘CRSI Design Handbook,’’ Concrete Reinforcing Steel
Institute.
For pile clusters without moment, the pile load Pu for strength design of the
footing is obtained by dividing the factored column load by the number of piles n.
The factored load equals 1.4D  1.7L, where D is the dead load, including the
weight of the pile cap, and L is the live load. For pile clusters with moment, the
factored load on the rth pile is
1 eCr P 
 (1.4D  1.7L)  (9.95) n ur n 2 	 C 
 r
1
where e 
 eccentricity of resultant load with respect to neutral axis of pile group,
in.
CONCRETE CONSTRUCTION 9.117
Cr 
 distance between neutral axis of pile group and center of nth pile, in.
n 
 number of piles in cluster
9.81 DRILLED-PIER FOUNDATIONS
A drilled-pier foundation is used to transmit loads to soil at lower levels through
end bearing and, in some situations, side friction. (See also Art. 9.74.) It can be
FIGURE 9.49 Bell-bottom drilled pier with
dowels for a column.
constructed in firm, dry earth or clay
soil by machine excavating an unlined
hole with a rotating auger or bucket with
cutting vanes and filling the hole with
plain or reinforced concrete. Under favorable
conditions, pier shafts 12 ft in
diameter and larger can be constructed
economically to depths of 100 ft and
more. Buckets with sliding arms can be
used to form bells at the bottom of the
shaft with a diameter as great as 3 times
that of the shaft (Fig. 9.49).
Some building codes limit the ratio
of shaft height to shaft diameter to a
maximum of 30. They also may require
the bottom of the bell to have a constant
diameter for the bottom foot of height,
as shown in Fig. 9.49.
The compressive stress permitted on
plain-concrete drilled piers with lateral
support from surrounding earth varies
with different codes. The BOCA National
Building Code/1999, limits the
computed bearing stress based on service loads to is the specified 0.33?
, where ?
 c c
concrete compressive strength.
Reinforced-concrete drilled piers can be designed as flexural members with axial
load, as indicated in Art. 9.82.
Allowable unfactored loads on drilled piers with various shaft and bell diameters,
supported by end bearing on soils of various allowable bearing pressures, are given
in Table 9.23. For maximum-size bells (bell diameter 3 times shaft diameter) and
a maximum concrete stress ?c1 
 for unfactored loads, the required concrete 0.33?
c
strength, psi, is 19% of the allowable soil pressure, psf.
COLUMNS
Column-design procedures are based on a comprehensive investigation reported by
American Concrete Institute Committee 105 (‘‘Reinforced Concrete Column Investigation,’’
ACI Journal, February 1933) and followed by many supplemental tests.
The results indicated that basically the total capacity for axial load can be predicted,
9.118 SECTION NINE
TABLE 9.23 Allowable Service (Unfactored) Loads on Drilled Piers, kips*
Shaft dia, ft Shaft area, in2 
 3000 ?
c 
 4000 ?
c 
 5000 ?
c 
 6000 ?
c
1.5 254 251 335 419 503
2.0 452 447 597 746 895
2.5 707 700 933 1167 1400
3.0 1018 1008 1344 1680 2016
3.5 1385 1371 1828 2285 2742
4.0 1810 1792 2389 2987 3584
4.5 2290 2267 3023 3778 4534
5.0 2827 2799 3732 4665 5597
5.5 3421 3387 4516 5645 6774
6.0 4072 4031 5375 6719 8063
Safe allowable service-load bearing pressure on soil, psf
Bell dia, ft Bell area, ft2 10,000 12,000 15,000 20,000 25,000 30,000
1.5 1.77 18 21 27 35 44 53
2.0 3.14 31 38 47 63 79 94
2.5 4.91 49 59 74 98 123 147
3.0 7.07 71 85 106 141 177 212
3.5 9.62 96 115 144 192 241 289
4.0 12.57 126 151 188 251 314 377
4.5 15.90 159 191 239 318 398 477
5.0 19.64 196 236 295 393 491 589
5.5 23.76 238 285 356 475 594 713
6.0 28.27 283 339 424 565 707 848
6.5 33.18 332 398 498 664 830 995
7.0 38.48 385 462 577 770 962 1155
7.5 44.18 442 530 663 884 1104 1325
8.0 50.27 503 603 754 1005 1257 1508
8.5 56.74 567 681 851 1135 1418 1702
9.0 63.62 636 763 954 1272 1590 1909
9.5 70.88 709 851 1063 1418 1772 2126
10.0 78.54 785 942 1178 1571 1963 2356
10.5 86.59 866 1039 1299 1732 2165 2598
11.0 95.03 950 1140 1425 1901 2376 2851
11.5 103.87 1039 1246 1558 2077 2597 3116
12.0 113.10 1131 1357 1696 2262 2827 3393
over a wide range of steel and concrete strength combinations and percentages of
steel, as the sum of the separate concrete and steel capacities.
9.82 BASIC ASSUMPTIONS FOR STRENGTH
DESIGN OF COLUMNS
At maximum capacity, the load on the longitudinal reinforcement of a concentrically
loaded concrete column can be taken as the steel area Ast times steel yield
strength ?y. The load on the concrete can be taken as the concrete area in comCONCRETE
CONSTRUCTION 9.119
TABLE 9.23 Allowable Service (Unfactored) Loads on Drilled Piers, kips* (Continued)
Safe allowable service-load bearing pressure on soil, psf
Bell dia, ft Bell area, ft2 10,000 12,000 15,000 20,000 25,000 30,000
12.5 122.72 1227 1473 1841 2454 3068 3682
13.0 132.73 1327 1593 1991 2655 3318 3982
13.5 143.14 1431 1718 2147 2863 3578 4294
14.0 153.94 1539 1847 2309 3079 3848 4618
14.5 165.13 1651 1982 2477 3303 4128 4954
15.0 176.15 1767 2121 2651 3534 4418 5301
15.5 188.69 1887 2264 2830 3774 4717 5661
16.0 201.06 2011 2413 3016 4021 5027 6032
16.5 213.82 2138 2566 3207 4276 5344 6415
17.0 226.98 2270 2724 3405 4540 5675 6809
17.5 240.53 2405 2886 3608 4811 6013 7216
18.0 254.47 2545 3054 3817 5089 6362 7634
*?c1 
 . 0.33?
c
NOTE: Bell diameter preferably not to exceed 3 times the shaft diameter. Check shear stress if bell
slope is less than 2:1. (Courtesy Concrete Reinforcing Steel Institute.)
pression times 85% of the compressive strength of the standard test cylinder. ?
c
The 15% reduction from full strength accounts, in part, for the difference in size
and, in part, for the time effect in loading of the column. Capacity of a concentrically
loaded column then is the sum of the loads on the concrete and the steel.
The ACI 318 Building Code applies a strength-reduction factor 	 
 0.75 for
members with spiral reinforcement and 	 
 0.70 for other members. For small
axial loads where Ag 
 gross area of column), 	may be increased (P  0.10?
A , u c g
proportionately to as high as 0.90. Capacity of columns with eccentric load or
moment may be similarly determined, but with modifications. These modifications
introduce the assumptions made for strength design for flexure and axial loads.
The basic assumptions for strength design of columns can be summarized as
follows.
1. Strain of steel and concrete is proportional to distance from neutral axis (Fig.
9.50c).
2. Maximum usable compression strain of concrete is 0.003 in / in (Fig. 9.50c).
3. Stress, psi, in longitudinal reinforcing bars equals steel strain s times 29,000,000
for strains below yielding, and equals the steel yield strength ?y, tension or
compression, for larger strains (Fig. 9.50?).
4. Tensile strength of concrete is negligible.
5. Capacity of the concrete in compression, which is assumed at a maximum stress
of , must be consistent with test results. A rectangular stress distribution 0.85?
c
(Fig. 9.50d) may be used. Depth of the rectangle may be taken as a 
 1c,
where c is the distance from the neutral axis to the extreme compression surface
and 1 
 0.85 for psi and 0.05 less for each 1000 psi that exceeds ?
  4000 ?
 c c
4000 psi, but 1 should not be taken less than 0.65.
In addition to these general assumptions, design must be based on equilibrium
and strain compatibility conditions. No essential difference develops in maximum
capacity between tied and spiral columns, but spiral-reinforced columns show far
9.120 SECTION NINE
FIGURE 9.50 Stresses and strains in a reinforcedconcrete
column.
more toughness before failure. Tied-column failures have been relatively brittle and
sudden, whereas spiral-reinforced columns that have failed have deformed a great
deal and carried a high percentage of maximum load to a more gradual yielding
failure. The difference in behavior is reflected in the higher value of 	 assigned to
spiral-reinforced columns.
Additional design considerations are presented in Arts. 9.83 to 9.87. Following
is an example of the application of the basic assumptions for strength design of
columns.
Example. Determine the capacity of the 20-in-square reinforced-concrete column
shown in Fig. 9.50a. The column is reinforced with four No. 18 bars, with ?y 

60 ksi, and lateral ties. Area of rebars total 16 in2. Concrete strength is ?
 
 c
Assume the factored load Pu to have an eccentricity of 2 in and that slen- 6 ksi.
derness can be ignored.
To begin, assume c 
 24 in. Then, with the depth  
 0.75 for ?
 
 6000 psi, 1 c
of the compression rectangle is a 
 0.75  24 
 18 in. This assumption can be
CONCRETE CONSTRUCTION 9.121
checked by computing the eccentricity e 
 	Mn / 	Pn, where 	Mn is the design
moment capacity, ft-kips, and 	Pn is the design axial load strength, kips.
Since the strain diagram is linear and maximum compression strain is 0.003 in
/ in the strains in the reinforcing steel are found by proportion to be 0.00258 and
0.00092 in / in (Fig. 9.50c). The strain at yield is 60/29,000 
 0.00207  0.00258
in / in. Hence, the stresses in the steel are 60 ksi and 0.00092  29,000 
 26.7 ksi.
The maximum concrete stress, which is assumed constant over the depth
a 
 18 in, is 
 0.85  6 
 5.1 ksi (Fig. 9.50d). Hence, the compression 0.85?
c
force on the concrete is 5.1  20  18 
 1836 kips and acts at a distance 20/2
 18/2 
 1 in from the centroid of the column (Fig. 9.50e). The compression
force on the more heavily loaded pair of reinforcing bars, which have a crosssectional
area of 8 in2, is 8  60 less the force on concrete replaced by the steel
8  5.1, or 439 kips. The compression force on the other pair of bars is 8(26.7 
5.1) 
 173 kips (Fig. 9.50?). Both pairs of bars act at a distance of 20/2  3.375

 6.625 in from the centroid of the column.
The design capacity of the column for vertical load is the sum of the nominal
steel and concrete capacities multiplied by a strength-reduction factor 	
 0.70.
	P 
 0.70(1836  173  439) 
 1714 kips n
The capacity of the column for moment is found by taking moments of the steel
and concrete capacities about the centerline of the column.
1 6.625
	M 
 0.70 1836 (439  173) 
 209 ft-kips  	 n 12 12
The eccentricity for the assumed value of c 
 24 in is
209  12
e
 
1.46  2 in
1714
If for a new trial, c is taken as 22.5 in, then Pu 
 1620 kips, Mu 
 272 ft-kips,
and e checks out close to 2 in. If sufficient load-moment values for other assumed
positions of the neutral axis are calculated, a complete load-moment interaction
diagram can be constructed (Fig. 9.51).
The nominal maximum axial load capacity Po of a column without moment
equals the sum of the capacities of the steel and the concrete.
P 
 0.85?
(A  A )  ? A (9.96) o c g st y st
where Ag 
 gross area of column cross section and Ast 
 total area of longitudinal
steel reinforcement. For the 20-in-square column in the example:
P 
 0.85  6(400  16)  60  16 
 2918 kips o
The maximum design axial-load strength permitted by the ACI 318 Building Code
is
	P 
 0.80 	[0.85?
(A  A )  ? A ] n(max) c g st y st (9.97)

 0.80  0.70[(0.85  6(400  16)  60  16] 
 1634 kips
9.122 SECTION NINE
FIGURE 9.51 Load-moment interaction diagram for determination of design strength of a rectangular
reinforced-concrete column.
9.83 DESIGN REQUIREMENTS FOR COLUMNS
The ACI 318 Building Code contains the following principal design requirements
for columns, in addition to the basic assumptions (Art. 9.82):
1. Columns must be designed for all bending moments associated with a loading
condition.
CONCRETE CONSTRUCTION 9.123
TABLE 9.24 Minimum Cover, in, for Column Reinforcement*
Type of construction Reinforcement
Not exposed
to weather†
Exposed to
weather*
Cast-in-place Longitudinal 11?2 2
Ties, spirals 11?2 11?2
Precast Longitudinal 5?8  db  11?2‡ 11?2
Ties, spirals 3?8 11?4
Prestressed Longitudinal 11?2 11?2
Ties, spirals 1 11?2
*From ACI 318-99.
† See local code; fire protection may require greater thickness.
‡ db 
 nominal bar diameter, in.
2. For corner columns and other columns loaded unequally on opposite sides
in perpendicular directions, biaxial bending moments must be considered.
3. All columns are designed for an eccentricity of the factored load Pu because
the maximum design axial load strength cannot be larger than 0.80Po for tied columns,
or 0.85Po for spiral columns, where Po is given by Eq. (9.96).
4. The minimum ratio of longitudinal-bar area to total cross-sectional area of
column Ag is 0.01, and the maximum ratio is 0.08. For columns with a larger crosssection
than required by loads, however, a smaller Ag, but not less than half the
gross area of the columns, may be used for calculating both load capacity and
minimum longitudinal bar area. This exception allows reuse of forms for largerthan-
necessary columns, and permits longitudinal bar areas as low as 0.005 times
the actual column area. At least four longitudinal bars should be used in rectangular
reinforcement arrangements, and six in circular arrangements.
5. The ratio of the volume of spiral reinforcement to volume of concrete within
the spiral should be at least
A  A ?
 g c c
 
 0.45 (9.98)    s A ? c y
where Ag 
 gross cross-sectional area of concrete column, in2
Ac 
 area of column within outside diameter of spiral, in2

 ?
c specified concrete compressive strength, psi
?y 
 specified yield strength of spiral steel, psi (maximum 60,000 psi)
6. For tied columns, minimum size of ties is No. 3 for longitudinal bars that
are No. 10 or smaller, and No. 4 for larger longitudinal bars. Minimum vertical
spacing of sets of ties is 16 diameters of longitudinal bars, 48 tie-bar diameters, or
the least thickness of the column. A set of ties should be composed of one round
tie for bars in a circular pattern, or one tie enclosing four corner bars plus additional
ties sufficient to provide a corner of a tie at alternate interior bars or at bars spaced
more than 6 in from a bar supported by the corner of a tie.
7. Minimum concrete cover required for column reinforcement is listed in Table
9.24.
9.124 SECTION NINE
9.84 COLUMN TIES AND TIE PATTERNS
For full utilization, all ties in tied columns must be fully developed (for full tie
yield strength) at each corner enclosing a vertical bar or, for circular ties, around
the full periphery.
Splices. The ACI 318 Building Code provides arbitrary minimum sizes and maximum
spacings for column ties (Art. 9.83). No increases in size nor decrease in the
spacings is required for Grade 40 materials. Hence, the minimum design requirements
for splices of ties may logically be based on Grade 40 reinforcing steel.
The ordinary closed, square or rectangular, tie is usually spliced by overlapping
standard tie hooks around a longitudinal bar. Standard tie patterns require staggering
of hook positions at alternate tie spacings, by rotating the ties 90 or 180. (‘‘Manual
of Standard Practice,’’ Concrete Reinforcing Steel Institute). Two-piece ties are
formed by lap splicing or anchoring the ends of U-shaped open ties. Lapped bars
should be securely wired together to prevent displacement during concreting.
Tie Arrangements. Commonly used tie patterns are shown in Figs. 9.52 to 9.54.
In Fig. 9.53, note the reduction in required ties per set and the improvement in
bending resistance about both axes achieved with the alternate bundled-bar arrangements.
Bundles may not contain more than four bars, and bar size may not exceed
No. 11.
Tie sizes and maximum spacings per set of ties are listed in Table 9.25.
Drawings. Design drawings should show all requirements for splicing longitudinal
bars, that is, type of splice, lap length if lapped, location in elevation, and layout
in cross section. On detail drawings (placing drawings), dowel erection details
should be shown if special large longitudinal bars, bundled bars, staggered splices,
or specially grouped bars are to be used.
9.85 BIAXIAL BENDING OF COLUMNS
If column loads cause bending simultaneously about both principal axes of a column
cross-section, as for most corner columns, a biaxial bending analysis is required.
For rapid preliminary design, Eq. (9.99) gives conservative results
M M y x   1 (9.99)
M M ox oy
where Mx, My 
 factored moments about x and y axes, respectively
Mox, Moy 
 design capacities about x and y axes, respectively
For square columns with equal longitudinal reinforcement in all faces, Mox 

Moy, and the relation reduces to:
M  M x y
 1 (9.100)
Mox
Because Mx 
 exPu and My 
 eyPy, the safe biaxial capacity can be taken from
CONCRETE CONSTRUCTION 9.125
FIGURE 9.52 Circular concrete columns. (a) Tied column. Use ties
when core diameter dc  s. (b) Spiral-reinforced column, for use when
dc  s. (c) Rectangular tie for use in columns with four longitudinal
bars. (d) Circular tie.
uniaxial load-capacity tables for the load Pu and the uniaxial bending moment
Mu 
 (ex  ey)Pu. Similarly, for round columns, the moment capacity is essentially
equal in all directions, and the two bending moments about the principal axes may
be combined into a single uniaxial factored moment Mu which is then an exact
solution
2 2 M 
 
M  M (9.101) u x y
The linear solution always gives a safe design, but becomes somewhat overconservative
when the moments Mx and My are nearly equal. For these cases, a more
exact solution will be more economical for the final design.
9.86 SLENDERNESS EFFECTS
ON CONCRETE COLUMNS
The ACI 318 Building Code requires that primary column moments be magnified
to provide safety against buckling failure. Detailed procedures, formulas, and design
aids are provided in the Code and Commentary.
9.126 SECTION NINE
FIGURE 9.53 Ties for square concrete columns. Additional single bars may be placed between
any of the tied groups, but clear spaces between bars should not exceed 6 in.
FIGURE 9.54 Ties for wall-like columns. Spaces between corner bars and interior groups of
three bars may vary to accommodate average spacing not exceeding 6 in. A single additional bar
may be placed in any of such spaces if the average spacing does not exceed 6 in.
CONCRETE CONSTRUCTION 9.127
TABLE 9.25 Maximum Spacing of Column
Ties*
Vertical
bar
size,
number
Size and spacing of
ties, in
No. 3 No. 4 No. 5
5 10
6 12
7 14
8 16 16
9 18 18
10 18 20
11 † 22 22
14 † 24 27
18 † 24 30
*Maximum spacing not to exceed least column
dimensions.
† Not allowed.
For most unbraced frames, an investigation will be required to determine the
magnification factor to allow for the effects of sidesway and end rotation. The
procedure for determination of the required increase in primary moments, after the
determination that slenderness effects cannot be neglected, is complex. For direct
solution, the requirements of Sec. 10.10, ACI 318-99 can be met by a P- analysis.
(See, for example, J. G. MacGregor and S. E. Hage, ‘‘Stability Analysis and Design
of Concrete,’’ Journal of the Structural Division, ASCE, Vol. 103, No. ST10,
October 1977.)
The direct P- method of MacGregor and Hage is based upon an equation for
a geometric series that was derived for the final second-order deflection as a function
of the first-order elastic deflection. This direct P- analysis provides a very
simple method for computing the moment magnifier  when the stability index Q
is greater than 0.04 but equal to or less than 0.22.

 1/(1  Q) 0.04  Q  0.22 (9.102)
where Q 
 Puu / (Huhs)
Pu 
 sum of the factored loads in a given story
u 
 elastically computed first-order lateral deflection due to Hu (neglecting
P- effects) at the top of the story, relative to the bottom
Hu 
 total factored lateral force (shear) within the story
hs 
 height of story, center-to-center of floors or roof
The approximate method of ACI 318-99 may also be used to determine the
moment magnifier. This approximate method is a column-by-column correction
based upon the stiffness of the column and beams, applied primary design column
end moments, and consideration of whether the entire structure is laterally braced
against sidesway by definition. (See ACI 318-99, Sec. 10.11).
The ACI 318 Building Code permits slenderness effects to be neglected only
for very short, braced columns, with the following limitations for columns with
square or rectangular cross-sections:
9.128 SECTION NINE
Ly  6.6h for bending in single curvature
Lu  10.2h for bending in double curvature with unequal end moments
Lu  13.8h for bending in double curvature with equal end moments
and for round columns, five-sixths of the maximum lengths for square columns,
where Lu is the unsupported length and h the depth or overall thickness of column
in the direction being considered.
These limiting heights are based on the ratio of the total stiffness of the columns
to the total stiffnesses of the flexural members, Kc /KB 
 50, at the joint at each
end of a column. As these ratios become less, the limiting heights can be increased.
When the total stiffnesses of the columns and the floor systems are equal at each
end of the column (a common assumption in routine frame analysis), the two ratios

 1.00, and the limiting heights increase about 30%. With this increase, the slenderness
effects can be neglected for most columns in frames braced against sidesway.
A frame is considered braced when other structural elements, such as walls,
provide stiffness resisting sidesway at least 6 times the sum of the column stiffnesses
resisting sidesway in the same direction in the story being considered.
9.87 ECONOMY IN COLUMN DESIGN
Actual costs of reinforced-concrete columns in place per linear foot per kip of loadcarrying
capacity vary widely. The following recommendations based on relative
costs are generally applicable:
Formwork. Use of the same size and shape of column cross-section throughout
a floor and, for multistory construction, from footing to roof will permit mass
production and reuse for economy. Within usual practicable maximum building
heights, about 60 stories or 600 ft, increased speed of construction and saving in
formwork will save more than the cost of the excess concrete volume over that for
smaller column sizes in upper stories.
Concrete Strength. Use of the maximum concrete compressive strength required
to support the factored loads with the minimum allowed reinforcing steel area results
in the lowest cost. The minimum size of a multistory column is established
by the maximum concrete strength reliably available locally and the limit on maximum
area of vertical bars. (Concrete with a compressive strength of 17,000 psi ?
c
is commercially available in many areas of the United States.) If the acceptable
column size is larger than the minimum possible at the base of the multistory stack,
the steel ratio can begin with less than the maximum limit (Art. 9.83). At successive
stories above, the steel ratio can be reduced to the minimum, and thereafter, for
additional stories, the concrete strength can be reduced. Near the top, as loads
reduce further, a further reduction in the steel area to 0.005 times the concrete area
may be made (Art. 9.83).
Reinforcing Steel. Comparative cost estimates should be made for combinations
of different strengths of concrete and reinforcing bars. For high-rise buildings, using
concrete with a high combined with Grade 75 vertical bars should provide the ?
c
CONCRETE CONSTRUCTION 9.129
greatest economy. Minimum tie requirements can be achieved with four-bar or fourbundle
(up to four bars per bundle) arrangements, or by placing an intermediate
bar between tied corners not more than 6 in (clear) from the corner bars. For these
arrangements, no interior ties are required; only one tie per set is needed. (See Fig.
9.53 and Art. 9.83.) With no interior ties, low-slump concrete can be placed and
consolidated more easily, and the cost and time for assembly of column reinforcement
cages are greatly reduced. Note that, for small quantities, the local availability
of Nos. 14 and 18 bars should be investigated before they are specified.
Details of Column Reinforcement. Where Nos. 14 and 18 bars are used in compression
only, end-bearing mechanical splices usually save money. If the splices are
staggered 50%, as with two-story lengths, the tensile capacity of the columns will
also be adequate for the usual bending moments encountered. For unusually large
bending moments, where tensile splices of No. 10 bars and larger are required,
mechanical splices are usually least expensive in place. For smaller bar sizes, lap
splices, tensile or compressive, are preferred for economy. Some provision for staggered
lap splices for No. 8 bars and larger may be required to avoid Class B tension
lap splices (Art. 9.49.7).
Where butt splices are used, it will usually be necessary to assemble the column
reinforcement cage in place. Two-piece interior ties or single ties with end hooks
for two bars (see Art. 9.84) will facilitate this operation.
Where the vertical bar spacing is restricted and lap splices are used, even with
the column size unchanged, offset bending of the bars from below may be required.
However, where space permits, as with low steel ratios, an additional saving in
fabrication and erection time will be achieved by use of straight column verticals
offset one bar diameter at alternate floors.
SPECIAL CONSTRUCTION
9.88 DEEP BEAMS
The ACI 318 Building Code defines deep beams as flexural members with clear
span-depth ratios less than 2.5 for continuous spans and 1.25 for simple spans.
Some types of building components behave as deep beams and require analysis for
nonlinear stress distribution in flexure. Some common examples are long, precast
panels used as spandrel beams; below-grade walls, with or without openings, distributing
column loads to a continuous slab footing or to end walls; and storyheight
walls used as beams to eliminate lower columns in the first floor area.
Shear. When the clear span-depth ratio is less than 5, beams are classified as deep
for shear reinforcement purposes. Separate special requirements for shear apply
when span-depth ratio is less than 2 or between 2 and 5. The critical section for
shear should be taken at a distance from face of support of 0.15Ln  d for uniformly
loaded deep beams, and of 0.50a  d for deep beams with concentrated loads,
where a is the shear span, or distance from concentrated load to face of support,
Ln the clear span, and d the distance from extreme compression surface to centroid
of tension reinforcement. Shear reinforcement required at the critical section should
be used throughout the span.
9.130 SECTION NINE
The nominal shear strength of the concrete can be taken as
V 
 2 
?
 b d (9.103) c c w
where 
 ?
c specified concrete compressive strength, psi
bw 
 width of beam web
d 
 distance from extreme compression fiber to the centroid of the tension
reinforcement
The ACI 318 Building Code also presents a more complicated formula that permits
the concrete to carry up to 6 
?
 b d. c w
Maximum nominal shear strength when Ln /d  2 should not exceed
V 
 V  V 
 8 
?
 b d (9.104) n c s c w
where Vs 
 nominal shear strength provided by shear reinforcement. When Ln /d
is between 2 and 5 maximum nominal shear strength should not exceed
2 Ln V 
 10  
?
 b d (9.105)   n cw 3 d
Required area of shear reinforcement should be determined from
A 1  L /d A 11  L /d v n vh n ? d  
V / 	 V (9.106)     	 y u c s 12 s 12 2
where Av 
 area of shear reinforcement perpendicular to main reinforcement
within a distance s
	
 strength-reduction factor 
 0.85
s 
 spacing of shear reinforcement measured parallel to main reinforcement
Avh 
 area of shear reinforcement parallel to main reinforcement within a
distance s2
s2 
 spacing of shear reinforcement measured perpendicular to main reinforcement
? 
 yield strength of shear reinforcement
Spacing s should not exceed d/5 or 18 in. Spacing s2 should not exceed d/3 or 18
in. The area of shear reinforcement perpendicular to the main reinforcement should
be a minimum of
A 
 0.0015b s (9.107) v w
where bw 
 width of beam compression face. Area of shear reinforcement parallel
to main reinforcement should be at least
CONCRETE CONSTRUCTION 9.131
FIGURE 9.56 Shear and normal forces acting on a longitudinal
section through a shear wall.
FIGURE 9.55 Reinforcement for deep beams.
When the beam thickness exceeds 10 in, a layer
of vertical rebars should be provided near each
face of the beam.
A 
 0.0025b s (9.108) vh w2
When bw  10 in. shear reinforcement
should be placed in each face of the
beam. If the beam has a face exposed to
the weather, between one-half and twothirds
of the total shear reinforcement
should be placed in the exterior face.
Bars should not be smaller than No. 3.
Bending. The area of steel provided
for positive bending moment in a deep
beam should be at least
200b d w A 
 (9.109) s ?y
where ?y 
 yield strength of flexural reinforcement, psi. This minimum amount can
be reduced to one-third more than that required by analysis.
A safe assumption for preliminary design is that the extreme top surface in
compression is 0.25 of the overall depth h below the top of very deep beams for
computation of a reduced effective depth d for flexure (Fig. 9.55).
(J. G. MacGregor, ‘‘Reinforced Concrete Mechanics and Design,’’ 2d ed., Prentice-
Hall, Englewood Cliffs, NJ.)
9.89 SHEAR WALLS
Cantilevered shear walls used for bracing structures against lateral displacement
(sidesway) are a special case of deep beams. They may be used as the only lateral
bracing, or in conjunction with beam-column frames. In the latter case, the lateral
displacement of the combination can be calculated with the assumption that lateral
forces resisted by each element can be distributed to walls and frames in proportion
to stiffness. For tall structures, the effect of axial shortening of the frames and the
contribution of shear to lateral deformation of the shear wall should not be neglected.
Figure 9.56 indicates the forces assumed to be acting on a horizontal cross
section of a shear wall.
9.132 SECTION NINE
Reinforcement required for flexure of shear walls as a cantilever should be proportioned
as for deep beams (Art. 9.88). Shear reinforcement is usually furnished
as a combination of horizontal and vertical bars distributed evenly in each story
(for increment of load). For low shear (where the factored shear force Vu at a section
is less than 0.5	Vc, where Vc is the nominal shear permitted on the concrete), the
minimum shear reinforcement required and its location in a wall are the same as
for bearing walls (Art. 9.68). Maximum spacing of horizontal shear reinforcement,
however, should not exceed Lw/5, 3h, or 18 in, where Lw is the horizontal length
of wall and h the overall wall thickness (Fig. 9.56). Maximum spacing of the
vertical reinforcement should not exceed Lw/3, 3h, or 18 in.
A thickness of at least Lw/25 is advisable for walls with high shear.
The factored horizontal shear force Vu acting on a section through the shear wall
must not exceed the nominal shear strength Vn multiplied by 	
 0.85.
V  (	V 
 	V  	V ) (9.110) u n c s
where Vc 
 nominal shear strength of the concrete and Vs 
 nominal shear strength
provided by reinforcement. The horizontal shear strength at any section should not
be taken larger than
V 
 10 
?
 hd (9.111) n c
where 
 ?
c specified concrete compressive strength, psi
d 
 effective depth of wall, but not to be taken larger than 80% of the wall
length
h 
 wall thickness
Shear carried by the concrete should not exceed the smaller of the values of Vc
computed from Eq. (9.112) or (9.113).
N d u V 
 3.3 
?
 hd  (9.112) c c 4Lw
where Nu 
 factored vertical axial load on wall acting with Vu, including tension
due to shrinkage and creep (positive for compression, negative for tension).
L (1.25 
?
  0.2N /L h) w c u w V 
 0.6 
?
  hd (9.113)  	 c c M /V  L /2 u u w
where Mu 
 factored moment at section where Vu acts.
Alternatively, Vc 
 may be used if Nu causes compression. Shear 2 
?
 hd c
strength Vc computed for a section at a height above the base equal to Lw/2 or onehalf
the wall height, whichever is smaller, may be used for all lower sections.
When Vu  0.5	Vc, the area of horizontal shear reinforcement within a distance
s2 required for shear is given by
(V / 	 V )s u s 2 A 
 	 0.0025hs (9.114) h 2 ? d y
where s2 
 spacing of horizontal reinforcement (max  Lw/5  3h  18 in) and
?y 
 yield strength of the reinforcement.
Also, when Vu  0.5	Vc, the area of vertical shear reinforcement with spacing
s should be at least
CONCRETE CONSTRUCTION 9.133
FIGURE 9.57 Components of a fixed arch.
L A h h A 
 0.0025  0.5 2.5 0.0025 hs 	 0.0025hs (9.115)    	 vh L nL w h
where Lh is the wall height. But Avh need not be larger than Ah computed from Eq.
(9.114). Spacing s should not exceed Lw/3, 3h, or 18 in.
9.90 REINFORCED-CONCRETE ARCHES
Arches are used in roofs for such buildings as hangars, auditoriums, gymnasiums,
and rinks, where long spans are desired. An arch is essentially a curved beam with
the loads, applied downward in its plane, tending to decrease the curvature. Arches
are frequently used as the supports for thin shells that follow the curvature of the
arches. Such arches are treated in analysis as two-dimensional, whereas the thin
shells behave as three-dimensional elements.
The great advantage of an arch in reinforced concrete construction is that, if the
arch is appropriately shaped, the whole cross section can be utilized in compression
under the maximum (full) load. In an ordinary reinforced concrete beam, the portion
below the neutral axis is assumed to be cracked and does not contribute to the
bending strength. A beam can be curved, however, to make its axis follow the lines
of thrust very closely for all loading conditions, thus virtually eliminating bending
moments.
The component parts of a fixed arch are shown in Fig. 9.57. For a discussion
of the different types of arches and the stress analyses required for each, see Art.
5.14.
Because the depth of an arch and loading for maximum moments generally vary
along the length, several cross sections must be chosen for design, such as the
crown, springing, haunches, and the quarter points. Concrete compressive stresses
and shear should be checked at each section, and reinforcement requirements determined.
The sections should be designed as rectangular beams or T-beams subjected
to bending and axial compression, as indicated in Arts. 9.82 to 9.84.
When an arch is loaded, large horizontal reactions, as well as vertical reactions,
are developed at the supports. For roof arches, tie rods may be placed overhead, or
in or under the ground floor, to take the horizontal reaction. The horizontal reaction
may also be resisted externally by footings on sound rock or piles, by reinforced
concrete buttresses, or by adjoining portions of the structure, for example a braced
floor or roof at springing level.
9.134 SECTION NINE
Hinged arches are commonly made of structural steel or precast concrete. The
hinges simplify the arch analysis and the connection to the abutment, and they
reduce the indeterminate stresses due to shrinkage, temperature, and settlements of
supports. For cast-in-place reinforced concrete, hingeless (fixed) arches are often
used. They eliminate the cost of special steel hinges needed for hinged concrete
arches and permit reduced crown thicknesses, to provide a more attractive shape.
Arches with spans less than 90 ft are usually constructed with ribs 2 to 4 ft
wide. Each arch rib is concreted in a continuous operation, usually in 1 day. The
concrete may be placed continuously from each abutment toward the crown, to
obtain symmetrical loading on the falsework.
For spans of 90 ft or more, however, arch ribs are usually constructed by the
alternate block, or voussoir, method. Each rib is constructed of blocks of such size
that each can be completed in one casting operation. This method reduces the
shrinkage stresses. The blocks are cast in such order that the formwork will settle
uniformly. If blocks close to the crown section are not placed before blocks at the
haunch and the springing sections, the formwork will rise at the crown, and placing
of the crown blocks will then be likely to cause cracks in the haunch. The usual
procedure is to cast two blocks at the crown, then two at the springing, and alternate
until the complete arch is concreted.
In construction by the alternate block method, the block sections are kept separate
by timber bulkheads. The bulkheads are kept in place by temporary struts
between the voussoirs. Keyways left between the voussoirs are concreted later. Near
piers and abutments where the top slopes exceed about 30 with the horizontal, top
forms may be necessary, installed as the casting progresses.
If the arch reinforcement is laid in long lengths, settlement and deformation of
the arch formwork can displace the reinforcing steel. Therefore, depending on the
curvature and total length, lengths of bars are usually limited to about 30 ft. Splices
should be located in the keyways. Lap splices of adjacent bars should be staggered
(50% stagger), and located where tension is small.
Upper reinforcement in arch rings may be held in place with spacing boards
nailed to props, or with wires attached to transverse timbers supported above the
surface of the finished concrete.
Forms for arches may be supported on a timber falsework bent. This bent may
consist of joists and beams supported by posts that are braced together and to solid
ground. Wedges or other adjustment should be provided at the base of the posts so
that the formwork may be adjusted if settlement occurs, and so that the entire
formwork may be conveniently lowered after the concrete has hardened sufficiently
to take its own load.
(‘‘Guide to Formwork for Concrete,’’ ACI 347R, American Concrete Institute.)
9.91 REINFORCED-CONCRETE THIN SHELLS
Thin shells are curved slabs with thickness very small compared with the other
dimensions. A thin shell possesses three-dimensional load-carrying characteristics.
The best natural example of thin-shell behavior is that of an ordinary egg, which
may have a ratio of radius of curvature to thickness of 50. Loads are transmitted
through thin shells primarily by direct stresses—tension or compression—called
membrane stresses, which are almost uniform throughout the thickness. Reinforcedconcrete
thin-shell structures commonly utilize ratios of radius of curvature to thickCONCRETE
CONSTRUCTION 9.135
FIGURE 9.58 Continuous cylindrical concrete shell.
ness about 5 times that of an eggshell. Because concrete shells are always reinforced,
their thickness is usually determined by the minimum thickness required to
cover the reinforcement, usually 1 to 4 in. Shells are thickened near the supports
to withstand localized bending stresses in such areas. (See also Art. 5.15.)
Shells are most often used as roofs for such buildings as hangars, garages, theaters,
and arenas, where large spans are required and the loads are light. The advantages
of reinforced-concrete thin shells may be summarized as follows:
Most efficient use of materials.
Great freedom of architectural shapes.
Convenient accommodation of openings for natural lighting and ventilation.
Ability to carry very large unbalance of forces.
High fireproofing value due to lack of corners, thin ribs, and the inherent fire
resistance of reinforced concrete.
Reserve strength due to many alternative paths for carrying load to the supports.
One outstanding example withstood artillery fire punctures with only local damage.
Common shapes of reinforced-concrete thin shells used include cylindrical (barrel
shells), dome, grained vault, or groinior, elliptical paraboloid, and hyperbolic
paraboloid (saddle shape).
Cylindrical shells may be classified as long if the radius of curvature is shorter
than the span, or as short (Fig. 9.58). Long cylindrical shells, particularly the continuous,
multiple-barrel version which repeats the identical design of each bay (and
permits reuse of formwork) in both directions, are advantageous for roofing rectangular-
plan structures. Short cylindrical shells are commonly used for hangar roofs
with reinforced-concrete arches furnishing support at short intervals in the direction
of the span.
Structural analysis of these common styles may be simplified with design aids.
(‘‘Design of Cylindrical Concrete Shell Roofs,’’ Manual No. 31, American Society
of Civil Engineers; ‘‘Design Constants for Interior Cylindrical Concrete Shells,’’
EB020D: ‘‘Design Constants for Ribless Concrete Cylindrical Shells,’’ EB028D;
‘‘Coefficients for Design of Cylindrical Concrete Shell Roofs’’ (extension of ASCE
Manual No. 31), EB035D; ‘‘Design of Barrel Shell Roofs,’’ IS082D, Portland Cement
Association; ‘‘Concrete Shell Structures—Practice and Commentary,’’ ACI
334.1R, American Concrete Institute.
The ACI 318 Building Code includes specific provisions for thin shells. It allows
an elastic analysis as an accepted basis for design and suggests model studies for
9.136 SECTION NINE
FIGURE 9.60 Typical shapes of concrete folded plates.
FIGURE 9.59 Reinforcements in a long cylindrical shell. Folded plates are
similarly reinforced.
complex or unusual shapes, prescribes minimum reinforcement, and prohibits use
of the working-stress method for design, thus prescribing selection of all shear and
flexural reinforcement by the strength-design method with the same load factors as
for design of other elements. Figure 9.59 shows a typical reinforcement arrangement
for a long cylindrical shell. (See also F. S. Merritt, ‘‘Standard Handbook for Civil
Engineers,’’ Sec. 8, ‘‘Concrete Design and Construction,’’ and D. P. Billington,
‘‘Thin-Shell Concrete Structures,’’ 2d ed., McGraw-Hill Publishing Company, New
York.)
9.92 CONCRETE FOLDED PLATES
Reinforced-concrete, folded-plate construction is a versatile concept applicable to
a variety of long-span roof construction. Applications using precast, simple V
folded plates include segmental construction of domes and (vertically) walls (Fig.
9.60). Inverted folded plates have also been widely used for industrial storage bins.
(‘‘Standard Practice for Design and Construction of Concrete Silos and Stacking
Tubes for Storing Granular Materials,’’ ACI 313, and ‘‘Commentary,’’ ACI 313R,
American Concrete Institute.) Determination of stresses in folded-plate construction
is described in Art. 5.15.5.
Formwork for folded plates is far simpler than that for curved thin shells. Precasting
has also been a simpler process to save formwork, permit mass-production
construction, and achieve sharp lines for exposed top corners (vees cast upside
down) to satisfy aesthetic requirements. For very long spans, posttensioned, draped
tendons have been used to reduce the total depth, deflection, and reinforcing-steel
CONCRETE CONSTRUCTION 9.137
requirements. The tendons may be placed in the inclined plates or, more conveniently,
in small thickened edge beams. For cast-in-place, folded-plate construction,
double forming can usually be avoided if the slopes are less than 35 to 40.
Since larger transverse bending moments develop in folded plates than in cylindrical
shells of about the same proportions, a minimum thickness less than 4 in
creates practical problems of placing the reinforcing steel. A number of area in the
plates will require three layers of reinforcing steel and, near the intersections of
plates, top and bottom bars for transverse bending will be required. Ratios of span
to total depth are similar to those for cylindrical shells, commonly ranging from 8
to 15. (See also F. S. Merritt, ‘‘Standard Handbook for Civil Engineers,’’ Sec. 8,
‘‘Concrete Design and Construction,’’ McGraw-Hill Publishing Company, New
York.)
9.93 SLABS ON GRADE
Slabs on ground are often used as floors in buildings. Special use requirements
often include heavy-duty floor finish (Art. 9.35) and live-load capacity for heavy
concentrated (wheel) load or uniform (storage) loads, or both.
Although slabs on grade seem to be simple structural elements, analysis is extremely
complicated. For design load requirements that are unusually heavy and
outside common experience, design aids are available. Occasionally, the design will
be controlled by wheel loads only, as for floors in hangars, but more frequently by
uniform warehouse loadings. (‘‘Design of Slabs on Grade,’’ ACI 360R; American
Concrete Institute; ‘‘Concrete Floors on Ground,’’ EB075D, Portland Cement Association;
‘‘Design of Floors on Ground for Warehouse Loadings,’’ Paul F. Rice,
ACI Journal, August 1957, paper No. 54-7.)
A full uniform load over an entire area causes no bending moment if the boundaries
of the area are simple construction joints. But actual loads in warehouse usage
leave unloaded aisles and often alternate panels unloaded. As a result, a common
failure of warehouse floors results from uplift of the slab off the subgrade, causing
negative moment (top) cracking. In lieu of a precise analysis taking into account
live-load magnitude, joint interval and detail, the concrete modulus of elasticity, the
soil modulus, and load patterns, a quick solution to avoid uplift is to provide a slab
sufficiently thick so that its weight is greater than one-fifth the live load. Such a
slab may be unreinforced, if properly jointed, or reinforced for temperature and
shrinkage stresses only. Alternatively, for very heavy loadings, an analysis and
design may be performed for the use of reinforcement, top and bottom, to control
uplift moments and cracking. (‘‘Design of Floors on Ground for Warehouse Loadings,’’
Paul F. Rice, ACI Journal, Aug., 1957, paper No. 53-7.)
Shrinkage and temperature change in slabs on ground can combine effects adversely
to create warping, uplift, and top crackling failures with no load. Closely
spaced joint intervals, alternate-panel casting sequence, and controlled curing will
avoid these failures. Somewhat longer joint spacings can be specified if reinforcement
with an area of about 0.002 times the gross section area of slab is provided
in perpendicular directions.
With such reinforcement, warping will usually be negligible if the slab is cast
in alternate lanes 12 to 14 ft wide, and provided with contraction joints at 20- to
30-ft spacings in the direction of casting. The joints may be tooled, formed by joint
filler inserts, or sawed. One-half the bars or wires crossing the contraction joints
9.138 SECTION NINE
should be cut accurately on the joint line. The warping effect will be aggravated if
excess water is used in the concrete and it is forced to migrate in one direction to
top or bottom of the slab, for example, when the slab has been cast on a vapor
barrier or on a very dry subgrade. For very long slabs, continuous reinforcement,
approximately 0.006 times the gross area, is used to eliminate transverse joints in
highway and airport pavement. (‘‘Design of Continuously Reinforced Concrete for
Highways’’ and ‘‘Construction of Continuously Reinforced Concrete Pavements,’’
Concrete Reinforcing Steel Institute; and ‘‘Suggested Specifications for Heavy-duty
Concrete Floor Topping,’’ IS021B; ‘‘Design of Concrete Floors on Ground,’’
IS046B; ‘‘Suggested Specifications for Single-course Floors on Ground,’’ IS070B,
Portland Cement Association.)
9.94 SEISMIC-RESISTANT
CONCRETE CONSTRUCTION
The ACI 318 Building Code contains special seismic requirements for design that
apply only for areas where the probability of earthquakes capable of causing major
damage to structures is high, and where ductility reduction factors for lateral seismic
loads are utilized (ACI 319-99, Chap. 21). The general requirements of ACI 318-
99 for reinforced concrete provide sufficient seismic resistance for seismic zones
(or seismic performance categories) where only minor seismic damage is probable
and no reduction factor for ductility is applied to seismic forces. Designation of
seismic zones (or seismic performance categories) is prescribed in general building
codes, as are lateral force loads for design. (See also Art. 5.18.7.)
Special ductile-frame design is prescribed to resist lateral movements sufficiently
to create ‘‘plastic’’ hinges and permit reversal of direction several times. These
hinges must form in the beams at the beam-column connections of the ductile.
Shear walls used alone or in combination with ductile beam-column frames must
also be designed against brittle (shear) failures under the reversing loads (‘‘Commentary
on ACI 318-99’’).
Ductility is developed in reinforced concrete by:
Conservative limits on the net flexural tension-steel ratio   0.025, to ensure
underreinforced behavior. At least two continuous bars must be provided at both
top and bottom of flexural members.
Heavy confining reinforcement extending at joints through the region of maximum
moment in both columns and beams, to include points where hinges may
form. This confining reinforcement may consist of spirals or heavy, closely spaced,
well-anchored, closed ties (hoops) with hooked ends engaging the vertical bars or
the tie at the far face.
(‘‘ACI Detailing Manual,’’ SP-66, American Concrete Institute.)
9.95 COMPOSITE FLEXURAL MEMBERS
Reinforced- and prestressed-concrete, composite flexural members are constructed
from such components as precast members with cast-in-place flanges, box sections,
and folded plates.
Composite structural-steel-concrete members are usually constructed of cast-inplace
slabs and structural-steel beams. Interaction between the steel beam and conCONCRETE
CONSTRUCTION 9.139
crete slab is obtained by natural bond if the steel beam is fully encased with a
minimum of 2 in of concrete on the sides or soffit. If the beam is not encased, the
interaction may be accomplished with mechanical anchors (shear connectors). Requirements
for composite structural-steel-concrete members are given in the AISC
‘‘Specification for Structural Steel for Buildings—Allowable Stress Design and
Plastic Design,’’ and AISC ‘‘Load and Resistance Factor Design Specification for
Structural Steel Buildings,’’ American Institute of Steel Construction.
The design strength of composite flexural members is the same for both shored
and unshored construction. Shoring should not be removed, however, until the supported
elements have the design properties required to support all loads and limit
deflections and cracking. Individual elements should be designed to support all
loads prior to the full development of the design strength of the composite member.
Premature loading of individual precast elements can cause excessive deflections
as the result of creep and shrinkage.
According to the ACI 318 Building Code, the factored horizontal shear force
for a composite member may be transferred between individual concrete elements
by contact stresses or anchored ties, or both. The factored shear force Vu at the
section considered must be equal to or less than the nominal horizontal shear
strength Vnh multiplied by 	
 0.85.
V  	 V (9.116) u nh
When Vu  	80bvd, where bv is the section width and d the distance from the
extreme compression surface to the centroid of tension reinforcement, the factored
shear force may be transferred by contact stresses without ties, if the contact surfaces
are clean, free of laitance and intentionally roughened. Otherwise, if the contact
surfaces are clean but not intentionally roughened, fully anchored minimum
ties [Eq. (9.81)], spaced not over 24 in or 4 times the least dimension of the
supported element are required when Vu  	80bvd.
When fully anchored minimum ties are provided and the contact surfaces are
clean, free of laitance and intentionally roughened to a full amplitude of about 1?4
in, the Code permits transferring a factored shear force equal to 	(260  0.6
v?y) 
bvd but not more than 	(500 bvd), where v is the ratio of tie reinforcement
area to the area of the contact surface, ?y is the yield strength of shear reinforcement,
and 
 is defined under Eq. (9.117).
When Vu exceeds 	(500bvd), the factored shear force may be transferred by
shear-friction reinforcement placed perpendicular to assumed cracks. Shear force
Vu should not exceed 800Ac or Ac, where Ac is the area of the concrete section 0.2?
c
resisting shear transfer, and is the specified concrete compressive strength. Re- ?
c
quired reinforcement area is
Vu A 
 (9.117) v? 	?  y
where ?y 
 yield strength of shear reinforcement

 coefficient of friction

 1.4 
 for monolithic concrete

 1.0 
 for concrete cast against hardened concrete with surface intentionally
roughened to a full amplitude of about 0.25 in

 0.7 
for concrete anchored by headed studs or rebars to as-rolled structural
steel (clean and without paint)

 0.6 
 for concrete cast against hardened concrete not intentionally
roughened
9.140 SECTION NINE


 1.0 for normal-weight concrete

 0.85 for sand-lightweight concrete

 0.75 for all-lightweight concrete
PRECAST-CONCRETE MEMBERS
Precast-concrete members are assembled and fastened together on the jobsite. They
may be unreinforced, reinforced, or prestressed. Precasting is especially advantageous
when it permits mass production of concrete units. But precasting is also
beneficial because it facilitates quality control and use of higher-strength concrete.
Form costs may be greatly reduced, because reusable forms can be located on a
casting-plant floor or on the ground at a construction site in protected locations and
convenient positions, where workmen can move about freely. Many complex thinshell
structures are economical when precast, but would be uneconomical if cast in
place.
9.96 DESIGN METHODS FOR
PRECAST MEMBERS
Design of precast-concrete members under the ACI 318 Building Code follows the
same rules as for cast-in-place concrete. In some cases, however, design may not
be governed by service loads, because transportation and erection loads on precast
members may exceed the service loads.
Design of joints and connections must provide for transmission of any forces
due to shrinkage, creep, temperature, elastic deformation, gravity loads, wind loads,
and earthquake motion.
(‘‘Design and Typical Details of Connections for Precast and Prestressed Concrete,’’
2d ed., Precast / Prestressed Concrete Institute.)
9.97 REINFORCEMENT COVER
IN PRECAST MEMBERS
Less concrete cover is required for reinforcement in precast-concrete members manufactured
under plant control conditions than in cast-in-place members because the
control for proportioning, placing, and curing is better. Minimum concrete cover
for reinforcement required by ACI 318-99 is listed in Table 9.26.
For all sizes of reinforcement in precast-concrete wall panels, minimum cover
of 3?4 in is acceptable at nontreated surfaces exposed to weather and 3?8 in at interior
surfaces.
9.98 TOLERANCES FOR
PRECAST CONSTRUCTION
Dimensional tolerances for precast members and tolerances on fitting of precast
members vary for type of member, type of joint, and conditions of use. See ‘‘PCI
CONCRETE CONSTRUCTION 9.141
TABLE 9.26 Minimum Reinforcement Cover for Precast Members, in
Concrete exposed to earth or weather:
Wall panels:
No. 14 and No. 18 bars 11?2
No. 11 bars and smaller 3?4
Other members:
No. 14 and No. 18 bars 2
No. 6 through No. 11 bars 11?2
No. 5 bars, 5?8-in wire and smaller 11?4
Concrete not exposed to weather or in contact with the ground:
Slabs, walls, joists:
No. 14 and No. 18 bars 11?4
No. 11 bars and smaller 5?8
Beams, girders, columns:
Principal reinforcement:
Diameter of bar db but not less than 5?8 in and need not be more than 11?2 in
Ties, stirrups or spirals 3?8
Shells and folded-plate members:
No. 6 bars and larger 5?8
No. 5 bars, 5?8-in wire and smaller 3?8
Design Handbook,’’ and ‘‘Design and Typical Details of Connections for Precast
and Prestressed Concrete,’’ Precast / Prestressed Concrete Institute; and ‘‘Standard
Specifications for Tolerances for Concrete Construction and Materials,’’ ACI 117,
American Concrete Institute.
9.99 ACCELERATED CURING
For strength and durability, precast concrete members require adequate curing. They
usually are given some type of accelerated curing for economic reuse of forms and
casting space. At atmospheric pressure, curing temperatures may be held between
125 and 185F for 12 to 72 h. Under pressure, autoclave temperatures above 325F
for 5 to 36 h are applied for fast curing. Casting temperatures, however, should not
exceed 90F. See Fig. 9.5.
(‘‘Standard Practice for Curing Concrete,’’ ACI 308; ‘‘Accelerated Curing of
Concrete at Atmospheric Pressure—State of the Art,’’ ACI 517.2R, American Concrete
Institute.)
9.100 PRECAST FLOOR AND ROOF SYSTEMS
Long-span, precast-concrete floor and roof units are usually prestressed. Short members,
30 ft or less, are often made with ordinary reinforcement. Types of precast
units for floor and roof systems include solid or ribbed slabs, hollow-core slabs,
single and double tees, rectangular beams, L-shaped beams, inverted-T-beams, and
I-beams.
Hollow-core slabs are usually available in normal-weight or structural lightweight
concrete. Units range from 16 to 96 in. in width, and from 4 to 12 in. in
9.142 SECTION NINE
depth. Hollow-core slabs may come with grouted shear keys to distribute loads to
adjacent units over a slab width as great as one-half the span.
Manufacturers should be consulted for load and span data on hollow-core slabs,
because camber and deflection often control the serviceability of such units, regardless
of strength.
(‘‘PCI Design Handbook,’’ Precast / Prestressed Concrete Institute.)
9.101 PRECAST RIBBED SLABS, FOLDED
PLATES, AND SHELLS
Curved shells and folded plates have a thickness that is small compared with their
other dimensions. Such structures depend on their geometrical configuration and
boundary conditions for strength.
Thickness. With closely spaced ribs or folds, a minimum thickness for plane
sections of 1 in is acceptable.
Reinforcement. Welded-wire fabric with a maximum spacing of 2 in may be used
for slab portions of thin-section members, and for wide, thin elements 3 in thick
or less. Reinforcement should be preassembled into cages, using a template, and
placed within a tolerance of 0 in or 1?8 in from the nearest face. The minimum
clear distance between bars should not be less than 11?2 times the nominal maximum
size of the aggregate. For minimum concrete cover of reinforcement, see Art. 9.97.
Compressive Strength. Concrete for thin-section, precast-concrete members protected
from the weather and moisture and not in contact with the ground should
have a compressive strength of at least 4000 psi at 28 days. For elements in other
locations, a minimum of 5000 psi is recommended.
Analysis. Determination of axial stresses, moments, and shears in thin sections is
usually based on the assumption that the material is ideally elastic, homogeneous,
and isotropic.
Forms. Commonly used methods for the manufacture of thin-section, precastconcrete
members employ metal or plastic molds, which form the bottom of the
slab and the sides of the boundary members. Forms are usually removed pneumatically
or hydraulically by admitting air or water under pressure through the bottom
form.
(‘‘Architectural Precast Concrete,’’ Precast / Prestressed Concrete Institute.)
9.102 WALL PANELS
Precast-concrete wall panels include plain panels, decorative panels, natural stonefaced
panels, sandwich panels, solid panels, ribbed panels, tilt-up panels, loadbearing
and non-load-bearing panels, and thin-section panels. Prestressing, when
used with such panels, makes it possible to handle and erect large units and thin
sections without cracking.
CONCRETE CONSTRUCTION 9.143
Forms required to produce the desired size and shape of panel are usually made
of steel, wood, concrete, vacuum-formed thermoplastics, fiber-reinforced plastics,
or plastics formed into shape by heat and pressure, or any combination of these.
For complicated form details, molds of plaster, gelatin, or sculptured sand can be
used.
Glossy-smooth concrete finish can be obtained with forms made of plastic. But,
for exterior exposure, this finish left untreated undergoes gradual and nonuniform
loss of its high reflectivity. Textured surfaces or smooth but nonglossy surfaces
obtained by early form removal are preferred for exterior exposure.
Exposed-aggregate monolithic finishes can be obtained with horizontal-cast panels
by initially casting a thin layer containing the special surface aggregates in the
forms and then casting regular concrete backup. With a thickness of exposed aggregate
of less than 1 in, the panel can also be cast face up and the aggregate
seeded over the fresh concrete or hand placed in a wet mortar. Variations of exposed
surface can be achieved by use of set retardant, acid washes, or sandblasting.
Consolidation of the concrete in the forms to obtain good appearance and durability
can be attained by one of the following methods:
External vibration with high-frequency form vibrators or a vibrating table.
Internal or surface vibration with a tamping-type or jitterburg vibrator.
Placing a rich, high-slump concrete in a first layer to obtain uniform distribution
of the coarse aggregate and maximum consolidation, and then making the mix
for the following layers progressively stiffer. This allows absorption of excessive
water from the previous layer.
Tilt-up panels can be economical if the floor slab of the building can be designed
for and used as the form for the panels. The floor slab must be level and
smoothly troweled. Application of a good bond-breaking agent to the slab before
concrete is cast for the panels is essential to obtain a clean lift of the precast panels
from the floor slab.
If lifting cables are attached to a panel edge, large bending moments may develop
at the center of the wall. For high panels, three-point pickup may be used.
To spread pickup stresses, specially designed inserts are cast into the wall at pickup
points.
Another method of lifting wall panels employs a vacuum mat—a large steel mat
with a rubber gasket at its edges to contact the slab. When the air between mat and
panel is pumped out, the mat adheres to the panel, because of the resulting vacuum,
and can be used to raise the panel. The method has the advantage of spreading
pickup forces over the mat area.
Panels, when erected, must be temporarily braced until other construction is in
place to provide required permanent bracing.
(‘‘Tilt-Up Concrete Structures,’’ ACI 551.R, American Concrete Institute.)
Joints. Joint sealants for panel installations may be mastics or elastomeric materials.
These are extensible and can accommodate the movement of panels.
Recommended maximum joint widths and minimum expansions for the common
sealants are listed in Table 9.27.
The joint sealant manufacturer should be asked to advise on backup material for
use with a sealant and which shape factor should be considered. A good backup
material is a rod of sponge material with a minimum compression of 30%, such as
foamed polyethylene, polystyrene, polyurethane, polyvinyl chloride, or synthetic
rubber.
9.144 SECTION NINE
TABLE 9.27 Maximum Joint Widths for Sealants
Type of Sealant
Maximum joint
width, in
Maximum
movement,
tension, and
compression, %
Butyl 3?4 10
Acrylic 3?4 15–25
One-part polyurethane 3?4 20
Two-part polyurethane 3?4 25
One-part polysulfide 3?4 25
Two-part polysulfide 3?4 25
(‘‘PCI Manual for Structural Design of Architectural Precast Concrete,’’ Precast/
Prestressed Concrete Institute.)
9.103 LIFT SLABS
Lift slabs are precast-concrete floor and roof panels that are cast on a base slab at
ground level, one on top of the other, with a bond-breaking membrane between
them. Steel collars are embedded in the slabs and fit loosely around the columns.
After the slabs have cured, they are lifted to their final position by a patented jack
system supported on the columns. The embedded steel collars then are welded to
the steel columns to hold the lift slabs in place. This method of construction eliminates
practically all formwork.
PRESTRESSED-CONCRETE CONSTRUCTION
Prestressed concrete is concrete in which internal stresses have been introduced
during fabrication to counteract the stresses produced by service loads. The prestress
compresses the tensile area of the concrete to eliminate or reduce the tensile stresses
caused by the loads.
9.104 BASIC PRINCIPLES OF
PRESTRESSED CONCRETE
In the application of prestress, the usual procedure is to tension high-strength-steel
elements, called tendons, and anchor them to the concrete, which resists the tendency
of the stretched steel to shorten after anchorage and is thus compressed. If
the tendons are tensioned before concrete has been placed, the prestressing is called
pretensioning. If the tendons are tensioned after the concrete has been placed the
prestressing is called posttensioning.
Prestress can prevent cracking by keeping tensile stresses small, or entirely
avoiding tension under service loads. The entire concrete cross-section behaves as
CONCRETE CONSTRUCTION 9.145
an uncracked homogeneous material in bending. In contrast, in nonprestressed,
reinforced-concrete construction, tensile stresses are resisted by reinforcing steel,
and concrete in tension is considered ineffective. It is particularly advantageous
with prestressed concrete to use high-strength concrete.
Loss of Prestress. The final compression force in the concrete is not equal to the
initial tension force applied by the tendons. There are immediate losses due to
elastic shortening of the concrete, friction losses from curvature of the tendons, and
slip at anchorages. There are also long-time losses, such as those due to shrinkage
and creep of the concrete, and possibly relaxation of the prestressing steel. These
losses should be computed as accurately as possible or determined experimentally.
They are deducted from the initial prestressing force to determine the effective
prestressing force to be used in design. (The reason that high-strength steels must
be used for prestressing is to maintain the sum of these strain losses at a small
percentage of the initially applied prestressing strain.) (See also Art. 9.107.)
Stresses. When stresses in prestressed members are determined, prestressing
forces can be treated as other external loads. If the prestress is large enough to
prevent cracking under design loads, elastic theory can be applied to the entire
concrete cross section (Fig. 9.61).
Prestress may be applied to a beam by straight tendons or curved tendons.
Stresses at midspan can be the same for both types of tendons, but the net stresses
with the curved tendons can remain compressive away from midspan, whereas they
become tensile at the top fiber near the ends with straight tendons. For a prestressing
force Ps applied to a beam by a straight tendon at a distance e1 below the neutral
axis, the resulting prestress in the extreme surface throughout is
P Pec s s 1 ? 
  (9.118)
A I c g
where Ps /Ac is the compressive stress on a cross section of area Ac, and Pse1c/ Ig
is the bending stress induced by Ps (positive for compression and negative for
tension), as indicated in Fig. 9.61. If stresses Mc/ Ig due to moment M caused by
external gravity loads are superimposed at midspan, the net stresses in the extreme
fibers can become zero at the bottom and compressive at the top. Because the
stresses due to gravity loads are zero at the beam ends, the prestress is the final
stress there and the top surface of the beam at the ends is in tension.
If the tensile stresses at the ends of beams with straight tendons are excessive,
the tendons may be draped, or harped, in a vertical curve. Stresses at midspan will
be substantially the same as with straight tendons (if the horizontal component of
prestress is nearly equal to Ps) and the stresses at the beam ends will be compressive,
because the prestressing force passes through or above the centroid of the end
sections (Fig. 9.61). Between midspan and the ends, the cross sections will also be
in compression.
9.105 LOSSES IN PRESTRESS
Assumptions in design of total losses in tendon stress of 35,000 psi for pretensioning
and 25,000 psi for posttensioning to allow for elastic shortening, frictional
losses, slip at anchorages, shrinkage, creep, and relaxation of the prestressing steel
9.146 SECTION NINE
FIGURE 9.61 Prestressed-concrete beam: (a) with straight tendons; (b)
with curved tendons; (c) midspan stresses with straight or curved tendons;
(d) stresses between midspan and supports with curved tendons.
Net stresses near the supports become tensile with straight tendons.
usually gives satisfactory results. Losses greater or smaller than these values have
little effect on the design strength but can affect service-load behavior, such as
cracking load, deflection, and camber.
Elastic Shortening of Concrete. In pretensioned members, when the tendons are
released from fixed abutments and the steel stress is transferred to the concrete by
bond, the concrete shortens under the compressive stress. The decrease in unit stress
in the tendons equals PsEs /AcEc 
 n?c, where Es is the modulus of elasticity of
the steel, psi; Ec the modulus of elasticity of the concrete psi; n the modular ratio,
Es /Ec; ?c the unit stress in the concrete, psi; Ps the prestressing force applied by
the tendons; and Ac the cross-sectional area of the member.
In posttensioned members, the loss due to elastic shortening can be eliminated
by using the members as a reaction in tensioning the tendons.
Frictional Losses. In posttensioned members, there may be a loss of prestress
where curved tendons rub against their enclosure. The loss may be computed in
terms of a curvature-friction coefficient . Losses due to unintentional misalignment
CONCRETE CONSTRUCTION 9.147
may be calculated from a wobble-friction coefficient K (per lin ft). Since the coefficients
vary considerably, they should, if possible, be determined experimentally.
A safe range of these coefficients for estimates is given in the ‘‘Commentary on
ACI 318-99,’’ American Concrete Institute.
Frictional losses can be reduced by tensioning the tendons at both ends, or by
initial use of a larger jacking force which is then eased off to the required initial
force for anchorage.
Slip at Anchorages. For posttensioned members, prestress loss may occur at the
anchorages during the anchoring. For example, seating of wedges may permit some
shortening of the tendons. If tests of a specific anchorage device indicate a shortening
L, the decrease in unit stress in the prestressing steel is equal to Es L/L,
where L is the length of the tendon. This loss can be reduced or eliminated by
overtensioning initially by an additional strain equal to the estimated shortening.
Shrinkage of Concrete. Change in length of a member caused by concrete shrinkage
results in a prestress loss over a period of time. This change can be determined
from tests or experience. Generally, the loss is greater for pretensioned members
than for posttensioned members, which are prestressed after much of the shrinkage
has occurred. Assuming a shrinkage of 0.0002 in / in of length for a pretensioned
member, the loss in tension in the tendons is 0.0002Es 
 0.0002  30  106 

6000 psi.
Creep of Concrete. Change in length of concrete under sustained load induces a
prestress loss proportional to the load over a period of time depending greatly on
the aggregate used. This loss may be several times the elastic shortening. An estimate
of this loss may be made with an estimated creep coefficient Ccr equal to
the ratio of additional long-time deformation to initial elastic deformation determined
by test. The loss in tension for axial prestress in the steel is, therefore, equal
to Ccrn?c. Values ranging from 1.5 to 2.0 have been recommended for Ccr.
Relaxation of Prestressing Steel. A decrease in stress under constant high strain
occurs with some prestressing steels. Steel tensioned to 60% of its ultimate strength
may relax and lose as much as 3% of the prestressing force. This type of loss may
be reduced by temporary overtensioning, which artificially accelerates relaxation,
reducing the loss that will occur later at lower stresses.
(P. Zia et al., ‘‘Estimating Prestress Loss,’’ Concrete International, June 1979,
p. 32, American Concrete Institute; ‘‘PCI Design Handbook,’’ Precast / Prestressed
Concrete Institute.)
9.106 ALLOWABLE STRESSES AT
SERVICE LOADS
At service loads and up to cracking loads, straight-line theory may be used for
computing stresses in prestressed beams with the following assumptions:
Strains vary linearly with depth through the entire load range.
At cracked sections, the concrete does not resist tension.
Areas of unbonded open ducts should not be considered in computing section
properties.
9.148 SECTION NINE
TABLE 9.28 Allowable Stresses for Prestressed Concrete
Concrete:
Temporary stresses after transfer of prestress but before prestress losses:
Compression 0.60?
ci
Tension in members without auxiliary reinforcement in tension zone,
except at ends of simply-supported members
3 
?
 * ci
Tension at ends of simply-supported members 6 
?
ci
Service-load stresses after prestress losses:
Compression for sustained service live load 0.45?
c
Compression for transient or temporary service live load 0.60?
c
Tension in precompressed tensile zone 6 
?
† c
Prestressing steel:
Due to jacking force 0.94?py‡
Pretensioning tendons immediately after transfer 0.82?py**
Posttensioning tendons immediately after anchoring 0.70?pu
* Where the calculated tension stress exceeds this value, bonded reinforcement should be provided to
resist the total tension force on the concrete computed for assumption of an uncracked section.
†May be taken as for members, except two-way slab systems, for which computations based 12 
?
c
on the transformed cracked section and on bilinear moment-deflection relationships show that immediate
and long-term deflection do not exceed the limits given in Table 9.14.
‡?py 
 specified yield strength of tendons but not greater than the lesser of 80% of the specified tensile
strength ?pu and the maximum value recommended by the manufacturer of the tendons or anchorages.
** But not more than 0.74?pu.
The transformed area of bonded tendons and non-prestressed reinforcing steel
may be included in pretensioned members and, after the tendons have been bonded
by grouting, in posttensioned members.
Flexural stresses must be limited to ensure proper behavior at service loads.
Limiting these stresses, however, does not ensure adequate design strength.
In establishing permissible flexural stresses, the ACI 318 Building Code recognizes
two service-load conditions, that before and that after prestress losses.
Higher stresses are permitted for the initial state (temporary stresses) than for loadings
applied after the losses have occurred.
Permissible stresses in the concrete for the initial load condition are specified as
a percentage of the compressive strength of the concrete, psi, at time of initial ?
 , ci
prestress. This strength is used as a base instead of the usual , 28-day strength ?
c
of concrete, because prestress is usually applied only a few days after concrete has
been cast. The allowable stresses for prestressed concrete, as given in ACI 318-99,
are tabulated in Table 9.28.
Bearing Stresses. Determination of bearing stresses at end regions around posttensioning
anchorages is complicated, because of the elastic and inelastic behavior
of the concrete and because the dimensions involved preclude simple analysis under
the St. Venant theory of linear stress distribution of concentrated loads. The ACI
318 Building Code formula for bearing stresses [Eq. (9.89)] does not apply to
posttensioning anchorages.
Lateral reinforcement may be required in anchorage zones to resist bursting,
horizontal splitting, and spalling forces. Expanded design requirements for posttensioned
tendon anchorage zones were introduced into the ACI 318-99 Building
Code. The Code’s design requirements are compatible with comprehensive proviCONCRETE
CONSTRUCTION 9.149
sions adopted previously in the ‘‘AASHTO Standard Specifications for Highway
Bridges,’’ American Association of State Highway and Transportation Officials.
9.107 DESIGN PROCEDURE FOR
PRESTRESSED-CONCRETE BEAMS
Beam design involves choice of shape and dimensions of the concrete member,
positioning of the tendons, and selection of amount of prestress.
After a concrete shape and dimensions have been assumed, determine the geometrical
properties—cross-sectional area, center of gravity, distances of kern and
extreme surface from the centroid, moment of inertia, section moduli, and dead
load of the member per unit length.
Treat the prestressing force as a system of external forces acting on the concrete.
Compute bending stresses due to service dead and live loads. From these, determine
the magnitude and location of the prestressing force required at sections
subject to maximum moment. The prestressing force must result in sufficient compressive
stress in the concrete to offset the tensile stresses caused by the bending
moments due to dead and live service loads (Fig. 9.61). But at the same time, the
prestress must not create allowable stresses that exceed those listed in Table 9.28.
Investigation of other sections will guide selection of tendons to be used and determine
their position and profile in the beam.
After establishing the tendon profile, prestressing forces, and tendon areas, check
stresses at critical points along the beam immediately after transfer, but before
losses. Using strength-design methods (Art. 9.108), check the percentage of steel
and the strength of the member in flexure and shear.
Design anchorages, if required, and shear reinforcement.
Finally, check the deflection and camber under service loads. The modulus of
elasticity of high-strength prestressing steel should not be assumed equal to
29,000,000 psi, as for non-prestressed reinforcement, but should be determined by
test or obtained from the manufacturer.
9.108 FLEXURAL-STRENGTH DESIGN OF
PRESTRESSED CONCRETE
Flexural design strength should be based on factored loads and the assumptions of
the ACI 318 Building Code, as explained in Art. 9.44. The stress ?ps in the tendons
at factored load (1.4D  1.7L, where D is the dead load and L the live load),
however, should not be assumed equal to the specified yield strength. High-strength
prestressing steels lack a sharp and distinct yield point, and ?ps varies with the
ultimate (tensile) strength of the prestressing steel ?pu, the prestressing steel percentage
p, and the concrete strength at 28 days. A stress-strain curve for the ?
c
prestressing steel being used is necessary for stress and strain compatibility computations
of ?ps. For unbonded tendons, successive trial-and-error analysis of tendon
strain for strength design is straightforward but tedious. Assume a deflection at
failure by crushing of the concrete (strain 
 0.003 in / in). Determine from the
stress-strain curve for the tendon steel the tendon stress corresponding to the total
9.150 SECTION NINE
tendon strain at the assumed deflection. Proceed through successive trials, varying
the assumed deflection, until the algebraic sum of the internal tensile and compressive
forces equals zero. The moment of the resulting couple comprising the
tensile and compressive forces times 	
 0.90 is the design moment strength.
Stress in Bonded Tendons. When such data are not available, and the effective
prestress, after losses, ?se is at least half the specified ultimate strength ?pu of the
tendons, the stress ?ps in bonded tendons at nominal strength may be obtained from
p ? 
? 1 R (9.119)   ps pu 1
? d? pu y R 
   (  
) (9.120) p ?
 d ?
 c pc
where p 
 factor for type of tendon

 0.55 for ?py/?pu 	 0.80

 0.40 for ?py/?pu 	 0.85

 0.28 for ?py/?pu 	 0.90
1 
 0.85 for  4000 psi, reduce 1 by 0.05 for each ?
  4000 psi; for ?
 c c
1000 psi that exceeds 4000 psi but not to less than 0.65 ?
c
p 
 Aps /bdp
Aps 
 area of tendons in tension zone
b 
 width of compression face of member
dp 
 distance from extreme compression surface to centroid of tendons

 As /bd
d 
 distance from extreme compression surface to centroid of nonprestressed
tension reinforcement
As 
 area of nonprestressed tension reinforcement

 
 /bd A
s

 A
s area of compression reinforcement
?y 
 specified yield strength of nonprestressed reinforcement
If the area of compression reinforcement is included in the calculation of ?ps from
Eq. (9.119), R should not exceed 0.17 nor should the distance d
 from the extreme
compression surface to the centroid of the compression reinforcement exceed
0.15dp.
Stress in Unbonded Tendons. When the ratio of span to depth of a prestressed
flexural member with unbonded tendons is 35 or less, the stress in the tendons at
nominal strength is given by
? 
 ?  10,000  ?
 /100   ?  60,000 (9.121) ps se c p se
where ?se is the effective stress in the tendons after allowance for prestress losses,
but ?ps should not exceed the specified yield strength ?py of the tendons.
When the ratio of span to depth is larger than 35,
? 
 ?  10,000  ?
 /300   ?  30,000 (9.122) ps se c p se
but ?ps should not exceed ?py.
CONCRETE CONSTRUCTION 9.151
Nonprestressed reinforcement conforming to ASTM A615, A706, A185, A496,
or A497, when used, in combination with tendons, may be assumed equivalent, at
factored moment, to its area times its yield strength, but only if
  0.36  (9.123) p 1
  (d/d )( 
)  0.36  (9.124) p p 1
  (d/d )(  
 )  0.36  (9.125) pw p w w 1
where p 
 p?ps/?
c

 ?y/?
c

 
 
?y/?
c
w, pw, 
 
w reinforcement indices for flanged sections, computed as for , p,
and 
, except that b is the web width, and the reinforcing steel
area is that required to develop the compressive strength of the web
only
Design and Cracking Loads. To prevent an abrupt flexural failure by rupture of
the prestressing steel immediately after cracking without a warning deflection, the
total amount of prestressed and nonprestressed reinforcement should be adequate
to develop a factored load in flexure of at least 1.2 times the cracking load, calculated
on the basis of a modulus of rupture ?r. For normal-weight concrete, this
modulus may be taken as
? 
 7.5 
?
 (9.126) r c
and for lightweight concrete as
? 
 1.12?  7.5 
?
 (9.127) r ct c
where ?ct 
 average splitting tensile strength of lightweight concrete. When the
value for ?ct is not available, the modulus of rupture of lightweight concrete can
be computed for sand-lightweight concrete from
? 
 6.375 
?
 (9.128) r c
and for all-lightweight concrete from
? 
 5.625 
?
 (9.129) r c
(‘‘PCI Design Handbook,’’ Precast / Prestressed Concrete Institute.)
9.109 SHEAR-STRENGTH DESIGN OF
PRESTRESSED CONCRETE
The ACI 318 Building Code requires that prestressed concrete beams be designed
to resist diagonal tension by strength theory. There are two types of diagonal-tension
cracks that can occur in prestressed-concrete flexural members: flexural-shear cracks
initiated by flexural-tension cracks, and web-shear cracks caused by principal tensile
stresses that exceed the tensile strength of the concrete.
9.152 SECTION NINE
The factored shear force Vu computed from Eq. (9.38) can be used to calculate
the diagonal-tension stress. The distance d from the extreme compression surface
to the centroid of the tension reinforcement should not be taken less than 0.80 the
overall depth h of the beam.
When the beam reaction in the direction of the applied shear introduces compression
into the end region of the member, the shear does not need to be checked
within a distance h/2 from the face of the support.
Minimum Shear Reinforcement. The ACI 318 Building Code requires that a
minimum area of shear reinforcement be provided in prestressed-concrete members,
except where the factored shear force Vu is less than 0.5	Vc, where 	Vc is the
assumed shear that can be carried by the concrete; or where the depth h of the
member is less than 10 in, 2.5 times the thickness of the compression flange, or
one-half the thickness of the web; or where tests show that the required nominal
(ultimate) flexural and shear capacity can be developed without shear reinforcement.
When shear reinforcement is required, the amount provided perpendicular to the
beam axis within a distance s should be not less than Av given by Eq. (9.81). If,
however, the effective prestress force is equal to or greater than 40% of the tensile
strength of the flexural reinforcement, a minimum area Av computed from Eq.
(9.130) may be used.
A ? s d ps pu A 
 (9.130) v  80 ? d b y w
where Aps 
 area of tendons in tension zone
?pu 
 ultimate (tensile) strength of tendons
?y 
 yield strength of nonprestressed reinforcement
s 
 shear reinforcement spacing measured parallel to longitudinal axis of
member
d 
 distance from extreme compression surface to centroid of tension reinforcement
bw 
 web width
The ACI 318 Building Code does not permit the yield strength ?y of shear
reinforcement to be assumed greater than 60,000 psi except the design yield strength
of deformed welded wire fabric should not exceed 80,000 psi. The Code also requires
that stirrups be placed perpendicular to the beam axis and spaced not farther
apart than 24 in or 0.75h, where h is the overall depth of the member.
The area of shear reinforcement required to carry the shear in excess of the shear
that can be carried by the concrete can be determined from Eq. (9.40a).
Maximum Shear. For prestressed concrete members subjected to an effective
prestress force equal to at least 40% of the tensile strength of the flexural reinforcement,
the shear strength provided by the concrete is limited to that which would
cause significant inclined cracking and, unless Eqs. (9.132) and (9.133) are used,
can be taken as equal to the larger of 2 
?
b d or c w
V d u V 
 0.60 
?
  700 b d  5 
?
 b d (9.131)   c c w c w Mu
where Mu 
 factored-load moment at section and Vu 
 factored shear force at
section. The factored moment Mu occurs simultaneously with the shear Vu at the
section. The ratio Vud/Mu should not be taken greater than 1.0.
CONCRETE CONSTRUCTION 9.153
If the effective prestress force is less than 40% of the tensile strength of the
flexural reinforcement, or if a more accurate method is preferred, the value of Vc
should be taken as the smaller of the shear forces causing inclined flexure-shear
cracking Vci or web-shear Vcw, but need not be smaller than bwd. 1.7 
?
c
V 
 0.6 
?
 b d  V  VM /M (9.132) ci c w d i cr max
V 
 (3.5 
?
  0.3 ? ) b d  V (9.133) cw c pc w p
where Vd 
 shear force at section caused by dead load
Vi 
 shear force at section occurring simultaneously with Mmax
Mmax 
 maximum bending moment at the section caused by externally applied
factored loads
Mcr 
 cracking moment based on the modulus of rupture (Art. 9.51)
bw 
 width of web
?pc 
 compressive stress in the concrete, after all prestress losses have occurred,
at the centroid of the cross section resisting the applied loads,
or at the junction of web and flange when the centroid lies within the
flange
Vp 
 vertical component of effective prestress force at section considered
In a pretensioned beam in which the section h/2 from the face of the support
is closer to the end of the beam than the transfer length of the tendon, the reduced
prestress in the concrete at sections falling within the transfer length should be
considered when calculating Vcw. The prestress may be assumed to vary linearly
along the centroidal axis from zero at the beam end to the end of the transfer
length. This distance can be assumed to be 50 diameters for strand and 100 diameters
for single wire.
(‘‘PCI Design Handbook,’’ Precast / Prestressed Concrete Institute.)
9.110 BOND, DEVELOPMENT, AND GROUTING
OF TENDONS
Three- or seven-wire pretensioning strand should be bonded beyond the critical
section for a development length, in, of at least
2 L 
 (?  ?3? )d (9.134) d ps se b
where dp 
 nominal diameter of strand, in
?ps 
 stress in tendons at nominal strength, ksi
?se 
 effective stress in tendons after losses, ksi
(The expression in parentheses is used as a constant without units.) Investigations
for bond integrity may be limited to those cross sections nearest each end of the
member that are required to develop their full strength under factored load. When
bonding does not extend to the end of the member, the bonded development length
given by Eq. (9.134) should be doubled.
Minimum Bonded Reinforcement. When prestressing steel is unbonded, the ACI
318 Building Code requires that some bonded reinforcement be placed in the precompressed
tensile zone of flexural members and distributed uniformly over the
tension zone near the extreme tension surface. The amount of bonded reinforcement
9.154 SECTION NINE
that should be furnished for beams, one-way slabs, and two-way slabs, except for
two-way flat plates, is
A 
 0.004A (9.135) s
For two-way flat plates, where tension stress in the concrete under service loads is
not greater than bonded reinforcement is not required in positive moment 2 
?
, c
areas. When the tension stress in the concrete under service load exceeds 2 
?
, c
the minimum amount of bonded reinforcement provided in positive moment areas
should be
Nc A 
 (9.136) s 0.5?y
where A 
 area of that part of the cross section between the flexural tension face
and centroid of gross section
Nc 
 tensile force in the concrete under actual dead load plus live load
?y 
 yield strength of bonded reinforcement, but not more than 60,000 psi
In the negative moment regions of two-way flat plates at column supports, the
minimum amount of bonded reinforcement provided in the top of the slab in each
direction should be
A 
 0.00075A (9.137) s c?
where Ac? 
 larger gross cross-sectional area of the slab-beam strips of the two
orthogonal equivalent frames intersecting at a column of a two-way
flat plate
The Code requires the bonded reinforcement computed by Eq. (9.137) to be distributed
between lines that are 1.5h outside opposite faces of the column support,
and that at least four bars be provided in each direction spaced not over 12 in,
where h is the depth of the flat plate. Requirements are included in the Code for
minimum lengths and extensions of the bonded reinforcement computed by Eqs.
(9.135), (9.136) and (9.137).
Grouting of Tendons. When posttensioned tendons are to be bonded, a cement
grout is usually injected under pressure (80 to 100 psi) into the space between the
tendon and the sheathing material of the duct. The grout can be inserted in holes
in the anchorage heads and cones, or through buried pipes. To ensure filling of the
space, the grout can be injected under pressure at one end of the member until it
is forced out the other end. For long members, it can be injected at each end until
it is forced out a vent between the ends.
Grout provides bond between the posttensioning tendons and the concrete member
and protects the tendons against corrosion.
Members should be above 35F in temperature at the time of grouting. This
minimum temperature should be maintained until field-cured 2-in cubes of grout
reach a minimum compressive strength of 800 psi.
Tendon Sheaths. Ducts for grouted or unbonded tendons should be mortar-tight
and nonreactive with concrete, tendons, or filler material. To facilitate injection of
the grout, the duct should be at least 1?4 in larger than the diameter of a single
posttensioning tendon. For multiple strand, bar or wire tendons, the duct should
have an internal area at least twice the gross area of the prestressing steel.
CONCRETE CONSTRUCTION 9.155
TABLE 9.29 Minimum Concrete Cover in in Prestressed Members
Concrete cast against and permanently exposed to earth 3
Concrete exposed to earth or weather:
Wall panels, slabs, and joists 1
Other members 11?2
Concrete not exposed to weather or in contact with the ground:
Slabs, walls, joists 3?4
Beams, girders, columns:
Principal reinforcement 11?2
Ties, stirrups, or spirals 1
Shells and folded-plate members:
Reinforcement 5?8 in. and smaller 3?8
Other reinforcement db but not less
than 3?4 in.
9.111 APPLICATION AND MEASUREMENT
OF PRESTRESS
The actual amount of prestressing force applied to a concrete member should be
determined by measuring the tendon elongation, also by checking jack pressure on
a calibrated gage or load cell, or by use of a calibrated dynamometer. If the discrepancy
in force determination exceeds 5%, it should be investigated and corrected.
Elongation measurements should be correlated with average load-elongation curves
for the particular prestressing steel being used.
9.112 CONCRETE COVER IN
PRESTRESSED MEMBERS
The minimum thicknesses of cover required by the ACI 318 Building Code for
prestressed and nonprestressed reinforcement, ducts, and end fittings in prestressed
concrete members are listed in Table 9.29.
The cover for nonprestressed reinforcement in prestressed concrete members
under plant control may be that required for precast members (Table 9.26). When
the general code requires fire-protection covering greater than that required by the
ACI 318 Building Code, such cover should be used.
(‘‘PCI Design Handbook,’’ Precast / Prestressed Concrete Institute.)
10.1
SECTION TEN
WOOD CONSTRUCTION
John ‘‘Buddy’’ Showalter
American Forest & Paper Association
Washington, D.C.
Thomas G. Williamson
APA—The Engineered Wood Association
Tacoma, Washington
Wood is the only renewable source for building materials. It comes from forests
that are continually being replanted as they are harvested. This practice ensures a
plentiful supply of wood for construction and for a myriad of other uses.
Compared to other building materials, wood has a very high ratio of strength to
weight. This makes it very economical for use in all types of construction. Wood
also has an aesthetic quality and natural warmth unequalled by other building materials.
Wood has inherent characteristics with which construction users should be familiar.
For example, as a consequence of its biological origin, it is nonhomogeneous.
Also, properties of pieces of wood from different species of tree may be
considerably different, and even properties of pieces of wood from the same tree
may differ. In the past, determination of engineering properties depended heavily
on visual inspection, keyed to averages, of wood pieces. Research, however, has
made possible better estimates of these properties. It is no longer necessary to rely
so heavily on visual inspection. Greater accuracy in determination of engineering
properties has been made possible by mechanical grading procedures.
Improvements in adhesives for wood also have contributed to the betterment of
wood construction. These advances in adhesion technology combined with a desire
to utilize more efficiently available wood-fiber resources have led to increasing use
of such products as oriented strand board (OSB), glued-laminated timber (glulam),
wood I joists, and structural composite lumber (SCL).
10.1 BASIC CHARACTERISTICS OF WOOD
Wood differs in several significant ways from other building materials. Its cellular
structure is responsible, to a considerable degree, for these differences. Because of
10.2
TABLE 10.1 Shrinkage Values of Wood Based on Dimensions When Green
Species
Dried to 20% MC*
Radial,
%
Tangential,
%
Volumetric,
%
Dried to 6% MC†
Radial,
%
Tangential,
%
Volumetric,
%
Dried to 0% MC
Radial,
%
Tangential,
%
Volumetric,
%
Softwood:‡
Cedar:
Alaska 0.9 2.0 3.1 2.2 4.8 7.4 2.8 6.0 9.2
Incense 1.1 1.7 2.5 2.6 4.2 6.1 3.3 5.2 7.6
Port Orford 1.5 2.3 3.4 3.7 5.5 8.1 4.6 6.9 10.1
Western red 0.8 1.7 2.3 1.9 4.0 5.4 2.4 5.0 6.8
Cypress, southern 1.3 2.1 3.5 3.0 5.0 8.4 3.8 6.2 10.5
Douglas fir:
Coast region 1.7 2.6 3.9 4.0 6.2 9.4 5.0 7.8 11.8
Inland region 1.4 2.5 3.6 3.3 6.1 8.7 4.1 7.6 10.9
Rocky Mountain 1.2 2.1 3.5 2.9 5.0 8.5 3.6 6.2 10.6
Fir, white 1.1 2.4 3.3 2.6 5.7 7.8 3.2 7.1 9.8
Hemlock:
Eastern 1.0 2.3 3.2 2.4 5.4 7.8 3.0 6.8 9.7
Western 1.4 2.6 4.0 3.4 6.3 9.5 4.3 7.9 11.9
Larch, western 1.4 2.7 4.4 3.4 6.5 10.6 4.2 8.1 13.2
Pine:
Eastern white 0.8 2.0 2.7 1.8 4.8 6.6 2.3 6.0 8.2
Lodgepole 1.5 2.2 3.8 3.6 5.4 9.2 4.5 6.7 11.5
Norway 1.5 2.4 3.8 3.7 5.8 9.2 4.6 7.2 11.5
Ponderosa 1.3 2.1 3.2 3.1 5.0 7.7 3.9 6.3 9.6
Southern (avg.) 1.6 2.6 4.1 4.0 6.1 9.8 5.0 7.6 12.2
Sugar 1.0 1.9 2.6 2.3 4.5 6.3 2.9 5.6 7.9
Western white 1.4 2.5 3.9 3.3 5.9 9.4 4.1 7.4 11.8
Redwood (old growth) 0.9 1.5 2.3 2.1 3.5 5.4 2.6 4.4 6.8
Spruce:
Engelmann 1.1 2.2 3.5 2.7 5.3 8.3 3.4 6.6 10.4
Sitka 1.4 2.5 3.8 3.4 6.0 9.2 4.3 7.5 11.5
TABLE 10.1 Shrinkage Values of Wood Based on Dimensions When Green (Continued)
Species
Dried to 20% MC*
Radial,
%
Tangential,
%
Volumetric,
%
Dried to 6% MC†
Radial,
%
Tangential,
%
Volumetric,
%
Dried to 0% MC
Radial,
%
Tangential,
%
Volumetric,
%
10.3
Hardwoods:‡
Ash, white 1.6 2.6 4.5 3.8 6.2 10.7 4.8 7.8 13.4
Beech, American 1.7 3.7 5.4 4.1 8.8 13.0 5.1 11.0 16.3
Birch:
Sweet 2.2 2.8 5.2 5.2 6.8 12.5 6.5 8.5 15.6
Yellow 2.4 3.1 5.6 5.8 7.4 13.4 7.2 9.2 16.7
Elm, rock 1.6 2.7 4.7 3.8 6.5 11.3 4.8 8.1 14.1
Gun, red 1.7 3.3 5.0 4.2 7.9 12.0 5.2 9.9 15.0
Hickory:
Pecan§ 1.6 3.0 4.5 3.9 7.1 10.9 4.9 9.8 13.6
True 2.5 3.8 6.0 6.0 9.0 14.3 7.5 11.3 17.9
Maple, hard 1.6 3.2 5.0 3.9 7.6 11.9 4.9 9.5 14.9
Oak:
Red 1.3 2.7 4.5 3.2 6.6 10.8 4.0 8.2 13.5
White 1.8 3.0 5.3 4.2 7.2 12.6 5.3 9.0 15.8
Poplar, yellow 1.3 2.4 4.1 3.2 5.7 9.8 4.0 7.1 12.3
*MC 
 moisture content, as a percent of oven-dry wood. These shrinkage values have been taken as one-third the
shrinkage to the oven-dry condition as given in the last three columns of this table.
† These shrinkage values have been taken as four-fifths of the shrinkage to the oven-dry condition as given in the
last columns of this table.
‡ The total longitudinal shrinkage of normal species from fiber saturation to oven-dry condition is minor. It usually
ranges from 0.17 to 0.3% of the green dimensions.
§Average of butternut hickory, nutmeg hickory, water hickory, and pecan.
10.4 SECTION TEN
this structure, structural properties depend on grain orientation. While most structural
materials are essentially isotropic, with nearly equal properties in all directions,
wood has three principal grain directions—longitudinal, radial, and tangential.
Loading in the longitudinal direction is referred to as parallel to the grain, whereas
transverse loading is considered to be across the grain. Parallel to the grain, wood
possesses high strength and stiffness characteristics. Across the grain, strength and
stiffness are much lower. In tension, wood stressed parallel to the grain is 25 to 40
times stronger than when stressed across the grain. In compression, wood loaded
parallel to the grain is 6 to 10 times stronger than when loaded perpendicular to
the grain. Furthermore, a wood member has three moduli of elasticity, with a ratio
of largest to smallest as large as 150:1.
Wood undergoes dimensional changes from causes different from those in most
other structural materials. For instance, thermal expansion of wood is so small as
to be unimportant in ordinary usage. Significant dimensional changes, however,
occur because of gain or loss in moisture. Swelling and shrinkage caused by moisture
changes vary in the three grain directions; these size changes are about 5 to
11% tangentially, 3 to 7% radially, but only 0.1 to 0.3% longitudinally. Table 10.1
gives shrinkage values for some commonly used species of wood.
Wood offers numerous advantages in construction applications—warmth and
beauty, versatility, durability, workability, low cost per pound, high strength-toweight
ratio, good electrical insulation, low thermal conductance, and excellent
strength at low temperatures. It has high shock-absorption capacity. It can withstand
good wearing qualities, particularly on end grain. It can be bent easily to relatively
sharp curative. A wide range of finishes can be applied for decorative or protective
purposes. Wood can be used in both wet and dry applications. Preservative treatments
are available for use when necessary, as are fire retardants (not appropriate
for all wood products). Also, there is a choice of a wide range of species with a
range of unique properties.
In addition, a wide variety of wood framing systems is available. The intended
use of a structure, geographical location, configuration required, cost, and many
other factors determine the best framing system to be used for a particular project.
Wood is naturally resistant to many chemicals that are highly corrosive to other
materials. It is superior to many building materials in resistance to mild acids,
particularly at ordinary temperatures. It has excellent resistance to most organic
acids, notably acetic. However, wood is seldom used in contact with solutions that
are more than weakly alkaline. Oxidizing chemicals and solutions of iron salts, in
combination with damp conditions, should be avoided.
Wood is composed of roughly 50 to 70% cellulose, 25 to 30% lignin, and 5%
extractives with less than 2% protein. Acids such as acetic, formic, lactic, and boric
do not ionize sufficiently at room temperature to attack cellulose, and thus do not
harm wood.
When the pH of aqueous solutions of weak acids is 2 or more, the rate of
hydrolysis of cellulose is small and dependent on the temperature. A rough approximation
of this temperature effect is that, for every 20
F increase, the rate of
hydrolysis doubles. Acids with pH values above 2, or bases with pH below 10,
have little weakening effect on wood at room temperature, if the duration of exposure
is moderate.
Design Recommendations. The following recommendations aim at achieved economical
designs with wood framing:
Use standard sizes and grades of lumber. Consider using standardized structural
components, whether lumber, stock glued-laminated beams, or other framing
members designed for structural adequacy, efficiency, and economy.
WOOD CONSTRUCTION 10.5
TABLE 10.2 Typical Span Range for Main Wood Framing Members
Framing member
Typical
span range,
ft
Roof beams
Simple span:
Constant depth
Solid-sawn 10–25
SCL 10–40
Glulam 20–100
Tapered glulam 25–100
Double-tapered pitched and curved glulam beams 25–100
Curved glulam beams 25–100
Simple beam with overhangs (overhangs typically limited to 25% of main
span)
Solid-sawn 10–25
Glulam 10–100
Continuous span:
Solid-sawn 10–25
Glulam 10–50
Glulam arches:
Three-hinged:
Gothic 40–100
Tudor 40–120
A-frame 20–100
Three-centered 40–250
Parabolic 40–250
Radial 40–250
Two-hinged
Radial 50–200
Parabolic 50–200
Roof trusses:
Flat or parallel chord 25–100
Triangular or pitched 25–100
Bowstring 50–200
Domes 200–500
Simple-span floor beams:
Solid sawn 6–20
Glulam 10–40
SCL 10–40
Continuous floor beams 10–40
Roof sheathing and decking:
1-in sheathing 1–4
2-in sheathing 6–10
3-in roof deck 8–15
4-in roof deck 12–20
* Not applicable.
10.6 SECTION TEN
Use standard details wherever possible. Avoid specially designed and manufactured
connecting hardware.
Use as simple and as few joints as possible. Place splices, when required, in
areas of lowest stress. Do not locate splices where bending moments are large,
thus avoiding design, installation, and fabrication difficulties.
Avoid unnecessary variations in cross section of members along their length.
Use identical member designs repeatedly throughout a structure, whenever practicable.
Keep the number of different arrangements to a minimum.
Specify required design stresses to permit the widest range of products that can
be used for a given design situation.
Use wood products pressure treated with preservatives where service conditions
dictate. Such treatment need not be used where decay or insect attack hazards
do not exist. Fire-retardant treatments may be used to meet a specific flamespread
rating for interior finish, but are not necessary for large-cross-sectional
members that are widely spaced and have a natural resistance to fire because of
their relatively large size.
Instead of long, simple spans, consider using continuous or suspended spans or
simple spans with overhangs.
Select an appearance grade best suited to the project. Do not specify the highest
quality appearance grade available for all members if it is not required.
Table 10.2 may be used as a general guide to typical ranges of spans for roof
and main floor framing members (excluding repetitive member joist and rafter applications).
10.2 SECTIONAL PROPERTIES OF WOOD
PRODUCTS
Dressed sizes of sawn lumber are given in the grading rules of agencies that formulate
and maintain such rules and in Table 10.3. The nominal and dressed sizes
are developed in accordance with the American Softwood Lumber Standard, Voluntary
Product Standard PS 20-94. These sizes are generally available, but it is
good practice to consult suppliers before specifying sizes not commonly used to
find out what sizes are on hand or can be readily secured.
The supplement to the ‘‘National Design Specification
 for Wood Construction’’
published by the American Forest & Paper Association (formerly the National Forest
Products Association) presents tables of section properties of standard dressed
sawn lumber and glulam timber. Standard finished sizes of structural glulam timber
should be used to the extent that conditions permit. These standard finished sizes
are based on lumber sizes given in Voluntary Product Standard PS 20-94. Other
finished sizes may be used to meet the size requirements of a design, or to meet
other special requirements.
For the manufacture of glulam nominal 2-in-thick lumber, surfaced to 13?8 in or
11?2 in before gluing, is used to laminate straight members and curved members
having radii of curvature within the bending-radius limitations for the species. Nominal
1-in-thick lumber, surfaced to 3?4 in before gluing, may be used for laminating
WOOD CONSTRUCTION 10.7
TABLE 10.3 Nominal and Minimum Dressed Sizes of Sawn Lumber
Item
Thickness, in
Nominal
Minimum dressed
Dry* Green†
Face width, in
Nominal
Minimum dressed
Dry* Green†
Boards 1 3?4 25?32 2 11?2 19?16
11?4 1 11?32 3 21?2 29?16
11?2 11?4 19?32 4 31?2 39?16
5 41?2 45?8
6 51?2 55?8
7 61?2 65?8
8 71?4 71?2
9 81?4 81?2
10 91?4 91?2
11 101?4 101?2
12 111?4 111?2
14 131?4 131?2
16 151?4 151?2
Dimension 2 11?2 19?16 2 11?2 19?16
Lumber 21?2 2 21?16 3 21?2 29?16
3 21?2 29?16 4 31?2 39?16
31?2 3 31?16 5 41?2 45?8
4 31?2 39?16 6 51?2 55?8
41?2 4 41?16 8 71?4 71?2
10 91?4 91?2
12 111?4 111?2
14 131?4 131?2
16 151?4 151?2
Timbers 5 and
thicker
1?2 in
less
5 and
wider
1?2 in
less
* Dry lumber is defined as lumber seasoned to a moisture content of 19% or less.
† Green lumber is defined as lumber having a moisture content is excess of 19%.
curved members when the bending radius is too tight to permit use of nominal 2-
in-thick laminations. Other lamination thicknesses may be used to meet special
curving requirements.
Standard sizes and grades of structural panels are given in U.S. Product Standard
PS 1-95 for Construction and Industrial Plywood and ‘‘Performance Standard for
Wood-Based Structural-Use Panels,’’ Voluntary Product Standard, PS 2-92. See also
Art. 10.12.
Weight and Specific Gravity. Specific gravity is a reliable indicator of fiber content.
Also, specific gravity and the strength and stiffness of solid wood or laminated
products are interrelated. See Table 10.4 for weights and specific gravities of several
commercial lumber species.
10.8
TABLE 10.4 Weights and Specific Gravities of Commercial Lumber Species
Species
Specific
gravity
based on
oven-dry
weight
and volume
at 12%
moisture
content
Weight, lb per ft3
At 12%
moisture
content
At 20%
moisture
content
Adjusting
factor
for each
1% change
in moisture
content
Moisture
content
when
green
(avg), %
Specific
gravity
based on
oven-dry
weight
and volume
when
green
Weight
when
green,
lb per ft3
Softwoods:
Cedar:
Alaska 0.44 31.1 32.4 0.170 38 0.42 35.5
Incense 0.37 25.0 26.4 0.183 108 0.35 42.5
Port Orford 0.42 29.6 31.0 0.175 43 0.40 35.0
Western red 0.33 23.0 24.1 0.137 37 0.31 26.4
Cypress, southern 0.46 32.1 33.4 0.167 91 0.42 45.3
Douglas fir:
Coast region 0.48 33.8 35.2 0.170 38 0.45 38.2
Inland region 0.44 31.4 32.5 0.137 48 0.41 36.3
Rocky Mountain 0.43 30.0 31.4 0.179 38 0.40 34.6
Fir, white 0.37 26.3 27.3 0.129 115 0.35 39.6
Hemlock:
Eastern 0.40 28.6 29.8 0.150 111 0.41 43.4
Western 0.42 29.2 30.2 0.129 74 0.38 37.2
Larch, western 0.55 38.9 40.2 0.170 58 0.51 46.7
Pine:
Eastern white 0.35 24.9 26.2 0.167 73 0.36 35.1
Lodgepole 0.41 28.8 29.9 0.142 65 0.38 36.3
Norway 0.44 31.0 32.1 0.142 92 0.41 42.3
Ponderosa 0.40 28.1 29.4 0.162 91 0.38 40.9
Southern shortleaf 0.51 35.2 36.5 0.154 81 0.46 45.9
Southern longleaf 0.58 41.1 42.5 0.179 63 0.54 50.2
Sugar 0.36 25.5 26.8 0.162 137 0.35 45.8
Western white 0.38 27.6 28.6 0.129 54 9.36 33.0
TABLE 10.4 Weights and Specific Gravities of Commercial Lumber Species (Continued)
Species
Specific
gravity
based on
oven-dry
weight
and volume
at 12%
moisture
content
Weight, lb per ft3
At 12%
moisture
content
At 20%
moisture
content
Adjusting
factor
for each
1% change
in moisture
content
Moisture
content
when
green
(avg), %
Specific
gravity
based on
oven-dry
weight
and volume
when
green
Weight
when
green,
lb per ft3
10.9
Redwood 0.40 28.1 29.5 0.175 112 0.38 45.6
Spruce:
Engelmann 0.34 23.7 24.7 0.129 80 0.32 32.5
Sitka 0.40 27.7 28.8 0.145 42 0.37 32.0
White 0.40 29.1 29.9 0.104 50 0.37 33.0
Hardwoods:
Ash, white 0.60 42.2 43.6 0.175 42 0.55 47.4
Beech, American 0.64 43.8 45.1 0.162 54 0.56 50.6
Birch:
Sweet 0.65 46.7 48.1 0.175 53 0.60 53.8
Yellow 0.62 43.0 44.1 0.142 67 0.55 50.8
Elm, rock 0.63 43.6 45.2 0.208 48 0.57 50.9
Gum 0.52 36.0 37.1 0.133 115 0.46 49.7
Hickory:
Pecan 0.66 45.9 47.6 0.212 63 0.60 56.7
Shagbark 0.72 50.8 51.8 0.129 60 0.64 57.0
Maple, sugar 0.63 44.0 45.3 0.154 58 0.56 51.1
Oak:
Red 0.63 43.2 44.7 0.187 80 0.56 56.0
White 0.68 46.3 47.6 0.167 68 0.60 55.6
Poplar, yellow 0.42 29.8 31.0 0.150 83 0.40 40.5
10.10 SECTION TEN
10.3 DESIGN VALUES FOR LUMBER AND
TIMBER
Design values for an extensive range of sawn lumber and timber are tabulated in
the supplement to the ‘‘National Design Specification
 for Wood Construction,’’
(NDS), American Forest & Paper Association (AF&PA).
10.3.1 Lumber
Design values for lumber are contained in grading rules established by the National
Lumber Grades Authority (Canadian), Northeastern Lumber Manufacturers Association,
Northern Softwood Lumber Bureau, Redwood Inspection Service, Southern
Pine Inspection Bureau, West Coast Lumber Inspection Bureau, and Western Wood
Products Association. The rules and the design values in them have been approved
by the Board of Review of the American Lumber Standards Committee. They also
have been certified for conformance with U.S. Department of Commerce Voluntary
Product Standard PS 20-94 (American Softwood Lumber Standard).
In addition, design values for visually graded lumber may be established in
accordance with ASTM D1990, ‘‘Standard Practice for Establishing Allowable
Properties for Visually-Graded Dimensional Lumber from In-Grade Tests of Full-
Size Specimens.’’ Design values for visually graded timbers, decking, and some
species and grades of dimension lumber are based on provisions of ‘‘Establishing
Structural Grades and Related Allowable Properties for Visually Graded Lumber,’’
ASTM D245. ASTM D245 also specifies adjustments to be made in the strength
properties of small clear specimens of wood, as determined in accordance with
‘‘Establishing Clear Wood Strength Values,’’ ASTM D2555, to obtain design values
applicable to normal conditions of service. The adjustments account for the effects
of knots, slope of grain, splits, checks, size, duration of load, moisture content, and
other influencing factors. Lumber structures designed with working stresses derived
from D245 procedures and standard design criteria have a long history of satisfactory
performance.
Design values for machine stress-rated (MSR) lumber and machine-evaluated
lumber (MEL) are based on nondestructive tests of individual wood pieces. Certain
visual-grade requirements also apply to such lumber. The stress rating system used
for MSR lumber and MEL is checked regularly by the responsible grading agency
for conformance with established certification and quality-control procedures.
10.3.2 Glued-Laminated Timber
Design values for glulam timber, developed by the American Institute of Timber
Construction (AITC) and Engineered Wood Systems (EWS) in accordance with
principles originally established by the U.S. Forest Products Laboratory, are included
in the supplement to the NDS. The principles are the basis for the ‘‘Standard
Method for Establishing Stresses for Structural Glued-Laminated Timber (Glulam),’’
ASTM D3737 which specifies procedures for obtaining design values that account
for the effects of knots, slope of grain, density, size of member, curvature, number
of laminations, and other factors unique to glulam. The satisfactory performance
of structures made with glulam members conforming to AITC and EWS specifi-
cations and manufactured in accordance with ‘‘Structured Glued-Laminated TimWOOD
CONSTRUCTION 10.11
ber,’’ ANSI A190.1, demonstrates the validity of the methods used to establish
glulam design values.
10.4 STRUCTURAL GRADING OF WOOD
Strength properties of wood are closely related to moisture content and specific
gravity. Therefore, data on strength properties should be accompanied by corresponding
data on these physical properties.
The strength of wood is actually affected by many other factors, including loading
rate, load duration, temperature, grain direction, and position of growth rings.
Strength is also influenced by inherent growth characteristics, including knots, slope
of grain, shakes, and checks. Analysis and integration of available data have yielded
a comprehensive set of principles for grading structural lumber (Art. 10.3.1).
The same characteristics that reduce the strength of solid timber also affect the
strength of glued-laminated (glulam) members (Art. 10.3.2). There are, however,
additional factors peculiar to glulam flexural members that should be considered.
For example, knots located near the neutral axis, which is a region of low bending
stress, have less effect on strength than knots closer to the outer surfaces, where
bending stresses are higher. Thus, strength of a flexural member with low-grade
laminations can be improved by substitution of higher grade laminations at the top
and bottom of the member.
Dispersement of knots in laminated members has a beneficial effect on strength.
With sufficient knowledge of the occurrence of knots within a grade, mathematical
estimates of the effect may be established for members containing various numbers
of laminations.
10.5 ADJUSTMENT FACTORS FOR
STRUCTURAL MEMBERS
Design values obtained by the methods described in Art. 10.3 should be multiplied
by adjustment factors based on conditions of use, geometry, and stability. The adjustments
are cumulative, unless specifically indicated in the following.
The adjusted design value for extreme-fiber bending is given by Fb
F 
 F C C CC C C C CC C (10.1) b b D M t L F V fu r c ?
where Fb 
 design value for extreme-fiber bending
CD 
 load duration factor (Art. 10.5.1)
CM 
 wet service factor (Art. 10.5.2)
Ct 
 temperature factor (Art. 10.5.3)
CL 
 beam stability factor (Arts. 10.5.5 and 10.7.2)
CF 
 size factor—applicable only to visually graded, sawn lumber and round
timber flexural members (Art. 10.5.4)
CV 
 volume factor—applicable only to glulam flexural members (Art.
10.5.6)
Cfu 
 flat-use factor—applicable only to dimension-lumber beams 2 to 4 in
thick and glulam beams with loads applied parallel to the wide face
of the laminations (Art. 10.5.7)
10.12 SECTION TEN
Cr 
 repetitive member factor—applicable only to dimension-lumber beams
2 to 4 in thick (Art. 10.5.8)
Cc 
 curvature factor—applicable only to curved portions of glulam beams
(Art. 10.5.9)
C? 
 form factor (Art. 10.5.10)
For glulam beams, use either CL or CV, whichever is smaller, not both, in Eq. (10.1).
The adjusted design value for tension is given by Ft
F 
 FC C CC (10.2) t t D M t F
where Ft 
 design values for tension.
For shear, the adjusted design value is computed from FV
F 
 F C C CC (10.3) V V D M t H
where FV 
 design value for shear and CH 
 shear stress factor  1—permitted
for FV parallel to the grain for sawn lumber members (Art. 10.5.13).
For compression perpendicular to the grain, the adjusted value is obtained Fc

from
F 
F C CC (10.4) c
 c
 M t b
where 
 design value for compression perpendicular to the grain and Cb 
 Fc

bearing area factor (Art. 10.5.11).
For compression parallel to the grain, the adjusted design value is given by Fc
F 
 F C C CC C (10.5) c c D M t F p
where Fc 
 design value for compression parallel to grain and Cp 
 column stability
factor (Arts. 10.5.11 and 10.8.1).
For end grain in bearing parallel to the grain, the adjusted design value is Fg
computed from
F 
 F C C (10.6) g g D t
where Fg 
 design value for end grain in bearing parallel to the grain. See also
Art. 10.11.1.
The adjusted design value for modulus of elasticity E is obtained from
E 
 EC C C (10.7) M t T
where E 
 design value for modulus of elasticity
CT 
 buckling stiffness factor—applicable only to sawn lumber truss compression
chords 2  4 in or smaller, when subject to combined bending
and axial compression and plywood sheathing 3?8 in or more thick is
nailed to the narrow face (Art. 10.5.12).
10.5.1 Load Duration Factor
Wood has the capacity to carry substantially greater loads for short periods of time
than for long periods. Design values described in Art. 10.3 apply to normal load
duration, which is equivalent to application of full design load for a cumulative
WOOD CONSTRUCTION 10.13
TABLE 10.5 Frequently Used Load Duration
Factors CD
Load duration CD Typical design loads
Permanent 0.9 Dead load
10 years 1.0 Occupancy live load
2 months 1.15 Snow load
7 days 1.25 Construction load
10 minutes 1.6 Wind or seismic load
Impact 2.0 Impact load
duration of about 10 years. The full design load is one that stresses a member to
its allowable design value. When the cumulative duration of the full design load
differs from 10 years, design values, except Fc
 for compression perpendicular to
grain and modulus of elasticity E, should be multiplied by the appropriate load
duration factor CD listed in Table 10.5.
When loads of different duration are applied to a member, CD for the load of
shortest duration should be applied to the total load. In some cases, a larger-size
member may be required when one or more of the shorter-duration loads are omitted.
Design of the member should be based on the critical load combination. If the
permanent load is equal to or less than 90% of the total combined load, the normal
load duration will control the design. Both CD and the modification permitted in
design values for load combinations may be used in design.
The duration factor for impact does not apply to connections. Load duration
factors greater than 1.6 shall not apply to structural members pressure-treated with
fire retardants or with waterborne preservatives.
10.5.2 Wet Service Factor
Sawn-lumber design values apply to lumber that will be used under dry service
conditions; that is, where moisture content (MC) of the wood will be a maximum
of 19% of the oven-dry weight, regardless of MC at time of manufacture. When
the MC of sawn lumber or timbers in service will exceed 19% for an extended
period of time, design values published in the supplement to the ‘‘National Design
Specification
 for Wood Construction’’ should be multiplied by the appropriate wet
service factor listed in Table 10.6. This reduction factor for timber does not apply
to southern pine.
MC of 19% of less is generally maintained in covered structures or in members
protected from the weather, including windborne moisture. Wall and floor framing
and attached sheathing are usually considered to be such dry applications. These
dry conditions are generally associated with an average relative humidity of 80%
or less. Framing and sheathing in properly ventilated roof systems are assumed to
meet MC criteria for dry conditions of use, even though they are exposed periodically
to relative humidities exceeding 80%.
Glulam-timber design values apply when the MC in service is less than 16%,
as in most covered structures. When MC of glulam timber under service conditions
is 16% or more, design values should be multiplied by the appropriate wet service
factor CM in Table 10.6.
10.14 SECTION TEN
TABLE 10.6 Wet Service Factors CM
Design
value
CM for sawn
lumber*
CM for glulam
timber†
CM for
timber
Fb 0.85‡ 0.80 1.0
Ft 1.0 0.80 1.0
FV 0.97 0.875 1.0
Fe
 0.67 0.53 0.67
Fc 0.80§ 0.73 0.91
E 0.90 0.833 1.00
*For use where moisture content in service exceeds 19%.
†For use where moisture content in service exceeds 16%.
‡CM 
 1.0 when FbCF  1150 psi.
§CM 
 1.0 when FcCF  750 psi.
TABLE 10.7 Temperature Factors Ct
Design values and
in-service moisture
conditions T  100
F 100
F  T  125
F 125
F  T  150
F
Ft and E, wet or dry 1.0 0.9 0.9
Fb, FV, Fc, and Fc

Dry 1.0 0.8 0.7
Wet 1.0 0.7 0.5
10.5.3 Temperature Factor
Design values apply to members used in ordinary temperature ranges. (Occasional
heating to 150
F is permissible.) Strength properties of wood, however, increase
when it is cooled below normal temperatures and decrease when it is heated. Members
heated in use to temperatures up to 150
F return essentially to original strength
when cooled. Prolonged exposure to temperatures above 150
F, however, may result
in permanent loss of strength. Design values for structural members that will experience
sustained exposure to elevated temperatures up to 150
F should be multiplied
by the appropriate temperature factor Ct listed in Table 10.7.
10.5.4 Size Factor
For visually graded dimension lumber, design values Fb, Ft, and Fc published in
the supplement to NDS for all species and species combinations, except southern
pine should be multiplied by the appropriate size factor CF given in Table 10.8 to
account for the effects of member size. This factor and the factors used to develop
size-specific values for southern pine are based on the adjustment equation given
in ASTM D1990. These factors, based on in-grade test data, account for differences
in Fb, Ft, and Fc related to width and in Fb and Ft related to length (test span).
For visually graded timbers (5  5 in or larger), when the depth d of a stringer,
beam, post, or timber exceeds 12 in, the design value for bending for all species
should be adjusted by the size factor
WOOD CONSTRUCTION 10.15
TABLE 10.8 Size Factors CF for Sawn Lumber
Fb
Grades Width, in
Thickness, in
2 and 3 4 Ft Fc
2, 3, and 4 1.5 1.5 1.5 1.15
Select 5 1.4 1.4 1.4 1.1
Structural, 6 1.3 1.3 1.3 1.1
No. 1 and better, 8 1.2 1.3 1.2 1.05
No. 1, No. 2, 10 1.1 1.2 1.1 1.0
No. 3 12 1.0 1.1 1.0 1.0
14 and wider 0.9 1.0 0.9 0.9
Stud 2, 3 and 4 1.1 1.1 1.1 1.05
5 and 6 1.0 1.0 1.0 1.0
Construction
and Standard
2, 3 and 4 1.0 1.0 1.0 1.0
Utility 4 1.0 1.0 1.0 1.0
2 and 3 0.4 0.4 0.6
1 / 9 C 
 (12/d) (10.8) F
10.5.5 Beam Stability Factor
Design values Fb for bending should be adjusted by multiplying by the beam stability
factor CL specified in Art. 10.7.2. For glulam beams, the smaller value of CL
and the volume factor CV should be used, not both. See also Art. 10.5.6.
10.5.6 Volume Factor
Design values for bending Fb for glulam beams should be adjusted for the effects
of volume by multiplying by
1 / x 21 12 5.125
C 
 K (10.9) 
      V L L d b
where L 
 length of beam between inflection points, ft
d 
 depth, in, of beam
b 
 width, in, of beam

 width, in, or widest piece in multiple piece layups with various widths
(thus, b  10.75 in)
x 
 20 for southern pine

 10 for other species
KL 
 loading condition coefficient (Table 10.9)
For glulam beams, the smaller of CV and the beam stability factor CL should be
used, not both.
10.16 SECTION TEN
TABLE 10.9 Loading Condition Coefficient KL for Glulam
Beams
Single-span beams
Loading condition KL
Concentrated load at midspan 1.09
Uniformly distributed load 1.0
Two equal concentrated loads at third points of span 0.96
Continuous beams of cantilevers
All loading conditions 1.0
TABLE 10.10 Flat-Use Factors Cfu for
Dimension Lumber
Width, in
Thickness, in
2 and 3 4
2 and 3 1.0
4 1.1 1.0
5 1.1 1.05
6 1.15 1.05
8 1.15 1.05
10 and wider 1.2 1.1
TABLE 10.11 Flat-Use Factors Cfu for
Glulam Beams
Lamination
width, in Cfu
103?4 or 101?2 1.01
83?4 or 81?2 1.04
63?4 1.07
51?8 or 5 1.10
31?8 or 3 1.16
21?2 1.19
10.5.7 Flat-Use Factor
Design values for sawn lumber beams adjusted by the size factor Cfu assume that
load will be applied to the narrow face. When load is applied to the wide face
(flatwise) of dimension lumber, design values should be multiplied by the appropriate
flat-use factor given in Table 10.10. These factors are based on the sizeadjustment
equation in ASTM D245. Available test results indicate that this equation
yields conservative values of Cfu.
When a glulam member is loaded parallel to the wide face of the laminations
and the member dimension parallel to the face is less than 12 in, the design value
for bending for such loading should be multiplied by the appropriate flat-use factor
in Table 10.11.
10.5.8 Repetitive Member Factor
Design values for bending Fb may be increased when three or more members are
connected so that they act as a unit. The members may be in contact or spaced up
to 24 in c to c if joined by transverse load-distributing elements that ensure action
of the assembly as a unit. The members may be any piece of dimension lumber
subjected to bending, including studs, rafters, truss chords, joists, and decking.
When the criteria are satisfied, the design value for bending of dimension lumber
2 to 4 in thick may be multiplied by the repetitive member factor Cr 
 1.15.
WOOD CONSTRUCTION 10.17
This factor applies to three or more essentially parallel members of equal size
and with the same orientation that are in direct contact with each other. Transverse
connecting elements may be mechanical fasteners, such as through nails, nail gluing,
tongue-and-groove joints, or bearing plates, that ensure that the members act
together to resist applied bending moments.
For spaced members, the transverse distributing elements should be acceptable
to the applicable regulatory agency and should be capable, as demonstrated by test,
analysis, or experience, of transmitting design loads without unacceptable deflections
or indications of structural weakness. The load may be uniform or concentrated,
or both, applied on the surface of the distributing element.
A transverse element attached to the underside of framing members and supporting
no uniform load other than its own weight and other incidental light loads,
such as insulation, qualifies as a load-distributing element only for bending moment
associated with its own weight and that of the framing members to which it is
attached. Qualifying construction includes subflooring, finish flooring, exterior and
interior wall finish, and cold-formed metal siding with or without backing. Such
elements should be fastened to the framing members by approved means, such as
nails, glue, staples, or snap-lock joints.
Individual members in a qualifying assembly made of different species or grades
are each eligible for the repetitive-member increase in Fb if they satisfy all the
preceding criteria.
10.5.9. Curvature Factor and Radial Stresses
For the curved portions of glulam beams, the design value for bending should be
multiplied by the curvature factor
2 C 
 1  2000(t /R) (10.10) c
where t 
 lamination thickness, in, and R 
 radius of curvature, in, of inside face
of lamination. t /R should not exceed 0.01 for hardwoods and southern pine or 0.008
for other softwoods. The curvature factor does not apply to design values of Fb for
the straight portions of a member, regardless of curvature elsewhere.
Radial Tension or Compression. The radial stress induced by a bending moment
in a member of constant cross section may be computed from
3M
? 
 (10.11) r 2Rbd
where M 
 bending moment, in-lb
R 
 radius of curvature at centerline of member, in
b 
 width of cross section, in
d 
 depth of cross section, in
When M is in the direction tending to decrease curvature (increase the radius),
tensile stresses occur across the grain. For this condition, the allowable tensile stress
across the grain is limited to one-third the allowable unit stress in horizontal shear
for southern pine for all load conditions, and for Douglas fir and larch for wind or
earthquake loadings. The limit is 15 psi for Douglas fir and larch for other types
10.18 SECTION TEN
TABLE 10.12 Bearing Area Factors Cb
Bearing length, in 0.50 1.00 1.50 2.00 3.00 4.00 6 or more
Bearing area factor 1.75 1.38 1.25 1.19 1.13 1.10 1.00
of loading. These values are subject to modification for duration of load. If these
values are exceeded, mechanical reinforcement sufficient to resist all radial tensile
stresses is required.
When M is in the direction tending to increase curvature (decrease the radius),
the stress is compressive across the grain. For this condition, the allowable stress
is limited to that for compression perpendicular to grain for all species.
(K. F. Faherty and T. G. Williamson, ‘‘Wood Engineering and Construction
Handbook,’’ and D. E. Breyer, ‘‘Design of Wood Structures,’’ 2d ed., McGraw-Hill
Publishing Company, New York.)
10.5.10 Form Factor
Design values for bending Fb for beams with a circular cross section may be multiplied
by a form factor C? 
 1.18. For a flexural member with a square cross
section loaded in the plane of the diagonal (diamond-shape cross section), C? may
be taken as 1.414.
These form factors ensure that a circular or diamond-shape flexural member has
the same moment capacity as a square beam with the same cross-sectional area. If
a circular member is tapered, it should be treated as a beam with variable cross
section.
10.5.11 Column Stability and Bearing Area Factors
Design values for compression parallel to the grain Fc should be multiplied by the
column stability factor CP specified in Art. 10.8.1.
Design values for compression perpendicular to the grain Fc
 apply to bearing
surfaces of any length at the ends of a member and to all bearings 6 in or more
long at other locations. For bearings less than 6 in long and at least 3 in from the
end of a member, Fc
 may be multiplied by the bearing area factor
L  0.375 b C 
 (10.12) b Lb
where Lb 
 bearing length, in, measured parallel to grain. Equation (10.12) yields
the values of Cb for elements with small areas, such as plates and washers, listed
in Table 10.12. For round bearing areas, such as washers, Lb should be taken as
the diameter.
10.5.12 Buckling Stiffness Factor
The buckling stiffness of a truss compression chord of sawn lumber subjected to
combined flexure and axial compression under dry service conditions may be inWOOD
CONSTRUCTION 10.19
creased if the chord is 2  4 in or smaller and has the narrow face braced by
nailing to wood structural panel sheathing at least 3?8 in thick in accordance with
good nailing practice. The increased stiffness may be accounted for by multiplying
the design value of the modulus of elasticity E by the buckling stiffness factor CT
in column stability calculations. When the effective column length Le, in, is 96 in
or less, CT may be computed from
K L M e C 
 1  (10.13) T K E T
where KM 
 2300 for wood seasoned to a moisture content of 19% or less at time
of sheathing attachment

 1200 for unseasoned or partly seasoned wood at time of sheathing
attachment
KT 
 0.59 for visually graded lumber

 0.75 for machine evaluated lumber (MEL)

 0.82 for products with a coefficient of variation of 0.11 or less
When Le is more than 96 in, CT should be calculated from Eq. (10.13) with Le 

96 in. For additional information on wood trusses with metal-plate connections, see
design standards of the Truss Plate Institute, Madison, Wis.
10.5.13 Shear Stress Factor
For dimension-lumber grades of most species or combinations of species, the design
value for shear parallel to the grain FV is based on the assumption that a split,
check, or shake that will reduce shear strength 50% is present (Art. 4.34). Reductions
exceeding 50% are not required inasmuch as a beam split lengthwise at the
neutral axis will still resist half the bending moment of a comparable unsplit beam.
Furthermore, each half of such a fully split beam will sustain half the shear load
of the unsplit member. The design value FV may be increased, however, when the
length of split or size of check or shake is known and is less than the maximum
length assumed in determination of FV, if no increase in these dimensions is anticipated.
In such cases, FV may be multiplied by a shear stress factor CH greater than
unity.
In most design situations, CH cannot be applied because information on length
of split or size of check or shake is not available. The exceptions, when CH can be
used, include structural components and assemblies manufactured fully seasoned
with control of splits, checks, and shakes when the products, in service, will not
be exposed to the weather. CH also may be used in evaluation of the strength of
members in service. The ‘‘National Design Specifications for Wood Construction,’’
American Forest & Paper Association, lists values of CH for lumber and timber of
various species.
10.6 PRESSURE-PRESERVATIVE TREATMENTS
FOR WOOD
Wood members are considered to be permanent without pressure treatment if located
in enclosed buildings where good roof coverage, proper roof maintenance,
10.20 SECTION TEN
good joint details, adequate flashing, good ventilation, and a well-drained site assure
moisture content of the wood continuously below 20%.
Where wood is in contact with the ground or with water, where there is air and
the wood may be alternately wet and dry, a preservative treatment, applied by a
pressure process, is necessary to obtain an adequate service life. In enclosed buildings
where moisture given off by wet-process operations maintains equilibrium
moisture contents in the wood above 19%, wood structural members must be preservatively
treated. So must wood exposed outdoors without protective roof covering
and where the wood moisture content can go above 19% for repeated or
prolonged periods.
Where wood structural members are subject to condensation by being in contact
with masonry or concrete, preservative treatment may be necessary.
Design values for wood structural members apply to products pressure-treated
by an approved process and with an approved preservative. (The ‘‘AWPA Book of
Standards,’’ American Wood Preservers Association, Granbury, TX, describes these
approved processes.) Design values for pressure-preservative treated lumber are
modified with the usual adjustment factors described in Art. 10.5 with one exception.
Load duration factors greater than 1.6 (Table 10.5) do not apply to structural
members pressure treated with waterborne preservatives or to structural members
treated with fire-retardant chemicals.
Each type of preservative and method of treatment has certain advantages. The
preservative to be used depends on the service expected of the member for the
specific conditions of exposure. The minimum retentions given in the applicable
American Wood Preservers Association (AWPA) standards for specific products and
end-use applications may be increased where severe climatic or exposure conditions
are involved.
Creosote and creosote solutions have low volatility. They are practically insoluble
in water, and thus are most suitable for severe exposure, contact with ground
or water, and where painting is not a requirement or a creosote odor is not objectionable.
Oilborne chemicals are organic compounds dissolved in an approved petroleum
carrier oil, and are suitable for outdoor exposure or where leaching may be a factor,
or where painting is not required. Depending on the type of oil used, they may
result in relatively clean surfaces. While there is a slight odor from such treatment,
it is usually not objectionable.
Waterborne inorganic salts are dissolved in water or aqua ammonia, which evaporates
after treatment and leaves the chemicals in the wood. The strength of solutions
varies to provide net retention of dry salt required. These salts are suitable
where clean and odorless surfaces are required. The surfaces are paintable after
proper seasoning. See also Art. 4.36.
(‘‘Design of Wood-Frame Structures for Permanence,’’ WCD No. 6, American
Forest & Paper Association, Washington, D.C.)
Fire-retardant treatment with approved chemicals can make wood highly resistant
to the spread of fire. Although wood will char where exposed to fire or high
temperatures, even if it is treated with a fire retardant, chemicals will retard transmission
of heat and rate of destruction. Treated with adequate quantities of an
approved chemical, wood will not support combustion nor contribute fuel to a fire
and will cease to burn after the ignition source is removed. The fire retardant may
be applied as a paint or by impregnation under pressure. The latter is more effective.
It may be considered permanent if the wood is used where it will be protected from
the weather.
The effects of fire-retardant impregnation treatments on strength should be considered
in design. Design values, including those for connections, for lumber and
WOOD CONSTRUCTION 10.21
structural glued-laminated timber pressure treated with fire-retardant chemicals
should be obtained from the company providing the treatment and redrying service.
Load duration factors greater than 1.6 (Table 10.5) should not be applied to structural
members pressure-treated with fire-retardant chemicals.
10.7 DESIGN PROVISIONS FOR FLEXURAL
MEMBERS
Design of flexural members requires consideration primarily of bending and shear
strength, deflection, and end bearing.
10.7.1 Strength of Flexural Members
The stress induced in a beam (or other flexural member) when subjected to design
loads should not exceed the strength of the member. The maximum bending stress
?b at any section of a beam is given by the flexural formula
? 
 M/S (10.14) b
where M is the bending moment and S the section modulus. For a rectangular beam,
the section modulus is bd2 /6 and Eq. (10.14) transforms into
2 ? 
 6M/bd (10.15) b
where b is the beam width and d the depth. At every section of the beam, ?b should
be equal to or less than the design value for bending Fb adjusted for all end-use
modification factors (Art. 10.5).
Shear stress induced by design loads in a member should not exceed the allowable
design value for shear FV. For wood beams, the shear parallel to the grain,
that is, the horizontal shear, controls the design for shear. Checking the shear stress
perpendicular to the grain is not necessary inasmuch as the vertical shear will never
be a primary failure mode.
The maximum horizontal shear stress ?V in a rectangular wood beam is given
by
? 
 3V/2bd (10.16) V
where V is the vertical shear. In calculation of V for a beam, all loads occurring
within a distance d from the supports may be ignored. This is based on the assumption
that loads causing the shear will be transmitted at a 45
 angle through
the beam to the supports.
(K. F. Faherty and T. G. Williamson, ‘‘Wood Engineering and Construction
Handbook.’’ McGraw-Hill Publishing Company, New York.)
10.7.2 Beam Stability
Beams may require lateral support to prevent lateral buckling. Need for such bracing
depends on the unsupported length and cross-sectional dimensions of the members.
When buckling occurs, a member deflects in the direction of its least dimension b.
In a beam, b usually is taken as the width. If bracing precludes buckling in that
10.22 SECTION TEN
TABLE 10.13 Approximate Lateral-Support Rules for Lumber Flexural Members*
Depth-width ratio
(nominal dimensions) Rule
d/b  2 No lateral support required
2  d/b  4 Hold ends in position with full-depth blocking, bridging, hangers,
or other structural members
4  d/b  5 Hold ends in position and compression edge in line, e.g., with
direct connection of sheathing, decking, or joists
5  d/b  6 Hold ends in position and compression edge in line, as for 5 to
1, and provide adequate bridging or blocking at intervals not
exceeding 8 ft
6  d/b  7 Hold ends in position and both edges firmly in line
If a beam is subject to both flexure and compression parallel to grain, the ratio may be as
much as 5:1 if one edge is held firmly in line, e.g., by rafters (or roof joists) and
diagonal sheathing. If the combined loads will induce tension on the unbraced face of the
member, the ratio may be 6:1.
*From ‘‘National Design Specification for Wood Construction,’’ American Forest & Paper Association.
direction, deflection can still occur, but in the direction of the strong dimension.
Thus, the unsupported length L, width b, and depth d are key variables in formulas
for lateral support and for reduction of design values for buckling.
Design for lateral stability of flexural members is based on a function of Ld/b2.
The beam stability factor, CL, for lumber beams of rectangular cross section having
maximum depth-width ratios based on nominal dimensions, as summarized in Table
10.13, can be taken as unity.
No lateral support is required when the depth does not exceed the width of a
beam. In that case also, the design value for bending does not have to be adjusted
for lateral stability. Similarly, if continuous support prevents lateral movement of
the compression flange, and the ends at points of bearing are braced to prevent
rotation, then lateral buckling cannot occur and the design of value Fb need not be
reduced.
When the beam depth exceeds the width, lateral support should be provided at
end bearings. This support should be so placed as to prevent rotation of the beam
about the longitudinal axis. Unless the compression flange is braced at sufficiently
close intervals between supports, the design value should be adjusted for lateral
buckling.
The slenderness ratio RB for beams is defined by
L d e R 
 (10.17) B 2  b
The slenderness ratio should not exceed 50.
The beam stability factor CL may be calculated from
2 1  (F /F*) 1  (F /F*) F /F* bE b bE b bE b C
   (10.18) 
  L  1.9 1.9 0.95
WOOD CONSTRUCTION 10.23
TABLE 10.14 Effective Length Lc for Lateral Stability of Beams*
Loading Lu /d  7† Lu /d  7‡
Simple beam§
Uniformly distributed load 1.63Lu  3d 2.06Lu
Load concentrated at midspan 1.37Lu  3d 1.80Lu
Equal end moments 1.84Lu 1.84Lu
Equal concentrated loads at third points 1.68Lu 1.68Lu
Equal concentrated loads at quarter points 1.54Lu 1.54Lu
Equal concentrated loads at fifth points 1.68Lu 1.68Lu
Cantilever§
Uniformly distributed load 0.90Lu  3d 1.33Lu
Concentrated load on the end 1.44Lu  3d 1.87Lu
*As specified in the ‘‘National Design Specification for Wood Construction,’’
American Forest & Paper Association.
†Lu 
 clear span when depth d exceeds width b and lateral support is provided to
prevent rotational and lateral displacement at bearing points in a plane normal to the
beam longitudinal axis and no lateral support is provided elsewhere.
‡Lu 
 maximum spacing of secondary framing, such as purlins, when lateral support
is provided at bearing points and the framing members prevent lateral displacement
of the compression edge of the beam at the connections.
§For a conservative value of Le for any loading on simple beams or cantilevers,
use 2.06 Lu when Lu / d  7, and 1.63 Lu  3d when 7  Lu / d  14.3, and 1.84 Lu
when Lu / d  14.3.
where 
 F*b design value for bending multiplied by all applicable adjustment factors
except C?u, CV, and CL (Art. 10.5)
FbE 
 KbEE / 2 RB
KbE 
 0.438 for visually graded lumber

 0.561 for machine evaluated lumber (MEL)

 0.609 for products with a coefficient of variation of 0.11 or less
E 
 design modulus of elasticity multiplied by applicable adjustment factors
(Art. 10.5)
The effective length Le for Eq. (10.17) is given in Table 10.14 in terms of the
unsupported length of beam. Unsupported length is the distance between supports
or the length of a cantilever when the beam is laterally braced at the supports to
prevent rotation and adequate bracing is not installed elsewhere in the span. When
both rotational and lateral displacement are also prevented at intermediate points,
the unsupported length may be taken as the distance between points of lateral
support. If the compression edge is supported throughout the length of the beam
and adequate bracing is installed at the supports, the unsupported length is zero.
10.7.3 Deflection of Wood Beams
The design of many structural systems, particularly those with long span, may be
governed by deflection. Verifying structural adequacy based on allowable stresses
alone may not be sufficient to prevent excessive deflection. Limitations on deflection
may increase member stiffness.
10.24 SECTION TEN
TABLE 10.15 Recommended Beam-Deflection Limitations, in
(In Terms of Span, l, in)
Use classification Live load only
Dead load plus
live load
Roof beams:
Industrial l /180 l /120
Commercial and industrial:
Without plaster ceiling l /240 l /180
With plaster ceiling l /360 l /240
Floor beams:
Ordinary usage* l /360 l /240
Highway bridge stringers l /200 to l /300
Railway bridge stringers l /300 to l /400
* Ordinary usage classification is intended for construction in which walking
comfort, minimized plaster cracking, and elimination of objectionable springiness
are of prime importance. For special uses, such as beams supporting vibrating
machinery or carrying moving loads, more severe limitations may be
required.
Deflection of wood beams is calculated by conventional elastic theory. For example,
for a uniformly loaded, simple-span beam, the maximum deflection is computed
from
4  
 5wL /384EI (10.19)
where w 
 the uniform load
L 
 span
E 
 modulus of elasticity
I 
 moment of inertia
Deflection should not exceed limitations specified in the local building code nor
industry-recommended limitations. (See, for example, K. F. Faherty and T. G. Williamson,
‘‘Wood Engineering and Construction Handbook,’’ McGraw-Hill Publishing
Company, New York.) Deflections also should be evaluated with respect to
other considerations, such as possibility of binding of doors or cracking of partitions
or glass.
Table 10.15 gives recommended deflection limits, as a fraction of the beam span,
for timber beams. The limitation applies to live load or total load, whichever governs.
Glulam beams may be cambered to offset the effects of deflections due to design
loads. These members are cambered during fabrication by creation of curvature
opposite in direction to that of deflections under load. Camber, however, does not
increase stiffness. Table 10.16 lists recommended minimum cambers for glulam
beams.
Minimum Roof Slopes. Flat roofs have collapsed during rainstorms even though
they were adequately designed for allowable stresses and definite deflection limitations.
The failures were caused by ponding of water as increasing deflections
permitted more and more water to collect.
Roof beams should have a continuous upward slope equivalent to 1?4 in / ft between
a drain and the high point of a roof, in addition to minimum recommended
WOOD CONSTRUCTION 10.25
TABLE 10.16 Recommended Minimum Camber for
Glued-Laminated Timber Beams*
Roof beams† 11?2 times dead-load deflection
Floor beams‡ 11?2 times dead-load deflection
Bridge beams:§
Long span 2 times dead-load deflection
Short span 2 times dead-load plus 1?2 applied-load deflection
* Camber and Deflection, AITC 102, Appendix B, American Institute of Timber
Construction.
‡ The minimum camber of 11?2 times dead-load deflection will produce a
nearly level member under dead load alone after plastic deformation has occurred.
Additional camber is usually provided to improve appearance or provide necessary
roof drainage.
‡ The minimum camber of 11?2 times dead-load deflection will produce a
nearly level member under dead load alone after plastic deformation has occurred.
On long spans, a level ceiling may not be desirable because of the optical illusion
that the ceiling sags. For warehouse or similar floors where live load may remain
for long periods, additional camber should be provided to give a level floor under
the permanently applied load.
§ Bridge members are normally cambered for dead load only on multiple spans
to obtain acceptable riding qualities.
camber (Table 10.16), to avoid ponding. As a general guideline, when flat roofs
have insufficient slope for drainage (less than 1?4 in / ft), the stiffness of supporting
members should be such that a 5-lb / ft2 load will cause no more than 1?2-in deflection.
Because of ponding, snow loads or water trapped by gravel stops, parapet walls,
or ice dams magnify stresses and deflections from existing roof loads by
1
C 
 (10.20) p 3 4 1  WL /  EI
where Cp 
 factor for multiplying stresses and deflections under existing loads to
determine stresses and deflections under existing loads plus ponding
W 
 weight of 1 in of water on roof area supported by beam, lb
L 
 span of beam, in
E 
 modulus of elasticity of beam material, psi
I 
 moment of inertia of beam, in4
(Kuenzi and Bohannan, ‘‘Increases in Deflection and Stresses Caused by Ponding
of Water on Roofs,’’ Forest Products Laboratory, Madison, Wis.)
10.7.4 Bearing Stresses in Beams
Bearing stresses, or compression stresses perpendicular to the grain, in a beam occur
at the supports or at places where other framing members are supported on the
beam. The compressive stress in the beam ?c
 is given by
? 
 P/A (10.21) c

where P 
 load transmitted to or from the beam and A 
 bearing area. This stress
should be less than the design value for compression perpendicular to the grain Fc

10.26 SECTION TEN
multiplied by applicable adjustment factors (Art. 10.5). (The duration-of-load factor
does not apply to Fc
 for either solid sawn lumber of glulam timber.)
Limitations on compressive stress perpendicular to the grain are set to keep
deformations within an acceptable range. An expected failure mode is excessive
localized deformation rather than a catastrophic type of failure.
Design values for Fc
 are averages based on a maximum deformation of 0.04
in in tests conforming with ASTM D143. Design values Fc
 for glulam beams are
generally lower than for solid sawn lumber with the same deformation limit. This
is due partly to use of larger-size sections for glulam beams, length of bearing and
partly to the method used to derive the design values.
Where deformations are critical, the deformation limit may be decreased, with
resulting reduction in Fc
. For example, for a deformation maximum of 0.02 in.
the ‘‘National Design Specification for Wood Construction,’’ American Forest &
Paper Association, recommends that Fc
, psi, be reduced to 0.73 Fc
.
10.7.5 Example of Design of a Glulam Beam
Standard beam formulas for bending, shear, and deflection may be used to determine
beam sizes. Ordinarily, bending deflection governs design; but for short, heavily
loaded beams, shear may control.
Design values for bending are tabulated in the supplement to the ‘‘National
Design Specification for Wood Construction.’’ These values should be adjusted for
service conditions (Art. 10.5). Section properties for solid sawn lumber and timber
and glulam members are listed in the supplement to the ‘‘National Design Speci-
fication for Wood Construction,’’ American Forest & Paper Association, Washington,
D.C.
With the following data, design a straight glued-laminated roof beam, simply
supported and uniformly loaded: span, 28 ft; spacing, 9 ft c to c; live load, such
as snow, 30 lb / ft2; dead load, 5 lb/ ft2 for deck and 7.5 lb / ft2 for roofing. Allowable
design value for bending of glulam combination grade is 2400 psi, and for horizontal
shear is 195 psi, for modulus of elasticity E 
 1,800,000 psi. These are
typical for a generic grade of glulam that can be manufactured using several different
species. Deflection limitation for total load is L/180, where L is the span, ft.
Assume the beam is laterally supported by the deck throughout its length.
With a 15% increase for load duration, such as snow, the allowable bending
stress Fb becomes 2760 psi, and the allowable horizontal shear FV, 224 psi.
Assume the beam will weigh 22.5 lb / lin ft, equivalent to 2.5 lb / ft2 based on a
9-ft c to c spacing. Thus, the total uniform load comes to 45 psf. So the beam
carries w 
 45  9 
 405 lb / lin ft.
The end shear V 
 wL/2 and the maximum shearing stress 
 3V/2 
 3wL/4.
Hence, the required area, in2, for horizontal shear is
3wL wL 405  28 2 A
 
 
 
37.9 in
4F 299 299 v
The required section modulus, in3, is
2 2 1.5wL 1.5  405  28 3 S
 
 
 172.6 in
F 2760 b
If D 
 180, the reciprocal of the deflection limitation, then the deflection equals
WOOD CONSTRUCTION 10.27
FIGURE 10.1 Cantilevered beam systems. A is a single cantilever,
B is a suspended beam. C has a double cantilever, and D is a beam
with the end suspended.
5  1728wL4 /384EI  12L/D, where I is the moment of inertia of the beam cross
section, in4. Hence, to control deflection, the moment of inertia must be at least
3 3 1.875DwL 1.875  180  405  28 4 I
 
 
 1688 in (10.22)
E 1,800,000
Assume that the beam will be fabricated with 11?2-in laminations. From the table
of section properties in the supplement to ‘‘National Design Specification for Wood
Construction,’’ the most economical section satisfying all three criteria is 51?8 
161?2, with A 
 84.6, S 
 232.5, and I 
 1919. But it has a volume factor of
0.94%, assuming western species are used. So the allowable bending stress must
be reduced to 2760  0.94 
 2594 psi. And the required section modulus must be
increased accordingly to 172.6/0.94 
 183.6. The selected section still is adequate.
10.7.6 Cantilevered-Span Construction
Cantilever systems may be composed of any of the various types and combinations
of beam illustrated in Fig. 10.1. Cantilever systems permit longer spans or larger
loads for a given size member than do simple-span systems, if member size is not
controlled by compression perpendicular to grain at the supports or by horizontal
shear. Substantial design economies can be effected by decreasing the depths of the
members in the suspended portions of a cantilever system.
For economy, the negative bending moment at the supports of a cantilevered
beam should be equal in magnitude to the positive moment.
Consideration must be given to deflection and camber in cantilevered multiple
spans. When possible, roofs should be sloped the equivalent of 1?4 in per foot of
horizontal distance between the level of drains and the high point of the roof to
eliminate water pockets, or provisions should be made to ensure that accumulation
of water does not produce greater deflection and live loads than anticipated. Unbalanced
loading conditions should be investigated for maximum bending moment,
deflection, and stability.
(For further information on the design of cantilevered beam systems, see K. F.
Faherty and T. G. Williamson, ‘‘Wood Engineering and Construction Handbook,’’
2d ed., McGraw-Hill Publishing Company, New York; D. E. Breyer, ‘‘Design of
Wood Structures,’’ 3d ed., McGraw-Hill Publishing Company, New York; ‘‘Wood
Structural Design Data,’’ American Forest and Paper Association, Washington,
D.C.)
10.28 SECTION TEN
FIGURE 10.2 Behavior of wood columns depends on length-thickness or length-depth
ratios: (a) solid wood column; (b) spaced column (the end distance for condition a should
not exceed L1 / 20 and for condition b should be between L1 / 20 and L1 / 10); (c) shear-plate
connectors in the end-block of the spaced column; (d) built-up column.
10.8 WOOD COMPRESSION MEMBERS
The design of wood columns or other types of compression members requires
consideration of compressive strength parallel to the grain, end bearing, and stability,
or resistance to buckling. Compressive strength considerations are the same
regardless of the type of column, since the maximum compressive stress ?c induced
by loads must not exceed the design value for compression parallel to the grain,
Fc, multiplied by applicable adjustment factors for service conditions (Art. 10.5).
(For design for end bearing, see Art. 10.11.1, and for stability, see Art. 10.8.1).
Wood compression members may be a solid piece of lumber or timber (Fig.
10.2a), or spaced columns, connector joined (Fig. 10.2b and c), or built-up (Fig.
10.2d).
10.8.1 Solid Columns
These consist of a single piece of lumber or timber or of pieces glued together to
act as a single member. In general,
? 
 P/A  F (10.23) c g c
where P 
 axial load on the column
Ag 
 gross area of column

 Fc design value in compression parallel to grain multiplied by the applicable
adjustment factors, including column stability factor CP
WOOD CONSTRUCTION 10.29
There is an exception, however, applicable when holes or other reductions in area
are present in the critical part of the column length most susceptible to buckling;
for instance, in the portion between supports that is not laterally braced. In that
case, ?c should be based on the net section and should not exceed Fc, the design
value for compression parallel to grain, multiplied by applicable adjustment factors,
except CP; that is,
? 
 P/A  F (10.24) c n c
where An 
 net cross-sectional area.
The stability factor represents the tendency of a column to buckle and is a
function of the slenderness ratio. For a rectangular wood column, a modified slenderness
ratio, Le /d, is used, where Le is the effective unbraced length of column,
and d is the smallest dimension of the column cross section. The effective column
length for a solid column should be determined in accordance with good engineering
practice. The effective length Le may be taken as the actual column length
multiplied by the appropriate buckling-length coefficient Ke. For the solid column
in Fig. 10.2a, the slenderness ratio should be taken as the larger of the ratios Le1 /
d1 or Le2 /ds2, where each unbraced length is multiplied by the appropriate value of
Ke. For solid columns, Le /d should not exceed 50, except that during construction,
Le /d may be as large as 75.
The column stability factor CP is given by
2 1  (F / F*) 1  (F / F*) F /F* cE c cE c cE c C
   (10.25) 
  P  2c 2c c
where 
 F*c design value for compression parallel to the grain multiplied by all
applicable adjustment factors except CP
FcE 
 KcEE / (Le /d)2
E 
 modulus of elasticity multiplied by adjustment factors
KcE 
 0.3 for visually graded lumber

 0.384 for machine evaluated lumber (MEL)

 0.418 for products with a coefficient of variation less than 0.11
c 
 0.80 for solid sawn lumber

 0.85 for round timber piles

 0.90 for glulam timber
For a compression member braced in all directions throughout its length to prevent
lateral displacement, CP 
 1.0.
10.8.2 Built-up Columns
These often are fabricated by joining together individuals pieces of lumber with
mechanical fasteners, such as nails, spikes, or bolts, to act as a single member (Fig.
10.2d). Strength and stiffness properties of a built-up column are less than those of
a solid column with the same dimensions, end conditions, and material (equivalent
solid column). Strength and stiffness properties of a built-up column, however, are
much greater than those of an unconnected assembly in which individual pieces act
as independent columns. Built-up columns obtain their efficiency from the increase
in the buckling resistance of the individual laminations provided by the fasteners.
The more nearly the laminations of a built-up column deform together—that is, the
10.30 SECTION TEN
smaller the slip between laminations, under compressive load—the greater is the
relative capacity of the column compared with an equivalent solid column.
When built-up columns are nailed or bolted in accordance with provisions in
the ‘‘National Design Specification for Wood Construction,’’ American Forest &
Paper Association, the capacity of nailed columns exceeds 60% and of bolted builtup
columns, 75% of an equivalent solid column for all L/d ratios. The NDS contains
criteria for design of built-up columns based on tests performed on built-up
columns with various fastener schedules.
10.8.3 Spaced Columns
A wood spaced column consists of the following elements: (1) two or more individual,
rectangular wood compression members with their wide faces parallel; (2)
wood blocks that separate the members at their ends and one or more points between;
and (3) steel bolts through the blocks to fasten the components, with splitring
or shear-plate connectors at the end blocks (Fig. 10.2b). The connectors should
be capable of developing required shear resistance.
The advantage of a spaced column over an equivalent solid column is the increase
permitted in the design value for buckling for the spaced-column members
because of the partial end fixity of those members. The increased capacity may
range from 21?2 to 3 times the capacity of a solid column. This advantage applies
only to the direction perpendicular to the wide faces. Design of the individual
members in the direction parallel to the wide faces is the same for each as for a
solid column. The NDS gives design criteria, including end fixity coefficients, for
spaced columns.
10.9 TENSION MEMBERS
The tensile stress ?t parallel to the grain should be computed for the net section
area. This stress should not exceed the design value for tension parallel to grain Ft.
Designs that induce tensile stress perpendicular to the grain should be avoided.
The reason for this is that wood is weaker and more variable in tension perpendicular
to the grain than in other properties. Furthermore, these tensile properties have
not been extensively evaluated and published values are not readily available. When
tension perpendicular to grain cannot be avoided, mechanical reinforcement suffi-
cient to resist the stresses may be required. An example of a construction that
induces critical tensile stress perpendicular to grain is a load supported from a beam
from a point below the neutral axis. This practice should be avoided for medium
to heavy loads.
10.10 COMBINED BENDING AND AXIAL
LOADING
When a bending moment and an axial force act on a section of a structural member,
the effects of the combined stresses must be provided for in design of the member.
WOOD CONSTRUCTION 10.31
10.10.1 Bending and Axial Tension
Members subjected to combined bending and axial tension should be proportioned
to satisfy the interaction equations, Eqs. (10.26) and (10.27).
? ? t b   1 (10.26)
F F* t b
(?  ? )/ F**  1 (10.27) b t b
where ?t 
 tensile stress due to axial tension acting alone
?b 
 bending stress due to bending moment alone

 Ft design value for tension multiplied by applicable adjustment factors

 F*b design value for bending multiplied by applicable adjustment factors
except CL

 F** b design value for bending multiplied by applicable adjustment factors
except CV
Adjustment factors are discussed in Art. 10.5.
The load duration factor CD associated with the load of shortest duration in a
combination of loads with differing duration may be used to calculate . F and F* t b
All applicable load combinations should be evaluated to determine the critical load
combination.
10.10.2 Bending and Axial Compression
Members subjected to a combination of bending and axial compression (beamcolumns)
should be proportioned to satisfy the interaction equation, Eq. 10.28.
2 ? ? ? c b1 b2    1 (10.28)   2 F [1  (? /F )] F [1  (? /F )  (? /F ) ]F c c cE1 b1 c cE2 b1 bE b2
where ?c 
 compressive stress due to axial compression acting alone

 Fc design value for compression parallel to grain multiplied by applicable
adjustment factors, including the column stability factor
?b1 
 bending stress for load applied to the narrow face of the member
?b2 
 bending stress for load applied to the wide face of the member

 Fb1 design value for bending for load applied to the narrow face of the
member multiplied by applicable adjustment factors, including the
beam stability factor

 Fb2 design value for bending for load applied to the wide face of the member
multiplied by applicable adjustment factors, including the beam
stability factor
For either uniaxial or biaxial bending, ?c should not exceed
2 F 
K E/ (L /d ) (10.29a) cE1 cE e1 1
Also, for biaxial bending, ?c should not exceed
2 F 
K E/ (L /d ) (10.29b) cE2 cE e2 2
and ?b1 should not be more than
10.32 SECTION TEN
2 F 
K E /R (10.30) bE bE B
FIGURE 10.3 Beam-column.
where d1 
 width of the wide face (Fig.
10.3) and d2 
 width of the narrow face
(Fig. 10.3). Slenderness ratio RB for
beams is given by Eq. (10.17). KbE is
defined for Eq. (10.18). The effective
column lengths Le1 for buckling in the
d1 direction and Le2 for buckling in the
d2 direction, E, FcE1, and FcE2 should be
determined in accordance with Art.
10.8.1. Adjustment factors are discussed
in Art. 10.5. The load duration factor CD should be applied in calculation of
as indicated for combined bending and axial tension. F, and F , and F c b1 b2
10.11 BEARING STRESSES
These may occur in a wood structural member parallel to the grain (end bearing),
perpendicular to the grain, or at an angle to the grain.
10.11.1 Bearing Parallel to Grain
The bearing stress parallel to grain ?g should be computed for the net bearing area.
This stress may not exceed the design value for bearing parallel to grain Fg multiplied
by load duration factor CD and temperature factor Ct (Art. 10.5). The adjusted
design value applies to end-to-end bearing of compression members if they have
adequate lateral support and their end cuts are accurately squared and parallel to
each other.
When ?g exceeds 75% of the adjusted design value, the member should bear on
a metal plate, strap, or other durable, rigid, homogeneous material with adequate
strength. In such cases, when a rigid insert is required, it should be a steel plate
with a thickness of 20 ga or more or the equivalent thereof, and it should be inserted
with a snug fit between abutting ends.
10.11.2 Bearing Perpendicular to Grain
This is equivalent to compression perpendicular to grain. The compressive stress
should not exceed the design value perpendicular to grain multiplied by applicable
adjustment factors, including the bearing area factor (Art. 10.5.11). In the calculation
of bearing area at the end of a beam, an allowance need not be made for the
fact that, as the beam bends, it creates a pressure on the inner edge of the bearing
that is greater than at the end of the beam.
10.11.3 Bearing at an Angle to Grain
The design value Fg for bearing parallel to grain and the design value for bearing
perpendicular to grain Fc
 differ considerably. When load is applied at an angle 	
WOOD CONSTRUCTION 10.33
FIGURE 10.4 Load applied to a wood member at an angle
to the grain.
with respect to the grain, where 0  	  90
 (Fig. 10.4), the design value for
bearing lies between Fg and Fc
. The ‘‘National Design Specification for Wood
Construction,’’ American Forest & Paper Association, recommends that the design
value for such loading be calculated from the Hankinson formula:
FF g c
 F 
 (10.31) 	 2 2 F sin 	 F cos 	 g c

where 
 F	 adjusted design value for bearing at angle 	 to the grain (longitudinal
axis)

 Fg design value for end bearing multiplied by applicable adjustment factors

 Fc
 design value for compression perpendicular to grain multiplied by
applicable adjustment factors
10.12 STRUCTURAL PANELS
Wood-based structural panels are thin, flat, composite materials capable of resisting
applied loads in specific applications. Structural panels fall into three basic categories
based on the manufacturing process used: plywood, mat-formed panels (oriented
strand board, or OSB), and composite panels.
Plywood—a flat panel built up of sheets of veneer, called plies. These are united
under pressure by a bonding agent. The adhesive bond between plies is as strong
as or stronger than solid wood. Plywood is constructed of an odd number of layers
with the grain of adjacent layers perpendicular. Layers may consist of a single ply
or two or more plies laminated with parallel grain direction. Outer layers and all
odd-numbered layers generally have the grain direction oriented parallel to the long
dimension of the panel. The odd number of layers with alternating grain direction
equalizes strains, reduces splitting, and minimizes dimensional change and warping
of the panel.
Mat-formed panel—any wood-based panel that does not contain veneer but is
consistent with the definition of structural-use panels, including products such as
waferboard and oriented strand board.
Oriented strand board—an engineered structural wood panel composed of
compressed wood strands arranged in layers at right angles to one another and
bonded with fully waterproof adhesive.
Composite panel—any panel containing a combination of veneer and other
wood-based materials.
10.34 SECTION TEN
A structural panel may contain either softwoods or hardwoods. Panels approved
for use in building-code-regulated construction carry the trademark of a codeapproved
agency, such as APA—The Engineered Wood Association. Most construction
grades have either an Exterior or Exposure 1 durability classification and are
made with fully waterproof adhesives. Exposure classifications are defined as follows:
Exterior—panels that are suitable for permanent exposure to weather or moisture.
Exposure 1—panels that are suitable for uses not permanently exposed to the
weather but may be used where exposure durability to resist effects of moisture
due to construction delays, high humidity, water leakage, or other conditions of
similar severity is required.
Exposure 2—panels that are suitable for interior use where exposure durability
to resist effects of high humidity and water leakage is required.
Interior—panels that are suitable for interior use where they will be subjected
to only temporary, minor amounts of moisture.
10.12.1 Standards for Structural Panels
Structural panels approved for building-code-regulated construction are manufactured
under one or more of three standards:
1. U.S. Product Standard PS 1-95 for Construction & Industrial Plywood (PS
1). It applies to plywood only. This voluntary product standard covers the wood
species, veneer grading, glue bonds, panel construction and workmanship, dimensions
and tolerances, marking, moisture content, and packing of plywood intended
for construction and industrial uses. Also included are test methods to determine
compliance and a glossary of trade terms and definitions. A quality certification
program is provided, whereby qualified testing agencies inspect, sample, and test
products identified as complying with the standard. Information regarding generally
available sizes, methods of ordering, and reinspecting practices also is provided.
2. Voluntary Product Standard PS 2-92, Performance Standard for Wood-Based
Structural-Use Panels (PS 2). It applies to all types of wood-based panels (typically
plywood, OSB, and composite). It establishes requirements for assessing the acceptability
of wood-based structural-use panels for construction sheathing and single-
floor applications. It also provides a basis for common understanding among
the producers, distributors, and users of these products. It covers performance requirements,
adhesive bond durability, panel construction and workmanship, dimensions
and tolerances, marking, and moisture content of structural-use panels. The
standard also includes test methods to determine compliance and a glossary of trade
terms and definitions. A quality certification program is provided, whereby qualified
testing agencies inspect, sample, and test products for qualification under the standard.
3. APA Performance Standards and Policies for Structural-Use Panels (PRP
108). It is similar to PS 2 but also includes performance-based qualification procedures
for siding panels.
10.12.2 Plywood Grades
Plywood grades are generally identified in terms of the veneer grade used on the
face and back of the panel; for example, A-B, B-C, . . . , or by a name suggesting
WOOD CONSTRUCTION 10.35
TABLE 10.17 Veneer-Grade Designations
Grade Description
N Smooth surface ‘‘natural finish’’ veneer. Select, all heartwood or all sapwood.
Free of open defects. Allows not more than six repairs, wood only, per 4-  8-ft
panel, made parallel to grain and well matched for grain and color.
A Smooth, paintable. Not more than 18 neatly made repairs, boat, sled, or router
type, and parallel to grain, permitted. May be used for natural finish in lessdemanding
applications. Synthetic repairs permitted.
B Solid surface. Shims, circular repair plugs, and tight knots up to 1 in across grain
permitted. Some minor splits and synthetic repairs permitted.
C
Plugged
Improved C veneer with splits limited to 1?8-in width and knotholes and borer
holes limited to 1?4  1?2 in. Admits some broken grain. Synthetic repairs
permitted.
C
Tight knots to 11?2 in. Knotholes up to 1 in across grain and some up to 11?2 in if
total width of knots and knotholes is within specified limits. Synthetic or wood
repairs and discoloration and sanding defects that do not impair strength
permitted. Limited splits allowed. Stitching permitted.
D Knots and knotholes up to 21?2-in wide across grain and 1?2 in larger within
specified limits, limited splits, and stitching permitted. Limited to Exposure 1 or
interior panels.
the panel’s intended end use, such as APA Rated Sheathing or APA Rated Sturd-
I-Floor.
Veneer grades define veneer appearance in terms of natural, unrepaired-growth
characteristics and allowable number and size of repairs that may be made during
manufacture (Table 10.17). The highest quality veneer grades are N and A. The
minimum grade of veneer permitted in Exterior plywood is C grade. D-grade veneer
is used in panels intended for interior use or applications protected from permanent
exposure to weather.
Panels with B-grade or better veneer faces are always sanded smooth in the
manufacturing process to fulfill the requirements of their intended end use—
applications such as cabinets, shelving, furniture, and built-ins. Rated Sheathing
panels are unsanded since a smooth surface is not a requirement of their intended
end use. Still other panels, such as Underlayment, Rated Sturd-I-Floor, C-D
Plugged, and C-C Plugged, require only touch sanding for ‘‘sizing’’ to make the
panel thickness more uniform.
Unsanded and touch-sanded panels, and panels with B-grade or better veneer
on one side only, usually carry the trademark on the panel back. Panels with both
sides of B-grade or better veneer, or with special overlaid surfaces, such as High-
Density Overlay, usually carry the trademark on the panel edge.
10.12.3 Plywood Group Number
Plywood can be manufactured from over 70 species of wood. These species are
divided on the basis of strength and stiffness into five groups under U.S. Product
Standard PS 1-95. Strongest species are in Group 1; the next strongest in Group 2,
etc. The group number that appears in the trademark on some APA trademarked
10.36 SECTION TEN
panels, primarily sanded grades, is based on the species used for face and back
veneers. Where face and back veneers are not from the same species group, the
higher group number is used, except for sanded panels 3?8 in thick or less and
decorative panels of any thickness. These are identified by face species if C or D
grade backs are at least 1?8 in thick and are not more than one species group number
larger. Some species are used widely in plywood manufacture, others rarely.
OSB panels, being composed of flakes or strands instead of veneers, are graded
without reference to veneers or species, and composite panels are graded on an
OSB performance basis by end use and exposure durability. Typical panel trademarks
for all three panel types and an explanation of how to read them are shown
in Fig. 10.5.
The ‘‘Design/Construction Guide—Residential & Commercial,’’ APA—The Engineered
Wood Association, Tacoma, Wash., contains a comprehensive summary
of plywood grades and trademarks and their applications.
10.12.4 Span Ratings for Panels
APA Rated Sheathing, APA Rated Sturd-I-Floor, and APA Rated Siding carry numbers
in their trademarks called span ratings. These denote the maximum spacing,
in, c to c of supports for panels in construction applications. Except for Rated Siding
panels, the span rating in the trademark applies when the long panel dimension is
across supports, unless the strength axis is otherwise identified. The span rating in
the trademark of Rated Siding panels applies when they are installed vertically.
The span rating in Rated Sheathing trademarks appears as two numbers separated
by a slash (Fig. 10.5a), such as 32/16 and 48/ 24. The left-hand number
denotes the maximum recommended spacing of supports when the panel is used
for roof sheathing with the long dimension or strength axis of the panel across three
or more supports. The right-hand number indicates the maximum recommended
spacing of supports when the panel is used for subflooring with the long dimension
or strength axis of the panel across three or more supports. A panel marked 32/
16, for example, may be used for roof decking over supports 32 in c to c or for
subflooring over supports 16 in c to c. An exception is Rated Sheathing intended
for use as wall sheathing only. The trademarks for such panels contain only a single
number similar to the span rating for APA Rating Siding and Sturd-I-Floor.
The Span Ratings in the trademarks on APA Rated Sturd-I-Floor and APA Rating
Siding panels appear as a single number. Rated Sturd-I-Floor panels are designed
specifically for single-floor (combined subfloor-underlayment) applications
under carpet and pad. They are manufactured with span ratings of 16, 20, 24, 32,
and 48 in.
APA Rated Siding is available with span ratings of 16 and 24 in. Span-rated
panels and lap siding may be connected directly to studs, or over nonstructural wall
sheathing, or over nailable panel or lumber sheathing (double-wall construction).
Panels and lap siding with a span rating of 16 in may be applied directly to studs
spaced 16 in c to c. Those bearing a span rating of 24 in may be connected directly
to studs 24 in c to c. All APA Rated Siding panels may be applied horizontally
directly to studs 16 or 24 in c to c, if horizontal joints are blocked. The span rating
of APA Rated Siding panels refers to the maximum recommended spacing of vertical
rows of nails rather than to stud spacing when the panels are applied to nailable
structural sheathing.
10.37
FIGURE 10.5 Typical trademarks for structural panels. (a) APA Rated Sheathing with a thickness of 15?32 in
and a span rating of 32 in for use as roof decking and 16 in for use as subflooring, suitable for Exposure 1
conditions (not permanently exposed to weather). (b) APA Rated Siding, grade 303-18-S /W, with a span rating
of 16 in. (c) APA Plyform, intended for use in formwork for concrete. (d) APA high-density overlay (HDO),
abrasion resistant and suitable for exterior applications (used for concrete forms, cabinets, countertops, and
signs). (e) APA Marine, used for boat hulls.
10.38 SECTION TEN
FIGURE 10.6 Floor construction with APA Rated Sturd-I-Floor.
10.12.5 Availability of Panel Grades
Some panel grades, thicknesses, span ratings, or species may be difficult to obtain
in some areas. Check with your supplier for availability or include an alternative
panel in specifications. Standard panel dimensions are 4  8 ft, although some
mills also produce plywood panels 9 or 10 ft long or longer. OSB panels may be
ordered in lengths up to 24 ft in some market areas.
10.12.6 APA Rated Sturd-I-Floor
APA Rated Sturd-I-Floor (copyrighted name) is a span-rated product designed specifically
for use in single-layer floor construction beneath carpet and pad. The maximum
spacing of floor joists, or span rating, is stamped on each panel. Panels are
manufactured with span ratings of 16, 20, 24, 32, and 48 in. These assume the
panel continuous over two or more spans with the long dimension or strength axis
across supports (Fig. 10.6). The span rating in the trademark applies when the long
panel dimension is across supports unless the strength axis is otherwise identified.
Glue-nailing is recommended, though panels may be nailed only. Application
provisions for both methods are given in Table 10.18. Uniform live loads are given
in the APA ‘‘Design/Construction Guide—Residential & Commercial.’’
10.12.7 Panel Subflooring
The limiting factor in design of floors is deflection under concentrated loads at
panel edges. Nailing provisions for APA panel subflooring (Fig. 10.7) are given in
Table 10.19. Other code-approved fasteners, however, may be used. The span ratings
in Table 10.19 applied to Rated Sheathing or sheathing grades only and are
the minimum for the span indicated. The span ratings assume panels continuous
over two or more spans with the long dimension or strength axis across supports.
10.39
TABLE 10.18 Fastener Size, Type, and Spacing for APA Rated Sturd-I-Floora
Span rating
(maximum joist
spacing), in
Minimum
panel
thickness, inb
Glue Nailedc
Nail size
and type
Spacing, in
Supported
panel edges
Intermediate
supports
Nailed Only
Nail size
and type
Spacing, in
Supported
panel edges
Intermediate
supportsd
16 19?32 6d ring- or 12 12 6d ring- or 6 12
5?8 screw-shanke screw-shank
20 19?32 6d ring- or 12 12 6d ring- or 6 12
5?8 screw-shanke screw-shank
23?32 6d ring- or 12 12 6d ring- or 6 12
24
3?4 screw-shanke screw-shank
7?8 8d ring- or 6 12 8d ring- or 6 12
screw-shanke screw-shank
32 7?8 8d ring- or 6 12 8d ring- or 6 12
screw-shanke screw-shank
48 3?32 8d ring- or 6 g 8d ring- or 6 g
1?8 screw-shank? screw-shank
a Heavy traffic and concentrated loads may require construction in excess of the minimum values in the table.
bPanels of a specific thickness may have more than one span rating. Panels with a span rating larger than the joist
spacing may be substituted for panels of the same thickness with a span rating equal to the joist spacing.
c Adhesives should conform to APA Specification AFG-01. Only solvent-based glues should be used for nonveneer
panels with sealed surfaces and edges.
d Local building code may require nail spacing 10 in c to c at intermediate supports for floors.
e 8d common nails may be used if these nails are not available.
? 10d common nails may be used with 11?8-in panels if supports are well seasoned.
g Nails should be spaced 6 in c to c for 48-in spans and 12 in c to c for 32-in spans.
10.40 SECTION TEN
FIGURE 10.7 Subfloor constructed of structural panels.
TABLE 10.19 Spans and Nailing for APA Panel Subflooringa
(APA Rated Sheathing)
Span rating
or group no.
Minimum panel
thickness, in
Maximum
span, in
Nail size
and typeb
Nail spacing, in
At
supported
edges
At
intermediate
supportsc
24/16 7?16 16 6d common 6 12
32/16 15?32, 1?2 16d 8d commone 6 12
40/20 19?32, 5?8 20d,? 8d common 6 12
48/24 23?32, 3?4 24 8d common 6 12
aFor recommendations for subfloors under ceramic tile, see the APA ‘‘Design / Construction Guide—
Residential and Construction.’’ For subfloors under gypsum concrete, obtain data from topping producers.
b Other code-approved fasteners may be used
c Local building codes may require nail spacing 10 c to c at intermediate supports for floors.
dA 24-in span may be used if 3?4-in-thick wood strip flooring is installed perpendicular to joists.
e If the panel is 1?2 in or less thick, 6d common nails are permitted.
?A 24-in span may be used if at least 11?2 in of lightweight concrete is applied over the panels.
Panel subflooring may also be glued for added stiffness and to reduce squeaks
if it satisfied nailing provisions in Table 10.18. Long edges should be tongue-andgroove
or supported with blocking unless:
1. A separate underlayment layer is installed with its joints offset from those in
the subfloor. The minimum thickness of underlayment should be 1?4 in for subfloors
on spans up to 24 in and 11?32 in or more on spans longer than 24 in.
2. A minimum of 11?2 in of lightweight concrete is applied over the panels.
3. A 3?4-in wood strip flooring is installed over the subfloor.
In some nonresidential buildings, greater traffic and heavier concentrated loads
may require construction in excess of the minimums given. Where joists are 16 in
WOOD CONSTRUCTION 10.41
FIGURE 10.8 Wall built of wood studs and APA Rated Siding panels. (a) Vertical panel siding.
If permitted by the local building and energy codes, no building paper is required when panel
edges are shiplapped, battened, and caulked. If caulking is not used with unbattened square butt
joints, apply a water repellent to panel edges. Caulk around windows and doors. (b) Horizontal
lap siding. Diagonal bracing or other code-approved bracing methods for the wall should be
provided. For engineered shear-wall segments, use APA Rated Sheathing under the lap siding.
(c) Siding joint details at a window.
c to c, for example, panels with a span rating of 40/20 or 48/24 provide greater
stiffness. For beams or joists 24 or 32 in c to c, 11?8-in-thick panels provide additional
stiffness.
10.12.8 Wall Systems
Rated siding (panel or lap) may be applied directly to studs or over nonstructural
fiberboard, or gypsum or rigid-foam-insulation sheathing. Nonstructural sheathing
is defined as sheathing not recognized by building codes as meeting both bending
and racking-strength requirements.
A single layer of panel siding, since it is strong and rack resistant, eliminates
the cost of installing separate structural sheathing or diagonal wall bracing. Panel
sidings are normally installed vertically (Fig. 10.8a), but most may also be placed
horizontally (long dimension across supports) if horizontal joints are blocked (Fig.
10.8b). Maximum stud spacings for both applications are given in Table 10.20.
10.42
TABLE 10.20 Recommended Installation of APA Rated Sturd-I-Wall
Siding
Descriptiona
Nominal
thickness, in,
or span rating
Maximum stud
spacing, in
Long
dimension
vertical
Long
dimension
horizontal
Nail size
(nonstaining
box, siding or
casing nails)b,c
Nail spacing,d in
At
panel edges
At
intermediate
supports
Panel
siding
APA MDO Exterior
APA Rated Siding
Exterior
11?32 and 3?8
15?32 and thicker
16
24
16
24
16
24
24
24
16e
24
6d for siding
1?2 in thick
or less;
8d for thicker
siding.
6e 12?
Lap
siding
APA Rating Siding—
Lap Exterior
16
24
16
24
6d for siding
1?2 in thick
or less;
8d for thicker
siding.
16 along
bottom edge
24 along
bottom edge
a Recommendations apply to all species groups for veneered APA Rated Siding, including APA 303 siding.
bNext regular size nailing should be used if panel siding is applied over foam-insulation sheathing. If lap siding is
installed over such sheathing up to 1 in thick, 10d (3-in) nails should be used for 3?8- or 7?16-in siding, 12d (31?4-in) nails
for 16?32- or 1?2-siding, and 16d (31?2-in) nails for 19?32-in or thicker siding. Nonstaining box nails should be used for
siding installed over foam-insulation sheathing.
c Hot-dipped or hot-tumbled galvanized steel nails are recommended for most siding applications, but electrically or
mechanically galvanized nails are acceptable if the plating meets or exceeds thickness requirements of ASTM A641
Class 2 coatings and is protected by a yellow chromate coating. For best performance, stainless steel or aluminum nails
are an alternative. Galvanized nails may react adversely under wet conditions with some wood species and cause staining
if left unfinished. Such staining can be minimized if the siding is finished in accordance with APA recommendations
or if the siding is protected by a roof overhang from direct exposure to moisture and weathering.
d Recommendations of siding manufacturers may vary.
e Nails should be spaced 3 in c to c along panel edges for a braced wall section with 11?32- or 3?8-in panel siding
applied horizontally over studs spaced 24 in c to c.
? Where wind velocity exceeds 80 mph, nails attaching siding to intermediate studs within 10% of the width of the
narrow side from wall corners should be spaced 6 in c to c.
g Stud spacing may be 24 in for veneer-faced siding panels.
WOOD CONSTRUCTION 10.43
FIGURE 10.9 Application of structural panels as sheathing. Building paper
is not required over the sheathing, except under stucco and brick veneer.
TABLE 10.21 Recommended Installation of APA Panel Wall Sheathinga
Panel
span rating
Maximum stud
spacing, in Nail sizeb
Nail spacing, in
At
supported
panel edges
At
intermediate
supports
12/0, 16/0, 20/0 or
Wall-16 in c to c
24/0, 24/16, 32/16
or Wall-24 in c to c
16
24
6d panels 1?2 in thick
or less; 8d for
thicker panels
6 12
a Applies to APA Rated Sheathing panels that are continuous over two or more spans. Different requirements
may apply to nailable panel sheathing when the exterior covering is to be nailed to the sheathing.
See the APA Design / Guide.
bFor common, smooth, annular, spiral-thread, or galvanized box nails. Other code approved fasteners,
however, may be used.
Rated Sheathing meets building-code wall-sheathing requirements for bending
and racking strength without let-in corner bracing. Installation provisions are given
in Table 10.21 and Fig. 10.9. When 1?2-in gypsum or fiberboard sheathing is used,
APA Rated Sheathing corner panels of the same thickness can also eliminate costly
let-in bracing. The APA Rated Sheathing, 15?32 or 1?2 in thick, should be nailed to
studs spaced 16 or 24 in c to c with 6d common nails spaced 6 in c to c along
panel edges and 12 in c to c at intermediate supports. When corner panels are PS
1 plywood, 11?2-in roofing nails at 4 in along panel edges and 12 in at intermediate
supports may be used.
10.44 SECTION TEN
TABLE 10.22 Typical APA Panel Considerations*
Span rating
Plywood
3-Ply 4-Ply 5-Ply† COM-PLY OSB
APA Rated Sheathing
24/0 X X
24/16 X
32/16 X X X X
40/20 X X X X
48/24 X X X
APA Rated Sturd-I-Floor
16 in c to c
20 in c to c X X X X
24 in c to c X X X X
32 in c to c X X X
48 in c to c X X X
* Constructions may not be available in every area. Check with suppliers
concerning availability.
† Applies to plywood with five or more layers.
Building paper is generally not required over wall sheathing, except under stucco
or under brick veneer where required by the local building code. Recommended
wall sheathing spans with brick veneer and masonry are the same as those for
nailable panel sheathing.
10.12.9 Allowable Loads for APA Structural-Use Panels
Because it is sometimes necessary to have engineering design information for structural
panel products for conditions not specifically covered in other literature, APA
publishes separate design-section capacities for the various span ratings for these
products. These values are listed in APA Technical Note N375, ‘‘Design Capacities
of APA Performance-Rated Structural-Use Panels.’’ The APA ‘‘Plywood Design
Specification’’ contains load-span tables that apply to APA trademarked structuraluse
panels qualified and manufactured in accordance with PS 2-92 or APA PRP-
108, ‘‘Performance Standards and Policies for Structural-Use Panels.’’ These panels
include plywood, composite, and mat-formed products, such as oriented strand
board. Loads are provided for applications where the panel strength axis is applied
across or parallel to supports. For each combination of span L and Span Rating,
loads are given for deflections of L/360, L/240 and L/180, and maximum loads
controlled by bending and shear capacity. The values may be adjusted for panel
type, load duration, span conditions, and moisture. Table 10.22 is provided to assist
in selecting panel constructions for specific span ratings.
Some structural-panel applications are not controlled by uniform loads. Residential
floors are a good example. They are commonly designed for 40-psf live
load. The allowable uniform floor load on panels with maximum span according
to APA recommendations is greatly in excess of typical design loads. This excess
does not mean that floor spans for structural panels can be increased, but only that
there is considerable reserve strength and stiffness for uniform loads. Actually, the
WOOD CONSTRUCTION 10.45
recommendations for panel floors are based on performance under concentrated
loads, how the floor ‘‘feels’’ to passing foot traffic, and other subjective factors that
relate to public acceptance. The maximum floor and roof spans for structural panels
should always be checked before a final panel selection is made for these applications.
10.12.10 Panel Shear Walls
While the wall systems described in Art. 10.12.8 will provide sufficient strength
under normal conditions in residential and light-frame construction, shear walls may
be desirable or required in areas with frequent seismic activity or high wind loads.
Shear walls are also advisable in commercial and industrial construction.
Either Rated Sheathing or all-veneer plywood Rated Siding can be used in shear
walls. Table 10.23 gives maximum shears for walls with Rated Sheathing, with
plywood Rated Siding installed directly to studs (Sturd-I-Wall), or with panels applied
over gypsum sheathing for walls required to be fired rated from the outside.
To design a shear wall, follow these steps:
1. Determine lateral loads and resulting shears with appropriate allowances for
openings.
2. Determine the required panel grade and thickness and the nailing schedule
from Table 10.23. Check the anchor bolts in the sill plate for shear.
3. Check wall framing on each end of the shear wall and design a foundation
anchor or hold-down, if required (see Fig. 10.10).
10.12.11 Panel Roof Sheathing
Table 10.24 lists maximum uniform roof live loads for APA Rated Sheathing Exposure
1, and Structural I Rated Sheathing, Exposure 1 or Exterior. Uniform-load
deflection limits are 1?180 of the span under live load plus dead load, and 1?240 under
live load only. Panels are assumed continuous over two or more spans with the
long dimension or strength axis across supports (Fig. 10.11). Special conditions,
such as heavy concentrated loads, may require constructions in excess of these
minimums, or allowable live loads may have to be decreased for dead loads greater
than 10 psf, for example, for tile roofs.
Good performance of built-up, single-ply, or modified bitumen roofing applied
on low-slope roofs requires a stiffer deck than does prepared roofing applied on
pitched roofs. Although Span-Rated panels used as roof sheathing at maximum
span are adequate structurally, an upgraded system is recommended for low-slope
roofs. Table 10.25 lists maximum spans for low-slope roof decks. Live loads can
be determined from Table 10.24, and minimum fastener requirements are given in
Table 10.26.
Rated Sheathing is equally effective under built-up roofing, asphalt or glass-fiber
shingles, tile roofing; or wood shingles or shakes. Roof trusses spaced 24 in c to c
are widely recognized as the most economical construction for residential roofs,
particularly when 3?8- or 7?16-in, 24/0 sheathing with panel clips is used. However,
use of fewer supports with thicker panels, for example, 23?32- or 3?4-in, 48/24 panels
over framing 48 in c to c, is also cost-effective for long-span flat or pitched roofs.
Live loads are given in Table 10.24. Nailing provisions are given in Table 10.26.
10.46
TABLE 10.23 Maximum Shear, lb / ft, for APA Panel Shear Walls for Wind or Seismic Loadinga
(For framing of Douglas fir, larch, or southern pine)b
Panel grade
Minimum
nominal
panel thickness,
in
Minimum nail
penetration
in framing,
in
Panels applied directly to framing
Nail size
(common or
galvanized
box)
Nail spacing at panel
edges, in
6 4 3 2c
Panels applied over 1?2-in or 5?8-in
gypsum sheathing
Nail size
(common or
galvanized
box)
Nail spacing at
panel edges, in
6 4 3 2c
5?16 11?4 6d 200 300 390 510 8d 200 300 390 510
3?8 230d 366d 460d 610d
APA Structural I
grades
7?16 11?2 8d 255d 395d 505d 670d 10de 280 430 550 730
15?32 280 430 550 730
15?32 15?8 10de 340 510 665 870
10.47
5?16 or 1?4? 180 270 350 450 180 270 350 450
3?8 11?4 6d 200 300 390 510 8d 200 300 390 510
APA Rated Sheathing;
APA Rated Siding
and other APA
gradesg except
species Group 5
3?8
7?16
15?32
11?2 8d
220d
240d
260
320d
350d
380
410d
450d
490
530d
585d
640
10de 260 380 490 640
15?32 310 460 600 770
19?32 15?8 10de 340 510 665 870
APA Rating Siding
and other APA
gradesg except
species Group 5
5?16f
3?8
11?4
11?2
Nail size
(galvanized
casing)
6d
8d
140
160
210
240
275
310
360
410
Nail size
(galvanized
casing)
8d
10d
140
160
210
240
275
310
360
410
a All panel edges should be backed with framing, which should have a nominal width of 2 in or more. The plywood
may be installed horizontally or vertically. Space nails 6 in c to c along intermediate framing members for 3?8-in and
7?16-in panels attached to studs that are spaced 24 in c to c. For other conditions and panel thicknesses, space nails 12
in c to c on intermediate supports.
bFor framing of other species, determine the species group of the lumber from the AF&PA National Design Specification
for Wood Construction. Then, proceed as follows: For common or galvanized box nails, find the shear value
from the above table for the nail size for Structural I panels, regardless of the actual grade. For galvanized casing nails,
use the shear value given in the table. Next, multiply this value by 0.82 for Lumber Group III or 0.65 for Lumber
Group IV.
c Framing at adjoining edge panels should have a nominal width of 3 in or more and nails should be staggered.
d If studs are spaced at most 16 in c to c or if panels are applied with the long dimension across the studs, shears
may be increased to the values shown for 15?32-in-thick sheathing with the same nail spacing.
e Framing at adjoining panels should have a nominal width of 3 in or more and nails with a penetration into the
framing exceeding 15?8-in and 3-in spacing c to c should be staggered.
? For 3?8-in-thick siding or APA Rated Siding when used as exterior siding applied directly to the framing, stud
spacing of 16 in c to c is recommended.
gValues apply to all-veneer plywood APA Rated Siding panels only. For APA Rated Siding on framing spaced 16
in c to c, the plywood may be 11?32 in thick, 3?8 in thick, or thicker. Thickness at the point of nailing on panel edges
governs shear values.
Panel grade
Minimum
nominal
panel thickness,
in
Minimum nail
penetration
in framing,
in
Panels applied directly to framing
Nail size
(common or
galvanized
box)
Nail spacing at panel
edges, in
6 4 3 2c
Panels applied over ?2-in or ?8-in
gypsum sheathing
Nail size
(common or
galvanized
box)
Nail spacing at
panel edges, in
6 4 3 2c
10.48 SECTION TEN
FIGURE 10.10 Foundation anchor for a wood shear wall.
TABLE 10.24 Maximum Uniform Roof Live Loads, psf,a for APA Rated Sheathingb and
APA Rated Sturd-I-Floor
(Long dimension perpendicular to supports)c
(a) APA Rated Sheathingb
Panel
span
rating
Minimum
panel
thickness,
in
Maximum span, in
With edge
supportd
Without edge
support
Spacing of supports, in, c to c
12 16 20 24 32 40 48 60
12/0 5?16 12 12 30
16/0 5?16 16 16 70 30
20/0 5?16 20 20 120 50 30
24/0 3?8 24 20e 190 100 60 30
24/16 7?16 24 24 190 100 65 40
32?16 15?32, 1?2 32 28 325 180 120 70 30
40/20 19?32, 5?8 40 32 305 205 130 60 30
48/24 23?32, 3?4 48 36 280 175 95 45 35
(b) APA Rated Sturd-I-Floor
Stud
spacing,
in
Minimum
panel
thickness,
in
Maximum span, in
With edge
support
Without edge
support
Spacing of supports, in, c to c
12 16 20 24 32 40 48 60
16 oc 19?32, 5?8 24 24 185 100 65 40
20 oc 19?32, 5?8 32 32 270 150 100 60 30
24 oc 23?32, 3?4 40 36 240 160 100 50 30 25
32 oc 7?8 48 40 295 185 100 60 40
48 oc 13?32, 11?8 60 48 290 160 100 65 40
aMaximum loads include an assumed 10 psf for dead load.
b Includes APA Rated Sheathing Ceiling Deck.
c Applies to panels 24 in or more wide.
d Edge support is provided by such means as tongue-and-groove edges, panel edge clips (generally one
midway between each support but two equally spaced between supports that are 48 in c to c), or lumber or
other blocking.
eMaximum span is 24 in for 15?32-in and 1?2-in panels.
WOOD CONSTRUCTION 10.49
FIGURE 10.11 Structural panels installed as roof sheathing.
TABLE 10.25 Maximum Spans for APA Panel Roof Decks for Low-Slope Roofs*
(Panels set with long dimension perpendicular to supports and continuous over two or more
spans)
Grade
Minimum nominal
panel thickness,
in
Minimum
span rating
Maximum span,
in
Number of
panel clips
per span†
APA
Rated
Sheathing
15?32, 1?2
19?32, 5?8
22?32, 3?4
32/16
40/20
48/24
24
32
48
1
1
2
* Built-up, single-ply, or modified bitumen roofing systems may be used for low-slope roofs. For guaranteed
or warranted roofs, check with the membrane manufacturer for requirements for an acceptable deck.
† Edge support may also be provided by tongue-and-groove edges or solid blocking.
When support spacing exceeds the maximum length of an unsupported edge, as
given in Table 10.24, provide adequate block, tongue-and-groove edges, or other
edge support such as panel clips. Some types of panel clips, in addition to edge
support, automatically assure recommended panel spacing. When required, use one
panel clip per span of less than 28 in and two for 48-in or longer spans.
10.12.12 Preframed Roof Panels
Spans of 8 to 12 ft are usually the most practical with preframed panel construction
which are typically used in large low slope roof applications, although spans up to
30 ft are not uncommon. Unsanded 4  8-ft panels with stiffeners preframed at 16
or 24 in c to c are common. The long dimension of panels typically runs parallel
to supports. Stiffeners and roof purlins provide support for all panel edges. Minimum
nailing requirements for preframed panels are the same as for roof sheathing.
For preframed panels 8  8 ft or larger, the long panel dimension may run either
parallel or perpendicular to stiffeners spaced 16 or 24 in c to c. Placing the long
dimension across supports may require edge support such as panel clips or cleats
between stiffeners at midspan in accordance with Table 10.24.
10.50 SECTION TEN
TABLE 10.26 Minimum Fastening for APA Panel
Roof Sheathing (increased nail schedules may be
required in high wind areas)
Panel
thickness,†
in
Nailing*
Size
Spacing, in
Panel
edge Intermediate
5?16 to 1 8d 6 12‡
11?8 8d or 10d 6 12‡
* In general, use common smooth or deformed-shank nails
for panels up to 1 in thick. For 11?8-in-thick panels, use 8d
ring- or screw-shank or 10d common smooth-shank nails.
Other approved fasteners, however, may be used.
†For stapling asphalt shingles to panels 5?16 in or more
thick, use staples with a 15?16-in minimum crown width and a
1-in-long leg. Space the staples in accordance with the recommendations
of the shingle manufacturer.
‡For spans of 48 in or more, space the nails 6 in c to c
at all supports.
Deflection limits are 1/180 of the span for total load; 1/240 for live load only.
Nailing requirements for preframed panels are the same as for roof sheathing. See
‘‘APA Design/Construction Guide—Residential and Commercial,’’ APA—The Engineered
Wood Association, for recommended maximum roof loads.
10.12.13 Panel Diaphragms
With only slight design modifications, any panel roof-deck system described in
Arts. 10.12.11 and 10.12.12 will also function as an engineered roof or floor diaphragm
to resist wind and seismic loading.
The ability of a diaphragm to function effectively as a deep beam, transferring
lateral loads to shear walls, is related to the quality of the connections. Nailing is
critical, since shears are transmitted through these fasteners. Common nails provide
required strength. Other nail types may be used when their lateral bearing values
are considered in the design. Load-carrying capacity is highest when the diaphragm
is blocked.
Where 11?8-in roof panels are desired, such as for heavy timber construction,
shear values for 19?32-in panels are used. Blocked shear values for 11?8-in panels
may be obtained by specifying stapled tongue-and-groove (T&G) edges. Staples
should be 16 ga, 1 in long, with a 3?8-in crown. They should be driven through the
T&G edges 3?8-in from the joint so as to penetrate the tongue. Staples should be
spaced at one-half of the boundary nail spacing for Cases 1 and 2, and at one-third
the boundary nail spacing for Case 3 through 6, as illustrated in Table 10.27, which
gives panel and fastening recommendations for roof diaphragms. Panels and framing
are assumed already designed for perpendicular loads. To design a diaphragm,
follow these steps:
1. Determine lateral loads and resulting shears.
2. Determine the nailing schedule (Table 10.27). Consider the load direction with
respect to joints.
WOOD CONSTRUCTION 10.51
3. Compute the chord stress due to bending moment. Provide adequate splices.
Check deflections. Check the anchorage of boundary framing, for example, to
walls.
For situations where greater diaphragm capacities are necessary and framing
with a nominal thickness of 3 or 4 in is available, diaphragms may be constructed
using heavier nailing schedules, such as that given in the Uniform Building Code.
(‘‘Diaphragms,’’ APA—The Engineered Wood Association, Tacoma, Wash.)
10.13 DESIGN VALUES FOR MECHANICAL
CONNECTIONS
Nails, staples, spikes, wood screws, bolts, and timber connectors, such as shear
plates and split rings, are used for connections in wood construction. Because determination
of stress distribution in connections made with wood and metal is complicated,
information for design of joints has been developed from tests and experience.
The data indicate that design values and methods of design for mechanical
connections are applicable to both solid sawn lumber and laminated members. The
‘‘National Design Specification for Wood Construction,’’ (NDS) American Forest
& Paper Association, provides design equations and tabulates design values for
connections made with various types of fasteners. Design values for connections
made with more than one type of fastener, however, should be based on tests or
special analysis.
10.14 ADJUSTMENT OF DESIGN VALUES FOR
CONNECTIONS
Nominal design values for laterally loaded fasteners Z, withdrawal of fasteners W,
load parallel to grain P, and load perpendicular to grain Q should be multiplied by
applicable adjustment factors to determine adjusted design values Z, W, P, and
Q, respectively. Table 10.28 summarizes the adjustment factors that should be
applied to the design values Z, W, P, and Q for connections made with commonly
used types of fasteners. The load applied to a connection should not exceed the
adjusted design value.
10.14.1 Load Duration Factor
Nominal design values should be multiplied by the load duration factor CD specified
in Art. 10.5.1, except that CD may not exceed 1.6 or when the capacity of the
connection is controlled by the strength of metal. The impact load duration factor
shall not apply to connections.
10.52
TABLE 10.27 Maximum Shear, lb / ft, for APA Panel Diaphragms for Wind or Seismic Loading
(For Framing of Douglas fir, larch, or southern pine)*
Blocked diaphragms
Nail spacing, in, at
diaphragm boundaries (all
cases), at continuous panel
edges parallel to load
(Cases 3, 4), and at all
panel edges (Cases 5, 6)†
Unblocked diaphragms
Nails spaced 6 in max at
supported edges†
Minimum
Minimum
nominal
6 4 21?2‡ 2‡ Case 1 (no
unblocked
Common
Minimum nail
penetration in
nominal
panel
thicknes,
width of
framing
member,
Nail spacing, in, at other
panel edges (Cases 1, 2,
3, 4)
edges or
continuous
joints parallel
All other
configurations
(Cases 2, 3,
Panel grade nail size framing, in in in 6 6 4 3 to load) 4, 5, 6)
APA Structural I
grades
6d
8d
10d§
1