Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge
Design Code
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November 2006
Title: Commentary on CAN/CSA-S6-06, Canadian Highway Bridge Design Code
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S6.1-06
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
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Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Contents
Preface xxxvii
Summary of significant changes to the Code since the previous edition xxxviii
Section C1 — General 1
C1.1
Scope 4
C1.1.1
Scope of Code 4
C1.1.2
Scope of this Section 4
C1.2
Reference publications 4
C1.3
Definitions 4
C1.3.1
General 4
C1.3.2
General administrative definitions 5
C1.3.3
General technical definitions 5
C1.3.4
Hydraulic definitions 5
C1.4
General requirements 5
C1.4.1
Approval 5
C1.4.2
Design 6
C1.4.2.1
Design philosophy 6
C1.4.2.2
Highway class 7
C1.4.2.3
Design life 7
C1.4.2.4
Structural behaviour and articulation 7
C1.4.2.5
Single-load-path structures 8
C1.4.2.6
Economics 8
C1.4.2.7
Environment 8
C1.4.2.8
Aesthetics 8
C1.4.3
Evaluation and rehabilitation of existing bridges 8
C1.4.3.1
Evaluation 8
C1.4.3.2
Rehabilitation design 9
C1.4.4
Construction 9
C1.4.4.1
General 9
C1.4.4.2
Construction safety 9
C1.4.4.3
Construction methods 9
C1.4.4.4
Temporary structures 10
C1.4.4.5
Plans 10
C1.4.4.6
Quality control and assurance 10
C1.5
Geometry 10
C1.5.1
Planning 10
C1.5.2
Structure geometry 11
C1.5.2.1
General 11
C1.5.2.2
Clearances 11
C1.6
Barriers 11
C1.6.1
Superstructure barriers 11
C1.6.2
Roadside substructure barriers 11
C1.6.3
Structure protection in waterways 12
C1.6.4
Structure protection at railways 12
C1.7
Auxiliary components 12
C1.7.1
Expansion joints and bearings 12
C1.7.2
Approach slabs 12
C1.7.3
Utilities on bridges 12
C1.7.3.1
General 12
C1.7.3.2
Location and attachment 13
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© Canadian Standards Association
C1.7.3.3
C1.7.3.4
C1.7.3.5
C1.8
C1.8.1
C1.8.2
C1.8.2.1
C1.8.2.2
C1.8.2.3
C1.8.2.4
C1.8.2.5
C1.8.3
C1.8.3.1
C1.8.3.2
C1.8.3.3
C1.9
C1.9.1
C1.9.1.1
C1.9.1.2
C1.9.1.3
C1.9.1.4
C1.9.1.5
C1.9.1.6
C1.9.2
C1.9.3
C1.9.4
C1.9.4.1
C1.9.4.2
C1.9.4.3
C1.9.4.4
C1.9.4.5
C1.9.4.6
C1.9.4.7
C1.9.4.8
C1.9.5
C1.9.5.1
C1.9.5.2
C1.9.5.3
C1.9.5.4
C1.9.5.5
C1.9.5.6
C1.9.5.7
C1.9.6
C1.9.6.1
C1.9.6.2
C1.9.6.3
C1.9.6.4
C1.9.6.5
C1.9.7
C1.9.7.1
C1.9.7.2
C1.9.8
C1.9.8.1
C1.9.8.2
iv
© Canadian Standards Association
Highway utilities 13
Public utilities 13
Fluid-carrying utilities 13
Durability and maintenance 13
Durability and protection 13
Bridge deck drainage 13
General 13
Deck surface 14
Drainage systems 14
Subdrainage of wearing surface 15
Runoff and discharge from deck 15
Maintenance 15
Inspection and maintenance access 15
Maintainability 16
Bearing maintenance and jacking 16
Hydraulic design 16
Design criteria 16
General 16
Normal design flood 16
Check flood 16
Regulatory floods and relief flow 16
Design flood discharge 16
High-water levels 17
Investigations 19
Location and alignment 19
Estimation of scour 19
Scour calculations 19
Soils data 20
General scour 20
Local scour 21
Total scour 22
Degradation 22
Artificial deepening 22
Allowance for degradation or artificial deepening 22
Protection against scour 23
General 23
Spread footings 23
Piles 23
Sheet piling 24
Protective aprons 24
Paved inverts and revetments 24
Special protection against degradation 24
Backwater 24
General 24
High-water level 24
Assumed depth of scour 24
Waterway modification 25
Reduction of backwater by relief flow 25
Soffit elevation 26
Clearance 26
High-water level for establishing soffit elevation 26
Approach grade elevation 26
General 26
Freeboard 26
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S6.1-06
C1.9.8.3
C1.9.8.4
C1.9.9
C1.9.9.1
C1.9.9.2
C1.9.9.3
C1.9.9.4
C1.9.10
C1.9.10.1
C1.9.10.2
C1.9.11
C1.9.11.1
C1.9.11.2
C1.9.11.3
C1.9.11.4
C1.9.11.5
C1.9.11.6
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
High-water level for establishing approach grade 26
Freeboard for routes under structures crossing water 26
Channel erosion control 27
Slope protection 27
Stream banks 27
Slope revetments 27
Storm sewer and channel outlets 27
Stream stabilization works and realignment 27
Stream stabilization works 27
Stream realignment 27
Culverts 27
General 27
Culvert end treatment 27
Culvert extensions 28
Alignment of non-linear culverts 28
Open-footing culverts 28
Closed-invert culverts 28
Section C2 — Durability 33
C2.1
Scope 34
C2.3
Design for durability 34
C2.3.1
Design concept 34
C2.3.2
Durability requirements 35
C2.3.2.1
General 35
C2.3.2.2
Materials 35
C2.3.2.3
Structural details 35
C2.3.2.4
Bearing seats 35
C2.3.2.5
Bridge joints 35
C2.3.2.6
Drainage 36
C2.3.2.9
Access 36
C2.3.2.11 Inspection and maintenance 36
C2.3.3
Structural materials 36
C2.4
Aluminum 36
C2.4.1
Deterioration mechanisms 36
C2.4.2
Detailing for durability 37
C2.4.2.1
Connections 37
C2.4.2.2
Inert separators 37
C2.7
Waterproofing membranes 37
C2.8
Backfill material 37
C2.9
Soil and rock anchors 37
Section C3 — Loads 39
C3.1
Scope 41
C3.2
Definitions 41
C3.3
Abbreviations and symbols 41
C3.4
Limit states criteria 41
C3.4.2
Ultimate limit states 41
C3.4.3
Fatigue limit state 41
C3.4.4
Serviceability limit states 42
C3.5
Load factors and load combinations 48
C3.5.1
General 48
C3.5.2
Permanent loads 49
C3.5.2.1
General 49
C3.5.2.2
Overturning and sliding effects 49
C3.5.3
Transitory loads 50
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© Canadian Standards Association
C3.5.4
C3.6
C3.7
C3.8
C3.8.1
C3.8.2
C3.8.3
C3.8.3.1
C3.8.3.2
C3.8.3.3
C3.8.4
C3.8.4.1
C3.8.4.2
C3.8.4.3
C3.8.4.4
C3.8.4.5
C3.8.5
C3.8.6
C3.8.7
C3.8.8
C3.8.8.1
C3.8.8.2
C3.8.9
C3.8.10
C3.8.12
C3.9
C3.9.1
C3.9.2
C3.9.3
C3.9.4
C3.9.4.1
C3.9.4.2
C3.9.4.3
C3.9.4.4
C3.9.4.5
C3.10
C3.10.1.1
C3.10.1.2
C3.10.1.3
C3.10.1.4
C3.10.1.5
C3.10.1.6
C3.10.1.7
C3.10.2
C3.10.2.1
C3.10.2.2
C3.10.2.3
C3.10.2.4
C3.10.3
C3.10.3.1
C3.10.3.2
C3.10.3.3
C3.10.4
C3.10.4.1
vi
© Canadian Standards Association
Exceptional loads 50
Dead loads 50
Earth loads and secondary prestress loads 50
Live loads 50
General 50
Design lanes 51
CL-W loading 51
General 51
CL-W Truck 52
CL-W Lane Load 55
Application 62
General 62
Multi-lane loading 62
Local components 63
Wheels on the sidewalk 63
Dynamic load allowance 63
Centrifugal force 68
Braking force 68
Curb load 69
Barrier loads 69
Traffic barriers 69
Pedestrian and bicycle barriers 70
Pedestrian load 70
Maintenance access loads 70
Multiple-use structures 70
Superimposed deformations 71
General 71
Movements and load effects 71
Superstructure types 72
Temperature effects 72
Temperature range 72
Effective construction temperature 72
Positioning of bearings and expansion joints 75
Thermal gradient effects 76
Thermal coefficient of linear expansion 79
Wind loads 79
General 79
Reference wind pressure 80
Gust effect coefficient 80
Wind exposure coefficient 80
Non-uniform loading 81
Overturning and overall stability 81
Alternative methods 81
Design of the superstructure 81
General 81
Horizontal drag load 81
Vertical load 82
Wind load on live load 83
Design of the substructure 83
General 83
Wind loads transmitted from the superstructure 83
Loads applied directly to substructure 83
Aeroelastic instability 84
General 84
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S6.1-06
C3.10.4.2
C3.10.5
C3.10.5.1
C3.10.5.2
C3.11
C3.11.4
C3.11.4.2
C3.11.5
C3.11.7
C3.12
C3.12.1
C3.12.2
C3.12.2.1
C3.12.2.2
C3.12.2.3
C3.12.2.4
C3.12.3
C3.12.4
C3.12.5
C3.12.6
C3.13
C3.14
C3.14.1
C3.14.2
C3.14.5
C3.14.6
C3.14.7
C3.15
C3.16
C3.16.1
C3.16.2
C3.16.3
C3.16.4
C3.16.4.1
C3.16.4.2
C3.16.4.3
C3.16.5
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Criterion for aeroelastic instability 85
Wind tunnel tests 85
General 85
Load factors 85
Water loads 86
Stream pressure 86
Lateral effects 86
Wave action 86
Debris torrents 86
Ice loads 87
General 87
Dynamic ice forces 87
Effective ice strength 87
Crushing and flexural strength 87
Ice impact forces 87
Slender piers 88
Static ice forces 88
Ice jams 88
Ice adhesion forces 89
Ice accretion 89
Earthquake effects 90
Vessel collision 90
General 90
Bridge classification 90
Design vessel 90
Application of collision forces 90
Protection of piers 91
Vehicle collision load 91
Construction loads and loads on temporary structures 91
General 91
Dead loads 91
Live loads 92
Segmental construction 92
Erection loads 92
Construction live loads 92
Incremental launching 92
Falsework 92
Annexes
CA3.1 — Commentary on Annex A3.1 — Climate and environmental data 97
CA3.2 — Commentary on Annex A3.2 — Wind loads on highway accessory supports and slender
structural elements 100
CA3.3 — Commentary on Annex A3.3 — Vessel collision 106
CA3.4 — Commentary on Annex A3.4 — CL-625-ONT live loading 111
Section C4 — Seismic design 113
C4.1
Scope 115
C4.3
Abbreviations and symbols 115
C4.4
Earthquake effects 115
C4.4.1
General 115
C4.4.2
Importance categories 115
C4.4.3
Zonal acceleration ratio 116
C4.4.4
Seismic performance zones 116
C4.4.5
Analysis for earthquake loads 117
C4.4.5.2
Single-span bridges 117
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C4.4.5.3
C4.4.6
C4.4.6.1
C4.4.7
C4.4.7.1
C4.4.8
C4.4.8.1
C4.4.8.2
C4.4.9
C4.4.9.1
C4.4.9.2
C4.4.10
C4.4.10.1
C4.4.10.2
C4.4.10.3
C4.4.10.4
C4.4.10.5
C4.4.10.6
C4.5
C4.5.1
C4.5.3
C4.5.3.1
C4.5.3.2
C4.5.3.3
C4.5.3.4
C4.5.3.5
C4.6
C4.6.2
C4.6.3
C4.6.4
C4.6.5
C4.6.6
C4.7
C4.7.1
C4.7.2
C4.7.3
C4.7.4
C4.7.4.2
C4.7.4.3
C4.7.4.4
C4.8
C4.8.1
C4.8.2
C4.8.3
C4.8.4
C4.8.4.1
C4.8.4.3
C4.8.4.4
C4.8.5
C4.10
C4.10.1
C4.10.4
C4.10.5
C4.10.6
viii
© Canadian Standards Association
Multi-span bridges 117
Site effects 118
General 118
Elastic seismic response coefficient 118
General 118
Response modification factors 119
General 119
Application 120
Load factors and load combinations 120
General 120
Earthquake load cases 120
Design forces and support lengths 120
General 120
Seismic Performance Zone 1 121
Seismic Performance Zone 2 121
Seismic Performance Zones 3 and 4 121
Minimum support length requirements for displacements 122
Longitudinal restrainers 122
Analysis 122
General 122
Multi-span bridges 123
Uniform-load method 123
Single-mode spectral method 124
Multi-mode spectral method 124
Time-history method 125
Static pushover analysis 125
Foundations 125
Liquefaction of foundation soils 125
Stability of slopes 128
Seismic forces on abutments and retaining walls 128
Soil-structure interaction 130
Fill settlement and approach slabs 133
Concrete structures 133
General 133
Seismic Performance Zone 1 133
Seismic Performance Zone 2 134
Seismic Performance Zones 3 and 4 134
Column requirements 134
Wall-type piers 136
Column connections 136
Steel structures 137
General 137
Materials 138
Sway stability effects 138
Steel substructures 138
General 138
Seismic Performance Zone 2 138
Seismic Performance Zones 3 and 4 139
Other systems 142
Seismic base isolation 142
General 142
Site effects and site coefficient 144
Response modification factors and design requirements for substructure 144
Analysis procedures 144
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Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
C4.10.6.2 Uniform-load/single-mode spectral analysis 144
C4.10.6.3 Multi-mode spectral analysis 146
C4.10.6.4 Time-history analysis 146
C4.10.7
Clearance and design displacements for seismic and other loads 146
C4.10.8
Design forces for Seismic Performance Zone 1 147
C4.10.9
Design forces for Seismic Performance Zones 2, 3, and 4 147
C4.10.10 Other requirements 147
C4.10.10.1 Non-seismic lateral forces 147
C4.10.10.2 Lateral restoring force 147
C4.10.10.3 Vertical load stability 147
C4.10.11 Required tests of isolation system 147
C4.10.12 Elastomeric bearings — Design 147
C4.10.14 Sliding bearings — Design 148
C4.11
Seismic evaluation of existing bridges 152
C4.11.1
General 152
C4.11.2
Bridge classification 152
C4.11.3
Damage levels 153
C4.11.3.1 Moderate damage 153
C4.11.3.2 Significant damage 153
C4.11.4
Performance criteria 153
C4.11.5
Evaluation methods 153
C4.11.6
Load factors and load combinations for seismic evaluation 153
C4.11.8
Member capacities 153
C4.11.8.1 General 153
C4.11.8.4 Effects of deterioration 154
C4.11.9
Required response modification factor 154
C4.11.10 Response modification factor of existing substructure elements 154
C4.12
Seismic rehabilitation 155
Section C5 — Methods of analysis 161
C5.1
Scope 163
C5.3
Abbreviations and symbols 163
C5.4
General requirements 163
C5.4.2
Analysis for limit states 163
C5.4.4
Structural responses 163
C5.4.5
Factors affecting structural responses 165
C5.4.6
Deformations 167
C5.4.6.1
General 167
C5.4.6.2
Dead load deflections 167
C5.4.6.3
Live load deflections 167
C5.4.7
Diaphragms and bracing systems 168
C5.4.8
Analysis of deck slabs 168
C5.4.9
Analysis for redistribution of force effects 168
C5.4.10
Analysis for accumulation of force effects due to construction sequence 168
C5.4.11
Analysis for effects of prestress 168
C5.4.12
Analysis for thermal effects 168
C5.5
Requirements for specific bridge types 169
C5.5.1
General 169
C5.5.2
Voided slab — Limitation on size of voids 169
C5.5.4
Truss and arch 169
C5.5.5
Rigid frame and integral abutment types 169
C5.5.5.1
Rigid frame 169
C5.5.5.2
Integral abutment 170
C5.5.7
Box girder 170
C5.5.8
Single-spine bridges 171
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C5.6
C5.6.1
C5.6.1.1
C5.7
C5.7.1
C5.7.1.1
C5.7.1.2
C5.7.1.3
C5.7.1.4
C5.7.1.5
C5.7.1.6
C5.7.1.7
C5.7.1.8
C5.7.1.9
C5.7.1.11
C5.8
C5.8.1
C5.8.2
C5.8.2.1
C5.8.2.2
C5.8.3
C5.9
C5.9.1
C5.9.2
C5.9.3
C5.10
C5.10.1
C5.10.2
C5.10.3
C5.11
C5.11.1
C5.11.1.1
C5.11.1.2
C5.11.1.4
C5.11.2
C5.11.2.1
C5.11.2.2
© Canadian Standards Association
Dead load 171
Simplified methods of analysis (beam analogy method) 171
Conditions for use 171
Live load 172
Simplified methods of analysis 172
Conditions for use 172
Longitudinal bending moments in shallow superstructures 173
Longitudinal bending moments in multi-spine bridges 185
Longitudinal vertical shear in shallow superstructures 186
Longitudinal vertical shear in multi-spine bridges 186
Deck slab moments due to loads on the cantilever overhang 186
Transverse bending moments in decks 189
Transverse vertical shear 189
Analysis of stringers in truss and arch bridges 189
Analysis of orthotropic steel decks 190
Idealization of structure and interpretation of results 190
General 190
Effective flange widths for bending 190
Concrete slab-on-girders 190
Orthotropic steel decks 190
Idealization for analysis 191
Refined methods of analysis for short- and medium-span bridges 191
Selection of methods of analysis 191
Specific applications 191
Model analysis 192
Long-span bridges 192
General 192
Cable-stayed bridges 192
Suspension bridges 192
Dynamic analysis 193
General requirements of structural analysis 193
General 193
Distribution of masses 193
Damping 193
Elastic dynamic responses 193
Vehicle-induced vibrations 193
Wind-induced vibrations 194
Annex
CA5.1 — Commentary on Annex A5.1 — Factors affecting structural response 199
Section C6 — Foundations 201
C6.1
Scope 204
C6.3
Abbreviations and symbols 205
C6.3.2
Symbols 205
C6.4
Design requirements 206
C6.4.1
Limit states 206
C6.4.1.1
General 206
C6.4.1.2
Ultimate limit state 206
C6.4.1.3
Serviceability limit state 206
C6.4.2
Effects on surroundings 206
C6.4.3
Effects on structure 207
C6.4.4
Components 208
C6.4.5
Consultation 208
C6.4.6
Inspection and quality control 208
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S6.1-06
C6.5
C6.5.1
C6.5.2
C6.5.3
C6.5.4
C6.5.5
C6.5.6
C6.6
C6.6.1
C6.6.2
C6.6.2.1
C6.6.2.2
C6.6.2.3
C6.6.2.4
C6.6.3
C6.6.3.1
C6.6.3.3
C6.6.3.6
C6.7
C6.7.1
C6.7.2
C6.7.3
C6.7.3.1
C6.7.3.2
C6.7.3.3
C6.7.3.4
C6.7.4
C6.7.5
C6.8
C6.8.1
C6.8.2
C6.8.3
C6.8.4
C6.8.5
C6.8.5.1
C6.8.5.2
C6.8.5.3
C6.8.5.4
C6.8.5.5
C6.8.5.6
C6.8.6
C6.8.6.1
C6.8.6.2
C6.8.7
C6.8.7.1
C6.8.7.2
C6.8.7.3
C6.8.8
C6.8.8.2
C6.8.8.3
C6.8.8.5
C6.8.9
C6.8.9.2
C6.8.10
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Geotechnical investigation 209
General 209
Investigation procedures 209
Geotechnical parameters 210
Shallow foundations 210
Deep foundations 210
Report 211
Resistance and deformation 212
General 212
Ultimate limit state 215
Procedures 215
Geotechnical formulas 215
In-situ tests 216
Assessed value 216
Serviceability limit state 217
General 217
Tests 219
Calculation considerations 219
Shallow foundations 223
General 223
Calculated geotechnical resistance at ULS 225
Pressure distribution 227
Effective area 227
Pressure distribution at the ULS for structural design 227
Pressure distribution at the SLS 229
Eccentricity limit 230
Effect of load inclination 230
Factored geotechnical horizontal resistance 231
Deep foundations 232
General 232
Selection of deep foundation units 232
Vertical load transfer 233
Downdrag 233
Factored geotechnical axial resistance 235
General 235
Static analysis 235
Static pile load tests 236
Dynamic analysis and tests 237
Limitation for tension piles 237
Relaxation of driven piles 237
Group effects — Vertical loads 237
Load distribution 237
Group resistance 238
Factored geotechnical lateral resistance 238
General 238
Static analysis 240
Lateral deflection 241
Structural resistance 241
Unsupported length 241
Structural instability 241
Factored structural resistance 241
Embedment and spacing 241
Pile spacing 241
Pile shoes and splices 242
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C6.8.10.1
C6.8.10.2
C6.9
C6.9.1
C6.9.2
C6.9.2.1
C6.9.2.2
C6.9.2.3
C6.9.3
C6.9.4
C6.9.5
C6.10
C6.10.1
C6.10.2
C6.10.2.1
C6.10.2.2
C6.10.2.3
C6.10.3
C6.10.4
C6.10.4.1
C6.10.4.2
C6.11
C6.11.1
C6.11.2
C6.11.3
C6.11.3.1
C6.11.3.3
C6.11.3.4
C6.11.4
C6.12
C6.12.1
C6.12.2
C6.12.2.1
C6.12.2.2
C6.12.2.3
C6.12.3
C6.13
C6.13.1
C6.13.2
C6.13.2.1
C6.13.2.2
© Canadian Standards Association
Pile shoes or points 242
Splices 242
Lateral and vertical pressures 242
General 242
Lateral pressures 247
General 247
Calculated pressures 248
Equivalent fluid pressures 249
Compaction surcharge 249
Effects of loads 249
Surcharge 250
Ground anchors 250
Application 250
Design 252
General 252
Factored geotechnical resistance at the ULS and geotechnical reaction at the SLS 252
Spacing, bond length and free-stressing length 252
Materials and installation 253
Anchor testing 253
General 253
Acceptance criteria 253
Sheet pile structures 253
Application 253
Design 254
Ties and anchors 254
Deadman anchors 254
Tie load 255
Sagging of tie rods 255
Cellular sheet pile structures 255
MSE structures 255
Application 255
Design 255
General 255
Calibration 255
Factors for consideration 256
Backfill 256
Pole foundations 256
Application 256
Design 256
General 256
Assumptions 256
Section C7 — Buried structures 265
C7.1
Scope 267
C7.3
Abbreviations and symbols 267
C7.3.2
Symbols 267
C7.4
Hydraulic design 267
C7.5
Structural design 268
C7.5.1
Limit states 268
C7.5.2
Load factors 268
C7.5.3
Material resistance factors 268
C7.5.4
Geotechnical considerations 268
C7.5.4.1
Geotechnical investigation 269
C7.5.4.2
Soil properties 269
C7.5.4.3
Camber 269
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C7.5.4.4
C7.5.4.5
C7.5.5
C7.5.5.1
C7.5.5.2
C7.5.5.3
C7.5.5.4
C7.5.6
C7.6
C7.6.1
C7.6.2
C7.6.2.1
C7.6.2.2
C7.6.2.3
C7.6.3
C7.6.3.1
C7.6.3.2
C7.6.3.3
C7.6.3.4
C7.6.3.5
C7.6.3.6
C7.6.4
C7.6.4.1
C7.6.4.2
C7.6.4.3
C7.6.5
C7.6.5.1
C7.6.5.2
C7.6.5.3
C7.6.5.4
C7.6.5.5
C7.6.5.6
C7.6.6
C7.6.7
C7.7
C7.7.1
C7.7.3
C7.7.3.1
C7.7.3.2
C7.7.4
C7.7.4.1
C7.7.5
C7.7.5.1
C7.7.5.2
C7.7.6
C7.8
C7.8.1
C7.8.2
C7.8.3
C7.8.3.1
C7.8.3.2
C7.8.3.3
C7.8.3.4
C7.8.3.5
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Footings 269
Control of soil migration 270
Seismic requirements 270
General 270
Seismic design of soil-metal structures 270
Seismic design of metal box structures 270
Seismic design of concrete structures 271
Minimum clear spacing between conduits 271
Soil-metal structures 271
General 271
Structural materials 271
Structural metal plate 271
Corrugated steel pipe 271
Soil materials 272
Design criteria 274
Thrust 274
Wall strength in compression 275
Wall strength in bending and compression 277
Connection strength 277
Maximum difference in plate thickness 278
Radius of curvature 278
Additional design requirements 278
Minimum depth of cover 278
Foundation treatment for pipe-arches 279
Durability 279
Construction 280
General 280
Deformation during construction 280
Foundations 281
Bedding 281
Assembly and erection 281
Structural backfill 281
Special features 282
Site supervision and construction control 282
Metal box structures 282
General 282
Design criteria 283
Design criteria for crown and haunches 283
Design criteria for connection 284
Additional design considerations 285
Depth of cover 285
Construction 285
Structural backfill 285
Deformation during construction 285
Special features 285
Reinforced concrete buried structures 285
Standards for structural components 285
Standards for joint gaskets for precast concrete units 286
Installation criteria 286
Backfill soils 286
Minimum depth of cover for structures with curved tops 286
Compaction 286
Frost penetration 286
Standard installations for circular precast concrete pipes 286
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© Canadian Standards Association
C7.8.3.6
C7.8.3.7
C7.8.4
C7.8.4.1
C7.8.4.2
C7.8.5
C7.8.5.1
C7.8.5.2
C7.8.5.3
C7.8.6
C7.8.7
C7.8.7.1
C7.8.8
C7.8.8.1
C7.8.8.2
C7.8.9
C7.8.9.1
C7.8.10
C7.8.11
C7.8.11.1
C7.8.11.2
C7.8.12
C7.8.13
C7.8.14
Standard installations for precast and cast-in-place concrete boxes 287
Non-standard installations 287
Loads and load combinations 287
Load combinations 287
Earth load 287
Earth pressure distribution from loads 288
General 288
Circular pipe in standard installations 288
Box sections in standard installations 289
Analysis 289
Ultimate limit state 289
Additional factors 289
Strength design 290
Flexure 290
Design for shear 291
Serviceability limit state 293
Control of cracking 293
Fatigue limit state 293
Minimum reinforcement 294
Parallel to span 294
Perpendicular to span 294
Distribution reinforcement 294
Details of the reinforcement 294
Joint shear for top slab of precast concrete box sections with depth of cover less than
0.6 m 294
C7.8.15
Construction 294
C7.8.15.3 Bedding for precast concrete structures 294
C7.8.15.5 Structural backfill 295
C7.8.15.8 Trenches 295
Section C8 — Concrete structures 299
C8.1
Scope 304
C8.3
Symbols 304
C8.4
Materials 305
C8.4.1
Concrete 305
C8.4.1.1
Compliance with CAN/CSA-A23.1/CAN/CSA-A23.2 305
C8.4.1.2
Concrete strength 306
C8.4.1.3
Thermal coefficient 306
C8.4.1.4
Poisson’s ratio 306
C8.4.1.5
Shrinkage 307
C8.4.1.6
Creep 307
C8.4.1.7
Modulus of elasticity 308
C8.4.1.8
Cracking strength 308
C8.4.2
Reinforcing bars and deformed wire 309
C8.4.2.1
Reinforcing bars 309
C8.4.2.2
Steel wires and welded wire fabric 309
C8.4.3
Tendons 309
C8.4.3.1
General 309
C8.4.3.2
Stress-strain relationship 309
C8.4.4
Anchorages, mechanical connections, and ducts 309
C8.4.4.5
Ducts 310
C8.4.5
Grout 310
C8.4.5.1
Post-tensioning 310
C8.4.5.2
Other applications 310
C8.4.6
Material resistance factors 310
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S6.1-06
C8.5
C8.5.1
C8.5.2
C8.5.2.1
C8.5.2.2
C8.5.2.3
C8.5.3
C8.5.3.1
C8.5.3.2
C8.5.4
C8.6
C8.6.1
C8.6.2
C8.6.2.1
C8.6.2.2
C8.6.2.3
C8.6.2.4
C8.6.2.5
C8.6.2.6
C8.6.2.7
C8.6.3
C8.7
C8.7.1
C8.7.2
C8.7.3
C8.7.4
C8.7.4.1
C8.7.4.2
C8.7.4.3
C8.8
C8.8.2
C8.8.3
C8.8.4
C8.8.4.1
C8.8.4.2
C8.8.4.3
C8.8.4.4
C8.8.4.5
C8.8.4.6
C8.8.5
C8.8.5.1
C8.8.5.4
C8.8.5.5
C8.8.5.6
C8.8.5.8
C8.8.6
C8.8.7
C8.9
C8.9.1
C8.9.1.1
C8.9.1.2
C8.9.1.3
C8.9.1.4
C8.9.1.5
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Limit states 311
General 311
Serviceability limit states 311
General 311
Cracking 311
Deformation 311
Fatigue limit state 311
Reinforcing bars 311
Tendons 312
Ultimate limit states 312
Design considerations 312
General 312
Design 312
General 312
Member stiffness 313
Imposed deformations 313
Stress concentrations 313
Secondary effects due to prestress 313
Redistribution of force effects 313
Directional change of tendons 313
Buckling 316
Prestressing 317
Stress limitations for tendons 317
Concrete strength at transfer 317
Grouting 317
Loss of prestress 317
General 317
Losses at transfer 319
Losses after transfer 320
Flexure and axial loads 322
Assumptions for the serviceability and fatigue limit states 322
Assumptions for the ultimate limit states 323
Flexural components 323
Factored flexural resistance 323
Tendon stress at the ultimate limit states 324
Minimum reinforcement 324
Cracking moment 324
Maximum reinforcement 325
Prestressed concrete stress limitations 325
Compression components 325
General 325
Maximum factored axial resistance 327
Biaxial loading 327
Reinforcement limitations 327
Hollow rectangular components 327
Tension components 328
Bearing 328
Shear and torsion 328
General 328
Consideration of torsion 328
Regions requiring transverse reinforcement 328
Minimum amount of transverse reinforcement 328
Design yield strength of transverse reinforcement 328
Effective shear depth 329
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C8.9.1.6
C8.9.1.7
C8.9.1.8
C8.9.2
C8.9.2.1
C8.9.2.2
C8.9.2.3
C8.9.2.4
C8.9.2.5
C8.9.3
C8.9.3.1
C8.9.3.3
C8.9.3.4
C8.9.3.5
C8.9.3.6
C8.9.3.7
C8.9.3.8
C8.9.3.9
C8.9.3.10
C8.9.3.11
C8.9.3.12
C8.9.3.13
C8.9.3.14
C8.9.3.15
C8.9.3.17
C8.9.3.18
C8.9.3.19
C8.9.4
C8.9.4.1
C8.9.4.3
C8.9.5
C8.9.5.1
C8.9.5.2
C8.9.5.4
C8.10
C8.10.1
C8.10.2
C8.10.3
C8.10.3.2
C8.10.3.3
C8.10.3.4
C8.10.4
C8.10.4.2
C8.10.5
C8.10.5.1
C8.10.5.2
C8.10.6
C8.11
C8.11.1
C8.11.2
C8.11.2.1
C8.11.2.2
C8.11.2.3
C8.11.2.4
xvi
© Canadian Standards Association
Effective web width 329
Variable-depth components 329
Reduced prestress within transfer length 329
Design procedures 329
Flexural regions 329
Regions near discontinuities 329
Interface regions 329
Slabs, walls, and footings 330
Detailed analysis 330
Sectional design model 330
Sections near supports 330
Factored shear resistance 330
Determination of Vc 330
Determination of Vs 330
Determination of β and θ for non-prestressed components (simplified method) 330
Determination of β and θ (general method) 331
Determination of ε x 332
Proportioning of transverse reinforcement 333
Extension of longitudinal reinforcement 334
Longitudinal reinforcement on the flexural tension side 334
Longitudinal reinforcement on the flexural compression side 335
Compression fan regions 335
Anchorage of longitudinal reinforcement at exterior supports 336
Transverse reinforcement for combined shear and torsion 336
Factored torsional resistance 337
Cross-sectional dimensions to avoid crushing for combined shear and torsion 337
Determination of ε x for combined shear and torsion 337
Slabs, walls, and footings 337
Critical sections for shear 337
Two-way action 337
Interface shear transfer 337
General 337
Values of c and µ 338
Anchorage of shear-friction reinforcement 339
Strut-and-tie model 339
General 339
Structural idealization 340
Proportioning of a compressive strut 340
Effective cross-sectional area of strut 340
Limiting compressive stress in strut 340
Reinforced strut 342
Proportioning of a tension tie 342
Anchorage of tie 342
Proportioning of node regions 342
Stress limits in node regions 342
Satisfying stress limits in node regions 342
Crack control reinforcement 343
Durability 343
Deterioration mechanisms 343
Protective measures 344
Concrete quality 344
Concrete covers and tolerances 346
Corrosion protection for reinforcement, ducts, and metallic components 347
Sulphate-resistant cements 347
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S6.1-06
C8.11.2.6
C8.11.3
C8.11.3.1
C8.11.3.2
C8.11.3.3
C8.12
C8.12.1
C8.12.2
C8.12.3
C8.12.3.1
C8.12.3.2
C8.12.4
C8.12.5
C8.13
C8.13.1
C8.13.2
C8.13.3
C8.13.3.2
C8.13.3.3
C8.13.3.4
C8.14
C8.14.1
C8.14.2
C8.14.2.1
C8.14.2.2
C8.14.3
C8.14.4
C8.14.4.2
C8.14.5
C8.15
C8.15.1
C8.15.2
C8.15.3
C8.15.4
C8.15.5
C8.15.5.1
C8.15.5.3
C8.15.7
C8.15.9
C8.15.9.4
C8.16
C8.16.1
C8.16.2
C8.16.2.1
C8.16.2.2
C8.16.2.3
C8.16.3
C8.16.5
C8.16.6
C8.16.7
C8.16.7.1
C8.16.7.2
C8.16.7.3
C8.16.7.4
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Drip grooves 347
Detailing for durability 348
Reinforcement detailing 348
Confining reinforcement cage 348
Debonding of pretensioned strands 348
Control of cracking 349
General 349
Distribution of reinforcement 349
Reinforcement 349
Maximum crack width 349
Calculation of crack width 349
Crack control in the side faces of beams 349
Flanges of T-beams 350
Deformation 350
General 350
Dimensional changes 350
Deflections and rotations 350
Refined method 350
Simplified method 350
Total deflection and rotation 350
Details of reinforcement and special detailing requirements 351
Hooks and bends 351
Spacing of reinforcement 351
Reinforcing bars 351
Tendons 351
Transverse reinforcement for flexural components 352
Transverse reinforcement for compression components 352
Spirals 352
Reinforcement for shear and torsion 352
Development and splices 352
Development 352
Development of reinforcing bars and deformed wire in tension 352
Development of reinforcing bars in compression 352
Development of pretensioning strand 352
Development of standard hooks in tension 353
General 353
Factors modifying hook development length 353
Development of welded wire fabric in tension 353
Splicing of reinforcement 353
Splices of deformed bars in compression 354
Anchorage zone reinforcement 354
General 354
Post-tensioning anchorage zones 354
General 354
General zone 356
Local zone 366
Pretensioning anchorage zones 368
Intermediate anchorages 368
Anchorage blisters 368
Anchorage of attachments 369
General 369
Transfer of tensile load from anchor to concrete 369
Transfer of shear load from anchor to concrete 370
Reinforcement 371
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© Canadian Standards Association
C8.16.7.5
C8.16.7.6
C8.17
C8.18
C8.18.1
C8.18.2
C8.18.3
C8.18.4
C8.18.4.1
C8.18.4.2
C8.18.4.3
C8.18.4.4
C8.18.5
C8.18.6
C8.18.7
C8.19
C8.19.2
C8.19.3
C8.19.4
C8.19.4.1
C8.19.4.2
C8.19.4.3
C8.20
C8.20.1
C8.20.3
C8.20.4
C8.20.5
C8.21
C8.22
C8.22.1
C8.22.2
C8.22.2.2
C8.22.2.3
C8.22.4
C8.22.6
C8.22.6.1
C8.22.6.3
C8.22.6.4
C8.22.6.5
C8.22.7
C8.22.7.2
C8.23
C8.23.2
C8.23.4
C8.23.5
C8.23.7
C8.23.7.1
C8.23.7.2
C8.23.7.3
C8.23.7.4
© Canadian Standards Association
Compressive resistance of concrete 372
Design requirements for anchors 372
Seismic design and detailing 373
Special provisions for deck slabs 373
Design methods 373
Minimum slab thickness 373
Allowance for wear 374
Empirical design method 374
General 374
Cast-in-place deck slabs 374
Cast-in-place deck slabs on precast panels 374
Full-depth precast panels 374
Diaphragms 375
Edge stiffening 375
Distribution reinforcement 375
Composite construction 375
Flexure 375
Shear 375
Semi-continuous structures 376
General 376
Positive moments 376
Negative moments 378
Concrete girders 378
General 378
Flange thickness for T- and box girders 378
Isolated girders 378
Top and bottom flange reinforcement for cast-in-place T- and box girders 379
Multi-beam decks 379
Segmental construction 379
General 379
Additional ducts and anchorages 379
During construction 379
Future strengthening 380
Deviators for external tendons 380
Special provisions for various bridge types 380
Precast segmental 380
Balanced cantilever construction 380
Span-by-span construction 380
Incrementally launched construction 381
Precast segmental beam bridges 382
Joints 382
Concrete piles 383
Specified concrete strength 383
Splices 383
Pile dimensions 383
Prestressed concrete piles 383
Effective prestress 383
Concrete stress limitations 383
Factored resistance 383
Sections within development length 383
Section C9 — Wood structures 393
C9.1
Scope 395
C9.4
Limit states 395
C9.4.1
General 395
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C9.4.2
C9.4.4
C9.5
C9.5.1
C9.5.2
C9.5.3
C9.5.4
C9.5.5
C9.5.6
C9.5.7
C9.5.8
C9.6
C9.6.2
C9.6.3
C9.7
C9.8
C9.10
C9.11
C9.11.1
C9.11.1.1
C9.11.1.2
C9.11.1.3
C9.11.2
C9.12
C9.12.1
C9.12.2
C9.12.3
C9.12.4
C9.12.5
C9.12.6
C9.13
C9.13.1
C9.13.2
C9.14
C9.14.3
C9.14.4
C9.14.4.2
C9.14.4.3
C9.15
C9.15.1
C9.16
C9.17
C9.17.1
C9.17.2
C9.17.3
C9.17.4
C9.17.5
C9.17.6
C9.17.9
C9.17.11
C9.18
C9.19
C9.19.1
C9.19.3
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Serviceability limit states 395
Resistance factor 395
General design 395
Design assumption 395
Spans 395
Load-duration factor 396
Size-effect factors 396
Service condition 396
Load-sharing factor 396
Notched components 397
Butt joint stiffness factor 397
Flexure 397
Size effect 397
Lateral stability 397
Shear 397
Compression members 398
Compression at an angle to grain 399
Sawn wood 399
Materials 399
Species and species combinations 399
Grades of sawn wood 400
Identification of wood 400
Specified strengths and moduli of elasticity 400
Glued-laminated timber 403
Materials 403
Specified strengths and moduli of elasticity 403
Vertically laminated beams 404
Camber 404
Varying depth 404
Curved members 404
Structural composite lumber 404
Materials 404
Specified strengths and moduli of elasticity 404
Wood piles 405
Specified strengths and moduli of elasticity 405
Design 405
Embedded portion 405
Unembedded portion 405
Fastenings 405
General 405
Hardware and metalwork 405
Durability 405
General 405
Pedestrian contact 406
Incising 406
Fabrication 406
Pressure preservative treatment of laminated veneer lumber 406
Pressure preservative treatment of parallel strand lumber 406
Untreated round wood piles 406
Protective treatment of hardware and metalwork 406
Wood cribs 407
Wood trestles 407
General 407
Framed bents 407
November 2006
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© Canadian Standards Association
C9.19.3.3
C9.20
C9.20.2
C9.21
C9.21.1
C9.21.2
C9.21.2.1
C9.21.2.2
C9.22
C9.22.3
C9.22.4
C9.22.5
C9.22.5.1
C9.22.5.2
C9.23
C9.23.1
C9.23.2
C9.23.2.1
C9.23.2.2
C9.23.2.4
C9.23.3
C9.23.3.1
C9.23.3.2
C9.23.3.3
C9.23.3.4
C9.23.4
C9.23.4.1
C9.23.4.2
C9.23.4.3
C9.23.4.4
C9.23.5
C9.23.5.4
C9.23.5.5
C9.23.6
C9.23.7
C9.23.8
C9.23.8.1
C9.23.8.2
C9.24
C9.25
C9.25.1
C9.25.2
© Canadian Standards Association
Post connections 407
Stringers and girders 407
Diaphragms 407
Nail-laminated wood decks 407
General 407
Transversely laminated wood decks 407
General 407
Assembly 408
Wood-concrete composite decks 408
Concrete slab 408
Wood-concrete interface 408
Factored moment resistance 408
General 408
Factored positive moment resistance 408
Stress-laminated wood decks 408
General 408
Post-tensioning materials 409
Post-tensioning steel 409
Anchorages 409
Stress limitations 409
Design of post-tensioning systems 409
General 409
Steel/wood ratio 409
Distributed normal pressure on laminates 409
Stressing procedure 410
Design of distribution bulkhead 410
General 410
Factored bearing resistance to post-tensioning forces 410
Bearing area for post-tensioning force 410
Steel channel bulkhead 410
Laminated decks 410
Nailing 410
Support anchorage 411
Net section 411
Hardware durability 411
Design details 411
Curbs and barriers 411
Containment of failed prestressing components 411
Wearing course 411
Drainage 411
General 411
Deck 412
Section C10 — Steel structures 415
C10.1
Scope 420
C10.2
Definitions 420
C10.3
Abbreviations and symbols 420
C10.3.2
Symbols 420
C10.4
Materials 420
C10.4.1
General 420
C10.4.2
Structural steel 421
C10.4.5
Bolts 421
C10.4.11 Identification 421
C10.5
Design theory and assumptions 421
C10.5.2
Ultimate limit states 421
xx
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S6.1-06
C10.5.3
C10.5.4
C10.5.7
C10.5.8
C10.5.9
C10.5.9.2
C10.6
C10.6.2
C10.6.3
C10.6.4
C10.6.4.2
C10.6.4.3
C10.6.5
C10.6.7
C10.6.7.2
C10.6.7.5
C10.7
C10.7.1
C10.7.3
C10.7.4
C10.7.4.3
C10.7.5
C10.8
C10.8.1
C10.8.1.2
C10.8.1.3
C10.8.1.4
C10.8.2
C10.8.3
C10.8.4
C10.9
C10.9.1
C10.9.2
C10.9.3
C10.9.3.1
C10.9.3.2
C10.9.4
C10.9.5
C10.9.5.3
C10.9.5.4
C10.9.5.5
C10.9.5.6
C10.10
C10.10.1
C10.10.1.1
C10.10.1.2
C10.10.2
C10.10.2.1
C10.10.2.2
C10.10.2.3
C10.10.3
C10.10.3.4
C10.10.4
C10.10.5
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Serviceability limit states 421
Fatigue limit state 421
Resistance factors 422
Analysis 426
Design lengths of members 426
Compression members 426
Durability 427
Corrosion as a deterioration mechanism 427
Corrosion protection 427
Superstructure components 428
Structural steel 428
Cables, ropes, and strands 429
Other components 429
Detailing for durability 430
Interior bracing 430
Overpasses 430
Design detail 430
General 430
Floor beams and diaphragms at piers and abutments 431
Camber 431
Horizontally heat-curved rolled or welded beams 431
Welded attachments 431
Tension members 431
General 431
Slenderness 431
Cross-sectional areas 431
Pin-connected members in tension 432
Axial tensile resistance 432
Axial tension and bending 432
Tensile resistance of cables 432
Compression members 433
General 433
Width-to-thickness ratios of elements in compression 433
Axial compressive resistance 433
Flexural buckling 433
Torsional or flexural-torsional buckling 433
Axial compression and bending 434
Composite columns 434
Axial load on concrete 434
Compressive resistance 434
Bending resistance 434
Axial compression and bending resistance 434
Beams and girders 435
General 435
Cross-sectional area 435
Flange cover plate restrictions 435
Class 1 and Class 2 sections 435
Width-to-thickness ratios 435
Laterally supported members 436
Laterally unbraced members 436
Class 3 sections 439
Class 4 sections 439
Stiffened plate girders 440
Shear resistance 440
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© Canadian Standards Association
C10.10.5.1
C10.10.5.2
C10.10.6
C10.10.6.1
C10.10.6.2
C10.10.6.3
C10.10.6.4
C10.10.7
C10.10.7.1
C10.10.7.2
C10.10.8
C10.10.8.1
C10.10.9
C10.11
C10.11.1
C10.11.2
C10.11.3
C10.11.4
C10.11.5
C10.11.5.2
C10.11.5.3
C10.11.6
C10.11.6.2
C10.11.6.3
C10.11.7
C10.11.8
C10.11.8.1
C10.11.8.3
C10.11.8.4
C10.12
C10.12.1
C10.12.2
C10.12.3
C10.12.4
C10.12.5
C10.12.5.1
C10.12.5.2
C10.12.5.3
C10.12.5.4
C10.12.6
C10.12.6.1
C10.12.6.2
C10.12.6.3
C10.12.7
C10.12.7.1
C10.12.8
C10.12.8.1
C10.12.8.2
C10.12.8.3
C10.12.8.4
C10.12.8.5
C10.13
C10.13.1
C10.13.2
xxii
© Canadian Standards Association
Factored shear resistance 440
Combined shear and moment 441
Intermediate transverse stiffeners 441
General 441
Proportioning transverse stiffeners 441
Connection to web 441
Stiffener details at flanges 441
Longitudinal web stiffeners 442
General 442
Proportioning 442
Bearing stiffeners 442
Web crippling and yielding 442
Lateral bracing, cross-frames, and diaphragms 442
Composite beams and girders 443
General 443
Proportioning 443
Effects of creep and shrinkage 443
Control of permanent deflections 443
Class 1 and Class 2 sections 443
Positive moment regions 443
Negative moment regions 444
Class 3 sections 444
Positive moment regions 444
Negative moment regions 444
Stiffened plate girders 445
Shear connectors 445
General 445
Shear connector resistance 445
Longitudinal shear 445
Composite box girders 445
General 445
Effective width of tension flanges 445
Web plates 446
Flange-to-web welds 446
Moment resistance 446
Composite and non-composite sections 446
Unstiffened compression flanges 446
Compression flanges stiffened longitudinally 446
Compression flanges stiffened longitudinally and transversely 447
Diaphragms, cross-frames, and lateral bracing 447
Diaphragms and cross-frames within girders 447
Diaphragms and cross-frames between girders 447
Lateral bracing 447
Multiple box girders 448
General 448
Single box girders 448
General 448
Analysis 448
Bearings 448
Moment resistance 448
Combined shear and torsion 448
Horizontally curved girders 449
General 449
Special considerations 449
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S6.1-06
C10.13.2.1
C10.13.2.2
C10.13.2.3
C10.13.2.4
C10.13.3
C10.13.3.1
C10.13.3.2
C10.13.4
C10.13.5
C10.13.6
C10.13.6.1
C10.13.6.2
C10.13.7
C10.13.7.2
C10.13.7.3
C10.13.7.4
C10.14
C10.14.1
C10.14.3
C10.14.3.3
C10.14.3.6
C10.15
C10.15.1
C10.15.2
C10.15.3
C10.15.4
C10.16
C10.16.1
C10.16.3
C10.16.3.2
C10.16.3.3
C10.16.3.4
C10.16.4
C10.16.6
C10.16.6.1
C10.16.6.2
C10.16.6.3
C10.16.7
C10.17
C10.17.1
C10.17.2
C10.17.2.1
C10.17.2.2
C10.17.2.3
C10.17.2.4
C10.17.2.5
C10.17.2.6
C10.17.2.7
C10.17.2.8
C10.17.3
C10.17.3.2
C10.18
C10.18.1
C10.18.1.1
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Dynamic load allowance 449
Super-elevation and centrifugal forces 449
Thermal forces 449
Uplift 449
Design theory 449
General 449
Limiting curvature 450
Bearings 450
Diaphragms, cross-frames, and lateral bracing 450
Steel I-girders 450
Non-composite girder design 450
Composite I-girders 451
Composite box girders 452
Webs 452
Top flanges 452
Bottom flanges 452
Trusses 453
General 453
Bracing 453
Through-truss spans 453
Half-through trusses and pony trusses 453
Arches 454
General 454
Width-to-thickness ratios 454
Longitudinal web stiffeners 454
Axial compression and bending 454
Orthotropic decks 454
General 454
Superposition of local and global effects 454
Decks in longitudinal tension 454
Decks in longitudinal compression 454
Transverse flexure 454
Deflection 455
Design detail requirements 455
Minimum plate thickness 455
Closed ribs 455
Deck and rib details 455
Wearing surface 455
Structural fatigue 456
General 456
Live-load-induced fatigue 456
Calculation of stress range 456
Design criteria 456
Fatigue stress range resistance 457
Detail categories 459
Width-to-thickness ratios of transversely stiffened webs 459
Fatigue resistance of high-strength bolts loaded in tension 459
Fatigue resistance of stud shear connectors 459
Fatigue resistance of cables 459
Distortion-induced fatigue 460
Connection of diaphragms, cross-frames, lateral bracing, and floor beams 460
Splices and connections 461
General 461
General design considerations 461
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© Canadian Standards Association
C10.18.1.2
C10.18.1.3
C10.18.2
C10.18.2.2
C10.18.2.3
C10.18.2.4
C10.18.3
C10.18.4
C10.18.4.1
C10.18.4.2
C10.18.4.3
C10.18.4.4
C10.18.4.5
C10.18.4.6
C10.18.4.7
C10.18.4.8
C10.18.4.9
C10.18.4.10
C10.18.4.12
C10.18.5
C10.18.5.3
C10.19
C10.19.2
C10.20
C10.20.1
C10.20.2
C10.21
C10.21.2
C10.21.3
C10.21.3.1
C10.21.3.3
C10.21.3.4
C10.22
C10.22.2
C10.22.3
C10.22.4
C10.23
C10.23.1
C10.23.4
C10.23.5
C10.23.6
C10.24
C10.24.1
C10.24.2
C10.24.3
C10.24.3.2
C10.24.4
C10.24.5
C10.24.5.3
C10.24.5.6
C10.24.6
C10.24.6.1
C10.24.6.2
C10.24.6.3
xxiv
© Canadian Standards Association
Alignment of axially loaded members 461
Proportioning of connections and splices 461
Bolted connections 461
Bolts in tension 461
Bolted joints in shear 461
Bolts in shear and tension 462
Welds 462
Detailing of bolted connections 463
Contact of bolted parts 463
Hole size 463
Coatings 463
Bolt spacing 463
Sealing bolts 463
Stitch bolts 463
Stitch bolts at the ends of compression members 463
Minimum edge distance 463
Minimum end distance 463
Maximum edge or end distance 463
Fillers 464
Connection reinforcement and stiffening 464
Moment connections 464
Anchors 464
Anchor bolt resistance 464
Pins, rollers, and rockers 465
Bearing resistance 465
Pins 465
Torsion 465
Members of closed cross-section 465
Members of open cross-section 466
St. Venant torsional constant 466
Torsional resistance 466
Combined bending and torsion 466
Piles 466
Effective length 466
Splices 466
Composite tube piles 466
Fracture control 467
General 467
Welding of fracture-critical and primary tension members 469
Welding corrections and repairs to fracture-critical members 469
Nondestructive testing of fracture-critical members 470
Construction requirements for structural steel 470
General 470
Submissions 470
Materials 470
High-strength bolts, nuts, and washers 470
Fabrication 470
Welded construction 470
Primary tension and fracture-critical members 470
Complete joint penetration groove welds 471
Bolted construction 471
General 471
Assembly 471
Installation of bolts 471
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S6.1-06
C10.24.6.6
C10.24.6.7
C10.24.6.8
C10.24.10
C10.24.10.2
C10.24.10.7
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Turn-of-nut tightening 472
Inspection 472
Reuse of bolts 473
Erection 473
Falsework 473
Repairs to erected material 473
Section C11 — Joints and bearings 483
C11.1
Scope 485
C11.4
Common requirements 485
C11.4.1
General 485
C11.5
Deck joints 486
C11.5.1
General requirements 486
C11.5.1.1
Functioning requirements 486
C11.5.1.2
Design loads 486
C11.5.1.3
Structural requirements 486
C11.5.1.5
Maintenance 487
C11.5.2
Selection 487
C11.5.2.1
Number of joints 487
C11.5.2.2
Placement 487
C11.5.2.3
Types of deck joints 488
C11.5.3
Design 488
C11.5.3.1
Bridge deck movements 488
C11.5.3.2
Components 488
C11.5.4
Fabrication 489
C11.5.5
Installation 489
C11.5.7
Sealed joint drainage 489
C11.5.9
Volume control joint 490
C11.6
Bridge bearings 490
C11.6.1
General 490
C11.6.2
Metal back, roller, and spherical bearings 490
C11.6.2.1
General design considerations 490
C11.6.2.2
Materials 490
C11.6.2.3
Geometric requirements 491
C11.6.2.4
Contact pressure 491
C11.6.3
Sliding surfaces 491
C11.6.3.1
General 491
C11.6.3.2
PTFE layer 491
C11.6.3.3
Mating surface 491
C11.6.3.4
Attachment 491
C11.6.3.5
Minimum thickness 492
C11.6.3.6
Contact pressure 492
C11.6.3.7
Coefficient of friction 492
C11.6.4
Spherical bearings 493
C11.6.4.1
General 493
C11.6.4.2
Geometric requirements 493
C11.6.4.3
Lateral load capacity 493
C11.6.5
Pot bearings 493
C11.6.5.1
General 493
C11.6.5.2
Materials 493
C11.6.5.3
Geometric requirements 494
C11.6.5.4
Elastometric disc 494
C11.6.5.5
Sealing rings 495
C11.6.5.6
Pot 495
C11.6.5.7
Piston 495
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© Canadian Standards Association
C11.6.6
C11.6.6.2
C11.6.6.3
C11.6.6.5
C11.6.6.6
C11.6.6.7
C11.6.7
C11.6.7.1
C11.6.7.2
C11.6.7.4
C11.6.7.5
C11.6.8
C11.6.8.1
C11.6.8.2
C11.6.8.3
C11.6.8.4
C11.6.8.5
C11.6.8.6
C11.6.8.7
C11.6.10
C11.6.10.1
C11.6.10.2
C11.6.10.3
© Canadian Standards Association
Elastomeric bearings 496
Materials 496
Geometric requirements 496
Fabrication 496
Positive attachment 496
Bearing pressure 496
Disc bearings 497
General 497
Materials 497
Elastomeric disc 497
Steel plates 497
Guides for lateral restraints 497
General 497
Materials 498
Geometric requirements 498
Design loads 498
Load location 498
Contact pressure 498
Attachment of low-friction material 498
Load plates and attachments for bearings 498
Plates for load distribution 498
Tapered plates 499
Attachment 499
Section C12 — Barriers and highway accessory supports 501
C12.1
Scope 502
C12.4
Barriers 502
C12.4.1
General 502
C12.4.2
Barrier joints 503
C12.4.3
Traffic barriers 503
C12.4.3.1
General 503
C12.4.3.2
Performance level 503
C12.4.3.3
Geometry and end treatment details 505
C12.4.3.4
Crash test requirements 506
C12.4.3.5
Anchorages 523
C12.4.4
Pedestrian barriers 524
C12.4.5
Bicycle barriers 524
C12.4.6
Combination barriers 524
C12.5
Highway accessory supports 524
C12.5.1
General 524
C12.5.2
Vertical clearances 525
C12.5.3
Maintenance 525
C12.5.5
Design 525
C12.5.5.2
Ultimate limit states 525
C12.5.5.3
Serviceability limit states 526
C12.5.5.4
Fatigue limit state 526
C12.5.6
Breakaway supports 527
C12.5.6.1
General 527
C12.5.6.2
Crash test requirements 528
C12.5.6.3
Alternative crash test requirements 528
C12.5.6.4
Changes to crash-tested highway accessory supports 528
C12.5.6.5
Geometry 528
C12.5.7
Foundations 529
C12.5.7.2
Foundation investigation 529
C12.5.8
Corrosion protection 529
xxvi
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S6.1-06
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
C12.5.8.1 Steel 529
C12.5.8.3 Drainage and air circulation 529
C12.5.10 Camber 529
C12.5.11 Connections 530
C12.5.11.1 Bolts 530
C12.5.11.2 Circumferential welds 530
C12.5.11.4 Lapped joints 530
Section C13 — Movable bridges 533
C13.1
Scope 534
C13.5
General design requirements 535
C13.5.2
Type of deck 535
C13.6
Movable bridge components 535
C13.6.1
General features 535
C13.6.1.1 Counterweights 535
C13.6.2
Swing bridge components 535
C13.6.2.1 Centre bearing 535
C13.6.2.2 Rim bearing 535
C13.6.3
Bascule bridge components 535
C13.6.3.2 Locking devices 535
C13.6.5
Vertical lift bridge components 535
C13.6.5.1 Auxiliary counterweights 535
C13.6.5.4 Counterweight sheaves 536
C13.7
Structural analysis and design 536
C13.7.1
General 536
C13.7.3
Wind loads 536
C13.7.3.1 General 536
C13.7.3.6 Operator’s house and machinery house 536
C13.7.4
Seismic loads 536
C13.7.8
Swing bridges — Ultimate limit states 536
C13.7.9
Bascule (including rolling lift) bridges — Ultimate limit states 537
C13.7.10
Vertical lift bridges — Ultimate limit states 537
C13.8
Mechanical system design 538
C13.8.5
Power requirements for main machinery 538
C13.8.8
Frictional resistance 538
C13.8.8.2 Locks and wedges 538
C13.8.15
Design of wire ropes 538
C13.8.15.2 Sheaves and drums — Minimum diameters 538
C13.8.15.5 Limiting rope deviations 538
C13.8.15.6 Initial tension of operating ropes 538
C13.8.16
Shafting 538
C13.8.17
Machinery fabrication and installation 539
C13.8.17.5 Anti-friction bearings 539
C13.8.17.7 Welded parts 539
C13.8.20
Quality of work 539
C13.8.20.3 Surface finishes 539
C13.10
Electrical system design 539
C13.10.7
Motor torque for span operation 539
C13.10.9
Number of motors 539
C13.11
Construction 539
C13.11.3
Erection 539
C13.11.3.6 Counterweights 539
C13.13
Operating and maintenance manual 540
C13.14
Inspection 540
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© Canadian Standards Association
© Canadian Standards Association
Section C14 — Evaluation 541
C14.1
Scope 543
C14.3
Symbols 543
C14.4
General requirements 544
C14.4.1
Exclusions 544
C14.4.2
Expertise 544
C14.4.3
Future growth of traffic or future deterioration 544
C14.5
Evaluation procedures 544
C14.5.2
Limit states 544
C14.5.2.2 Ultimate limit states 544
C14.5.2.3 Serviceability limit states 544
C14.5.4
Procedures 545
C14.5.4.1 General 545
C14.6
Condition inspection 545
C14.6.1
General 545
C14.6.2
Plans 545
C14.6.4
Deterioration 546
C14.7
Material strengths 546
C14.7.1
General 546
C14.7.2
Review of original construction documents 546
C14.7.2.1 General 546
C14.7.2.2 Mill certificates 546
C14.7.3
Analysis of tests of samples 546
C14.7.3.4 Masonry mortar 546
C14.7.4
Strengths based on date of construction 547
C14.7.4.1 General 547
C14.7.4.2 Structural steel 547
C14.8
Permanent loads 547
C14.8.2
Dead load 547
C14.8.2.1 General 547
C14.8.2.2 Dead load distribution 548
C14.8.4
Shrinkage, creep, differential settlement, and bearing friction 548
C14.8.5
Secondary effects from prestressing 548
C14.9
Transitory loads 548
C14.9.1
Normal traffic 549
C14.9.1.6 Alternative loading 550
C14.9.2
Permit — Vehicle loads 550
C14.9.2.1 General 550
C14.9.2.2 Permit — Annual or project (PA) 550
C14.9.2.3 Permit — Bulk haul (PB) 550
C14.9.2.4 Permit — Controlled (PC) 550
C14.9.2.5 Permit — Single trip (PS) 551
C14.9.3
Dynamic load allowance for permit vehicle loads and alternative loading 551
C14.9.4
Multiple-lane loading 552
C14.9.4.1 Design lanes 552
C14.9.4.2 Normal traffic 552
C14.9.4.3 Permit vehicle with normal traffic 552
C14.9.5
Loads other than traffic 552
C14.9.5.1 Sidewalk loading 552
C14.9.5.2 Snow loads 552
C14.9.5.4 Temperature effects 552
C14.9.5.5 Secondary effects 553
xxviii
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S6.1-06
C14.10
C14.11
C14.12
C14.12.1
C14.12.2
C14.12.3
C14.12.4
C14.12.5
C14.13
C14.13.1
C14.13.2
C14.13.2.1
C14.13.3
C14.13.3.1
C14.13.3.2
C14.14
C14.14.1
C14.14.1.3
C14.14.1.4
C14.14.1.5
C14.14.1.6
C14.14.1.7
C14.14.1.8
C14.14.2
C14.14.3
C14.15
C14.15.1
C14.15.2
C14.15.2.3
C14.15.4
C14.16
C14.16.1
C14.16.2
C14.16.3
C14.16.3.2
C14.16.3.3
C14.16.4
C14.16.4.1
C14.16.4.2
C14.17
C14.17.1
C14.17.2
C14.17.3
C14.18
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Exceptional loads 553
Lateral distribution categories for live load 553
Target reliability index 553
General 553
System behaviour 556
Element behaviour 556
Inspection level 556
Important structures 556
Load factors 557
General 557
Permanent loads 557
Dead load 557
Transitory loads 557
Normal traffic 557
Permit vehicles 557
Resistance 557
General 557
Concrete deck slabs 557
Rivets 558
Masonry 558
Shear in concrete beams 558
Wood 559
Shear in steel plate girders with intermediate transverse stiffeners 559
Resistance adjustment factor 559
Effects of defects and deterioration 560
Live load capacity factor 561
General 561
Ultimate limit states 562
Mean load method for ultimate limit states (alternative method) 562
Combined load effects 562
Load testing 562
General 562
Instrumentation 562
Test load 563
Static load test 563
Dynamic load test 563
Application of load test results 563
Evaluation using observed behaviour 563
Live load capacity factors 564
Bridge posting 564
General 564
Calculation of posting loads 565
Posting signs 565
Fatigue 566
Annex
CA14.1 — Commentary on Annex A14.1 — Equivalent material strengths from tests of samples 571
Section C15 — Rehabilitation and repair 573
C15.3
General requirements 574
C15.3.1
Limit states 574
C15.5
Data collection 574
C15.6
Rehabilitation loads and load factors 574
C15.6.1
Loads 574
C15.6.1.2 Permanent loads 574
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C15.6.1.3 Rehabilitation design live loads 574
C15.6.1.5 Thermal, shrinkage, and creep effects 575
C15.6.1.7 Collision loads 575
C15.6.1.11 Component deterioration 576
C15.6.1.12 Loads induced by the rehabilitation 576
C15.6.2
Load factors and load combinations 576
C15.6.2.2 Minimum rehabilitation load factors 576
C15.6.2.4 Overall minimum load factor 576
C15.7
Analysis 576
C15.8
Resistance 576
Section C16 — Fibre-reinforced structures 579
C16.1
Scope 581
C16.2
Definitions 581
C16.3
Abbreviations and symbols 581
C16.3.1
Abbreviations 581
C16.3.2
Symbols 581
C16.4
Durability 582
C16.4.1
FRP tendons, primary reinforcement, and strengthening systems 582
C16.4.4
Cover to reinforcement 584
C16.4.5
Protective measures 584
C16.4.6
Allowance for wear in deck slabs 584
C16.4.8
Handling, storage, and installation of fibre tendons and primary reinforcement 585
C16.5
Fibre-reinforced polymers 585
C16.5.2
Confirmation of the specified tensile strength 585
C16.5.3
Resistance factor 585
C16.6
Fibre-reinforced concrete 588
C16.6.2
Fibre volume fraction 588
C16.7
Externally restrained deck slabs 588
C16.7.1
General 588
C16.7.2
Full-depth cast-in-place deck slabs 588
C16.7.3
Cast-in-place deck slabs on stay-in-place formwork 588
C16.7.4
Full-depth precast concrete deck slabs 589
C16.8
Concrete beams and slabs 589
C16.8.2
Deformity and minimum reinforcement 589
C16.8.2.1 Design for deformability 589
C16.8.2.2 Minimum flexural resistance 589
C16.8.2.3 Crack-control reinforcement 589
C16.8.3
Non-prestressed reinforcement 590
C16.8.4
Development length for FRP bars and tendons 590
C16.8.4.2 Splice length for FRP bars 590
C16.8.6
Tendons 590
C16.8.6.1 Supplementary reinforcement 590
C16.8.6.2 Stress limitations for tendons 590
C16.8.6.3 Capacity of anchors 590
C16.8.6.4 End zones in pretensioned components 590
C16.8.6.5 Protection of external tendons 590
C16.8.7
Design for shear 591
C16.8.8
Internally restrained cast-in-place deck slabs 591
C16.8.8.1 Design by empirical method 591
C16.8.8.2 Design for flexure 591
C16.9
Stressed wood decks 592
C16.9.1
General 592
C16.9.2
Post-tensioning materials 592
C16.9.2.1 Tendons 592
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C16.9.2.2
C16.9.2.3
C16.9.4
C16.9.5
C16.9.6
C16.9.6.1
C16.9.6.2
C16.9.6.3
C16.9.6.4
C16.9.6.5
C16.9.6.7
C16.10
C16.11
C16.11.1
C16.11.2
C16.11.2.1
C16.11.2.2
C16.11.2.3
C16.11.2.4
C16.11.2.5
C16.11.3
C16.11.3.1
C16.11.3.2
C16.12
C16.12.1
C16.12.2
C16.12.2.1
C16.12.2.2
C16.12.3
C16.12.3.1
C16.12.3.2
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Anchors 592
Stress limitations 592
Stressing procedure 592
Design of bulkheads 592
Stressed log bridges 592
General 592
Log dimensions 593
Splicing at butt joints 593
Frequency of butt joints 593
Holes in logs for an internal system 593
Surfacing 593
Barrier walls 593
Rehabilitation of existing concrete structures with FRP 595
General 595
Flexural and axial load rehabilitation 596
General 596
Assumptions for SLS and FLS calculations 596
Assumptions for ULS calculations 596
Flexural components 596
Compression components 598
Shear rehabilitation with externally bonded FRP systems 599
General 599
Factored shear resistance 599
Rehabilitation of timber bridges 599
General 599
Strengthening for flexure 599
Flexural strengthening with GFRP sheets 600
Flexural strengthening with GFRP NSMR 600
Strengthening for shear 600
Shear strengthening with GFRP sheets 600
Shear strengthening with embedded GFRP bars 601
Annexes
CA16.1 — Commentary on Annex A16.1 — Installation of FRP strengthening systems 607
CA16.2 — Commentary on Annex A16.2 — Quality control for FRP strengthening systems 608
Tables
C1.1 — Computation of design flood discharges 17
C1.2 — Local scour coefficients for piers, CL 21
C1.3 — Coefficients for skewed piers, CS 22
C2.1 — Typical service life of components 34
C3.1 — Configuration factor, K 47
C3.2 — MOU weight and dimension limits 52
C3.3 — Load factors for ASCE 30% heavy vehicles 59
C3.4 — Estimated live load factors for long span loads 59
C3.5 — Load effects due to restraint of thermal movements 75
C3.6 — Shielding factors, Kx, for trusses 82
C3.7 — Conservative horizontal load combinations 83
C4.1 — Performance requirements 116
C4.2 — Seismic performance zones 116
C5.1 — Analysis results for flexure — 3-lane slab-on-girder at ULS and SLS, B = 10.92 m 175
C5.2 — Analysis results for internal girders of 3-lane slab-on-girder with narrow lanes 182
C5.3 — Code equations for internal girders of 3-lane slab-on-girder bridges with narrow lanes 183
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C5.4
— Transverse moments in cantilever slabs due to horizontal railing loads in selected PL-3 and PL-2
barriers 188
C5.5 — Refined methods of analysis for short- and medium-span bridges 191
C6.1 — Reduction factors, R, to account for the effects of inclined loads 231
C6.2 — Downdrag calculations 235
C6.3 — Ranges of φ , β and Nt values 236
C6.4 — Assessed horizontal passive resistance and geotechnical reaction at SLS 240
C6.5 — Assumed strength of cohesive soils (CFEM 1992) 240
C6.6 — Movements required to mobilize various conditions (Ovesen 1981, Barker 1991,
NAVFAC DM-7.1 1982, Clayton and Militsky 1986) 244
C7.1 — Calculated and recommended kE and Es values 273
C7.2 — Non-saturated loss rates 280
C7.3 — Saturated loss rate (saturated soil area and water side inverts) 280
C8.1 — Typical thermal coefficients for concrete 306
C8.2 — Estimate of lump sum losses, MPa 318
C8.3 — Anchorage slip 319
C8.4 — Values of C 321
C8.5 — Effective length factor of compression components 326
C8.6 — Chemical attack of concrete by waters and soils containing aggressive agents 344
C8.7 — Proposed performance-based durability guideline for concrete materials 345
C8.8 — Multipliers for estimating long-time deflections 350
C10.1 — Allowable stress fraction, C, of specified minimum tensile strength, Fu for main cables of
suspension bridges 422
C10.2 — Ratios of live total load for suspension bridge cables 424
C10.3 — Ratios of live and dead loads to total load for various long-span cable-supported bridges, with
corresponding resistance factors for three values of C 425
C10.4 — Variation in life of coatings 428
C10.5 — Bolt tension 472
C12.1 — Test speeds, mph (kph) 516
C12.2 — Standard deviation modification factors 526
C13.1 — Swing bridges — Special load combinations and load factors 537
C13.2 — Bascule (including rolling lift) bridges — Special load combinations and load factors 537
C13.3 — Vertical lift bridges — Special load combinations and load factors 538
C14.1 — Statistical parameters for various dead loads 547
C14.2 — Statistical parameters for traffic loads 549
C14.3 — Statistical parameters for dynamic load allowance 551
C14.4 — Statistical parameters for lateral distribution categories for live load 553
C14.5 — Notional probability of failure for various reliability indices based on the normal probability
curve 555
C14.6 — δ R and VR values 560
C16.1 — Reactivity of fibres and matrices 583
C16.2 — Examples of variability of tensile strengths for CFRP and AFRP bars (Machida 1997) 585
C16.3 — Calculation of resistance factors 586
C16.4 — Comparison of resistance factors specified in the revised clauses with the product of F and
resistance factors in the previous edition of the Code 587
Figures
C1.1 — Reliability index 6
C1.2 — Typical abnormal flood discharge 18
C1.3 — General and local scour at a bridge 19
C1.4 — Typical scour at a bridge with spread footings 20
C1.5 — Clearance and freeboard for regulatory flood with maximum relief flow 25
C1.6 — Clearance and freeboard for regulatory flood with no relief flow possible 25
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Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
C3.1
— Comparison of measured deflections at edge of bridge, adjusted to design load, with deflection
criteria 42
C3.2 — Acceleration response of footbridge to pedestrian passage (Blanchard et al. 1977) 43
C3.3 — Acceleration limit for pedestrian bridge serviceability 44
C3.4 — Criteria for human response for steady vibration 44
C3.5 — Footfall impulse 46
C3.6 — Dynamic response factor as a function of span length and damping ratio, ζ 47
C3.7 — CS-W truck model in CAN/CSA-S6-88 53
C3.8 — OHBD truck models (OHBDC 1979, 1983, 1991) 53
C3.9 — Maximum observed overloads in Ontario during the 1970s 54
C3.10 — Critical vehicle configurations per the MOU (TAC 1991) 54
C3.11 — Comparison of the subconfigurations of the CL-625 Truck with the Ontario Bridge Formula and
the MOL 55
C3.12 — ASCE recommended loading, giving parameters P, U, and % HV (P = concentrated load per lane;
U = uniform load per lane; and % HV = average percentage of heavy vehicles in traffic flow) 57
C3.13 — Comparison of ASCE and Clause 12 of CAN/CSA-S6-88 truck populations 58
C3.14 — Factored loads compared 61
C3.15 — Dynamic load allowance frequency relationship 64
C3.16 — Loaded length for pedestrian load 70
C3.17 — Factors affecting thermal response of superstructure 73
C3.18 — Response of curved structures 73
C3.19 — Normal and transverse displacement across skew joint 74
C3.20 — Stationary point in straight and skewed superstructure 74
C3.21 — Stationary point in curved structure 75
C3.22 — Temperature during hydration and cooling 76
C3.23 — Components of thermal strain 77
C3.24 — Induced moments and reactions 77
C3.25 — Irregular support geometry 78
C3.26 — Plan view of pier showing direction of forces 86
C3.27 — Transverse ice load (floe flowing past a portion of a pier nose) 88
C4.1 — Seismic response coefficients for various soil profiles, normalized with respect to zonal
acceleration ratio A 118
C4.2 — Bridge deck subjected to assumed transverse and longitudinal loading 123
C4.3 — Typical relationship between stress ratio triggering liquefaction and (N1 )60 values for silty sand
(Seed et al. 1984) 126
C4.4 — Comparison of available and required resistance in terms of SPT or static cone resistance 127
C4.5 — Definition of β and i 129
C4.6 — Effect of soil friction angle on seismic active pressure coefficient (Elms and Martin 1979) 130
C4.7 — Variation of shear modulus with shear strain for sands (Seed et al. 1986) 131
C4.8 — Variation of shear modulus with shear strain for clays (Zen and Higuchi 1984) 132
C4.9 — Hoops and cross-tie arrangements 135
C4.10 — Details of interlocking spirals in oblong columns 136
C4.11 — Idealized force response curve 148
C4.12 — Idealized displacement response 149
C4.13 — Response curves for increasing damping 150
C4.14 — Characteristics of bilinear isolation bearings 151
C4.15 — Modified input response spectrum 152
C5.1 — Representative cross-sections and elevations of bridge types 164
C5.2 — Illustration of certain structural responses 165
C5.3 — Behaviour of box girder — Bending and torsional decomposition 170
C5.4 — Behaviour of box girder — Torsional components 171
C5.5 — Transverse variation of maximum longitudinal moment intensity in the idealized orthotropic
plate 173
C5.6 — Fm curves for slab and voided slab type — Narrow lane width 177
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C5.7 — Fm curves for slab-on-girder type — Narrow lane width 178
C5.8 — Fm curves for internal girders of slab-on-girder type at FLS 179
C5.9 — Fm curves for external girders of 3-lane narrow slab-on-girder type at FLS 180
C5.10 — Fm curves for external girders of slab-on-girder type at FLS 181
C5.11 — Vehicle edge distance correction — 3-lane slab-on-girders 184
C5.12 — Fm for 3-lane narrow slab and voided slab bridge at the fatigue and vibration limit state 185
C6.1 — Various load cases 208
C6.2 — Typical stress-strain curves for soil/rock 213
C6.3 — Load-deformation curve for footing 213
C6.4 — Typical resistance and reaction values 214
C6.5 — Total and differential settlement 217
C6.6 — Movements of components 218
C6.7 — Influence of an excavation for a new footing on an existing footing 224
C6.8 — Settlement caused by an adjacent excavation 224
C6.9 — Recommended locations for a new footing 224
C6.10 — Shallow foundation, effective contact area — Uniform pressure distribution 228
C6.11 — Shallow foundation, effective contact area — Linear pressure distribution 228
C6.12 — Pressure distributions, ULS structural design 229
C6.13 — Reaction at the SLS 230
C6.14 — Downdrag and the neutral plane 234
C6.15 — Idealized load vs. displacement relationships 238
C6.16 — Various earth pressures 243
C6.17 — Effect of ground slope — Active earth pressure 245
C6.18 — Effect of ground slope — Passive earth pressure 245
C6.19 — Backfill pressure after Broms and Ingold 246
C6.20 — Backfill for frost protection 247
C6.21 — Surcharge loading conditions 250
C6.22 — Ground anchor retaining wall schematic 251
C6.23 — Class I protection — Encapsulated anchor (PTI 1996) 251
C6.24 — Class II protection — Grout-protected anchor (PTI 1996) 252
C7.1 — Soil stress-strain relationships 272
C7.2 — Buried structure and soil section 273
C7.3 — Identification of W1 and W2 275
C7.4 — Longitudinal seam strengths of bolted steel plates with 152 × 51 mm corrugation profiles and
20 mm diameter bolts 278
C7.5 — Effective supporting length of pipe 289
C8.1 — Modulus of elasticity, Ec 308
C8.2 — Thrusts due to directional change of the prestressing steel 314
C8.3 — Resistance of concrete 315
C8.4 — Lateral forces due to strand bunching 316
C8.5 — Schematic diagram of stress levels during lifetime of a component 318
C8.6 — Force effects at a section 320
C8.7 — Prestress loss reduction in partially prestressed components 322
C8.8 — Strain and stress distribution and forces at ULS 323
C8.9 — Footing for which β = 0.18 331
C8.10 — Diagonal cracks in component with transverse reinforcement 331
C8.11 — More accurate calculation procedure for determining ε x 332
C8.12 — Assumed relationships between axial force in flange and axial strain of flange 333
C8.13 — Proportioning of transverse reinforcement 334
C8.14 — Free-body diagram of end region of beam 335
C8.15 — Force variation in longitudinal reinforcement near maximum moment locations 336
C8.16 — Box girder subjected to combined shear and torsion 336
C8.17 — Shear friction concept 338
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Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
C8.18 — Comparison of relationships between shear stress that can be transmitted across a crack and
compressive stress across the crack 339
C8.19 — Point load applied to a deep beam 340
C8.20 — Strut-and-tie truss model for a deep beam 341
C8.21 — Crushing strength of compressive strut as a function of the angle between strut and adjoining
tie 342
C8.22 — Deterioration process 343
C8.23 — Drip groove detail 348
C8.24 — Recommended spacing of ducts 351
C8.25 — Factors modifying hook development length 353
C8.26 — Anchorage terms 354
C8.27 — Geometry of the anchorage zone 355
C8.28 — General zone and local zone 356
C8.29 — Arrangement for bursting reinforcement 357
C8.30 — Edge tension forces 358
C8.31 — Arrangement of anchorage zone reinforcement 359
C8.32 — Principal stress field and strut-and-tie model 360
C8.33 — Strut-and-tie models for selected anchorage zones 361
C8.34 — Critical sections for nodes and compressive struts 362
C8.35 — Effect of discontinuity in anchorage zone 363
C8.36 — Edge distances 364
C8.37 — Local zone and strut interface 364
C8.38 — Closely spaced multiple anchorages 365
C8.39 — Terms used in expressions for Tbs and dbs 365
C8.40 — Determination of edge tension forces for eccentric anchorages 366
C8.41 — Geometry of the local zone 366
C8.42 — Area of supporting concrete surface for bearing stress 367
C8.43 — Effective bearing plate area for anchorage devices with separate wedge plate 368
C8.44 — Effective bearing plate area for anchorage device without separate wedge plate 368
C8.45 — Stress prismoids for tensile loading 369
C8.46 — Anchor head details 370
C8.47 — Effective shear stress area for shear towards a free edge 371
C8.48 — Reinforcement across potential failure surfaces 372
C8.49 — Equivalent bearing area 372
C8.50 — Coefficient of friction 373
C8.51 — Box girders without intermediate diaphragms 375
C8.52 — Haunch detail 376
C8.53 — Positive moment connection 377
C8.54 — Continuity moments due to external loads 378
C8.55 — Flange reinforcement 379
C8.56 — Shear keys 381
C8.57 — Location of launching pads 382
C8.58 — Eccentric reaction at launching pads 382
C9.1 — Shear load for a typical pile cap 398
C10.1 — Interaction diagram for axial compression and bending of composite columns 435
C10.2 — Monosymmetric I-section 437
C10.3 — Open-top box girder with sloping or vertical webs (typical box girder section) 438
C10.4 — Maximum strength of curved bottom flanges in compression 453
C10.5 — Stress range versus number of cycles 458
C10.6 — Schematic diagram showing relation between static and impact fracture toughness 469
C11.1 — Loads on a joint 486
C11.2 — Anchorage design factored load (factored resistance) 489
C11.3 — Pot bearing — Critical dimensions for clearances 494
C12.1 — Federal lands modified Kansas Corral 507
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C12.2 — Oregon side-mounted thrie beam 508
C12.3 — Glulam wood 508
C12.4 — California Type 115 509
C12.5 — Vertical concrete parapet (812 mm) 509
C12.6 — New Jersey shape concrete parapet (812 mm) 510
C12.7 — F shape concrete parapet (812 mm) 510
C12.8 — Illinois 2399 2-Rail 511
C12.9 — Vertical concrete parapet (1066 mm) 511
C12.10 — F shape concrete parapet (1066 mm) 512
C12.11 — Aluminum tru-beam 512
C12.12 — Oregon 2 tube 513
C12.13 — Wyoming 2 tube 513
C12.14 — Iowa concrete beam and post 514
C12.15 — Texas T101 514
C12.16 — North Carolina one-bar metal rail 515
C12.17 — Modified Texas C202 515
C12.18 — Flexbeam — Straight concrete wingwall transition (1) 517
C12.19 — Flexbeam — Straight concrete wingwall transition (2) 518
C12.20 — Flexbeam — Tapered concrete wingwall transition 519
C12.21 — Thrie beam — Straight concrete wingwall transition 520
C12.22 — Thrie beam — Tapered concrete wingwall transition (1) 521
C12.23 — Thrie beam — Tapered concrete wingwall transition (2) 522
C12.24 — Anchor bolts with and without preload 527
C12.25 — Maximum breakaway support projection 529
C12.26 — Chamfered edge of lapped plate 530
C14.1 — Relationship between risk and probability of failure 554
C14.2 — Typical posting signs in use in Ontario 565
C16.1 — PL-2 barrier wall with GFRP bars 594
C16.2 — PL-3 barrier wall with GFRP bars 595
C16.3 — Failure modes in flexure for external strengthening 597
C16.4 — Displacement of the tensile force curve in relation to the moment curve 598
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S6.1-06
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Preface
This is the third edition of CSA S6.1, Commentary on CAN/CSA-S6-06, Canadian Highway Bridge Design
Code. It supersedes the previous editions, published in 2000 under the title Commentary on
CAN/CSA-S6-00, Canadian Highway Bridge Design Code and in 1990 under the title Commentary on CSA
Standard CAN/CSA-S6-88, Design of Highway Bridges.
Throughout this Commentary, CAN/CSA-S6-06 is referred to as the “Code”. Other Codes are always
identified in a manner that allows them to be readily distinguished from the Code.
The purpose of this Commentary is to provide background on the design provisions of the Code and
thereby to help designers deal with issues not explicitly addressed in the Code.
Each section and clause in this Commentary bears the number of its corresponding section or clause in
the Code, with the addition of the prefix “C”. For example, Section C1 provides commentary on Section 1
of the Code, and within Section C1, Clause C1.1.1 provides commentary on Clause 1.1.1 of the Code. The
same approach is used in the numbering of annexes. Tables and figures are numbered sequentially (for
example, the first table in Section C3 is Table C3.1, which is followed by Table C3.2, etc.). However, they
do not correspond to the tables and figures bearing the same numbers (minus the “C”) in the Code.
The Code contains many clauses dealing with “Approval”, meaning approval in writing by the
Regulatory Authority having jurisdiction (see the definitions in Clause 1.3.2 of the Code). Where possible,
this Commentary provides guidance for Regulatory Authorities consulting such clauses.
This Special Publication was prepared by the Technical Committee on the Canadian Highway Bridge
Design Code.
November 2006
Notes:
(1) Use of the singular does not exclude the plural (and vice versa) when the sense allows.
(2) Although the intended primary application of this Special Publication is stated in its Preface, it is important to note that
it remains the responsibility of the users of this Special Publication to judge its suitability for their particular purpose.
(3) All enquiries regarding this Special Publication should be addressed to Canadian Standards Association,
5060 Spectrum Way, Suite 100, Mississauga, Ontario, Canada L4W 5N6.
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Summary of significant changes to
the Code since the previous edition
Note: There are no significant changes to Sections 6 and 15.
Section 1
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
Change
1.2.1
1.3.2
The definition of “Constructor” has been clarified
1.2.2
1.3.3
The definition of “Multiple-load-path structure” has been clarified
1.5.2.3
1.4.2.3
Bridge rehabilitations are no longer referred to
1.5.4.4
1.4.4.4
The temporary structures exceptions have been clarified
1.7.1
1.6.1
Temporary barriers are no longer referred to
1.9.2.2.1
1.8.2.2.1
This Clause has been rewritten
1.9.2.4
1.8.2.4
This Clause has been revised for greater specificity
Section 2
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
Change
2.2
2.2
A definition of “Durability” has been added
Section 3
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
Change
Table 3.5.1(a) Table 3.1
The definition of L in the legend has been modified to exclude reference
to the CL-625 Truck or Lane
3.8.8.1
3.8.8.1
This Clause has been clarified by adding that the dynamic load
allowance shall not be applied to the loads on barriers
Figure A3.1.2
Figure A3.1.2
All of the temperatures in the figure have been corrected from positive
to negative
(Continued)
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Section 3 (Concluded)
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
Table A3.2.2
Table A3.2.2
The drag coefficients for sign panels now also apply to noise barriers.
The equations for cylindrical and hexdecagonal (0 ≤ r < 0.26) sections of
single member or truss for the middle range [3.6 < D(qCe)0.5 < 7.2] have
been revised. Variable message signs have been included in the
definition of flat members.
A3.2.4.3.1
A3.2.4.3.1
In Item (a), the first equation for ai has been revised. In Item (b), the first
equation for ai (x1) has been revised.
Change
Section 4
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
4.4.1
4.4.1
A response modification factor of 1.0 and an importance factor of 1.0 have
been specified for determining displacements
4.4.3
4.4.3
This Clause has been revised to include the requirement that a qualified
specialist shall be consulted to determine the zonal acceleration ratio for sites
not only located close to active faults but also having peak horizontal ground
acceleration (PHA) values greater than 0.40
Change
4.4.10.4.2 4.4.10.4.2
This Clause has been revised to include a requirement that seismic design
forces for capacity-protected elements are to be determined using elastic
design forces with R and I both equal to 1.0, and that connectors are to be
designed to transmit the force effects determined from 1.25 times the elastic
seismic forces determined with R and I both equal to 1.0
4.5.1
4.5.1
This Clause has been revised to include a provision that either uncracked or
cracked cross-sectional properties shall be used when periods and seismic
force effects are calculated
4.7.4.1.1
4.7.4.2.2
The minimum area of longitudinal reinforcement in reinforced concrete
columns has been reduced from 0.01 to 0.008
4.7.4.1.2
4.7.4.2.3
The reduction in flexural resistance, as a function of the axial load level, has
been removed
4.7.4.1.6
4.7.4.2.7
Lap splices of longitudinal reinforcement in reinforced concrete columns are
now permitted within the centre half of the column height or in regions where
it is demonstrated that plastic hinge regions cannot occur
4.10.7
4.10.7
This Clause has been revised to include a requirement that thermal
movements shall also be considered when horizontal deflections of seismic
isolators are assessed
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Section 5
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
5.7.1.1
5.7.1.1
Change
Limits for using the simplified method for multi-spine box girders have
been specified
Tables 5.3
Tables
to 5.5
A5.7.1.2.1,
A5.7.1.2.2(a),
and
A5.7.1.2.2(b)
These Tables were formerly in Appendix A5.2
Table
5.7.1.6.1(a)
Table 5.10
The maximum cantilever moments have been revised
5.7.1.7.1
5.7.1.7.1
The equivalent span used with the simplified elastic method for
determining deck slab transverse bending moments has been redefined
Table
A5.2(a)(ii)
Table A5.2.2
Several of the expressions have been revised
Section 7
Clause/table/figure/
Annex designation
Previous Current
edition edition
Change
Tables 7.2
Tables
7.5.1 and and 7.3
7.5.3
Soil-metal structures have been divided into two types, i.e., soil-metal structures
with shallow corrugations and soil-steel structures with deep corrugations
7.5.4.4
7.5.4.4
For arch structures, footings are now required to resist development of
horizontal reactions due to soil pressures on the conduit wall
7.5.6
7.5.6
Controlled low strength material (CLSM) is now permitted between adjacent
conduits, with a smaller required minimum spacing between the conduits
7.6.1.3
7.6.2.3
The values for Es for soil compacted to different Standard Procter densities have
been revised. The values for Es for CLSM are now specified.
7.6.2.1.2
7.6.3.1.2
Extrapolation is now permitted to obtain values of Af for H/Dh < 0.2
7.6.2.1.3
7.6.3.1.3
The procedure for obtaining σL has been revised
—
7.6.3.3.2
This Clause is new
7.6.3.1
7.6.4.1
New depth of cover provisions have been provided for soil-metal structures
with deep corrugations
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Section 8
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
8.4.1.5
and
8.4.1.6
8.4.1.5
and
8.4.1.6
These Clauses have been rewritten to be consistent with the International
Federation for Structural Concrete CEB-FIP Model Code 90 (1993)
8.9
8.9
This Clause has been rewritten to be consistent with CSA A23.3-04, Design of
concrete structures
Table
8.11.2.1
Table 8.4
The requirements for minimum concrete strength have been removed
8.12.3
8.12.3
This Clause has been rewritten to be consistent with the current provisions of
Comité Européen de Normalisation (CEN) Eurocode 2: Design of Concrete
Structures (1992)
Change
Section 9
Clause/table/figure/
Annex designation
Previous Current
edition
edition
Change
9.5.6
9.5.6
The load-sharing factor, km , is now found in Table 9.2
—
Table 9.2
Values for km are lower
9.7.2
9.7.2
The size factor in shear, ksv, is now also obtained from Table 9.4 and is the same
as ksb for sawn wood
9.7.3
9.7.3
The formula for factored shear load, Vf , is now calculated only for
glued-laminated timber, not for sawn wood
9.8.3.3
9.8.3.3
The maximum slenderness ratio for columns is now 50 rather than 35
9.10
9.10
The text referring to the formula for the strength of wood in compression at an
angle to load has been clarified
Tables 9.12 The characteristic strengths for sawn timbers have been revised in accordance
Tables
with CAN/CSA-O86-01, Engineering design in wood. Shear strength, fvu , has
9.11.2(a), to 9.14
9.11.2(b),
been significantly increased for all sizes and grades.
and
9.11.2(c)
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Section 10
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
Change
10.5.7
10.5.7
New resistance factors and more precise definitions are now specified
10.9.5.5
10.9.5.5
A new version of this Clause has been provided to comply with
CAN/CSA-S16-01, Limit states design of steel structures
10.10.3.4
10.10.3.4
A sentence has been added for clarity
10.10.4.2
10.10.4.2
This Clause has been thoroughly rewritten to reflect new developments
10.11.6.3.1
and
10.12.5.3
10.11.6.3.1
and
10.12.5.3
These Clauses have been rewritten for clarity
Figure
10.11.6.3.1
Figure 10.4
This Figure has been revised for clarity
—
10.17.2.5
This is a new clause related to Clause 10.10.4.2
Table
10.7.2.4(a)
and Figure
10.17.2.4
Table 10.7
and
Figure 10.6
This Table and this Figure have been corrected
10.17.2.6
10.17.2.7
The equations have been corrected
Table
10.23.3.1
Table 10.12
This Table has been reorganized for compatibility with CSA G40.21-04,
Structural quality steel
10.23.4 and
10.23.5
10.23.4 and The references to Standards have been updated
10.23.5
Section 11
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
11.5.1.4
11.5.1.4
The surface of the joint exposed to pedestrian traffic is now required to be skid
resistant
11.5.6
11.5.6
The movements now include those at the serviceability and ultimate limit
states
11.6.1
11.6.1
Specifications are now given for the design-bearing rotation for bearings other
than elastomeric bearings. The Clause also now includes grout bedding for
bearings.
11.6.8.1
11.6.8.1
This Clause now specifies that the seismic design considerations specified in
Section 4 shall be applied as necessary
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Section 12
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
12.1
12.1
Change
This Clause has been revised to clarify that Section 12 applies only to
permanent barriers
Section 13
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
13.4.9
13.4.9
Change
ASTM A 325/A 325M and ASTM A 490/A 490M bolts are now included in this
Clause
13.6.1.1.2 13.6.1.1.2
Centre of gravity calculations for symmetrical and unsymmetrical bridges are
now included in this Clause
13.6.1.4
This Clause now provides that tail locks are to be provided only when
indicated by calculations
13.6.1.4
13.6.2.1.2 13.6.2.1.2
This Clause has been renamed
13.6.3.2
13.6.3.2
A minimum of two locking devices for end locks are now specified
13.6.3.3
13.6.3.3
Interference fitting and keying against rotation are now included
13.6.5.3.3 13.6.5.3.3
Counterweight guide shoe material is now required to be adjustable and
replaceable
13.7.6
13.7.6
The criteria for calculating the forces for hydraulic cylinder connections have
been revised
—
13.8.7.1.1
This new Clause has been added to describe the various types of brakes
13.8.17.5
13.8.17.5
Roller bearings now called anti-friction bearings
13.10.18.1 13.10.18.1
Manual, semi-automatic, and automatic sequence electrical controls are now
allowed
13.10.46
13.10.46
LED technology for navigation lights is now allowed
13.13
13.13
This Clause now requires an operating and maintenance manual (which is to
be kept up to date)
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Section 14
Clause/table/figure/
Annex designation
Previous
edition
Current
edition
Table
14.6.3.3
Table 14.2
14.13.1.2.2,
14.14.2,
and
14.14.2.1(a)
14.14.1.3.3, The symbol for factored resistance has been changed to Rr
14.15.2.1,
and
14.15.2.2.1
14.13.1.5
14.14.1.6
A transition has been provided for shear strength of beams that do not satisfy
the minimum transverse reinforcement requirements of Section 8. The
proportion of transverse reinforcement contributing to shear resistance has
been increased.
—
14.14.1.7
The size effect factor in wood has been increased for heavier wood beams in
the absence of cracks, shakes, and splits. Specified strengths under axial and
bending loads have been increased for larger wood members.
—
14.14.1.8
A method has been provided for determining the strength of steel plate
girders with one-sided stiffener plates having a width-to-thickness ratio
exceeding the limits of Section 10
Change
Changes have been made to reinforcing steel strengths for the years
1956–1972 (now grouped with the values for 1914–1972)
Table 14.3.2 Table 14.15 Some of the values have been revised
14.15
14.15.2.3
Corrections have been made to the symbols used in the equations for
coefficient of variation and standard deviation
Section 16
Clause/table/figure/
Annex designation
Previous Current
edition edition
Change
16.4.1
16.4.1
Glass-fibre-reinforced polymer (GFRP) is now permitted for primary
reinforcement and tendons. Wet glass transition temperature requirements
have been added for matrices and adhesives.
16.4.2
16.4.2
Thermoplastic polymers are now permitted
16.4.3
16.4.3
Additional fibre types are now permitted for fibre-reinforced concrete (FRC)
16.5.3
16.5.3
φFRP now depends on the application
—
Table 16.2
φFRP now depends on the application
16.6.1
16.6.2
The Ri values now depend on the application
—
Table 16.3
The Ri values now depend on the application
(Continued)
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Section 16 (Concluded)
Clause/table/figure/
Annex designation
Previous Current
edition edition
Change
16.7
16.7
The FRC deck slabs of the previous edition are now called “externally
restrained deck slabs”. The Clause has been reorganized to explicitly include
(a) full-depth cast-in-place concrete deck slabs;
(b) cast-in-place concrete deck slabs on stay-in-place formwork; and
(c) full-depth precast concrete.
A GFRP crack control grid in the externally restrained deck slab is now
required. Requirements for use of fibre-reinforced polymer (FRP) bars in edge
beams are now specified.
16.8.1
16.8.2
Requirements for minimum flexural resistance and crack control
reinforcement have been added
16.8.2
16.8.3
Factor F has been eliminated and new serviceability limit state limits have
been specified for non-prestressed reinforcement
16.8.5.2
16.8.6.2
The stress limitations for FRP tendons have been changed
16.8.6
16.8.7
The provisions for calculation of shear capacity have been revised
16.8.7
16.8.8
Deck slabs with reinforcement required for strength are now referred to as
”internally restrained deck slabs”
16.10
16.10
This Clause now provides for all of the reinforcement in the barrier wall
—
16.11, 16.12,
and Annexes
A16.1 and
A16.2
These Clauses and Annexes are new
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Canadian Highway Bridge Design Code
Section C1 — General
C1.1
C1.1.1
C1.1.2
C1.2
C1.3
C1.3.1
C1.3.2
C1.3.3
C1.3.4
C1.4
C1.4.1
C1.4.2
C1.4.2.1
C1.4.2.2
C1.4.2.3
C1.4.2.4
C1.4.2.5
C1.4.2.6
C1.4.2.7
C1.4.2.8
C1.4.3
C1.4.3.1
C1.4.3.2
C1.4.4
C1.4.4.1
C1.4.4.2
C1.4.4.3
C1.4.4.4
C1.4.4.5
C1.4.4.6
C1.5
C1.5.1
C1.5.2
C1.5.2.1
C1.5.2.2
C1.6
C1.6.1
C1.6.2
C1.6.3
C1.6.4
C1.7
C1.7.1
C1.7.2
C1.7.3
C1.7.3.1
C1.7.3.2
C1.7.3.3
C1.7.3.4
C1.7.3.5
C1.8
C1.8.1
Scope 4
Scope of Code 4
Scope of this Section 4
Reference publications 4
Definitions 4
General 4
General administrative definitions 5
General technical definitions 5
Hydraulic definitions 5
General requirements 5
Approval 5
Design 6
Design philosophy 6
Highway class 7
Design life 7
Structural behaviour and articulation 7
Single-load-path structures 8
Economics 8
Environment 8
Aesthetics 8
Evaluation and rehabilitation of existing bridges 8
Evaluation 8
Rehabilitation design 9
Construction 9
General 9
Construction safety 9
Construction methods 9
Temporary structures 10
Plans 10
Quality control and assurance 10
Geometry 10
Planning 10
Structure geometry 11
General 11
Clearances 11
Barriers 11
Superstructure barriers 11
Roadside substructure barriers 11
Structure protection in waterways 12
Structure protection at railways 12
Auxiliary components 12
Expansion joints and bearings 12
Approach slabs 12
Utilities on bridges 12
General 12
Location and attachment 13
Highway utilities 13
Public utilities 13
Fluid-carrying utilities 13
Durability and maintenance 13
Durability and protection 13
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C1.8.2
C1.8.2.1
C1.8.2.2
C1.8.2.3
C1.8.2.4
C1.8.2.5
C1.8.3
C1.8.3.1
C1.8.3.2
C1.8.3.3
C1.9
C1.9.1
C1.9.1.1
C1.9.1.2
C1.9.1.3
C1.9.1.4
C1.9.1.5
C1.9.1.6
C1.9.2
C1.9.3
C1.9.4
C1.9.4.1
C1.9.4.2
C1.9.4.3
C1.9.4.4
C1.9.4.5
C1.9.4.6
C1.9.4.7
C1.9.4.8
C1.9.5
C1.9.5.1
C1.9.5.2
C1.9.5.3
C1.9.5.4
C1.9.5.5
C1.9.5.6
C1.9.5.7
C1.9.6
C1.9.6.1
C1.9.6.2
C1.9.6.3
C1.9.6.4
C1.9.6.5
C1.9.7
C1.9.7.1
C1.9.7.2
C1.9.8
C1.9.8.1
C1.9.8.2
C1.9.8.3
C1.9.8.4
C1.9.9
C1.9.9.1
C1.9.9.2
2
© Canadian Standards Association
Bridge deck drainage 13
General 13
Deck surface 14
Drainage systems 14
Subdrainage of wearing surface 15
Runoff and discharge from deck 15
Maintenance 15
Inspection and maintenance access 15
Maintainability 16
Bearing maintenance and jacking 16
Hydraulic design 16
Design criteria 16
General 16
Normal design flood 16
Check flood 16
Regulatory floods and relief flow 16
Design flood discharge 16
High-water levels 17
Investigations 19
Location and alignment 19
Estimation of scour 19
Scour calculations 19
Soils data 20
General scour 20
Local scour 21
Total scour 22
Degradation 22
Artificial deepening 22
Allowance for degradation or artificial deepening 22
Protection against scour 23
General 23
Spread footings 23
Piles 23
Sheet piling 24
Protective aprons 24
Paved inverts and revetments 24
Special protection against degradation 24
Backwater 24
General 24
High-water level 24
Assumed depth of scour 24
Waterway modification 25
Reduction of backwater by relief flow 25
Soffit elevation 26
Clearance 26
High-water level for establishing soffit elevation 26
Approach grade elevation 26
General 26
Freeboard 26
High-water level for establishing approach grade 26
Freeboard for routes under structures crossing water 26
Channel erosion control 27
Slope protection 27
Stream banks 27
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C1.9.9.3 Slope revetments 27
C1.9.9.4 Storm sewer and channel outlets 27
C1.9.10 Stream stabilization works and realignment 27
C1.9.10.1 Stream stabilization works 27
C1.9.10.2 Stream realignment 27
C1.9.11 Culverts 27
C1.9.11.1 General 27
C1.9.11.2 Culvert end treatment 27
C1.9.11.3 Culvert extensions 28
C1.9.11.4 Alignment of non-linear culverts 28
C1.9.11.5 Open-footing culverts 28
C1.9.11.6 Closed-invert culverts 28
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Section C1
General
C1.1 Scope
C1.1.1 Scope of Code
The OHBDC (MTO 1991) was written for application within Ontario. CAN/CSA-S6-88 was generated with
interprovincial co-operation for use in the other provinces of Canada and was largely derived from the
preceding OHBDC edition. The provinces and CSA then agreed that the successor edition to both codes
would be the Code, published by CSA. The Code has been written using the earlier codes as source
documents and with the intention of retaining continuity.
The scope of the Code is a little broader than that of the third and last edition of the OHBDC
(MTO 1991). Long span bridges and movable bridges are included. In addition to incorporating newer
technology, more emphasis is placed on criteria related to seismic design, durability, access for inspection
and maintenance.
The Code Scope statement lists types of structures to which the Code is not intended to apply. The list is
not exhaustive. The application of the Code to the types of structures listed is not precluded where the
Owner or the Authority having jurisdiction over the structure has designated all or part of the Code as
being applicable.
C1.1.2 Scope of this Section
Geometrical provisions have been minimized by referring to the Geometric Design Guide for Canadian
Roads (TAC 1986).
Many catastrophic failures have been caused by scour at bridge piers and abutments. Good hydraulic
design is a fundamental requirement for bridges. Basic hydraulic requirements are specified in the Code,
and reference is made to the Guide to Bridge Hydraulics (TAC 1980) for guidance concerning good
hydraulic design and detailing.
C1.2 Reference publications
All specifications, standards, manuals, and similar documentation referred to in the Code are listed. Direct
reference in the Code to research reports, papers, and similar publications has been avoided. Such
references are given in this Commentary.
C1.3 Definitions
C1.3.1 General
Definitions are divided into three groups: General Administrative Definitions, General Technical
Definitions, and Hydraulic Definitions.
Abbreviations
The following abbreviations are used in this Commentary in addition to those used in the Code:
MLPS — multiple-load-path structure or structures
OHBDC — Ontario Highway Bridge Design Code
TAC
— Transportation Association of Canada, previously named the Roads and Transportation
Association of Canada (RTAC). These names and abbreviations may be used interchangeably in
the Code and Commentary
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SLPS
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Canadian Highway Bridge Design Code
— single-load-path structure or structures
Symbols
The following additional symbols should be noted:
dsp = the depth of local scour, which is measured below the anticipated level of general scour
adjacent to the pier
d t = the total scoured depth, which is measured from the high water level to the bottom of the scour
Wp = the width of the footing only if the footing is exposed to the stream flow
C1.3.2 General administrative definitions
These define a few basic terms used throughout the Code in connection with its application. These
terms begin with capital letters when the specified meaning is intended.
C1.3.3 General technical definitions
Definitions given in this clause are used in Section 1 or are used in more than one Section. Terms used
in only one Section or having a particular meaning therein are given in that Section.
Definitions are based on existing glossaries (MTO 1991, TAC 1986) wherever possible, but have
been modified where necessary to suit the purposes of the Code.
Bridge components are classified as primary, secondary, or auxiliary.
Substructure — substructures include all superstructure support components such as piers and
abutments, including the foundations, and earth-supporting components such as ballast walls and
wing walls. Soil-steel structures, because of their interaction with the ground, are considered to be
substructures in their entirety.
Superstructure — for articulated structures, superstructures consist of the components supported by
the bearings and the bearings themselves. For nonarticulated systems, the superstructure is deemed to
be all components supported by the legs of a frame or by columns; or, with the exception of soil-steel
structures, those supported by an arch, including the arch itself above the springing.
C1.3.4 Hydraulic definitions
For hydraulic terminology, the principal references are TAC (1980), ASCE (1962), and the
MTO Drainage Manual (MTO 1992a).
The “Regulatory Flood” is normally designated by an authority having jurisdiction over the
waterway, which is generally not the “Regulatory Authority” having jurisdiction over highways.
The Code is concerned only with structure sites and the term “Natural Scour” is not used nor
defined since it is included in the definition of “General Scour”.
C1.4 General requirements
C1.4.1 Approval
So as not to inhibit developments in design, materials, and components, Clause 1.4.1 establishes
general interpretation guidelines and permits departures and variations from the Code subject to
Approval.
The last paragraph warns against using prescriptive material from other codes to augment the Code
without assurance as to compatibility. Such use could result in dangerous errors. Establishing
compatibility or correcting for incompatibilities requires specialized knowledge of calibration
procedures. For any design criteria outside the Code limits that are submitted for Approval, the target
reliability index, β, should be 3.5 for the ULS.
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C1.4.2 Design
C1.4.2.1 Design philosophy
Clause 1.4.2.1 sets out fundamental principles. Safety is identified as the overriding concern. As in the
earlier source codes (see Clause C1.1.1), with certain exceptions the use of elastic methods of analysis is
required, and the limit states philosophy is the same, including the grouping of identified limit states as
follows:
(a) the ULS;
(b) the SLS, involving primarily deflection, cracking, and vibration; and
(c) the FLS, at which material fatigue is considered.
For new structures, the last two should not be regarded as less important than the ULS. Fatigue in
particular is as important a safety consideration, or perhaps more important, being a potential cause of
sudden and catastrophic failure. While the usual limit states are identified in the Code, the Engineer is
responsible for ensuring that all potentially critical limit states are properly investigated, particularly when
dealing with unusual structures or conditions.
In the calibration of the Code, as in earlier editions of the OHBDC (Nowak and Grouni 1994,
Nowak 1990, Nowak and Agarwal 1979, Agarwal and Cheung 1987, Kennedy et al. 1992), reliability is
measured by the reliability index β . The reliability index, the measure of structural safety, is the ratio of the
mean to the standard deviation of a random variable X. Figure C1.1 shows the relationship.
For the ULS, the random variable X is taken as the natural logarithm of R / S, where S is the load effect
and R is the corresponding resistance.
For the design of new bridges, components that will not fail suddenly or will retain post-failure capacity,
and whose failure will not lead to sudden collapse, the lifetime target value of the reliability index β has
been maintained as 3.5 as in the OHBDC; but the structure design life has been established as 75 years
instead of 50. For the OHBDC, the choice of 50 years was based on a statistical analysis of a selection of
existing bridges in Ontario (Nowak and Agarwal 1979) that were considered representative of present and
expected future construction. The above lifetime target value of the reliability index is consistent with CSA
S408-81 and is equivalent to an annual target reliability index of 3.75 for most bridge structures.
For the SLS, the variable X is taken as the safety margin, i.e.,
X=R–S
Region
of failure
b = Reliability index
sx = Standard deviation
bsx
Mean
Area =
probability
of failure
Frequency of occurrence
For this limit state, the target value of the safety index is selected as zero for the appropriate period.
The criteria for the FLS are as used for the OHBDC.
mx
x
Figure C1.1
Reliability index
(See Clause C1.4.2.1.)
6
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Except for live loads and wind loads, load and resistance factors in the Code have been determined
from those established for the 3rd edition of the OHBDC (MTO 1991) by adjustment to allow for the
longer structure design life. The calibration for the OHBDC (Nowak 1990) considered superstructures
of steel, concrete, prestressed concrete, and wood. Wood superstructures were found to exhibit a
somewhat larger deviation from the target safety index value. Substructures and soil-steel structures
were calibrated against previous performance.
Traffic loads have been specified at the regulatory level and live load factors have been determined
to meet the target reliability index by reliability analysis using vehicle load data from recent surveys in
various Canadian provinces from 1994 to 1997. Other live loads have been adjusted to make the live
load factor applicable to them. Load factors for wind have been calibrated to satisfy the target
reliability index using statistical data reported by Davenport (1983) and MacGregor et al. (1997).
Elastic methods of analysis are generally prescribed for determining the response of the structure at
the ULS. This is consistent with current North American codes, including Standard Specifications for
Highway Bridges (AASHTO 1994), codes of the American Concrete Institute, the National Building Code
of Canada, and most European codes. It is recognized that the structure does not behave elastically
throughout the whole load range and that plastic redistribution will normally occur before a ULS
condition is reached. However, inelastic methods of analysis are not yet well established and in general
use by designers and Approval is required for their use except where it is specifically allowed by the
Code, as in the case of yield line theory for slabs.
C1.4.2.2 Highway class
The highway class, determined from traffic counts, is an indicator of truck loading frequency and of
the loading intensity due to multiple truck presence. If known, the ADTT per lane count should be
used in preference to the ADT since it is the more relevant criterion.
Classes C and D were known as C1 and C2 in the OHBDC (MTO 1991).
All new bridges are designed to comply with Class A Highway requirements because most highways
have the potential to evolve as Class A Highways during the life of a structure and the cost of providing
for this possibility is not large at the design stage, but may be prohibitive if the structure has to be
upgraded at a later stage.
C1.4.2.3 Design life
In earlier codes, a 50-year design life was assumed but not explicitly stated. Increasing the structure
design life to 75 years was a pragmatic decision that took into account the desirability of having more
durable structures, consistency with other codes (AASHTO 1994), and the slowing of obsolescence
and renewal rates as highway systems approach maturity.
C1.4.2.4 Structural behaviour and articulation
Detailed design requirements for joints and bearing systems are given in Section 11.
Some types of bearings intended to permit rotation do so only while causing large bearing reaction
eccentricities. Clause 1.4.2.4 requires that the magnitude of such eccentricities be determined and the
effects considered if they are significant. It is also specified that in this determination, the
approximations involved in arriving at material elastic properties and time-dependent effects not be
overlooked.
In the past, almost all bridges have been electrically grounded through bearings, joints, or integral
connections. Even fairly dry concrete will pass high-voltage charges to ground. Modern elastomeric
bearing and joint designs are cause for concern in that they may enable a structure to hold a
high-voltage electrical charge long enough to be dangerous. Leakage from high voltage power cables
passing over or through the structure are potential sources, in addition to atmospheric discharges.
In most cases, a review of the design or structure will show that there is an adequate path to ground.
If not, an electrical engineer should be consulted.
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C1.4.2.5 Single-load-path structures
Normally, it is preferable not to use single-load-path structures (SLPS). These are defined as structures in
which the failure of a single primary component or connection would cause the structure to collapse. In
some cases, it may be obvious that a structure is a SLPS. In others, a detailed evaluation of the structure
and an examination of collapse mechanisms and of the after-failure performance of some members
(Tharmabala et al. 1996) may be required.
Single-box girders with two webs and two-girder systems are generally considered to be SLPS and a
MLPS alternative should be substituted. Multicellular void systems are considered to be MLPS. An example
of SLPS behaviour is the collapse of the US I-95 Mianus River crossing in Connecticut in 1983. In this case,
the failure of one hanger connection caused the collapse of a two-girder cantilevered span.
Bridges with single columns are SLPS. This type of structure is almost indispensable, however, in many
highway interchange situations and in large skew angle crossings. This configuration can be acceptable if
the structure complies with all requirements of the Code concerning substructure impact protection and
corrosion protection, and the column also has strength, additional to that required by the Code, sufficient
to ensure that it will not be the first member to fail.
Approval should be obtained in cases where an SLPS involves a primary flexural component, for
example, in single box girder superstructures, or if there is doubt as to whether the system to be used is of
the SLPS type.
C1.4.2.6 Economics
Clause 1.4.2.6 requires that the design not only meet the technical requirements of the Code, but also
provide an economical structure.
Economic considerations should include construction costs, design costs, lifetime maintenance costs,
and user costs where appropriate. The availability of competitive resources for the fabrication and
production of components and of their erection when and where required should be considered at the
design stage as part of this analysis.
C1.4.2.7 Environment
Clause 1.4.2.7 reaffirms the obligation to preserve and enhance the environment to the greatest extent
possible. It requires a consideration of any effect the structure may have on the environment. For some
jurisdictions (RSO 1990, MTO 1992b, MEA 1993) the procedures for environmental assessment have been
refined into a process developed by the Provincial Government and in co-operation with local authorities.
Examples of adverse environmental effects are flooding caused by the hydraulic restriction of a water
crossing, the leaching of wood preservatives or contaminated drainage runoff into streams or the ground,
or the destruction of fish habitat.
C1.4.2.8 Aesthetics
The visual effect of the bridge or structure itself on the surrounding landscape is an important design
consideration. Matters of taste should not be the subject of rigid specifications; however, it is legitimate
and appropriate to require that due attention be given to the appearance of the structure and the
suitability of the type, form, and geometry of the structure in relation to its surroundings (ACI 1990).
Where a full knowledge of costs and benefits and public preferences is assured, incurring moderate
additional costs to achieve an aesthetic improvement should not be precluded.
After safety and economics, appearance should be the determining consideration in selection of
alternatives.
C1.4.3 Evaluation and rehabilitation of existing bridges
C1.4.3.1 Evaluation
Section 14, covering the evaluation of existing bridges, gives pertinent load and other data so as to be
fairly self-contained. In general, Section 14 provides load and analysis requirements specific to evaluation
while referring to the remainder of the Code for other provisions.
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C1.4.3.2 Rehabilitation design
Most bridges that require rehabilitation were designed to editions of CSA S6 or AASHTO much older
than CAN/CSA-S6-88 and AASHTO (1994). In Ontario, some bridges designed to the early editions of
the OHBDC are being rehabilitated.
Because the older codes generally required lower load capacities, it is often necessary for economic
reasons to design the rehabilitation to a load level less than the Code specifies for new bridges.
Design criteria are given in Section 15 that permit rehabilitation design for a specific duration and
load level.
C1.4.4 Construction
C1.4.4.1 General
The Engineer is required to consider, for all stages of Construction, effects such as those due to built-in
stresses and the redistribution of stresses resulting from the erection or demolition sequence. By
definition, Construction includes reconstruction and demolition.
Changes in section strengths during Construction are of particular importance. Designers tend to
think of a member in its final form. It may have very different properties in one or more intermediate
stages of Construction. Composite steel and precast prestressed concrete girder bridges are well
known examples. During the casting of the concrete deck, the girders have a fraction of their final
strength and are required to support a weight of wet concrete that may cause the critical loading for
some parts of the section. More often overlooked is that they are not well braced to resist compression
flange buckling, lateral forces, or torque due to eccentric loading, nor such Construction loads as those
caused by concrete finishing machines.
Changes in loading effects during Construction also need to be considered. The casting sequence
for a concrete deck may be critical and needs to be established and investigated. Construction loads
for various forms of cantilever construction are prescribed, but the requirements presuppose that the
form and sequence of Construction is predetermined and adhered to.
The buckling of steel components during Construction has in the past been the cause of a number
of disastrous failures. Often these have resulted from flanges and webs designed to resist tension in the
completed structure being subjected to unanticipated compression during Construction. This can be
caused by deck casting sequence, forced fitting, or even temperature effects, and aggravated by
flatness or welding inaccuracies. The compression strength of a plate element may be a very small
fraction of its tensile strength.
C1.4.4.2 Construction safety
Shoring of excavation is not normally shown on the Plans. There are often alternative means of
construction, some of which may not require shoring. If there appears to be no method of
construction that will not jeopardize an adjacent facility open to the public without shoring, then
protection of that facility in the form of a shoring scheme, a diversion, or support should be indicated.
Methods of construction should be envisaged in their entirety during the design process and
designs that of necessity involve high-risk construction work, regardless of economic benefits, should
be avoided.
C1.4.4.3 Construction methods
For common types of structures, construction procedures are well established. For less well-known
types of structures, the possibility of deviations from the construction methods assumed in design
must be considered. Such deviations may cause load effects, built-in stresses, and component
resistances different from those anticipated. It is therefore prudent in such cases to make the intended
construction procedures clear so as to preclude the possibility of structural instability during
construction or a reduction of safety in the completed structure.
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C1.4.4.4 Temporary structures
The collapse of temporary structures, particularly falsework and access scaffolding, with resulting loss of
life or injuries has in the past been alarmingly common. This collapse is often attributable to poor
definition of responsibilities because such structures are not part of the final structure. Particular attention
is therefore directed to the clarification of responsibility for the design, checking, Construction, and the
supervision of Construction and to the applicability of specifications.
The necessity for construction safety requires that the same engineering certification criteria be specified
for falsework as for permanent structures.
Temporary structures include modular bridges and earth-retaining structures used for Construction.
C1.4.4.5 Plans
By definition, the term “Plans” includes all forms of specifications.
The intent of Clause 1.4.4.5 is to ensure that a clear and verifiable understanding of the requirements
and intent of the design exists at the time of Construction, and that information is placed on record that
will facilitate any subsequent investigation, particularly in connection with evaluation and rehabilitation. It
is also important to document all changes to the Plans made during Construction. This is the beginning of
a process of documentation that should continue throughout the life of a bridge, whether the changes
occur through deterioration, damage, rehabilitation, widening, or other circumstance.
In the past, many bearing replacement projects have been complicated by a lack of adequate provision
for jacking. For this reason it is required that the articulation system and the locations for future jacking
points be shown on the drawings. It is relatively simple for the designer to indicate the intended system of
articulation and a practical method of jacking on the design drawings. These may be difficult to establish
at a later stage.
Requirements for signing and sealing drawings are left to the Regulatory Authority, but normal good
practice is for the Engineer and the Checker each to affix his or her Professional Engineer’s seal and
signature to provide assurance that the design, rehabilitation design, or evaluation is in accordance with
the Code.
It should not be assumed that the Constructor is obligated to comply with the provisions of the Code or
even be aware of them. Almost all Code provisions are intended to be implemented in the process of
design and Plan preparation. A few clauses specify that the Plans show certain provisions, in effect
requiring that the provisions be transferred into the Construction specifications. They directly require the
compliance of the Constructor and therefore need to be stated explicitly in the Plans to ensure
implementation. The purpose of the last paragraph of the Clause 1.4.4.5 is to require this treatment for
any other provisions if in particular circumstances this is necessary to ensure their implementation.
C1.4.4.6 Quality control and assurance
The provisions of the Code have been formulated and calibrated on the assumption that high standards of
construction will be adhered to. If this were not so, generally larger design loads and lower strengths
would have to be used, or lower safety levels accepted.
High standards of construction require that only competent and conscientious Constructors be
entrusted with the work, that the Plans include clear, comprehensive, and practicable specifications, and
that thereafter, testing and the supervision of Construction are such as to guarantee compliance.
C1.5 Geometry
C1.5.1 Planning
Widening a bridge to accommodate increasing vehicular traffic volume is generally not a desirable nor
cost-effective strategy unless the widening will not be required for many years after initial Construction.
Therefore, a traffic projection for the specified period from the completion of Construction is required as a
minimum. If the bridge is of a type that is difficult to widen, and twinning is not practicable, a longer
period is required. In some cases, initial Construction to suit the final width of the highway is justified.
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Horizontal alignments should be on tangent if possible and curvature of a constant radius is
preferable to a spiral or transition curve. Superelevation runout complicates the placing of deck
concrete and often results in a poor surface and ponding. Bridges that dry quickly after precipitation or
thaw runoff are less likely to deteriorate. At the planning stage, it is often possible to influence the
choice of vertical and horizontal alignment so as to avoid poor deck drainage. Sag vertical curves on
bridges should be avoided.
C1.5.2 Structure geometry
C1.5.2.1 General
Some Regulatory Authorities have well-established standards for structure geometry. In their absence,
the TAC Standards apply. Preference should always be given to the National Standards.
C1.5.2.2 Clearances
C1.5.2.2.1 Roadways and sidewalks
See Clause C1.5.2.1.
C1.5.2.2.2 Railways
Specific clearance requirements may vary, depending on the railway company. Detailed clearance
proposals should be approved by all affected railway companies prior to detailed design.
C1.5.2.2.3 Waterways
Clause 1.5.2.2.3 deals with navigable clearance, hydraulic clearance, and the water level to be
assumed.
C1.5.2.2.4 Construction
The timing and duration of the clearance restriction may be of considerable importance and should be
established before or together with the clearance values. For stream crossings in some areas, summer
Construction can take advantage of very low runoff and discharge.
C1.6 Barriers
C1.6.1 Superstructure barriers
All requirements for barriers on structures are in Section 12. Median barriers that are a continuation of
approach roadway median barriers, where there is no gap in the deck at the median, are not subject
to any Code requirements. The basal support of such barriers normally differs from that of the
approach roadway barrier and special attention should be given to the bridge deck waterproofing
system at this location.
If, at the median, there is an opening in the bridge deck or a gap between twin bridges that is large
enough for a vehicle or a vehicle wheel to enter, the median barrier should be considered as a roadside
barrier.
C1.6.2 Roadside substructure barriers
Where the full clear recovery zone is provided, no roadside guiderail protection between the roadway
edge and the structural component is required.
The minimum clearance specified to a structural component is to permit access for cleaning and
inspection. This is not required if the barrier is part of the structural component with no gap. In such
cases, the barrier is rigid and the component is designed to resist the barrier loading.
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C1.6.3 Structure protection in waterways
If fendering is provided, the deflection of the fendering required to develop its resistance should be
considered in determining the clearance between the fendering and the structure.
C1.6.4 Structure protection at railways
Most protection traditionally provided for substructures at railway crossings could do little more than
protect against light overhanging loads. A Jordan or safety rail of sufficient extent may at moderate cost
contain a derailment capable of destroying the structure.
C1.7 Auxiliary components
C1.7.1 Expansion joints and bearings
Expansion joints and bearings are small but critical components and Section 11 is devoted to their design
requirements. Corrosion, corrosion spalling and concrete scaling caused by runoff flow through joints, and
the accumulation of debris carried into the joint by the flow have been major contributors to the
premature deterioration of bridge components, particularly bearings and bearing seats. The failure of
bearings has caused bridge collapses in a few cases and in many others has required costly repairs.
C1.7.2 Approach slabs
When approach slabs are not provided, settlement of the backfill behind a bridge abutment can cause a
depression that can form or worsen quite rapidly. An approach slab maintains a smooth transition
between the approach pavement and the bridge deck even when settlement is substantial. This is an
important safety consideration and minimizes dynamic impact forces on expansion joints and decks.
Approach slab costs begin to increase rapidly with lengths beyond 7 m. A length of a little less than that
has been found adequate where settlement is minimized through compaction. In addition, for most
concrete pavement designs, no additional thickness is required and costs are limited to that of the
reinforcing steel. Some authorities provide top slab reinforcement near the abutment; however, bottom
reinforcement alone, designed assuming a simple span of three-quarters of the slab length, has performed
satisfactorily.
Approach slabs should be supported by a continuous ledge on the back face of the abutment and
dowels are necessary to prevent the slab from being pulled away from the abutment. Such a separation
can result in the sudden formation of a vertical face large enough to cause a disastrous vehicular impact.
The dowels are best located at the bottom of the slab to minimize stresses due to settlement of the other
end of the slab. The slab length recommended combined with good backfill compaction appears to keep
rotation at the joint within acceptable limits.
The approach slab should extend the full width of the roadway but should not be integral with curbs or
barriers that will not settle. Sealing to prevent the infiltration of large amounts of water is advisable.
Approach slabs are recommended for all urban and high speed rural highway classifications. On
unpaved roads that are regularly graded, approach slabs may be omitted.
C1.7.3 Utilities on bridges
C1.7.3.1 General
In exposed locations, particularly where salt is present in runoff or spray, it may be difficult to prevent the
corrosion of steel components that form part of utilities or their attachments. Galvanizing gives protection
for a limited period, sometimes less than ten years, before rust appears. Aluminum components partly
enclosed in concrete corrode rapidly and may cause bursting. Stainless steel fasteners have performed well
close to roadways. They have been costly, though costs are trending lower. Nonferrous and nonmetallic
materials and protected locations are generally preferable.
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C1.7.3.2 Location and attachment
If access is from above, either on the structure or on the structure approaches, side and median
locations minimize interference with traffic when work on the utility is required. If the utilities are
accessible from beneath the structure, spaces between beams provide protection and concealment.
Utilities are permitted in structural voids only when access to the void interiors is provided for bridge
inspection and maintenance purposes, as required by Clause 1.8.3.1.5. Where voids with accessible
interiors are not available and the utilities cannot be suspended between beams, they should be in
concrete-encased conduit. Conduits should be of a material not subject to any form of deterioration
nor expansion, and not likely to cause electrochemical activity. The preferred location for conduits is in
nonstructural components. If this is not possible, acceptable locations may be found in areas of
secondary components where stresses are low.
The surfaces of primary components should not be obscured in such a way as to hinder visual
examination and testing.
The low points of conduit and other potential water traps should be drained by weep holes or drain
tubes to reduce the likelihood of freezing and bursting. If tubes are used, a minimum diameter of
10 mm is recommended. All tubes should extend through the superstructure and discharge below the
soffit.
Despite protection and sealing, access openings, junction boxes, and other openings in or near the
upper surfaces of structures are a common source of problems due to salt water penetration,
accidental damage, e.g., from snow plows, and vandalism.
The requirement to allow for 15 mm vertical movement in utility joint couplings is to allow for
future bridge jacking operations during bearing replacement. All other movements that may take
place at joints should be considered in the joint design to ensure that there is no damage to the
couplings nor to the structure.
C1.7.3.3 Highway utilities
See Clause C1.7.3.4.
C1.7.3.4 Public utilities
Such provisions will generally prove economic and obviate unsightly attachments to the structure at a
later stage.
C1.7.3.5 Fluid-carrying utilities
Sewer and water lines should not be allowed inside bridge members such as box girders because of
the possibility of breakage. The pressure and loading caused by such breakage may lead to structural
damage or failure.
Gas and oil lines are prohibited because of fire and explosion hazards. In special situations where
economic or other safety considerations take precedence, Approval may be given for such
installations.
C1.8 Durability and maintenance
C1.8.1 Durability and protection
Code requirements pertaining exclusively to durability are in Section 2. Requirements elsewhere,
e.g., concerning bridge deck drainage, may involve durability in conjunction with other
considerations.
C1.8.2 Bridge deck drainage
C1.8.2.1 General
Bridge deck drainage affects vehicular safety and structural durability.
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Rapid clearance of runoff from the traffic lanes is most important to ensure tire grip (Marsalek and
Gruspier 1982), especially in winter conditions. Ice often forms on bridge decks in advance of that on the
approach roadways because of the more rapid cooling of the superstructure.
Currently, the primary cause of concrete deck deterioration is the corrosion of deck reinforcing steel.
Corrosion is most rapid in wet concrete that is impregnated with salt. It is slowed or stopped in dry
concrete. Waterproofing membranes can be effective, but leakage is common and the asphalt wearing
surfaces required to protect the membranes retain salt and water. If surface water is removed quickly,
allowing drying to begin, the duration of corrosion activity is minimized. These reasons justify higher
drainage standards and more attention to detail for bridge decks than for approach roadways.
C1.8.2.2 Deck surface
C1.8.2.2.1 Crossfall and grades
The slopes specified are necessary to ensure rapid flow and to reduce ponding due to irregularities in the
deck finishing.
C1.8.2.2.2 Deck finish
Irregularities in finished deck surfaces are undesirable. Depressions may trap moisture, or lead to excessive
thickness of waterproofing membrane. High points on the deck surface may reduce membrane thickness
or require raising wearing surface elevations over a large area in order to maintain the minimum asphalt
thickness. Surface grinding can be a useful expedient to correct and discourage inaccuracies in deck
finishing.
C1.8.2.3 Drainage systems
C1.8.2.3.1 General
Although deck drains can cause problems, it is necessary to provide them for longer bridges to prevent the
encroachment of water onto the traffic lanes. The extent of the permissible encroachment and the width
of available shoulder or side clearance determine their size and spacing (Marsalek and Gruspier 1982).
Many bridges have side or median clearances or shoulders sloping towards gutters at the exterior side of
the roadway; this normally provides adequate width for gutter flow without unacceptable encroachment
on the traffic lanes, even without deck drains. The specified maximum encroachment should leave
sufficient room for safe travel within the curb lane at the reduced speeds normal during heavy rainfall.
C1.8.2.3.2 Deck drain inlets
The most effective transverse location for deck drain inlets is in the area of deepest flow. This is usually
adjacent to the curb. Inlets completely recessed into the curb are less obtrusive and less dangerous for
cyclists but are not usually as effective.
Drains with inlets 150 mm in diameter or least dimension have proven ineffective. A 200 mm least
dimension is recommended as a minimum for small drains used to prevent local ponding. For the
collection of significant quantities of water, much larger gratings are necessary.
For the protection of pedestrians, one dimension of every opening should be no more than 75 mm.
Cyclists find openings greater than 75 mm measured in their direction of travel uncomfortable and
openings of any width greater may cause loss of control.
Dishing the wearing surface around drain inlets to a depth greater than 25 mm may cause vehicular
impact, difficulties in maintaining minimum concrete cover to reinforcement, or difficulties with asphalt
wearing surface placement.
C1.8.2.3.3 Downspouts and downpipes
The diameter or least dimension specified has been found to be the desirable minimum in order to reduce
maintenance required to keep downpipes clear of sand and debris washed from the road surface, and to
avoid problems caused by the freezing of water in the pipes.
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The projection of downspouts below the superstructure should be minimized for the sake of
appearance, but needs to ensure that discharge will be clear of the structure. The projection specified
is suitable for most locations. For very high superstructures where winds are stronger and the
projection is less visible, a larger projection should be considered.
C1.8.2.4 Subdrainage of wearing surface
Water accumulates within the wearing surface of bridge decks and can be trapped there if not drained.
This occurs where pockets are formed by curbs and expansion joint dams. Drains of the type specified
also serve to prevent ponding on the membrane prior to placing the wearing surface.
Typically, these drains discharge slowly and continue to drip almost incessantly, or long after the
deck surface has dried. The drains should project a little below the soffit. This is easily achieved by
setting a coupler of the type used for joining small diameter PVC pipe in the soffit form and
connecting the drain to it. After the form is stripped, an extension pipe may be attached to the coupler
if the projection length or the discharge location are not satisfactory.
C1.8.2.5 Runoff and discharge from deck
Runoff crossing the area where the bridge joins the approaches can be particularly destructive. The
area is vulnerable to damage due to joints, discontinuities, and steep slopes. Inadequate provisions for
runoff can lead to serious erosion; the undermining of abutments, approach slabs, and slope paving;
and traffic hazards and inconvenience to pedestrians, cyclists, and traffic passing underneath.
C1.8.3 Maintenance
C1.8.3.1 Inspection and maintenance access
C1.8.3.1.1 General
Periodic inspection of structures is necessary to detect deterioration and to determine when preventive
maintenance is needed (MTO 1993). Clause 1.8.3.1.1 is concerned with the provision of features
required to facilitate inspection and maintenance.
C1.8.3.1.2 Removal of formwork
Clause 1.8.3.1.2 exists primarily to facilitate inspection of the underside of decks and of box girder
interiors. A further consideration is that forms left in place may trap and hold salt and water in contact
with the concrete surface, thus accelerating deterioration.
Inspection of box girder interiors is not considered feasible if the inside vertical dimension is less
than that specified. It is also difficult to remove the formwork in such cases.
C1.8.3.1.3 Superstructure accessibility
The cost of providing the means of access should be reasonable in relation to the cost of the structure,
the expected frequency of use, and the probable cost of providing alternative temporary inspection
access when needed.
C1.8.3.1.4 Access to expansion joints
The space prescribed is the minimum acceptable for most situations.
Temporary formwork used under or in expansion joints, including materials such as polystyrene
foam, should be removed.
C1.8.3.1.5 Access to primary component voids
It is recommended that wherever possible, there should be interconnection between access points to
facilitate inspection and air circulation.
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Access hatches are normally provided on the sides of webs or in bottom flanges. Access from above may
be more convenient, but even with allegedly watertight gasket seals there have been problems due to
leakage of salt water into the voids.
C1.8.3.2 Maintainability
Components that may require replacement or repair during the required design life of the structure should
be removable, or at least accessible if on-site repair is likely to be acceptable. Past performance will
generally be the best basis for assessing probable life. All bearings, expansion joints, coatings, railings,
wearing surfaces, waterproofing membranes, external drainage fixtures, covers, gratings, utilities, and
lighting and sign fixtures should be replaceable.
C1.8.3.3 Bearing maintenance and jacking
See also Clause C1.4.4.5.
Actual jacking forces as much as double those calculated have been reported as being necessary to lift
superstructures off their supports.
C1.9 Hydraulic design
C1.9.1 Design criteria
C1.9.1.1 General
The Regulatory Authority may be prepared to accept stated risks in order to reduce initial costs. These may
include risks affecting the level of service during severe flood conditions, or the need for restorative work
after flooding. They do not include risks affecting safety.
C1.9.1.2 Normal design flood
The Regulatory Authority may specify a normal design flood having a return period greater than or less
than 50 years. The return period may be less than the specified design life for structures. The low
probability of design flood conditions being attained more than once during the structure life may be
acceptable.
C1.9.1.3 Check flood
Most failures of bridges and open-footing culverts are caused by hydraulic effects, principally scour. The
reason for considering the check flood is to ensure that the foundations and the approach embankment
will not fail as a result of a flow somewhat larger than the normal design flood. Consideration of a check
flood is not normally required if the structure is designed to the larger regulatory flood criteria.
C1.9.1.4 Regulatory floods and relief flow
In some cases, designing to the regulatory flood criteria (MTO 1992a) may necessitate almost doubling
the hydraulic opening of the bridge. This increase in size and cost can be avoided if flow over the
approach road is allowed and if nonhydraulic considerations permit the grade to be placed at a suitable
elevation.
C1.9.1.5 Design flood discharge
Methods used for calculating design flood discharges depend on the size of the basin, the type of terrain,
the magnitude of flood involved, and whether the basin is rural or urban. No method is completely
satisfactory in all circumstances. Approval for the methods proposed should be obtained for the specific
site. Table C1.1 lists some methods considered suitable for a range of the more common runoff
conditions.
Absence of specific mention of a method does not necessarily imply that it is inferior to those listed.
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Table C1.1
Computation of design flood discharges
(See Clause C1.9.1.5.)
Method
Comments
Station frequency analysis
Preferred method where suitable flow records are available,
for any size of basin, and return periods up to 100 years
Modified index
Based on regional frequency analysis. For use where station
frequency analysis cannot be used, for basins generally over
25 km2 and for return periods up to 100 years.
Runoff equations
Comments similar to those for Modified Index Method
Unit hydrographs
For return periods exceeding 100 years, particularly where
large regulatory floods must be considered. Hydrographs
based on recorded data are preferred to synthetic
hydrographs whenever circumstances permit.
Rational method
2
For basin areas up to 25 km where other methods are not
feasible. Can give acceptable results in many cases if
properly used; reliability is significantly less for sandy soils
and retentive watersheds.
Miscellaneous methods
For checking design flood estimates made by other
methods, and for calculating runoff in special cases where
normal hydrologic methods are not applicable.
C1.9.1.6 High-water levels
Selection of appropriate high-water levels for various segments of the hydraulic design requires careful
consideration. Use of an incorrect value can in some cases have serious consequences, including
structure failure.
Changes in high-water level during the life of a structure may result from various factors including
urbanization, deforestation, channel diking, and the construction of flood control structures.
Use of an incorrect high-water level at a crossing that experiences abnormal flood conditions can
result in excessive scour and failure of the structure.
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Approaches
Ma
in s
tre
am
Flood plain
Tributary stream
a
Plan of site
Approach grade
CL
Freeboard
Clearance
HWL
HWL
NWL
NWL
Tributary
streambed
Note: Soffit and approach grade
elevations are based on HWL shown
Main stream
HWL with main stream in flood
CL
HWL
Soffit
HWL
NWL
NWL
Tributary
streambed
Main stream
Scour calculation
based on HWL shown
HWL with only tributary in flood
Figure C1.2
Typical abnormal flood discharge
(See Clause C1.9.1.6.)
Figure C1.2 shows a typical situation where the high water level of the tributary crossed by the bridge
and used for the scour computations differs considerably from that of the main stream which establishes
the soffit elevation and approach grade. Abnormal flood discharge conditions may also be encountered
just upstream from lakes and reservoirs, where the design discharge in the river may coincide with either a
high or a low water level downstream.
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C1.9.2 Investigations
An example of the type and extent of investigations required can be found in Chapter J of the
Drainage Manual (MTO 1992a).
C1.9.3 Location and alignment
The location of a structure and its alignment relative to the flow can significantly influence the
long-term cost of maintenance of the structure and its approaches. Attention is drawn to the following
points:
(a) Failure to predict and allow for future channel shifts can create serious problems.
(b) Concentration of flow through a structure opening can cause downstream channel erosion and
damage to downstream structures.
(c) Failure to take account of conditions associated with the site, such as ice jam formation, can cause
serious maintenance problems and even loss of the structure.
(d) The requirements of established boating, shipping, hydroelectric power, logging and other
interests must be accommodated. These sometimes govern the span arrangement and structure
alignment.
(e) Occasionally, the agency having jurisdiction over a river or other body of water has proposals for
channel realignments, flood control schemes and other works that must be considered in the
hydraulic design of the crossing. Failure to do so could result in avoidable costs to the public.
(f) Discharge from dams and other flow restrictions can cause serious damage to downstream
facilities, depending on velocity and distance.
C1.9.4 Estimation of scour
C1.9.4.1 Scour calculations
Inadequate attention to the prediction or prevention of scour is a common cause of failure for bridges
and open-footing culverts. An example of scour-related collapse is that of the Scholarie Creek bridge
on US I-90 in New York state (ENR 1987).
General scour, caused by constriction of the flow, is the most common type of scour at stream
crossings. Local scour, mostly caused by substructures, must be added to general scour, as illustrated
by Figures C1.3 and C1.4.
Abutment
Road grade
Abutment
Design HWL
Flood plain
Average original streambed
Original
streambed
Total depth
of scour
NWL
General
scour
Total depth of scour
= general scour + local scour
Depth of
general scour
Local scour
Figure C1.3
General and local scour at a bridge
(See Clauses C1.9.4.1 and C1.9.4.4.)
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Abutment
Road grade
Abutment
HWL
Flood
plain
Average original bed
dsm
Original bed
dsa
ds
Footing
Average
general scour
Footing
dsp
Legend
dsa = average depth of general scour
dsm = maximum depth of general scour
dsp = depth of local scour
ds = total depth of scour
Figure C1.4
Typical scour at a bridge with spread footings
(See Clauses C1.9.4.1 and C1.9.4.4.)
C1.9.4.2 Soils data
Scour calculations are approximate and must therefore be conservative. Scour predictions should be
exceeded seldom and by small amounts. Large errors could occur however if, for example, a highly
erodible stratum were located just below the predicted maximum depth of scour in a much less erodible
soil. In this case, there could be disastrous consequences if the actual scour penetrated into the erodible
soil.
For this reason, it is essential to obtain detailed information on materials underlying the streambed
unless the bed is inerodible. Soils investigations should therefore be carried out for all structures having an
erodible streambed.
C1.9.4.3 General scour
C1.9.4.3.1 Average depth
The original streambed is defined as the bed as it was before man-made alterations or restriction of the
channel. In the replacement of an existing structure, the original bed is considered the general level of the
streambed, excluding scour caused by the old bridge. This is an important consideration in the
determination of spread footing depths.
The competent velocity method has been found suitable for calculating average depths of general scour
at stream crossings in most locations. Competent velocity values are given in the Guide to Bridge Hydraulics
(TAC 1980).
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C1.9.4.3.2 Maximum depth
During the life of a bridge, a meandering channel passing through highly erodible alluvial soil may
change its course drastically, causing the deepest scour location to shift from one side of a bridge to
the other. Scour protection should be provided in such cases.
Restriction of a channel by ice can increase flow velocity under the ice, thereby creating general
scour if the bed is erodible. This possibility should be considered in determining the scoured bed
elevation.
C1.9.4.4 Local scour
Local scour is illustrated in Figures C1.3 and C1.4.
In noncohesive silt or sand, the depth of local scour at a pier may be calculated by the following
formula:
dsp = CLCSWp
where values of CL and CS are given by Tables C1.2 and C1.3, respectively.
The above formula and Tables C1.2 and C1.3 are based on information in the Guide to Bridge
Hydraulics (TAC 1980).
Other methods of predicting local scour were established by Richardson and Richardson (1989) and
Melville and Sutherland (1988).
Satisfactory methods of predicting local scour at abutments and at piers in cohesive materials are
not yet available. Tables C1.2 and C1.3 may be used with a reduction factor to allow for the less
scourable material; but measurements of local scour at existing structures provide the best guidance.
Table C1.2
Local scour coefficients for piers, CL
(See Clause C1.9.4.4.)
Piers aligned parallel to flow
Local scour coefficient CL*
Pier shape in plan†
Pier shape in profile
dt ≤ 5Wp
dt > 5Wp
Rectangular with round ends
Round column
Rectangular
Elliptical ends
Rectangular with round ends
Rectangular with round ends
Vertical ends
Vertical
Vertical ends
Vertical ends
Obtuse > 20°
Acute ≤ 20°
1.5
1.5
2.0
1.2
1.0
2.0
2.3
2.3
3.0
1.8
1.5
3.0
*Coefficients are applicable for piers in noncohesive sands and silts.
†Where scour is likely to expose the footing to the flow, Wp shall be taken as the width of the footing.
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Table C1.3
Coefficients for skewed piers, CS
(See Clause C1.9.4.4.)
Piers skewed at an angle θ
to flow
Skew angle
Length-to-width ratio of pier
θ degrees
4
8
12
0
15
30
45
1.0
1.5
2.0
2.5
1.0
2.0
2.5
3.5
1.0
2.5
3.5
4.5
C1.9.4.5 Total scour
It is conservative to assume that the maximum depth of general scour will occur at the location of the local
scour. An additional allowance must be made for degradation or artificial deepening as described in
Clause C1.9.4.8.
C1.9.4.6 Degradation
Degradation, or general lowering of a streambed over a long period, can be a serious problem and should
be considered for structures on susceptible channels.
The amount of degradation on some streams may exceed 10 m over a period of several decades. There
appears to be no reliable method of calculating degradation analytically at present, and field observations
provide the best guidance. This approach is described in Chapter J of the Drainage Manual (MTO 1992a).
FHWA (1980) is also of interest concerning the prediction of degradation.
C1.9.4.7 Artificial deepening
Artificial deepening of municipal drains has, in the past, caused undermining and failure of structures.
Every effort should be made to anticipate it. This is particularly necessary in developing areas, where urban
drainage schemes sometimes necessitate deepening by several metres. If drainage plans are not available,
field observations, discussions with local authorities, and investigation of past developments in similar
situations may be helpful.
Where costs are substantial, allowance for major deepening should be made only when definite plans
for the deepening are on record.
C1.9.4.8 Allowance for degradation or artificial deepening
(a) Where a concrete or other inerodible invert is not provided to stabilize an actively degrading
streambed, depths of spread footings must be based on the ultimate bed elevation, allowing for
degradation and scour. Because the probability that the maximum scour will coincide with the
maximum degradation is small, only half the estimated scour is used in determining the ultimate bed
elevation.
(b) Maximum scour is more likely to occur in conjunction with maximum artificial deepening, especially
if the deepening is undertaken early in the life of the structure. Therefore, the full amount of
estimated scour should be added to the expected amount of deepening. This should not result in
excessive footing depths, as the amount of scour on channels subjected to artificial deepening is
usually small.
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C1.9.5 Protection against scour
C1.9.5.1 General
Protection against undermining of structure foundations may be achieved by locating spread footings
at an appropriate depth, or by the use of piles, sheet piling, or paved inverts.
C1.9.5.2 Spread footings
C1.9.5.2.1 Depth of footings
Spread footings in erodible soils may be vulnerable to floods larger than the normal design flood, but
where the soil bearing capacity is suitable, their lower initial cost usually favours their use, except on
highly scourable soils such as sand, silt, or fine gravel.
The following comments relate to the corresponding Item (a), (b), (c), etc. in Clause 1.9.5.2.1.
(a) The depths specified in Clause 1.9.5.2.1(a)(i) represent current practice. They apply to all
substructure footings that may be exposed to scour, including those of training works and wing
walls. The factor specified in Clause 1.9.5.2.1(a)(ii) allows a theoretical safety margin of at least
0.4 times the depth of footing before the footing begins to become undermined. The margin is
intended to allow for inexact design assumptions, the approximate nature of scour computations,
and the probability that during the structure lifetime, a flood larger than the design flood will
occur.
(b) For bedrock that is subject to erosion or weathering, the footings are normally set into the
bedrock by an amount greater than the conservatively estimated maximum depth of erosion.
(c) The reductions in footing depth for temporary gabion or timber crib substructures are based on
past practice.
(d) It is very unlikely that a flood causing the predicted scour depth at a bridge would coincide with
the maximum expected bed degradation. As degradation progresses it obliterates earlier scour;
thus, in determining the required footing depth, it is reasonable to use half the predicted scour
depth. Multiplying this value by the factor of 1.7 gives a footing depth below the degraded bed
of 0.85 times the estimated scour, which has been rounded off to 1.0.
(e) Because a channel might be artificially deepened at any stage in the life of a bridge, it is prudent
to add the full depth of scour to the predicted amount of deepening. In practice, artificial
deepening is seldom required at locations on channels that are subject to scour.
C1.9.5.2.2 Protection of spread footings
Structures with spread footings on highly erodible soils are very vulnerable to failure caused by scour
and undermining, and should not be used without the sheet piling or other protection specified.
Clause 1.9.5.4 requires that sheet piling used for this purpose should have sufficient stiffness and
strength to maintain the bearing capacity of the soil within the sheet piling with the soil outside the
sheet piling at the ultimate bed elevation.
Spread footings close to the channel and without protection should be considered likely to be
exposed to stream flow. Footings some distance from the channel and founded on erodible material at
a level higher than the streambed are vulnerable to failure if the stream banks become eroded, as is
often the case. The bank protection required in such situations needs to remain effective for the design
life of the bridge.
C1.9.5.3 Piles
C1.9.5.3.1 General
Piles do not provide an absolute assurance against scour failure, but can withstand much greater
depths of scour than spread footings.
The increased resistance to scour failure may also permit a reduction of span below that required for
spread footings. Pile foundations also have the advantage that the footings can often be placed at a
shallower depth, thereby reducing dewatering costs.
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C1.9.5.3.2 Penetration and strength
Reduction of the bearing capacity attributable to skin friction, and the reduction of structural strength due
to the removal of buckling restraint are possibilities that should be considered.
C1.9.5.3.3 Abutments supported on piles
Although pile abutments are relatively safe even if the footings are undermined, the fill behind the
abutments should be prevented from washing out and causing a hazardous cavity in or below the road
surface.
C1.9.5.4 Sheet piling
These provisions are intended to prevent failure due to scouring of the stream bed and the fill in front of
the footing or piling. If sheet piles are required in the dewatering of footing excavations, to leave them in
place permanently as scour protection may be an economic option.
C1.9.5.5 Protective aprons
The provisions of Clause 1.9.5.5 are based on the Guide to Bridge Hydraulics (TAC 1980). Procedures for
determining the size of stone are given in Appendix IV of the Guide.
C1.9.5.6 Paved inverts and revetments
Protection is essential at all ends or edges of paved inverts and revetments that may be exposed to stream
flow.
C1.9.5.7 Special protection against degradation
On actively degrading streams, it is desirable to stabilize the bed at a culvert or small bridge in order to
protect the foundations and prevent upstream progression of the gully. On very active gullies, the amount
of deepening may be 10 m or more during the life of a structure.
It is important that the downstream end of the invert be protected against undermining. In extreme
cases, a drop outlet structure or other device may have to be installed to prevent failure of the structure.
C1.9.6 Backwater
C1.9.6.1 General
Backwater should be considered at crossings downstream of buildings or land that is likely to be
developed within twenty years. Some Provincial Government regulations require that the regulatory flood
be used for calculations in such cases.
Where the value of affected property is low, it may be more economical to purchase the property rather
than increase the size of the bridge. The requirements of regulatory agencies should be reviewed to ensure
that the extra cost to the Owner is commensurate with the benefits produced by a larger structure.
C1.9.6.2 High-water level
Conditions that determine critical backwater level will generally not be the same as those used in the
consideration of scour.
C1.9.6.3 Assumed depth of scour
The increase of bridge waterway area created by scouring of the stream bed has the beneficial effect of
reducing backwater. However, scour is time-dependent and the calculated depth of scour may not
develop during a single flood. For this reason, only half the calculated average depth of general scour is
used in the backwater calculations.
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C1.9.6.4 Waterway modification
Artificial enlargement of the bridge waterway opening by widening or deepening the channel may be
beneficial in reducing backwater, but care should be taken not to create erosion or deposition
problems in the upstream or downstream channel. Inappropriate enlargement of the bridge opening
may become ineffective after a few years because of sedimentation and the growth of vegetation.
C1.9.6.5 Reduction of backwater by relief flow
Relief flow over the approach road to a structure can greatly reduce backwater during a regulatory
flood and should, therefore, be maximized by keeping the grade as low as possible, provided that the
minimum freeboard requirements for the normal design flood are satisfied. The comparison in bridge
size between crossings with and without relief flow is illustrated by Figures C1.5 and C1.6.
Freeboard
HWL for regional design flood
Relief flow
Clearance
Road grade
HWL for normal design flood
HWL
Flood plain
NWL
Figure C1.5
Clearance and freeboard for regulatory flood with
maximum relief flow
(See Clauses C1.9.6.5 and C1.9.8.1.)
Freeboard less than
the minimum required
Freeboard exceeds
the minimum required
Road grade
HWL for regional design flood
HWL for normal design flood
Flood plain
NWL
Zero clearance from
regional design flood
Figure C1.6
Clearance and freeboard for regulatory flood
with no relief flow possible
(See Clauses C1.9.6.5 and C1.9.8.1.)
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C1.9.7 Soffit elevation
C1.9.7.1 Clearance
The clearances specified are in accordance with common practice.
Specifying standard clearances for arch structures is impracticable because of the wide range of
circumstances. For open-spandrel steel arches, a buildup of water and ice against the superstructure is not
permissible. For concrete arches, it is often acceptable to have some of the soffit submerged. Bridges of
this type should be considered individually, together with the effects of stream flow and ice loads at the
appropriate water level.
The minimum clearance from the normal water level ensures that sufficient clearance is available at low
flows to keep the structure from being submerged in most conditions and to permit inspection of the
underside of the structure.
C1.9.7.2 High-water level for establishing soffit elevation
C1.9.7.2.1 General
The critical high-water level for determining the soffit elevation is in some cases caused by ice jams and
may be considerably higher than that under ice-free conditions.
C1.9.7.2.2 Flooding and relief flow
Clause C1.9.7.2.2 may require the superstructure to be submerged for the regulatory flood. This may be
acceptable provided the amount of relief flow is sufficient to prevent damage to the bridge. If relief flow is
not possible, the soffit elevation determination may have to be based on the regulatory flood level.
Clause C1.9.8.1 offers some guidance for cases where only a moderate amount of relief flow is possible.
C1.9.8 Approach grade elevation
C1.9.8.1 General
It is usual practice to keep highways passable during the normal design flood, but to permit relief flow over
the approach grade during floods much larger than the normal design flood.
If concern for the flooding of upstream property dictates consideration of the regulatory flood, the
required size of structure may be reduced by allowing relief flow. This may not be possible if, because of
other considerations, the approach grade cannot be placed low enough. In such a case, a larger opening
will be required to reduce backwater to an acceptable level.
This situation is illustrated in Figures C1.5 and C1.6. If sufficient relief flow is possible during a regulatory
flood, the structure cost can be greatly reduced by designing it to accommodate only the normal design
flood. However, if the vertical alignment of the road is such that relief flow is not possible, the structure
opening must be high enough and large enough to accommodate the regulatory flood without exceeding
the permissible backwater. In cases where only a moderate amount of relief flow is possible, the structure
opening may have to be designed for a discharge between the normal and the regulatory flood.
C1.9.8.2 Freeboard
The specified minimum freeboard values conform to current practice.
C1.9.8.3 High-water level for establishing approach grade
See Clause C1.9.7.2.
On the upstream side of an opening causing backwater, the estimated backwater is included in
determining the high-water level used to establish minimum freeboard.
C1.9.8.4 Freeboard for routes under structures crossing water
Clause 1.9.8.4 may require setting the bridge soffit elevation higher to provide the required traffic
clearance.
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For access roads and pathways or similar routes under a bridge or culvert, high maintenance costs
caused by frequent flooding may justify increased freeboard.
C1.9.9 Channel erosion control
C1.9.9.1 Slope protection
The control of slope erosion at bridges is important where erosion may lead to undermining of
foundations or cause structural damage. In these cases, appropriate slope protection should be
provided.
C1.9.9.2 Stream banks
Clause 1.9.9.2 concerns stream bank erosion that would endanger a structure or approach
embankment.
C1.9.9.3 Slope revetments
Toe protection is an essential part of slope revetment, but is sometimes overlooked.
C1.9.9.4 Storm sewer and channel outlets
Storm sewers and channels discharging into or adjacent to a bridge or open-footing culvert opening
may cause serious undermining unless concrete aprons or other erosion control devices are provided.
C1.9.10 Stream stabilization works and realignment
C1.9.10.1 Stream stabilization works
Stabilization works should not be provided without compelling justification. They are initially costly
and may require repairs and maintenance. Future widening of the structure may require their removal
and replacement.
C1.9.10.2 Stream realignment
Diversions may cause harmful erosion and sedimentation, as well as adverse environmental and
hydrologic effects.
C1.9.11 Culverts
C1.9.11.1 General
Some Regulatory Authorities have comprehensive requirements for the design of culverts. Chapter D
of the Ontario Drainage Manual (MTO 1992a) covers all normal aspects of the hydraulic design,
including manual and computer procedures for conventional and improved-inlet culverts, fish passage
considerations, relief flow computations, and the design of end treatment.
Experience has shown that open-footing culverts with scourable inverts are vulnerable to failure
resulting from undermining of the footings by scour, degradation, and artificial deepening. Properly
designed and installed closed-invert culverts are virtually indestructible, and should survive floods
much greater than the design flood unless the road itself washes out. For this reason, closed-invert
culverts should be used wherever possible. The open-footing type is sometimes necessary when the
channel will be deepened by an indeterminate amount some time in the future.
C1.9.11.2 Culvert end treatment
In general, the comments pertaining to stream stabilization works in Clause C1.9.10.1 apply to some
extent to culvert end treatment. However, for closed-invert culverts that can sustain high velocity flow,
possible economic benefits dictate special consideration.
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The full potential of improved culvert inlets in reducing culvert costs is often overlooked. In some cases,
such inlets can double culvert capacities, or culvert openings may be reduced accordingly. The reduction
in culvert cost must be weighed against the increased cost of the inlet and outlet structures. Properly
bevelled edges should be provided on inlets of all cast-in-place concrete box culverts, whether
conventional or improved inlets are provided, since they are inexpensive and effective.
General backwater considerations pertinent to culverts are discussed in Clause C1.9.6.1.
It is common practice to permit conventional closed-invert culverts to flow full at the inlet. Permitting
such culverts to flow submerged during design floods is sometimes undesirable due to the difficulty of
removing debris under flood conditions, the reduced safety factor, and the possibility of embankment
failure due to piping through the fill. However, in some cases submergence of an existing culvert or its
extension may obviate the need for an expensive replacement structure. Submergence may also be
permissible at crossings where, for example, a large river downstream produces a water level at the site
several metres higher than that created by the culvert.
In the case of improved inlet culverts, the allowable backwater is generally determined by consideration
of potential flooding of upstream property and, for maximum economy, the inlet may be submerged
provided that piping through the fill is controlled.
C1.9.11.3 Culvert extensions
Extension of an existing multispan culvert by a single span upstream, or extension of a single-span culvert
by multiple spans downstream, can create serious debris blockage problems inside the culvert during
floods, and should be avoided.
Changes of cross-sectional shape should be accomplished by providing gradual, snag-free transitions.
C1.9.11.4 Alignment of non-linear culverts
The maximum changes of direction specified are those suggested in the Hydraulic Design of Culverts
(AASHTO 1979). The limitation is necessary to prevent an accumulation of debris inside the culvert and to
prevent undue loss of head in culverts operating with high velocities. Some flexibility is allowed for sites
where the optimum alignment cannot be attained.
C1.9.11.5 Open-footing culverts
C1.9.11.5.1 Inerodible inverts
Open-footing culverts often have footings and inverts on bedrock that is assumed to be inerodible. If the
rock is susceptible to erosion or weathering, the footings must be embedded into the rock a depth
sufficient to ensure that they will not be exposed during the design life of the structure.
C1.9.11.5.2 Vertical clearance
Provision of clearance from high water level is beneficial in providing additional waterway area during a
large flood. It also reduces the risk of blockage by debris.
C1.9.11.6 Closed-invert culverts
C1.9.11.6.1 Invert elevation
Experience has shown the desirability of placing inverts below the general channel invert.
C1.9.11.6.2 Artificial deepening
This requirement may save replacement of the culvert, but will add to the initial cost. Costs and the
probability of deepening should be evaluated.
C1.9.11.6.3 Degrading channel
If the invert is placed below the bed of a degrading channel, gullying will proceed upstream unless a sill is
provided. Cutoff walls are essential for preventing the undermining and failure of structures on degrading
streams. The provisions of Clause 1.9.5.7 apply in this case.
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C1.9.11.6.4 Piping
There have been numerous failures initiated by piping through the fill surrounding culverts. Piping
may cause progressive loss of support at the springing of soil-steel structures, leading to structural
failure. It may initiate the washout of soil behind an abutment, leading to embankment failure and
perhaps also to structural failure. Clay seals can provide an inexpensive and effective means of
preventing piping.
C1.9.11.6.5 Concrete box structures
Failures of closed-invert culverts usually occur as a result of uplift or undermining of culvert ends.
Cutoff walls at the ends of concrete box culverts are necessary in all cases to prevent undermining and
possible collapse of the culvert ends.
C1.9.11.6.6 Soil-steel structures
End treatment
The flexibility and light weight of soil-steel culverts make them particularly vulnerable to failure due to
hydraulic uplift of the inlet or upward buckling of the invert. To ensure structural stability, special end
treatment should be provided. The end treatment should include collars, cutoff walls, and proper
finishing and geometry of the steel plates at the ends. The attachment of concrete collars and cutoff
walls to the culvert is important. Lack of attachment has been a factor in uplift failures.
Concrete cutoff walls and headwalls have proved to be very successful and are the preferred means
of preventing uplift. However, where concrete is not readily available, or where placing concrete is not
practicable, other acceptable methods of end treatment may be devised.
The simplest means of reducing the possibility of uplift is grading the fill to minimize the uncovered
length of pipe. This is particularly necessary in the case of heavily skewed culverts, where the exposed
length is greatly increased. Culvert ends projecting from the fill to accommodate future widening
should also be covered by fill unless other precautions against uplift are taken (Abdel-Sayed et al.
1993).
Camber
This is an important consideration where anticipated settlement of the structure is significant in
relation to the height of the opening.
References
CSA (Canadian Standards Association)
CAN/CSA-S6-88 (withdrawn)
Design of highway bridges
S408-1981 (R2001)
Guidelines for the development of limit states design
Other publications
AASHTO. 1979. Highway Drainage Guidelines, Vol. IV — Hydraulic Design of Culverts. American
Association of State Highway and Transportation Officials, Washington, DC.
AASHTO. 1994. Standard Specifications for Highway Bridges. American Association of State Highway
and Transportation Officials, Washington, DC.
Abdel-Sayed, G., Bakht, B., and Jaeger, L.G. 1993 Soil-Steel Bridges. McGraw-Hill Inc., New York.
ACI. 1990. Esthetics in Concrete Bridge Design. American Concrete Institute.
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Agarwal, A.C., and Cheung, M.S. 1987. “Development of Loading-truck Model and Live-load Factor for
the Canadian Standards Association CSA S6 Code.” Canadian Journal of Civil Engineering, Vol. 14, No. 1,
pp. 58–67.
ASCE. 1962. Nomenclature for Hydraulics. American Society of Civil Engineers, New York.
Davenport, A.G. 1983. “The Relationship of Reliability to Wind Loading.” Journal of Wind Engineering and
Industrial Aerodynamics, Vol. 13, pp. 3–27.
ENR. 1987. “Scouring Suspected in Collapse (Scholarie Creek, New York).” Engineering News Record,
Vol. 219, No. 15, p. 13, April 9, 1987.
FHWA. 1980. Stream Channel Degradation and Aggradation, FHWA-RD-80-159, U.S. Federal Highway
Administration, Washington, DC.
Kennedy, D.J.L., Gagnon, D.P., Allen, D.E., and MacGregor, J.G. 1992. “Canadian Highway Bridge
Evaluation: Load and Resistance Factors.” Canadian Journal of Civil Engineering, Vol. 19, No. 6,
pp. 992–1006.
Macgregor, J.G., Kennedy, D.J.L., Bartlett, F.M., Chernenko, D., Maes, M.A., and Dunaszegi, L. 1997.
“Design Criteria and Load Resistance Factors for the Confederation Bridge.” Canadian Journal of Civil
Engineering, Vol. 24, No. 6, pp. 882–897.
Marsalek, J., and Gruspier, J.E. 1982. Road and Bridge Deck Drainage Systems. Research & Development
Branch Report RR-228, Ministry of Transportation of Ontario, Downsview, Ontario.
MEA. 1993. Class Environmental Assessment for Municipal Road Projects. Municipal Engineers Association,
Ontario.
Melville, B.W., and Sutherland, A.J. 1988. “Design Method for Local Scour at Bridge Piers.” Journal of
Hydraulic Engineering, Vol. 114, No. 10. ASCE. October, 1988.
MTO. 1991. Ontario Highway Bridge Design Code (OHBDC), 3rd ed. Ministry of Transportation of
Ontario, Downsview, Ontario.
MTO. 1992a. Drainage Manual. Ministry of Transportation of Ontario, Downsview, Ontario.
Chapter B — Design Flood Estimation for Small Watersheds 1984.
Chapter C — Open Channel Design 1992.
Chapter D — Hydraulic Design of Culverts 1985.
Chapter E — Pavement Drainage and Storm Sewer Design 1983.
Chapter H — Design Flood Estimation for Medium and Large Watersheds 1988.
Chapter I — Hydraulic Design of Bridges 1986.
Chapter J — Field Investigations for Water Crossings 1986.
MTO. 1992b. Environmental Manual — Provincial Highway Class Environmental Assessment Process, Ministry
of Transportation of Ontario. Ronen Publishing, Toronto.
MTO. 1993. Ontario Structure Inspection Manual, (OSIM) Ministry of Transportation of Ontario. Ronen
Publishing, Toronto.
Nowak, A. 1990. Calibration of Load and Resistance Factors for Ontario Highway Bridge Design Code.
Research Report UMCE 90–06, Department of Civil Engineering, College of Engineering, University of
Michigan, Ann Arbor.
Nowak, A.S., and Agarwal, A.C., 1979. Calibration of the Ontario Highway Bridge Design Code. R&D Branch
report SRR-81-01, Ministry of Transportation of Ontario, Downsview, Ontario.
Nowak, A.S., and Grouni, H. 1994. “Calibration of the Ontario Highway Bridge Design Code 1991
Edition.” Canadian Journal of Civil Engineering, Vol. 21, No. 1, January 1994. pp. 25–35. Canadian Society
for Civil Engineering, Montréal.
30
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Richardson, E.V., and Richardson, J.R. 1989. Proceedings of the Bridge Scour Symposium, Report No.
FWHA-RD-90-035, Civil Engineering Department, Colorado State University, Ft. Collins, December
1989.
RSO. 1990. The Environmental Assessment Act. Revised Statutes of Ontario 1990, Chapter E18 and
amendments thereto, Toronto.
TAC. 1980. Guide to Bridge Hydraulics. Roads and Transportation Association of Canada, 1973, as
revised by Metric Supplement, 1980. University of Toronto Press, Toronto.
TAC. 1986. Geometric Design Guide for Canadian Roads. Metric Edition. Transportation Association of
Canada, Ottawa.
Tharmabala, T., Reel, R.S., and Nowak, A.S. 1996. Single and Multiple Load Path Bridges. Structural
Office Report SO-96-09, Ministry of Transportation of Ontario, Downsview, Ontario.
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Canadian Highway Bridge Design Code
Section C2 — Durability
C2.1
Scope 34
C2.3
Design for durability 34
C2.3.1
Design concept 34
C2.3.2
Durability requirements 35
C2.3.2.1 General 35
C2.3.2.2 Materials 35
C2.3.2.3 Structural details 35
C2.3.2.4 Bearing seats 35
C2.3.2.5 Bridge joints 35
C2.3.2.6 Drainage 36
C2.3.2.9 Access 36
C2.3.2.11 Inspection and maintenance 36
C2.3.3
Structural materials 36
C2.4
Aluminum 36
C2.4.1
Deterioration mechanisms 36
C2.4.2
Detailing for durability 37
C2.4.2.1 Connections 37
C2.4.2.2 Inert separators 37
C2.7
Waterproofing membranes 37
C2.8
Backfill material 37
C2.9
Soil and rock anchors 37
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Section C2
Durability
C2.1 Scope
In the past, insufficient attention has been given in the design phase to durability. There has also been a
lack of investigation and systematic reporting on the performance of the various structure types and
details. Section 2 calls attention to durability as a design requirement.
The high cost of repairs and replacements is a compelling reason to focus attention on durability. On
heavily travelled highways, it is increasingly difficult to obtain access to or possession of roadways in order
to carry out the necessary repairs or replacement. The danger posed by repairs to workers and to the
travelling public is another major consideration, as is the increasing cost of delays and detours.
C2.3 Design for durability
C2.3.1 Design concept
The design life of all new structures is specified as 75 years in Section 1. The past performance of some
types of bridges indicates that additional measures would be required to achieve this specified design life.
For example, soil steel structures may require additional material thickness in addition to galvanizing;
concrete decks may require waterproofing and paving; certain components of wood bridges may require
additional protection to prevent environmental exposure or wear and tear due to vehicular traffic or ice.
For main structural components such as foundations, piers, abutments, superstructure, and decks, the
service life should be 75 years.
The design life of components that are envisaged to be replaced before the end of the design life of the
bridge should be clearly defined at the start of the design process.
It would be unrealistic to expect that all components will last for their design life without any repair or
possible replacement. Components may need total replacement during the design life of the structure.
Based on past experience, the typical service life of some components is specified in Table C2.1.
Table C2.1
Typical service life of components
(See Clause C2.3.1.)
34
Component
Service life, years
Asphaltic concrete pavement
15–20
Hot applied rubberized waterproofing membrane
25–30
Concrete overlays with waterproofing
30
Steel coating systems
10–20
Timber wearing surfaces
5–10
Expansion joints
15–30
Expansion joint seals
5–15
Bearings under expansion or fixed joints
25–40
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In some cases, the construction of a new facility will change the environmental conditions at the
site. For example, a new highway will result in the use of de-icing salts, which cannot be measured by
an investigation of the site. In such cases, reference should be made to exposure conditions in
comparable facilities.
Measures should be taken to protect the structure against premature deterioration. A multistage
protection strategy may be established, based on the adverse effects of the environment and the type
and rate of deterioration.
C2.3.2 Durability requirements
C2.3.2.1 General
Many decisions taken early in the design process greatly influence the durability of the final product.
This whole process of creating structures and keeping them in serviceable condition requires a
coordinated effort by the following parties, in roughly the sequence indicated:
(a) The Owner, by defining his present and future needs.
(b) The Planner, by choosing alignments that will result in rapid drying of the decks and other
components of the bridge.
(c) The Designer, by selecting the optimum structure type that meets the Owner’s requirements at a
reasonable cost and by preparing the design specifications.
(d) The Contractor, by building the structure according to the specifications and controlling the
quality of construction and materials.
(e) The Owner once again, by instituting a regular maintenance program.
C2.3.2.2 Materials
Each material responds differently to aggressive environmental agents (MTO 1989).
In order to design durable structures, it is important to consider the following for the design life of
the structure:
(a) the expected adverse effects of the environment on the structure and structural materials;
(b) the various deterioration mechanisms that may occur and the processes of deterioration;
(c) steps that can be taken to slow down the processes of deterioration, or possible strategies that
can be adopted at the design stage to alleviate environmental actions.
C2.3.2.3 Structural details
By paying attention to structural details during the design stage, the service life of the structure can be
enhanced considerably without any appreciable increase in cost.
Stray current from electric power distribution systems is thought to accelerate the corrosion of
buried metallic components. Early detection of deterioration and determination of its cause are very
important in limiting the damage and the cost of repair.
Thorough investigation of the effectiveness of protective systems or counteractive measures is also
important. The efficacy of protective measures should never simply be assumed.
C2.3.2.4 Bearing seats
Sloping the concrete surfaces around bearings by 5% towards the faces of the abutments or piers
helps to prevent a buildup of salt and debris and accelerates drying. The slope should be increased to
15% under open joints. Bearings may also be placed on raised pedestals.
Where large expanses of abutment or pier faces are visible, it may be desirable to contain the runoff
and to channel it into grooves or drain pipes.
C2.3.2.5 Bridge joints
C2.3.2.5.1 Expansion and/or fixed joints in decks
Poorly designed, improperly installed bridge joints and their chronic lack of maintenance are the
biggest causes of premature deterioration of bridge components under the joints. It may not be
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possible to design joints that are completely watertight for the design life of the structure, but it is essential
to provide details that will prevent the water from dripping on to bearing seats or anchors. Expansion
joints should be designed to facilitate replacement of the joint seals. Bridges with integral abutments and
continuous bridges that eliminate unnecessary expansion joints are inherently more durable.
To prevent water from expansion joints from travelling along exterior surfaces of girders, consideration
should be given to extending the end diaphragm past the exterior face of the outside girder.
C2.3.2.6 Drainage
Proper drainage and waterproofing are the key to preventing most durability problems. The number of
drains provided should be kept to a minimum.
In exposed locations, longer downspouts may be required to prevent wind-blown spray from wetting
adjacent members.
C2.3.2.9 Access
All components that are susceptible to damage must be accessible for inspection and maintenance, and
must be replaceable. Voids in decks should have a minimum height of 1200 mm for access purposes.
Access hatches should be provided to all box girders deeper than 1200 mm and should be located away
from travelled portions of the roadway, where practicable, to prevent unnecessary interference with traffic.
On high bridges, access to the superstructure may be provided via travelling platforms.
Access to buried parts of the substructure is not required.
C2.3.2.11 Inspection and maintenance
It is unlikely that any structure will achieve its design life without routine inspection, maintenance, repair,
or rehabilitation. The level of maintenance planned for the structure is an economic decision based on
established policies or the bridge management system in place. However, rational decisions made early in
the design process can extend the service life of a structure without much additional cost.
Investigation of the effectiveness of protective systems or counteractive measures is important. The
efficacy of protective measures should never be simply assumed. A comprehensive bridge management
system can help in making rational decisions regarding protection and rehabilitation strategies on the
basis of life-cycle costs.
C2.3.3 Structural materials
The durability requirements of structural materials are affected by the environmental exposure and the
deterioration mechanisms of the materials.
Default values of environmental exposure should be based on local conditions.
The deterioration mechanisms for structural materials are identified in the appropriate material sections.
C2.4 Aluminum
C2.4.1 Deterioration mechanisms
Corrosion in aluminum is usually a uniform, gradual oxidation of the surface in the presence of air and
moisture. Aluminum has a strong resistance to corrosion deterioration after the initial formation of
aluminum oxide which protects the underlying metal and inhibits further corrosion (MTO 1989).
Galvanic corrosion occurs when aluminum comes into contact with other metals in the presence of an
electrolyte. Galvanic corrosion does not occur when aluminum is in contact with galvanized or stainless
steel.
Chemical corrosion occurs when aluminum is in contact with concrete. Deterioration mechanisms for
aluminum, other than corrosion, are related to stresses, detailing, and material quality.
36
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C2.4.2 Detailing for durability
C2.4.2.1 Connections
Coating with paint or bitumastic material between the galvanized bolt and aluminum helps to isolate
dissimilar metals and prolong the service life of the components (AGA 1990).
C2.4.2.2 Inert separators
Nylon or neoprene may be used to separate aluminum from other metals in order to prevent galvanic
corrosion. Nylon, neoprene, or bitumastic coating may be used to separate aluminum from concrete
to prevent chemical corrosion.
C2.7 Waterproofing membranes
Some of the waterproofing membranes in use are as follows:
(a) hot rubberized asphalt membrane;
(b) sheet membranes; and
(c) polymer membranes.
C2.8 Backfill material
If the backfill material is suspect, its electrochemical resistivity and pH values should be checked
(AASHTO 1994).
C2.9 Soil and rock anchors
Rock anchor tie backs need to be protected with a double corrosion protection system. The anchors
should be encased in corrugated PVC sheathing and pregrouted prior to installation. A smooth PVC
tubing should fit snugly over the corrugated sheathing in the free-stressing length. The annular space
between the sheathing should be grouted over its full length prior to its installation.
References
Other publications
AASHTO. 1994. LRFD Bridge Design Specifications. American Association of State Highway and
Transportation Officials, Washington, DC.
AGA. 1990. Galvanizing for Corrosion Protection. American Galvanizers Association.
MTO. 1989. Ontario Structure Inspection Manual. Ministry of Transportation of Ontario, Downsview,
Ontario.
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Canadian Highway Bridge Design Code
Section C3 — Loads
C3.1
C3.2
C3.3
C3.4
C3.4.2
C3.4.3
C3.4.4
C3.5
C3.5.1
C3.5.2
C3.5.2.1
C3.5.2.2
C3.5.3
C3.5.4
C3.6
C3.7
C3.8
C3.8.1
C3.8.2
C3.8.3
C3.8.3.1
C3.8.3.2
C3.8.3.3
C3.8.4
C3.8.4.1
C3.8.4.2
C3.8.4.3
C3.8.4.4
C3.8.4.5
C3.8.5
C3.8.6
C3.8.7
C3.8.8
C3.8.8.1
C3.8.8.2
C3.8.9
C3.8.10
C3.8.12
C3.9
C3.9.1
C3.9.2
C3.9.3
C3.9.4
C3.9.4.1
C3.9.4.2
C3.9.4.3
C3.9.4.4
C3.9.4.5
C3.10
C3.10.1.1
C3.10.1.2
C3.10.1.3
C3.10.1.4
C3.10.1.5
Scope 41
Definitions 41
Abbreviations and symbols 41
Limit states criteria 41
Ultimate limit states 41
Fatigue limit state 41
Serviceability limit states 42
Load factors and load combinations 48
General 48
Permanent loads 49
General 49
Overturning and sliding effects 49
Transitory loads 50
Exceptional loads 50
Dead loads 50
Earth loads and secondary prestress loads 50
Live loads 50
General 50
Design lanes 51
CL-W loading 51
General 51
CL-W Truck 52
CL-W Lane Load 55
Application 62
General 62
Multi-lane loading 62
Local components 63
Wheels on the sidewalk 63
Dynamic load allowance 63
Centrifugal force 68
Braking force 68
Curb load 69
Barrier loads 69
Traffic barriers 69
Pedestrian and bicycle barriers 70
Pedestrian load 70
Maintenance access loads 70
Multiple-use structures 70
Superimposed deformations 71
General 71
Movements and load effects 71
Superstructure types 72
Temperature effects 72
Temperature range 72
Effective construction temperature 72
Positioning of bearings and expansion joints 75
Thermal gradient effects 76
Thermal coefficient of linear expansion 79
Wind loads 79
General 79
Reference wind pressure 80
Gust effect coefficient 80
Wind exposure coefficient 80
Non-uniform loading 81
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C3.10.1.6
C3.10.1.7
C3.10.2
C3.10.2.1
C3.10.2.2
C3.10.2.3
C3.10.2.4
C3.10.3
C3.10.3.1
C3.10.3.2
C3.10.3.3
C3.10.4
C3.10.4.1
C3.10.4.2
C3.10.5
C3.10.5.1
C3.10.5.2
C3.11
C3.11.4
C3.11.4.2
C3.11.5
C3.11.7
C3.12
C3.12.1
C3.12.2
C3.12.2.1
C3.12.2.2
C3.12.2.3
C3.12.2.4
C3.12.3
C3.12.4
C3.12.5
C3.12.6
C3.13
C3.14
C3.14.1
C3.14.2
C3.14.5
C3.14.6
C3.14.7
C3.15
C3.16
C3.16.1
C3.16.2
C3.16.3
C3.16.4
C3.16.4.1
C3.16.4.2
C3.16.4.3
C3.16.5
© Canadian Standards Association
Overturning and overall stability 81
Alternative methods 81
Design of the superstructure 81
General 81
Horizontal drag load 81
Vertical load 82
Wind load on live load 83
Design of the substructure 83
General 83
Wind loads transmitted from the superstructure 83
Loads applied directly to substructure 83
Aeroelastic instability 84
General 84
Criterion for aeroelastic instability 85
Wind tunnel tests 85
General 85
Load factors 85
Water loads 86
Stream pressure 86
Lateral effects 86
Wave action 86
Debris torrents 86
Ice loads 87
General 87
Dynamic ice forces 87
Effective ice strength 87
Crushing and flexural strength 87
Ice impact forces 87
Slender piers 88
Static ice forces 88
Ice jams 88
Ice adhesion forces 89
Ice accretion 89
Earthquake effects 90
Vessel collision 90
General 90
Bridge classification 90
Design vessel 90
Application of collision forces 90
Protection of piers 91
Vehicle collision load 91
Construction loads and loads on temporary structures 91
General 91
Dead loads 91
Live loads 92
Segmental construction 92
Erection loads 92
Construction live loads 92
Incremental launching 92
Falsework 92
Annexes
CA3.1 — Climate and environmental data 97
CA3.2 — Wind loads on highway accessory supports and slender structural elements 100
CA3.3 — Vessel collision 106
CA3.4 — CL-625-ONT live loading 111
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Section C3
Loads
C3.1 Scope
The Code is applicable to all highway bridges in Canada, including those with long spans.
C3.2 Definitions
The definitions include terms used in Annexes A3.1 to A3.4.
C3.3 Abbreviations and symbols
Symbols that are introduced in this Commentary are defined as they occur.
C3.4 Limit states criteria
C3.4.2 Ultimate limit states
The statement that a factored resistance shall always exceed the total factored load can be expressed
mathematically by the following:
φ Rn ≥ largest Sj
where
φ is the resistance factor,
Rn is the unfactored resistance, and
Sj is the total of the load effects due to factored loads.
For structures that behave linearly
Sj = Σ α ij times the effect of the i th load in loading case j
where
α ij is the load factor for load i in loading case j.
All possible unrestrained movements including overturning, sliding, and uplift should be
investigated. Normally, these will involve ULS considerations and the load effects and resistances will
accordingly be factored. Some tie-down systems could involve fatigue considerations.
C3.4.3 Fatigue limit state
Fatigue is the process of permanently induced progressive localized structural change occurring in a
material subjected to conditions that produce fluctuating stresses at some point or points and that
may culminate in cracks or fracture after a sufficient number of stress fluctuations. In bridge
components, this fluctuation of stresses is caused by the application of transitory loads.
In real life, bridge components are subjected to variable load cycles. However, in design, the fatigue
limit state is defined by the application of a specified number of cycles of a fixed characteristic
transitory load such that the cumulative fatigue effect is equivalent to that of the expected variable
load cycles during the lifetime of the bridge structure, without causing failure.
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C3.4.4 Serviceability limit states
No general formulation is possible for the requirements of serviceability limit states.
Superstructure vibration
The acceleration due to a representative load traversing the superstructure has been taken as a
serviceability limit state for highway and pedestrian bridges. Limitations on the depth-to-span ratio, or on
the live load deflection as a function of span, are not considered as providing for serviceability. The intent
of such limitations has been to control vibration, prevent fatigue, limit stresses in secondary members, and
account for dynamic loading. All these are provided for explicitly in the Code.
For highway bridges, acceleration limits have been converted to equivalent static deflection limits, to
simplify the design process.
Highway bridges
The development of Clause 3.4.4 is based on the examination of the weight of trucks likely to cross
bridges with the three different types of pedestrian use; the calculation of dynamic deflection values due
to these typical vehicles; and the vibration limits appropriate to each of the three types of pedestrian use.
A vehicle loading similar to that of the fatigue limit state, where the truck is assumed to be in a travelled
lane, was selected for all uses, it being noted that, in general, bridges with frequent pedestrian use are
usually crossed by traffic at low speeds (60 km/h or less).
Values of acceleration of a typical superstructure with typical approach irregularities under the action of
a typical vehicle cannot be easily calculated. Hence, the criteria for acceleration are expressed in terms of a
calculated static deflection against first flexural frequency. The conversion of acceleration to static
deflection was made on the basis of field observations of dynamic response of bridges to traffic in a
travelled lane. Data from early studies (Wright and Green 1964) indicate that an average vehicle load of
150 kN results in an average dynamic deflection of 12 to 15% of the static deflection. More recent
observations (Green et al. 1982, Billing 1982) for a wide range of bridge types and vehicle loads from
100 to 600 kN confirm this and show that existing bridges, whether designed with sidewalks or not, are
generally satisfactory, as shown in Figure C3.1.
30.0
Bridge with sidewalk
Static deflection, mm
20.0
10.0
Little pedestrian use
Significant pedestrian use
1.0
0.5
0
2
4
6
8
10
12
First flexural frequency, Hz
Figure C3.1
Comparison of measured deflections at edge of bridge,
adjusted to design load, with deflection criteria
(See Clause C3.4.4.)
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Acceleration, m/s2
For a bridge with sidewalks, and significant pedestrian use, and where there is concern about
possible traffic-induced vibration, careful attention should be given in design and, by quality control,
during Construction, to minimize bumps at the joints and undulations in the approach pavements.
Curbs and parapet walls, constructed with or without joints, can have a significant effect on the
deflection at the sidewalk (Green et al. 1982). If a bridge satisfies the deflection criterion with the
structural model used for design, there is no need to consider alternatives. However, if the deflection
criterion appears to govern, it will usually be more economical to recompute the deflection using an
analysis that reflects bridge response under single truck loading, rather than to increase the stiffness of
the main longitudinal members. The analysis procedures outlined in Section 5 for fatigue limit state
loading can be used for the majority of beam-and-slab, or slab type bridges.
Where a refined analysis is required for strength calculations, the fatigue limit state loading case can
easily be included. The deflection criteria will normally be satisfied for bridges of conventional design
with the longest span no greater than 20 m, or with a first flexural frequency above 6 Hz. For bridges
of slab-and-girder construction, deflection may be computed at the closest girder to the specified
location, if the girder is within 1.5 m of that location. For bridges of slab construction, or with long
cantilevers supporting the sidewalk, account should be taken of deflection due to torsion or transverse
flexure resulting from an eccentric load.
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
0
2
4
6
8
10
12
14
Time, s
Figure C3.2
Acceleration response of footbridge to pedestrian passage
(Blanchard et al. 1977)
(See Clause C3.4.4.)
Pedestrian bridges
The repeated footfall of a pedestrian crossing a flexible footbridge with little damping may result in a
buildup of vibration as shown in Figure C3.2. Pedestrian bridges can have less than 1% critical
damping so that footfall-induced vibration may be significant. The intent of Clause 3.4.4 is to limit
such vibration to a level acceptable to other pedestrians. The following method has previously been
applied for this purpose.
The basic criterion is that a single pedestrian weighing 700 N should not produce an acceleration
exceeding the limit given in Figure C3.3, as a function of the first flexural frequency of the
superstructure.
It should be assumed that the pedestrian walks with a footfall frequency, f f , that is the lesser of the
first flexural frequency of the structure or 4 Hz. The stride assumed should be 0.9 m or that which,
taken with the assumed footfall frequency, results in a speed of 2.5 m/s, whichever is the lesser. The
footfall force in newtons is taken as 180 sin (2/f f t).
Static values of the material properties should be used for the dynamic analysis.
A close parallel exists between the excitation and response of floors in buildings and pedestrian
bridges, so experience with human response to floor vibration as well as bridge vibration can be
applied (Allen 1974, Wheeler 1980). A selection of criteria is shown in Figure C3.4. The various criteria
given recognize that the dominant mode of vibration of a continuous structure may not be the first,
and the criterion given above may be restrictive in some cases. People walking alone, or in unison,
have footfall frequencies of up to 3 Hz.
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10.0
Acceleration, m/s2
5.0
Unacceptable
2.0
1.5
1.0
0.5
Acceptable
0.25
0.2
0.1
1.0
2.0
5.0
10.0
First flexural frequency, Hz
Figure C3.3
Acceleration limit for pedestrian bridge serviceability
(See Clause C3.4.4.)
10.0
8.0
6.0
(Reiher & Meister, 1946)
“disturbing” × 10
4.0
1/2 f
Acceleration, m/s2
2.0
(Blanchard et al., 1977)
(Wheeler, 1980)
(Allen & Rainer, 1976) × 10
(Leonard, 1966)
1.0
0.8
0.6
0.4
0.2
0.1
(Reiher & Meister, 1946)
“strongly perceptible”
1
2
4
6
8 10
20
First flexural frequency, Hz
Figure C3.4
Criteria for human response for steady vibration
(See Clause C3.4.4.)
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Pedestrian bridges with natural frequencies less than approximately 4 Hz should be given special
consideration in design. If a pedestrian bridge is to be extensively used by joggers as well as walkers, a
detailed analysis may be warranted.
Studies of floor vibration indicate a low probability that two or more persons will walk in phase, and
a walking or standing person tends to act as a damper for vibration excited by others (Allen 1974). The
same result has been found for pedestrian bridges, so the acceleration limit is based on a loading of
one typical pedestrian weighing 700 N.
The acceleration due to the typical pedestrian can be calculated by a full dynamic analysis, using
either the footfall impulse given in Figure C3.5 for an energetic walk (Wheeler 1980, Blanchard et al.
1977) or a pulsating point load of 180 N, which is approximately equivalent to the fluctuating portion
of the footfall impulse (Blanchard et al. 1977). The assumed footfall frequency is equal to the lesser of
the first flexural frequency of the superstructure, or 4 Hz, which is an upper limit for joggers. The
pedestrian is assumed to move at a speed of 2.5 m/s or 0.9f 1 m/s, whichever is less (Blanchard
et al. 1977), where the latter represents a 0.9 m stride at the fundamental frequency of the bridge
(Tilly 1977).
For the majority of pedestrian bridges, a beam model neglecting any torsional effects is appropriate.
For an N-span continuous bridge, at least the first N longitudinal flexural modes should be used in any
analysis. For wider bridges, or bridges having similar torsional and flexural frequencies, the significant
torsional modes should be included.
If a full dynamic analysis is not performed, the following simplified procedure, applicable to one,
two, or three span structures that act as beams, may be used to calculate acceleration (Blanchard et al.
1977):
a = 4π 2f 1 2ws K Ψ
where
a = acceleration, m/ s2
f1 = first flexural frequency, Hz
ws = maximum static superstructure deflection due to a vertical concentrated force of 700 N, m
K = configuration factor from Table C3.1
Ψ = dynamic response factor, a function of damping, from Figure C3.6.
In the absence of more precise information, the following percentage values of critical damping
should be used (Blanchard et al. 1977):
(a) steel superstructure with asphalt paving: 0.5%;
(b) composite concrete-steel superstructures: 0.6%; and
(c) prestressed or reinforced concrete superstructure: 0.8%.
For values of f 1 greater than 4 Hz, the calculated maximum acceleration may be reduced by an
amount varying from zero at 4 Hz to 70% reduction at 5 Hz or greater.
If the application of the above criterion results in an uneconomical structure or if an existing
pedestrian bridge is perceived to vibrate excessively, consideration should be given to the inclusion of
devices to increase the damping of the structure (Brown 1977).
Superstructures of pedestrian bridges that rest on slender piers may have rigid-body modes of
vibration at low frequencies. In these modes, the entire superstructure may move longitudinally,
transversely, or yaw due to flexibility of the piers. A multi-span continuous bridge may also exhibit a
transverse flexural mode over the entire length of the bridge if slender supports do not provide
sufficient stiffness. Slender piers should be avoided or adequately braced to avoid such modes of
vibration in the frequency range of pedestrian footfalls.
To avoid coupling between the vertical mode and the transverse and longitudinal modes of
vibration, a frequency separation between the vertical mode and the other modes is required, and
pedestrian bridges should be designed so that the longitudinal and the lateral frequency of vibration
of the superstructure are not less than 1.5 times the first flexural frequency of the superstructure, nor
less than 4 Hz.
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Stiffness values or the mass distribution need not be adjusted for frequencies greater than 4 Hz, as the
footfall frequency of pedestrians seldom exceeds 2.5 Hz, which is about two-thirds of 4 Hz. The transverse
and longitudinal modes of vibration of the superstructure will be influenced by the substructure. The
restraint provided by the substructure should be included in frequency calculations for the superstructure,
with the appropriate degree of flexibility that such a restraint would contribute.
Sway vibration in pedestrian bridges
A number of bridges, including the recently built Millennium footbridge in London (New Civil Engineer,
2000) and the Interprovincial bridge in Ottawa (Ottawa Citizen, 2000), have experienced lateral sway
vibration at a frequency of approximately 0.7 to 1.1 Hz as a result of a crowd of people walking across the
bridge. As a result of human reaction to the sway vibration, some footbridges, including the Millennium
footbridge, have been closed to enable the problem to be mitigated by stiffening the bridge or by
applying tuned mass dampers (Fujino et al. 1993, and Bachmann 1992). The sway vibration is generated
by footstep forces, where each footstep applies an equal but opposite lateral force to the previous
footstep, so that people who walk at a normal step frequency of 2 Hz can excite a lateral vibration at 1 Hz.
Annoying large lateral vibration occurs when a natural lateral frequency of the bridge matches the forcing
frequency in the range 0.7 to 1.1 Hz. It has been observed that, although people in a crowd initially do
not walk in step with each other, once they perceive a lateral vibration generated by some of the people or
by some other source such as wind, many people tend to stabilize themselves by walking in step with the
lateral vibration that they feel, resulting in a buildup of resonance vibration (Fujino et al. 1993).
The only available design criteria for sway vibration due to people walking are contained in Eurocode 5:
Design of Timber Structures (1997) for timber bridges. As a result of the Millennium footbridge experience,
research is being carried out in the United Kingdom to develop new design criteria. In the meantime, it is
recommended that footbridges intended for use by crowds of people be analyzed to determine the lateral
bridge frequencies. It is recommended that the bridge be designed to ensure that lateral bridge
frequencies be outside the range 0.5 to 1.3 Hz, or that a strategy for mitigating unacceptable sway
vibration due to resonance be developed at the design stage.
Force, kN
1.0
0.7
Next
pace
0.35
0
0
0.1
0.2
0.3
0.4
0.5
Time, s
Figure C3.5
Footfall impulse
(See Clause C3.4.4.)
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Dynamic response factor, y
18
z = 0.3%
16
z = 0.5%
14
z = 0.6%
12
z = 0.8%
10
8
6
4
2
0
0
10
20
30
40
50
Main span, m
Figure C3.6
Dynamic response factor as a function of span length
and damping ratio, ζ
(See Clause C3.4.4.)
Table C3.1
Configuration factor, K
(See Clause C3.4.4.)
Side span ratio a
2-span continuous
3-span continuous
1.0
0.8
0.6
0.4
0.2
0.70
0.92
0.96
0.96
0.95
0.60
0.82
0.92
0.92
0.90
Notes:
(1) Configurations are shown below.
(2) K = 1.0 for simple spans.
L
Single span simply supported
L
aL
2-span continuous
aL
L
aL
3-span continuous
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C3.5 Load factors and load combinations
C3.5.1 General
The objective of the Code is to ensure a prescribed uniform level of reliability. For various limit states, the
load factors are determined on the basis of an acceptable probability of the factored loads being exceeded
during a specified time period. The limit states considered in the Code are divided into three categories:
(a) ultimate limit states: these include the limit states pertaining to structural safety;
(b) serviceability limit states: these include the limit states that may affect the life, appearance, or use of a
bridge; and
(c) fatigue limit state: this comprises a limit state that may lead to the formation of cracks as a result of
the repeated application of load.
Fatigue can be regarded as a safety consideration; however, the loading conditions that must be
considered are quite different from those considered at the ultimate limit state and it is more convenient
to treat fatigue formally as a separate limit state.
For the ultimate limit states, load factors are selected so that the maximum effect of each specified load
multiplied by its load factor has a small probability of being exceeded in the bridge lifetime of 75 years;
the probability is in the order of 1%.
For the fatigue limit state, the factored live load effect is expected to be exceeded an average of once
every five minutes on a Class A highway. Dynamic effects at the fatigue limit state are generally higher
than those for the other limit states because dynamic amplifications for the stress range are higher than
those for the peak stress and the fatigue limit state reflects lighter vehicles. The live load factor for the
fatigue limit state includes these increased dynamic effects. For serviceability limit states, the maximum
effect of each specified load multiplied by its load factor has a probability of cracking in prestressed
concrete components in the order of 10% to 20% of being exceeded within one week, and a probability
of inelastic deformations in structural steel components in the same order of being exceeded within
10 years. The higher probability of the serviceability limit states is acceptable because the consequences of
exceeding a serviceability limit state are less severe than they are for an ultimate limit state.
Table 3.1 is self-explanatory and follows traditional lines in many respects. Most other codes make use
of a combination factor, which is a multiplier of load factors for each load combination. A similar approach
was used initially for the OHBDC (OHBDC 1983), but the load factors now shown have already been
multiplied by combination factors, where appropriate.
It should be noted that the load factors given in Table 3.1 result from a calibration process using the
CL-625 live loading. The use of these load factors with a different live load will not necessarily produce a
structure with the same safety level.
Within the Code, the word “loads” has the very general meaning given in the definitions, and includes
movements. In calculating movements for the sizing of bearings or expansion joints at the serviceability
limit states, the load factors are applied to the movements.
Older codes listed effects such as shrinkage and creep separately, but then generally prescribed the
same load factor. The grouping of such loads under the load identifier, K, somewhat simplifies the process
of identifying combined critical responses.
K has not been included in every ultimate limit state combination, as some redistribution of the stresses
from the K effects takes place at this limit state.
The load factor for K is also prescribed for the horizontal forces transmitted by sliding bearings when
such forces have the upper bound value determined by limiting friction. This approach is adopted for
simplicity, since it would otherwise be necessary to consider various load combinations capable of
inducing slip. Unfactored vertical loads are used in calculating friction, since to do otherwise would involve
double factoring. The load factor or factors prescribed for the loads tending to cause movement apply to
horizontal forces that are not large enough to cause sliding bearings to slip, to forces transmitted by
bearing stops designed to limit travel, and to forces arising from the shear stiffness of elastomeric bearings.
Attention is drawn to the definition of factored load effect. In principle, it is the load that is factored
rather than the effect; however, in most cases responses are linear and it is convenient to factor the
calculated effects.
Most modern methods of analysis consider elastic distortion as an integral part of the solution and it
would be difficult to factor such effects in any way other than that prescribed.
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In earlier codes, the load factors for wind were based on typical past practice. For the Code, the
wind load factors have been derived from calibration to a target safety wider for the first time. The
derived load factors are higher than before, with the factor for ULS 4 being 1.65 compared to 1.3 in
the OHBDC. A major reason for the increase is the higher coefficient of variation in the wind speed
data.
There is some concern over construction stages that may be investigated, in which all major loads
are subject to load factors of 1.25 or less. It is possible that a structure may have an insufficient reserve
of strength to cover loads that are not considered, e.g., the strain that is induced by force-fitting
components, locked-in stresses, transverse temperature differential, hidden or unobserved minor
defects, or small unauthorized construction loads.
The global factor requirement of 1.25 may be waived if Approval is obtained, which normally
requires a detailed review of the structure and the analysis.
As the Code now covers long span bridges for which dead load can dominate, ULS Combination 9
has been added to ensure an adequate factor of safety under the sole action of permanent loads. This
combination need not be applied during erection. ULS Combination 9 should not be applied to
cable-supported bridges where an adequate factor of safety has been covered by the use of a low
resistance factor for cables (see Clause C3.8.3.3).
C3.5.2 Permanent loads
C3.5.2.1 General
It can be important to consider stages in which assumed dead loads are not yet present in full or are
partially present over the structure. For example, near points of contraflexure, temporary conditions
during an erection stage may produce bending moments opposite in sign to those produced during
the final stage. This could be catastrophic for a section designed only for the final loading stage,
particularly if flanges of a steel girder, proportioned only for tension and thus having low buckling
resistance, are subjected to compression during an erection stage.
Minimum values of dead load factors need rarely be considered. When normal standards of
construction and supervision are applied, the variations in nominal dimensions and unit weights are
small and random, and tend consistently towards larger than the assumed values. Therefore minimum
values of the load factors are to be used only in the rare cases where permanent load effects are critical
and where the probability that consistently low loads will occur is high.
Although the use of minimum values of dead load factors given in Table 3.2 is seldom justified,
values of unity should be used whenever they yield results more critical than when the maximum
values are used. For example, in the design of piers or footings, if dead load imparts stability to the
system or reduces tension in reinforcement due to longitudinal forces such as earthquake or braking or
centrifugal effects, a load factor of unity for the dead load should be considered together with the
appropriate load factors for the longitudinal forces. Except when specified otherwise, it is adequate to
apply the same load factors to loads in different spans.
To allow for variations in dead load and the effects of vertical accelerations, at the ultimate limit state
load combination for earthquake effects (ULS Combination 5), maximum and minimum values of α D
equal to 1.25 and 0.8 respectively, whichever produces the most unfavourable effect, shall be used.
C3.5.2.2 Overturning and sliding effects
It is reasonable to assume that, in cantilever earth-retaining structures, the weight of soil acts
concurrently with the horizontal earth pressure, although both may not be at a maximum value.
In some cases, such as backfill pressures that oppose one another, the full value of soil pressures in
different locations may not be simultaneously developed. In such instances, it is appropriate to apply
the minimum values of the load factors.
In balanced cantilever construction, since the variation of segment weights may not be randomly
distributed within the limits specified, the correction of any cumulative imbalance is required during all
stages of erection.
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C3.5.3 Transitory loads
Transitory loads include those that are occasionally present, or that vary in their magnitude, position, or
direction, and whose application with the specified magnitude may be considered as a normal rather than
exceptional possibility.
C3.5.4 Exceptional loads
These loads rarely occur or rarely achieve the magnitude specified, and the possibility of more than one
occurring simultaneously can be neglected. Simultaneous occurrence of one exceptional load and one or
more transitory loads is probable, but a consideration of the types of structures involved, the parts of the
structures significantly affected by the various loads, and the relative magnitudes of the effects suggests
that it is not normally necessary to consider combinations other than that of ice accretion and wind load.
Note 3 has been added to Table 3.1 for ULS Combination 6, however, as a combination of ice load F
and wind load W could govern for some long span bridges. At present, calibration of F and W for long
span bridges has yet to be carried out.
For ultimate limit states, with the exception of earthquake loads, the maximum effect of each specified
load multiplied by its load factor has a small probability, in the order of 1%, of being exceeded in the
bridge lifetime of 75 years.
C3.6 Dead loads
Dead load consists of the weight of all permanent structural and non-structural parts of the bridge,
including any additional parts expected in the future. For the design of a highway bridge having an
exposed concrete wearing surface, an added bituminous wearing surface should be considered even
though there is no immediate intention to place such a layer. The weight of stay-in-place forms and future
additions should not be overlooked.
Unit material weights given in Clause 3.6 are close to average values. The additional weight of any
substantial structural steel sections embedded in concrete should be considered.
C3.7 Earth loads and secondary prestress loads
Reference should be made to Sections C6 to C8 for further clarification.
C3.8 Live loads
C3.8.1 General
Design live loads should reflect actual vehicle loads and bear a direct relationship to the legal loads on the
highway. Highway traffic consists of a large number of light vehicles and a comparatively smaller number
of heavy vehicles. Modern heavy vehicles include a wide variety of vehicle types, ranging from short
two-axle trucks to multi-axle long truck trains.
The critical loading for deck components and short-span structural components with span lengths up to
8 m is generally caused by a single wheel load or axle loads. Axle loads in this context include single axles,
tandem axles, and tridem axles.
Critical loading for main longitudinal components and support systems for bridges, with span lengths
varying from 8 m to 25 m, is generally caused by single heavy vehicles or a group of axle loads within a
vehicle. For longer medium span bridges, the multiple presence of vehicles in a design lane for the free
flowing condition may be critical.
For longer span bridges, with span length exceeding 125 m, multiple presence of vehicles in a design
lane, particularly in traffic jams, constitutes the critical loading condition.
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C3.8.2 Design lanes
During the lifetime of a bridge, the number, position, and direction of travel of actual traffic lanes may
change, depending upon the highway use during normal operations or its use during special or
emergency situations. The bridge should be capable of supporting the maximum number of loaded
lanes that can be accommodated on the bridge within the full deck width. Therefore, the design lanes
are derived from the deck width, without regard for the way lanes are initially marked for traffic use.
Provisions for the design lanes were adopted from the OHBDC (OHBDC 1991) and CAN/CSA-S6-88.
The concept was originally adopted from the AASHTO Standard (AASHTO 1973).
It has been found that the design of the central girder of a three-lane, three-girder bridge could in
fact be governed by a symmetrical two-lane layout, and the footnote has been added to Table 3.4 to
cover this possibility.
C3.8.3 CL-W loading
C3.8.3.1 General
The legal traffic loads vary from one province to another across Canada. Even within a province, traffic
conditions may vary from one locality to another. It is therefore prudent to specify a certain minimum
standard for the highways that carry interprovincial traffic, and allow flexibility of selecting a load level
suitable for other roads and highways. The specified loading has the flexibility to adopt an appropriate
level of loading at the discretion of the provincial authorities.
The Code also allows the development of loading models based on site-specific vehicle and traffic
conditions, established by vehicle load surveys. Such models must provide the level of safety intended
by the provisions in the Code.
The specified traffic loads should model the following:
(a) heavy wheel loads;
(b) heavy axle loads in a design lane;
(c) one heavy vehicle in a design lane;
(d) multiple presence of vehicles in a design lane; and
(e) simultaneous presence of vehicles or axle loads in more than one design lane.
The traffic loads specified in the Code are based on three primary characteristics, i.e., simplicity in
design applications, efficiency in modelling actual highway loads, and flexibility in adopting a load
level based on the site-specific conditions. Another consideration is that the subconfigurations of the
design truck model should be suitable for use as the truck models for various evaluation levels specified
in Section 14. These considerations resulted in a traffic load system consisting of two alternative
components of the Canadian Loading (CL), namely, the CL-W Truck and corresponding CL-W Lane
Load.
CAN/CSA-S6-88 specified a live load truck model based on the Council of Ministers’ loading
(Agarwal and Cheung 1987) for interprovincial transportation agreed to in 1981. This model, shown
in Figure C3.7, therefore reflects a regulatory level of vehicle loads in Canada. The OHBDC (OHBDC
1983) Truck model, on the other hand, includes maximum observed overloads in Ontario, thus
reflecting a load level higher than the regulatory level. As a result, the corresponding live load factors
for design in the two codes are different: the Code uses 1.60, whereas OHBDC uses 1.40.
The main reason to include overloads in the OHBD Truck model, shown in Figure C3.8, was that the
percentage overload observed on axles are generally larger than for the whole vehicle. The Ontario
experience during the 1970s is depicted in Figure C3.9. It can be seen that while the overload on
single axles (equivalent base length equal to zero) can be as much as 100% on tandems up to 60%
and on tridems up to 50%, yet it is only about 20% for the gross weight. By including observed
overload in the live load model, it was possible to achieve a uniform reliability level using a single live
load factor for all bridge components, which is a considerable simplification in bridge design.
However, the degree and nature of overloads may vary from one province to another and the
observations in Ontario may not be directly applicable to other provinces. Therefore, the live load
model for the Code has been adopted at a regulatory load level, except that the model includes a
heavy dual axle in the truck model with some degree of overload in order to make the model more
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efficient in achieving a uniform reliability for all ranges of span length and all types of bridges. A similar
approach has been adopted in the new loading for AASHTO-LRFD Specifications which consists of the
existing HS Truck and, alternatively, a heavy design tandem (NCHRP 1991).
C3.8.3.2 CL-W Truck
The CL-W Truck is based on a set of regulations for interprovincial transportation contained in the
Memorandum of Understanding on Vehicle Weights and Dimensions (MOU) signed by all Canadian
provinces, initially in 1988 and amended in 1991 (TAC 1991). The MOU gives weight and dimension
limits for straight trucks (single unit trucks), tractor/semitrailer combinations, and trains. These represent
minimum values of the maximum loads any province must allow on its principal highways carrying
interprovincial traffic. The B-train is permitted as the largest load among the trains due to its greater
stability. Table C3.2 summarizes the relevant limits, and Figure C3.10 shows the critical vehicle
configurations in accordance with the MOU.
Regulatory loads vary quite widely across Canada, and each province seems to have some particular
area in which loads are allowed to exceed the levels of the MOU. These higher loads may apply only to
some vehicles, specific to commodities, roads, or during certain times of the year. They are sufficiently
widespread that MOU cannot strictly be considered the regulatory level; it is more like a lower bound to
the regulatory levels. However, it may be important that the proposed National Highway Policy would
support a road network to the minimum level demanded by the MOU. This minimum standard is
represented by the CL-625 Truck with a gross weight of 625 kN.
Any province could adopt a different standard, depending upon the local situation, by using a different
load level such as CL-600, CL-650, CL-700, etc. However, calibration of load factors, load combinations,
and resistance factors are based on the CL-625 truck. Hence, the same safety level should be ensured at all
times.
The CL-625 Truck and its subconfigurations are displayed in Figure C3.11 for comparison with the
Ontario Bridge Formula, which is the basis of the regulatory loads in Ontario, and the maximum observed
load (MOL) level, which is the basis of the OHBD Truck model (OHBDC 1983, Agarwal et al. 1978).
Table C3.2
MOU weight and dimension limits
(See Clause C3.8.3.2.)
Item
Straight truck
Tractor
A-train
B-train
C-train
Axle weight, kN
Steering axle
Single axle
Tandem axle
54
89
167
54
89
167
54
89
167
54
89
167
54
89
167
Tridem axle weight, kN
2.4 m to 3.0 m
3.0 m to 3.6 m
3.6 m to 3.7 m
Minimum inter-axle spacings, m
Single-single
Single-tandem
Tandem-tandem
Tandem-Tridem
206
225
235
3.0
3.0
3.0
3.0
5.0
5.5
Sum of axle loads on second trailer, kN
Full vehicle
Gross weight, kN
Overall length, m
52
206
225
235
3.0
3.0
5.0
3.0
3.0
5.0
5.5
157
221
12.5
456
23.0
525
23.0
3.0
3.0
5.0
206
613
23.0
574
23.0
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1
2
3
4
0.1W
0.3W
0.3W
0.3W
Axle no.
Axle load, kN
Gross load, W•kN
6.0 m
4.0 m
6.0 m
16.0 m
Figure C3.7
CS-W truck model in CAN/CSA-S6-88
(See Clause C3.8.3.1.)
1
2
3
4
5
60
140 140
200
160 Axle load, kN
30
70
70
100
80
Axle No.
Wheel load, kN
Gross load, 700 kN
1.2
m
3.6 m
6.0 m
7.2 m
18.0 m
(a) First Edition (1979) and Second Edition (1983)
1
2
3
4
5
60
160 160
200
160 Axle load, kN
30
80
80
100
80
Axle No.
Wheel load, kN
Gross load, 740 kN
3.6 m
1.2
m
6.0 m
7.2 m
18.0 m
(b) Third Edition (1991)
Figure C3.8
OHBD truck models (OHBDC 1979, 1983, 1991)
(See Clause C3.8.3.1.)
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Range for common tandems
2.0
Range for common tridems
MOL/OBF ratio
1.8
Multi-axle groups
in Ontario
1.6
Vehicle combinations
and trains
1.4
1.2
1.0
0
5
10
15
20
25
Equivalent base length, m
Figure C3.9
Maximum observed overloads in Ontario during the 1970s
(See Clause C3.8.3.1.)
Figure C3.10
Critical vehicle configurations per the MOU (TAC 1991)
(See Clause C3.8.3.2.)
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1000
CL-625 Truck loading:
50
250
3.6
175
150
6.6
6.6
1.2
= 625 kN
= 18.0 m
2
800
3
4
Load on axle group, kN
5
7
6
6
7
600
5
Maximum observed
load (MOL)
400
4
Ontario
Bridge Formula (OBF)
3
2
200
1
0
0
5
10
15
20
25
Equivalent base length, m
Figure C3.11
Comparison of the subconfigurations of the CL-625 Truck
with the Ontario Bridge Formula and the MOL
(See Clause C3.8.3.2.)
C3.8.3.3 CL-W Lane Load
The CL-W Lane Load is based on traffic loading for long span bridges recommended by the American
Society of Civil Engineers Committee on Loads and Forces on Bridges (Buckland, Ed. 1981), informally
referred to as the “ASCE loading”.
The ASCE loading was based on measurements in the greater Vancouver area. The first step was to
take samples of registered Gross Vehicle Weights (GVW). At this point, there was no attempt to
measure actual weights; only legal allowable weights, registered and painted on the cab doors, were
surveyed. These were recorded, along with the total number of trucks crossing the Second Narrows
Bridge. This bridge was selected because trucks are banned from the only other crossing of Vancouver
Harbour, the Lions’ Gate Bridge, and consequently Second Narrows could have a higher than average
amount of truck traffic.
The second step was to attend at weigh stations and record for each truck its GVW, its actual
weight, and its overall length bumper-to-bumper. It should be noted that on long spans actual axle
spacings are not important.
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Thus, for each group of GVW (a group being a range of 12 000 lb [53 kN], such as 48 000 [212 kN] to
60 000 lb [265 kN]), distributions were determined for length and actual weight.
This work has been described in more detail by Buckland et al. (1978, 1980).
It was found that less than 7.5% of all vehicles were “heavy vehicles” (HV), i.e., greater than 12 000 lb
(53 kN). However, in order to test the sensitivity of the loading to this assumption, the simulation program
was run with 30% of all vehicles being heavy and, for the upper limit, with 100% of all vehicles being
heavy.
The comparison can be seen in Figure C3.12. The differences are not as great as the changes in
percentages of HV, as these percentages are average values. With random selection and higher
percentages of trucks during certain hours of the day, the peak percentages of trucks in the traffic did not
differ greatly.
Several times the validity of the 7.5% HV assumption has been queried, but subsequent traffic counts in
the lower mainland of British Columbia have not revealed HV percentages as high as 7.5.
Since data on truck weights had been gathered independently for the preparation of Clause 12 of
CAN/CSA-S6-88, a comparison was made of the data used for the ASCE study and that used for Clause 12
of CAN/CSA-S6-88, which came mostly from Alberta in the 1980s.
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Loaded length (ft)
50
100
200
400
800
1600
3200
6400
40
P
U
2600
35
2400
2000
p (lbs)
p (kN)
2200
1800
180,000
1600
160,000
30
U (100% HV)
U (kN/m)
750
500
U (30% HV)
20
1400
P
15
1200
U (lbs/ft)
25
140,000
120,000
1000
100,000
800
80,000
600
60,000
400
40,000
200
20,000
0
0
10
250
5
0
U (7.5% HV)
0
15
30
61
122
244
488
975
1951
Loaded length (m)
Figure C3.12
ASCE recommended loading, giving parameters P, U,
and % HV (P = concentrated load per lane; U = uniform load per lane;
and % HV = average percentage of heavy vehicles in traffic flow)
(See Clause C3.8.3.3.)
Figure C3.13 shows the cumulative probability of truck weight for the two populations. From this it
can be seen, for example, that the maximum truck weight in the ASCE population is 544 kN, whereas
for the Clause 12 of CAN/CSA-S6-88 sample, it is 760 kN. Similarly, 50% of ASCE trucks are less than
about 130 kN, whereas only 23% of Clause 12 trucks (over 60 kN) are less than 130 kN.
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The implication of this is that the trucks in the Clause 12 of CAN/CSA-S6-88 population are generally
heavier than those in the ASCE population. The reason for this is unknown, but could be because trucks
have become heavier, trucks on truck routes are heavier than those on suburban routes, or there are
sampling errors.
Even if trucks in the Clause 12 of CAN/CSA-S6-88 population are heavier, the force effect on long spans
is unknown. If they are also longer, perhaps the net effect on long span loading is small. Unfortunately, the
data in Clause 12 of CAN/CSA-S6-88 do not include vehicle lengths.
In the study that produced the ASCE loading, the maximum loading for each three-month period was
found, and a Gumbel distribution was used to predict a 5-year return period loading. To assist in the
development of Clause 3.8.3.3, the original 3-month maxima and the same type of Gumbel distribution
were used to find 50-year return period loadings. Bias coefficients and standard deviations were then
calculated for various dead/live load ratios, from which live load factors are calculated, as shown in
Table C3.3.
As can be seen, the calculated value of α L varies with the live-load to dead-load ratio, LL/ DL, and with
loaded length. Certain LL /DL ratios, however, are more prevalent at particular lengths — i.e., long span,
LL /DL ≈ 0.2, short span, LL / DL ≈ 20. The weighted averages shown in Table C3.4 allowed for this trend,
having been derived from the values enclosed in the diagonal on Table C3.3.
Cumulative probability of occurring
1
0.9
0.8
Maximum ASCE truck
0.7
Maximum Clause 12 of
CAN/CSA-S6-88 truck
0.6
0.5
0.4
ASCE study trucks
Clause 12 of CAN/CSA-S6-88
study trucks
0.3
0.2
0.1
0
50
150
250
350
450
550
650
750
Truck weight (kN)
Figure C3.13
Comparison of ASCE and Clause 12 of CAN/CSA-S6-88 truck populations
(See Clause C3.8.3.3.)
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Table C3.3
Load factors for ASCE 30% heavy vehicles
(See Clause C3.8.3.3.)
Loaded length, m
15
30
60
120
245
490
975
1950
Live load bias
Live load COV
1.035
0.029
1.162
0.052
1.133
0.046
1.202
0.057
1.132
0.054
1.102
0.047
1.158
0.059
1.236
0.088
Fractions of dead
and live loads
LL Load Factor, α L
1.69
1.67
1.65
1.63
1.62
1.60
1.59
1.59
1.62
1.78
1.58
1.56
1.55
1.53
1.51
1.50
1.49
1.50
1.53
1.69
1.52
1.51
1.49
1.48
1.46
1.45
1.45
1.45
1.49
1.65
1.63
1.61
1.59
1.58
1.56
1.55
1.54
1.54
1.57
1.73
1.83
1.80
1.78
1.75
1.73
1.71
1.69
1.67
1.69
1.83
Dead
Live
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.41
1.39
1.38
1.37
1.36
1.35
1.35
1.36
1.40
1.57
1.62
1.60
1.59
1.57
1.55
1.54
1.53
1.54
1.57
1.73
1.57
1.55
1.54
1.52
1.51
1.49
1.49
1.49
1.53
1.69
Using:
(a)
(b)
(c)
(d)
5-year return model and 50-year return distributions.
Reliability index of 3.5.
Various dead to live load ratios.
Other input values as shown.
Dead Load Bias
Dead Load COV
Dead Analysis Bias
Dead Analysis COV
Live Analysis Bias
Live Analysis COV
φ
Resistance Bias
Resistance COV
α Dead
Beta
1.04
0.036
1
0
1.02
0.09
0.94
1.13
0.096
1.2
3.5
Table C3.4
Estimated live load factors for long span loads
(See Clause C3.8.3.3.)
% HV
Approximate range of α L
Weighted average
7.5
30
100
1.52 to 1.74
1.45 to 1.62
1.35 to 1.57
1.63
1.52
1.44
To check the reasonableness of these numbers, the statistics were compared with Clause 12 of
CAN/CSA-S6-88 type of traffic.
Bias coeff., δ C.O.V. αL (for β = 3.5, sophisticated analysis)
Load
ASCE 7.5% 1.168
0.068
0.068
1.63 — 50-year return
NP
1.36
0.069
0.069
1.75 — 1-year return
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PM
1.064
0.0086
0.0086
1.33 — 1-year return
PS
1.195
0.031
0.031
1.46 — 1-year return
where
(a) NP (non-permit) = normal “legal” traffic; maximum loads are not known with confidence;
(b) PM (permit, multiple-trip) = a series of overloaded vehicles on a special permit, usually a bulk haul,
from a mine, for example; individual legal axle loads are not exceeded; loads are usually well
controlled; and
(c) PS (permit, single-trip) = an overload for which a special permit is required, normally a large
indivisible load with axle loads exceeding legal limits; loads may not be well known.
The bias coefficient for ASCE loading is similar to that of PS traffic. The coefficient of variation for ASCE is
similar to that of NP traffic. We would thus expect α L for ASCE to be slightly more than α L for PS. Note
that if NP represents “legal” traffic and the Code truck represents “legal” traffic, we could expect α L to
be > 1.75 in the Code. The factor specified is 1.70.
It is generally accepted that at short loaded lengths a single truck will produce the maximum loading; at
long loaded lengths the maximum load will be produced by stationary traffic “bumper to bumper”.
Harman and Davenport (1979) suggest that the single truck governs up to somewhere in the range of
48 to 55 m, from there up to about 76 m two trucks govern, and at lengths longer than 76 m the load is
caused by stationary vehicles bumper to bumper. There is thus a transition zone in the range of 50 to 75 m
between the single truck case and the stationary case that is represented by the ASCE loading.
Note that when stationary bumper to bumper vehicles govern, no dynamic load allowance (DLA)
should be added.
Long span bridges are, by definition, likely to have serious consequences if they collapse. An importance
factor is therefore desirable; or, putting it another way, the required target value of β should be increased.
One way of accomplishing this is to use the following formula from CSA S408:
Pf =
TAK
W n
where
Pf = target probability of failure
T = return period, years
A = activity factor
K = coefficient
W = warning factor
n = number of people at risk
For Clause 12 of CAN/CSA-S6-88, n was assumed to be 10, except for PC traffic (controlled permit), in
which case n = 1. For a very long span bridge, say 2000 m, one might expect n to be much larger,
perhaps one person per 8 m per lane, which for a four lane bridge would give n = 1000. In this case, the
required Pf would be 10–1 times as great as for a small bridge, and the required β might increase by ~ 0.5,
say from 3.5 to 4.0. This can be accomplished without changing load factors if the design loading is
increased at long loaded lengths by about 8%.
Because of an apparent general increase in truck weights, and to allow for potential future growth in
truck traffic, and until the apparent inconsistencies are fully resolved, it was deemed by the Subcommittee
on Loads, sitting simultaneously with the Long Span Task Force, that it would be prudent to match the
ASCE (30%) loading for long loaded lengths.
The requirement is, therefore, to select a (factored) loading that approximates the (factored) effects of
ASCE (30%) loading above the transition zone — i.e., at lengths greater than 75 m, and matches the
(factored) effects of single truck loading below the transition zone — i.e., at lengths less than 50 m.
The adopted loading is the greater of
(a) 100% of the CL-625 truck with DLA; or
(b) 80% of the CL-625 truck and a uniform load of 9 kN/m, without DLA.
The effects of this loading can be seen in Figure C3.14. It matches the truck loading exactly up to 50 m,
and varies between 10% conservative and 3% nonconservative compared to ASCE (30%), above the
transition zone.
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Figure C3.14 also shows, for comparison, the CAN/CSA-S6-88 CS-623 loading, which is
conservative at all lengths greater than 30.5 m, and the ASCE (7.5%) which varies from 93% to 66%
of the ASCE (30%) load over its intended range. OHBDC-91 loading (not shown) matches closely the
proposed CL-625 loading. It should be remembered, however, that ASCE (7.5%) loading represents
what was actually measured.
The above study for the CL-W Lane Load was carried out before the final code calibration was
performed, and assumed that the live load factor would be 1.75, as shown on Figure C3.14. The final
calibrated factor was 1.70 and is sufficiently close that the study may still be considered valid.
Transition
1.6
Single vehicle
CAN/CSA-S6-88: CS-623
Impact = 0.3 (on truck)
Impact = 0.1 (on lane load)
aL = 1.6
Multiple stationary vehicles
Ratio of loading/ASCE 30%
1.4
1.2
1
0.8
ASCE 30%:
Impact = 0.0
aL = 1.5
0.6
Code: CL-625
Impact = 0.25 (on truck)
Impact = 0.0 (on lane load)
aL = 1.75 (assumed)
0.4
0.2
ASCE 7.5%:
Impact = 0.0
aL = 1.6
0
0
30.5
50
61
75
122
244
488
975
1950
Loaded length (m)
Legend:
Band width for target loading
Figure C3.14
Factored loads compared
(See Clause C3.8.3.3.)
As discussed in the preceding paragraphs, the target reliability index should be increased for long
spans. This can be accomplished by increasing either the load factor or the loading by 8%.
For simplicity, it is preferred to maintain a constant load factor. Figure C3.14 shows that the
proposed loading is 4% conservative compared to ASCE (30%) loading at about 2000 m loaded
length. However, ASCE (30%) loading is itself thought to be conservative, by an unknown amount not
exceeding 50%.
Finally, the effects on various bridge components must also be considered.
The longest bridges are suspension bridges. The various components are considered separately.
Cables
Cables are almost completely dominated by dead load, which is often 80% or 90% of the total. The
use of a dead load factor α D of around 1.2 would thus result in much smaller cables than has been
conventional practice. This may be satisfactory but one must move with caution as there are
secondary effects at cable bands, and cables are sensitive to corrosion.
The solution can be found in setting the appropriate resistance factor for cables. See Section C10.
ULS Combination 9, from Table 3.1, should not be applied for cable-supported bridges.
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Towers
Towers are governed by P-Δ effects where the vertical load, P, is largely governed by dead load as the case
for the cables, and Δ is governed almost exclusively by live load. Ideally, one could start by comparing
factored loading effects with past practice, but so far this has proved difficult. More work needs to be done
in this area.
Stiffening system
The stiffening trusses are generally governed by relatively short lengths of live load and therefore they are
not unduly affected by long span loading. They are, however, only affected by live load, so any load factor
greater than about 1.67 will result in conservatism, compared to past practice.
C3.8.4 Application
C3.8.4.1 General
To properly model an actual truck population, the truck axles and the uniformly distributed loads are
applied only where they increase the total load effects.
The fatigue limit state is concerned with fatigue in structural steel, aluminum, and reinforcement. This is
the cumulative effect of frequent crossing by heavy vehicles in a traffic stream. Although an average heavy
vehicle weighs much less than the legal limit, the number of passages of the heavy vehicles during the
bridge lifetime generally exceeds the two million cycles specified in most bridge design codes. The fatigue
loading provisions are so calibrated that the predicted cumulative effect of the actual loading during the
lifetime of a bridge shall not exceed the cumulative effect of 2 000 000 cycles of the specified loading. The
superstructure vibration limitations are based on the human response to bridge vibration under passage
by a single heavy vehicle. For both of the above, the limit states specified design load includes a single
vehicle on the bridge, loaded to near the legal limit. Since most vehicles would be travelling along the
centreline of a travelled lane, the Truck is placed at critical locations along the centreline of a travelled lane.
The ultimate limit states and the serviceability limit states other than the superstructure vibrations
correspond to the most critical loading pattern that can occur during a representative return period. This
includes simultaneous presence of vehicles within a lane, as well as in more than one lane. For simplicity of
design, the specified loading and loading patterns for both limit states are the same. The difference in the
return periods for the ultimate limit states and the serviceability limit states leads to different levels of
loading, which is reflected by the load factors.
C3.8.4.2 Multi-lane loading
The flow of traffic in a lane is not independent of the presence of vehicles in other lanes. Correlation of the
traffic flow in adjacent lanes is affected by a number of parameters including number of lanes, traffic
volume, speed, traffic mix and accident situations. The reduced probability of more than one lane being
critically loaded at the same time is accounted for by a reduction factor, ms , for multi-lane loading
(Davenport and Harman 1977), which is applied to the static force effects, and is given by
ms = l +
( 1− l )
( S Lk )
S Lk2
where
λ = a constant that is a function of correlation of traffic flow in adjacent lanes
Lk = live load effect due to loads in kth lane
The summation is carried out for the desired number of loaded lanes. For most conditions of traffic flow,
the value of λ varies from 0.5 to 0.7.
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It is further recognized that the vehicles in various lanes generally would not vibrate in harmony,
and hence, cumulative dynamic loads as percentage of the total static loads will be smaller for the
multi-lane loading as compared to the one lane loaded case. The dynamic load allowance reduction
factor was derived by assuming that the mean value of the dynamic effect of loading several design
lanes is no larger than the square root of the sum of squares of the contributing effects.
This assumption is made frequently in the analysis of dynamic response of structures and is valid
when the contributing effects are uncorrelated. Thus the modification factor, mI , for the DLA is
determined from
S Lk2
ml =
S Lk
The specified values of the modification factors were obtained from
mf =
ms (1+ ml )
( 1+ l )
where
I
= dynamic load allowance
Generally, the maximum effects are obtained by placing either trucks or lane loads in all of the
loaded design lanes. Simultaneous loading of different design lanes by truck and lane load need not be
considered.
C3.8.4.3 Local components
Trucks are assumed to remain entirely within their design lanes, as specified in Clause 3.8.2. This
would preclude the consideration of wheel loads closer than 0.6 m to a curb or barrier. In the design of
deck slabs and certain components of deck plate and grid systems, for which critical load effects are
mostly due to one or two wheel loads and increase rapidly as the wheels approach the curb or barrier,
it is prudent to consider the wheels in extreme position, such that they are almost in contact with the
curb or barrier and yet are still in motion to the extent that the dynamic load allowance applies. This
would be a rare event and is, therefore, considered only at the ultimate limit states.
Heavy overloaded single axle loads represented by the Axle No. 4 of the CL-W model occur in reality
either due to the operational overloads or are permitted under the special overweight permits.
However, probability of local small components incorporated in the decks, such as manhole covers,
drainage, grating, etc., being subjected to these heavy single axle loads is very low. Therefore, it is not
necessary to consider the effects of the Axle No. 4 on these components.
The modular expansion joints, decks, and other short components will undoubtedly carry the heavy
single axle loads. Therefore, Axle No. 4 should be considered for the design of these components.
C3.8.4.4 Wheels on the sidewalk
Situations in which the wheels of a heavily-loaded truck accidentally ride over the sidewalk may be
critical for the sidewalk and the structural components supporting the sidewalk. Such events are rare
and generally do not involve very heavy trucks, which permits a reduction in the axle loads assumed.
C3.8.4.5 Dynamic load allowance
The requirements specified in Clause 3.8.4.5 represent a refinement and considerable simplification in
the application of the same theoretical work on which the provisions of the 1983 edition of the Ontario
Highway Bridge Design Code (OHBDC 1983) were based. Central to those provisions was the use of the
dynamic load allowance/frequency relationship shown in Figure C3.15.
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A closer examination of the calibration methods previously used suggests that some reductions in the
dynamic load allowance values would be supportable, e.g., from 0.4 to 0.35; but in general, the
relationship seems to be correct, and indeed has since been corroborated by several other studies (Nowak
et al. 1991, Cantieni 1992, Rosler 1994, Drosnu et al. 1989).
The provisions of the 1983 edition were based on evidence obtained from field measurement and
analysis, tempered with experience, and reflected the physical process of vehicle-bridge interaction.
Extensive background material is given in the cited references (Biggs 1964, Billing 1982, Cantieni 1988,
1992, Csagoly et al. 1972, Green 1977, Green et al. 1982, Wright and Green 1964, and others). These
references include discussion of the calculation of natural frequencies of bridge superstructures, vehicle
and bridge dynamic interaction, damping, and human response to motion.
The term “dynamic load allowance” was introduced to reflect the various sources of dynamic loading,
including discrete and random irregularity of the riding surface, bridge static and vibratory deflections,
and the dynamic effects of interaction between a moving vehicle and the bridge.
The term “impact factor” was discarded as its literal interpretation is too narrow to describe the
phenomenon of dynamic loading.
0.40
Dynamic load allowance
0.40
0.25
0.20
0
0
1.0
2.5
4.5
6.0
10.0
First flexural frequency, Hz
Figure C3.15
Dynamic load allowance frequency relationship
(See Clause C3.8.4.5.)
The complex interaction between a bridge and traversing vehicles was described in AASHTO (1973) and
the 1974 edition of CSA S6 by the following simple expression developed in the late 1920s:
I = 15 / (L + 38)
where
I
= impact fraction, not to exceed 0.30
L
= span length in metres
This allowance for dynamic, vibratory, or impact effects is applied as a fraction of the live load in a
component and for some components can be taken as zero. Confusion can occur as to which component
should have the static effects of live load amplified for design purposes. The expression for impact fraction
is not representative of the response of bridges having fundamental frequencies in the 2 to 5 Hz range
(Csagoly et al. 1972, Green 1977, Wright et al. 1964, Green et al. 1982) under the loading of modern
commercial vehicles. Further, loads and load factors in the Code differ from those in other codes.
For convenience in design, and to maintain established practice, the dynamic load allowance is
described in terms of an equivalent static load that is a fraction of the CL-W Load. Thus, the force effects of
dynamic load due to the gravity portion of the CL-W Load can easily be calculated.
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Also, the effect of load on a member or component may be found without the designer having to
exercise judgement as to whether the dynamic allowance should be included for that member or
component.
Dynamic effects of load are associated with all parts of the structure where force effects due to the
gravity portion of moving loads may be present, including sidewalks, bearings, and substructures.
Buried structures are also considered.
Billing (1982) shows that dynamic load effects do not increase indefinitely with vehicle weight. The
mean dynamic amplification factor is shown to reduce almost linearly with increasing vehicle weight,
giving a fairly constant mean dynamic load. This trend is apparent in the results of other research
(e.g., Cantieni 1988), but is not as prominently noted and its importance appears to have been
overlooked in the earlier calibration process. During calibration of the OHBDC, it was shown by
simulation (Nowak et al. 1991) that the dynamic load is almost a constant value, irrespective of vehicle
weight. This value is around 80 to 90 kN, which is reflected in a higher percentage in lighter trucks and
a lower percentage in heavier trucks.
The values given in Clauses 3.8.4.5.3 to 3.8.4.5.4 were developed from tests (Csagoly et al. 1972,
Wright et al. 1964, Green et al. 1982, Billing 1982, Sheperd and Aves 1973) using identical values of
load factor for live load and dynamic load, and a mean-to-specified value of 0.5 to 0.6. This ratio of
0.5 to 0.6 might appear unusual in a limit states design code. If mean dynamic load allowance values
were specified for design, the corresponding load factor would be approximately 2.5. Mean values of
the dynamic component of response are approximately 0.20 of the static component of response for
structures with frequencies in the 2.5 to 4.5 Hz quasi-resonance range, and about 0.10 to 0.15 for
structures outside this range. Coefficients of variation of the dynamic component of 0.6 to 1.0 are
typical for the observed data (Billing 1982).
C3.8.4.5.1 General
The dynamic load allowance is an equivalent static load, expressed as a fraction of the CL-W Truck
load, which is considered for design purposes to be equivalent to the dynamic and vibratory effects of
the interaction of the moving vehicle and the bridge. Dynamic load allowance is not required for
centrifugal, braking, collision or pedestrian loads. The maintenance vehicle load, Clause 3.8.11,
includes an allowance for dynamic effects.
The Lane Load represents the CL-W Truck and additional traffic in the same lane. It is unlikely that all
axles of all these vehicles would be in phase, so the dynamic responses will be reduced from those for
a single truck. As the maximum intensity of the uniformly distributed portion of the lane load, 9 kN/m,
represents stationary vehicles, bumper-to-bumper, no dynamic load allowance is applied to the CL-W
Lane Load.
In design, the force effects transferred from one component to another should include the effects of
vibration and impact through the inclusion of the dynamic load allowance as part of such force effects.
Designers are advised to transfer the force effects of load, including the dynamic load allowance, to
the top of the foundations where earth cover provides damping and reduces the vibratory effects of
live load.
Consideration was given to the identification of components for which the dynamic load allowance
should be included. Such a component identification scheme was found to be intractable as there is
not a universally accepted definition for all components that uniquely defines a structural function. For
example, a diaphragm may connect two girders, transferring deck loads to the girders and thence
bearings, or a diaphragm may connect two girders and support both via a bearing. In each case the
nature of the force effects introduced into a similar component differs markedly.
Advanced dynamic analyses, or tests, either on structural models or existing structures, are usually
used only in special cases or where there are special conditions that warrant their use. Where such
analyses, or test results, are used, the data need to be calibrated before use to obtain an appropriate
dynamic load allowance (Green et al. 1982) and these values need to be Approved.
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C3.8.4.5.2 Buried structures
The dynamic load allowance specified assumes that the design of arch type buried structures is usually
based on a single or dual axle loading. The dynamic load allowance value of 0.4 is used for both loading
cases to reflect local irregularity in the pavement profile in the vicinity of the crown of the arch type
structure. Clause 3.8.4.5.2 is based on earlier practice in AASHTO (1973) and the 1974 edition of CSA S6.
As the depth of earth cover increases from zero to 2.0 m, a reduction in the dynamic load allowance is
applied. Recent field studies of soil-steel structures having various depths of cover from the paved riding
surface to the top of the structure indicate that the dynamic effects of load decrease with depth (Bakht
1980). A dynamic load allowance of 0.10 is appropriate for buried structures for depths of cover in excess
of 2 m because the soil mass has a high energy absorption capacity.
For box type buried structures, the dynamic load allowances also reduces with depth of cover, but for
more than one axle, the values are less than for the arch type as there is no crown effect.
C3.8.4.5.3 Components other than buried structures
Dynamic load is caused by a combination of
(a) bumps in the riding surface or expansion joints that result in direct impact to the bridge deck;
(b) dynamic variation in axle loads due to undulation and roughness in the riding surface; and
(c) dynamic response of the main longitudinal bridge components to the moving vehicle loads.
The effects of these factors are generally not independent, but the relative contribution from each may
vary significantly depending upon the component loaded and the characteristics of the vehicle traversing
the structure. The dynamic load allowance for a truck, or part thereof, is specified according to the
number of axles involved in generating the load effect, as follows:
(a) loading by a single axle load;
(b) loading by two axle loads, or axles 1, 2, and 3;
(c) loading by three or more axles, except for axles 1, 2, and 3, including loading by the entire truck.
Single-axle effect
Components governed by a single axle unit, or part thereof, may include slabs, such as concrete deck
slabs, pan fill floors, steel orthotropic decks and short-span supporting elements. Dynamic variation in axle
load due to roughness in the riding surface, and impact at bumps, is directly transferred to the
component, which results in a high dynamic load. The dynamic interaction of such components with the
moving load is generally very small, because vibration of the component has a short period compared to
the duration of loading.
The specified values of dynamic load allowance are based on test results (Page 1976, AASHTO/NRC
1962, Whittemore et al.), assuming that the approach riding surface and bridge deck have been paved to
acceptable standards.
If the approach is unlikely to be paved for an extended period of time, or if expansion joints between
the superstructure and approach pavement are not generally flush with the roadway riding surface,
vehicles will enter the bridge in a state of excitation. To allow for this, it is recommended that the dynamic
load allowance be increased from 0.4 to 0.5 within 3 m or one-tenth of the span length, whichever is
greater, from the location of the joint. This distance corresponds approximately to one half cycle of the
axle spring for a vehicle travelling at approximately 100 km/h. Where suspended spans are incorporated in
semi-continuous or continuous structures, and also where expansion joints are present within the length
of the structure, an increase in dynamic load allowance from 0.4 to 0.5 within 3 m or one-tenth of the
span length, whichever is greater, from the location of the joint is recommended.
Appreciable reduction in the dynamic effects of axle loads can be achieved by minimizing undulations,
potholes, and bumps, especially at or close to expansion joints. Repair of the approaches and deck should
be considered as part of any rehabilitation of a structure.
Earlier editions of the OHBDC recognized that high axle impact loads could occur in the region of deck
joints, due either to an unpaved approach or deck joints not flush with the roadway.
The OHBDC Commentary recommended as practice that dynamic load allowance be increased by 0.1
within 3 m or one tenth of the span length from the joint in these cases.
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Test of a modular deck joint suggested that a higher dynamic load allowance would be appropriate,
especially for fatigue loading (Agarwal 1991). The AASHTO Code specifies a dynamic load allowance
of 0.75 for deck joints (AASHTO 1994).
Two-axle effect
For longitudinal components whose design is governed by two-axle loads, the axles are not generally
in phase so that the impact effect is moderated. The dynamic response of the component to moving
loads results in some dynamic load amplification, but the spans of such components are substantially
less than 20 m and the frequencies are usually sufficiently high that a frequency match between
component and vehicle is unlikely. A consideration of either effect, however, would lead to about the
same value of dynamic load allowance.
A dynamic load allowance value for two axles can be derived similarly, but this loading is
intermediate between one that should clearly be considered with an impact allowance and one for
which a factor based on an assumption of dynamic interaction could be appropriate. The values
obtained using either approach are very close to one another and to the dynamic load allowance of
0.30 prescribed for spans of less than 22 m in OHBDC, 1983. It was decided to maintain this value.
The increase in the dynamic load allowance of 0.1 recommended for deck joints is also
recommended for suspended spans; the dynamic load allowance value for loading by two axles may
also be applied to expansion joints within spans.
Multiple-axle effect
For longer spans, for which the critical loading is due to three or more axles, a frequency match with a
vehicle suspension system is possible and the largest dynamic load effect is likely to involve dynamic
interaction between the structure and the vehicle. The effect of axle load impact is not likely to be
critical. The duration of loading is longer, and the bridge and vehicle may interact for more than one
cycle of vibration of the bridge frequency.
Tests have shown that structures with spans greater than about 20 m usually have a lower damping
ratio than shorter spans. Vibration, therefore, persists longer and vehicles have a greater probability of
entering a bridge already vibrating due to passage of a preceding vehicle. There is increased dynamic
response of bridge superstructures having natural frequencies in the range 2 to 5 Hz, a range typical of
the bounce frequencies of vehicles (Csagoly et al. 1972, Green et al. 1982). The increase is because of
interaction between the vehicle and bridge, and has many of the characteristics of resonance in an
oscillator undergoing simple harmonic notation. This is shown by the analytical model of a moving
pulsating load on a simple span (Fryba 1972, Biggs 1964).
The complex interaction response of the vehicle and bridge to the vehicle crossing is related to the
riding surface roughness, the frequencies of both, and many other factors (Green et al. 1982). The first
longitudinal flexural frequency of the main longitudinal components is an appropriate reference for
the dynamic response of the superstructure to vehicle load.
Examples are available where, under the action of traffic, superstructures vibrate in higher
longitudinal flexural modes, torsional modes, transverse flexural modes, a frequency associated with
the crossing vehicle, or some combination of these (Csagoly et al. 1972, Wright et al. 1964, Green et
al. 1982, Dorton 1976). However, the consideration of the higher modes of vibration and the
calculation of their frequencies can become complex and is not generally necessary in practice.
Values for dynamic load allowance must obviously be established with regard for the fact that it is to
be applied as a factor to the CL-W Truck and that the resulting load will be assumed simultaneously
present with the Truck weight. Values should therefore be determined that are appropriate to the very
heavy vehicles that the CL-W Truck represents.
The observed dynamic amplification values (Billing 1984) were due to trucks with an average
weight estimated to be in the order of 300 to 400 kN. The CL-W Truck now has a total weight of
625 kN and when allowance is made for this difference, assuming a more-or-less inverse linear
relationship between vehicle weight and structure dynamic response, a maximum dynamic load
allowance for the entire truck of less than 0.2 is obtained, even for a structure with a natural frequency
in the resonance-sensitive range.
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This supports the concept of a constant-force effect of about 80 to 90 kN, which yields a DLA factor of
about 0.20 for a 400 kN truck and of about 0.15 for a CL-W Truck. However, there was a reluctance to
prescribe a dynamic load allowance for the design of new structures any lower than 0.25 at the present
time, so this value is now specified for three or more axles and it is no longer necessary to consider the
resonance susceptibility of the structure.
The dynamic load allowance value specified assumes a structure for which coincidence of vehicle and
bridge frequencies is possible. The dynamic load allowance of 0.25 provides for the quasi-resonance effect,
and also for the duration of vibration of structures with low damping. It is conservative for the very heavy
vehicles that are represented by the CL-W Truck, and should be increased for lighter vehicles.
If vehicles of significantly lesser weight than the CL-W Truck were being considered, the dynamic load
allowance values prescribed would not be conservative. This becomes apparent when a more or less
constant force-effect DLA is used. The loads and factors specified for the fatigue and for the serviceability
limit states were reviewed with this in mind. It was found that the overall conservatism of the load
prescription was still satisfactory and, for simplicity, the dynamic load allowance for these limit states was
left the same as for the ULS, although the value for three or more axles should obviously be a little higher.
Caution should be exercised in special cases when vehicles much lighter than the CL-W Truck are being
considered. The specified value of dynamic load allowance for three or more axles should be increased to
allow for the lesser weight; but if the natural frequency of the structure is outside the resonance-sensitive
range, a decrease to reflect the non-resonance effect would tend to offset the increase to reflect the lighter
weight vehicles.
C3.8.4.5.4 Reduction for wood components
The wood components considered in Clause 3.8.4.5.4 include bridges fabricated largely of wood,
composite concrete and wood, and transversely or longitudinally laminated wood decks.
Wood bridges are usually short-span structures and the duration of loading is short. The impactive
effects of wheel loads on the deck element will be present.
In addition, for longer span structures, interaction between the vehicle and bridge is possible. The
dynamic load allowance has been reduced for wood in recognition of improved response to load applied
quickly (short-span structures) and of higher damping (long-span structures). For wood structures
supporting earth cover, a minimum allowance of 0.07 would apply.
C3.8.5 Centrifugal force
The magnitude of the centrifugal force is proportional to the square of the vehicle speed. Therefore, the
critical centrifugal force occurs in free traffic flow at high speed. In free traffic flow, vehicles tend to
maintain a clear distance of at least 1 m for every 2 km/h of vehicle speed. Therefore, for conventional
structures it is unnecessary to consider more than one truck in a lane for critical centrifugal forces. For a
very long curved structure in which transverse forces from several spans are resisted at one location,
special consideration is appropriate.
It will probably be found, however, that in many such cases earthquake loads control the design even if
more than one truck per lane is considered.
C3.8.6 Braking force
While braking, vehicles apply a transient longitudinal force to the top of the bridge deck. This force causes
a longitudinal motion of the superstructure that is restrained by support reactions. The magnitude of the
restraining forces depends upon the dynamic characteristics of the bridge superstructure, the vehicle, and
the bridge bearings and piers.
For simplicity in design, the braking force in the Code is specified as an equivalent static longitudinal
force that will cause load effects similar to those caused by the vehicles.
The vehicle braking force is a function of the coefficient of friction between the tires and the wearing
surface, which depends upon the skid resistance qualities of the wearing surface. Under extreme
conditions, the dynamic braking force due to an axle may be as much as 80% of the axle-load
(OHBDC 1991).
However, since all axles do not exert maximum braking force simultaneously, the peak value of the
braking force as a percentage of gross vehicle weight is smaller.
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Based on energy principles, and assuming uniform deceleration, maximum braking force from one
vehicle determined as a fraction of the vehicle weight is b = v2/2ga, where a is the stopping distance
with uniform deceleration (m), v is the initial speed (m/s), and b is the braking force fraction. NCHRP
provisions were developed using a stopping distance of 122 m (400 ft) at a speed of 88.5 km/h
(55 mph), which gives b = 0.253 (NCHRP 1992). Thus, braking force exerted by one vehicle would be
approximately 25% of the gross vehicle weight. Other vehicles, represented by the uniformly
distributed portion of the lane load, are generally expected to brake out of phase. However, they could
still result in a comparatively smaller increase in the total braking force.
A theoretical consideration of dynamic behaviour for typical structures suggests that although the
equivalent static force should be substantially smaller than the peak force exerted by the vehicles, it is
still quite large. Special consideration should be given to structures that are unduly susceptible to
longitudinal deck forces.
The braking force for multi-lane loading is affected by two considerations, i.e., the reduced
probability of having critical highway live load in more than one lane at the same time, and the
reduced probability of vehicles in all loaded lanes braking simultaneously. Approximate modification
factors to account for the above two effects are 1.00, 0.75, 0.50, and 0.35 for one, two, three, and
four lanes loaded cases, respectively (OHBDC 1991). These modification factors suggest that the
braking forces in three or more lanes is no more critical than in two lanes, and therefore, need not be
considered. Furthermore, because new bridge designs generally consist of two or more lanes, the
braking force corresponding to two lanes is specified irrespective of the width of the structure.
The live load factor accounts for the unknown overloads during the bridge lifetime and uncertainties
in the load analysis. Since braking is a rare event and likely not associated with the overloaded vehicles,
the load factor for the ultimate limit states should be somewhat lower for the braking force than for
the live load (Agarwal 1992). For design purposes, however, it was considered desirable to have the
same load factor for braking force as that for the highway live loads.
The specified braking force has been adjusted for this simplification.
Several codes (NCHRP 1992, AASHTO 1989, CAN/CSA-S6-88, IRC 1974) specify a height of force
application corresponding to the centre of mass of a truck, whereas some other codes (OHBDC 1991,
BSI 1978, NAASRS 1987) require the braking force to be applied at the deck surface. The effect of
applying force at a height above the deck surface would be to redistribute the axle loads within a
vehicle which would be within the degree of overloads considered for the calibration of the highway
live loads. Therefore, application of the load at the deck level is specified in the Code.
C3.8.7 Curb load
The loads of 20 kN/m and 32 kN were derived from values given in the 1974 edition of CSA S6
multiplied by a factor of 1.75. This factor was determined by considering curb resistance at the
ultimate limit state and at the working stress level and the various load and performance factors for
each method of design. Thus, the specified curb load in this Code will result in designs consistent with
earlier practice.
C3.8.8 Barrier loads
C3.8.8.1 Traffic barriers
The specified traffic loads on the barriers are based on vehicular impact at the performance levels
specified in Section 12. The loads are taken from the AASHTO LRFD Bridge Specification
(AASHTO 1994) adjusted for the different live load factors and converted into equivalent static loads
by dividing by a dynamic stress coefficient of 1.4 (NCHRP 1970), reflecting the relationship between
dynamic and static strength of the components.
The live load factor of 1.7 shall be applied, not the collision load factor of 1.0. No DLA need be
applied.
According to Section 12, the design of the barrier itself is based on its performance at a required
performance level evaluated through crash testing. Therefore, the specified traffic loads are to be used
for design of only the anchorages and the deck slab supporting the barrier.
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C3.8.8.2 Pedestrian and bicycle barriers
The pedestrian live load on railings are based on the requirements for railings for exits and stairs in the
National Building Code of Canada (NBC 1990), adjusted for the live load factor specified in Clause 3.5.1.
C3.8.9 Pedestrian load
Pedestrian live loads are not generally a major consideration for highway bridges and for simplicity the
Sidewalk and the Pedestrian Loads of the 1991 edition of the OHBDC have been consolidated into one
load.
The factored pedestrian load remains the same as in the 1991 edition of the OHBDC. The maximum
value of 5.0 kPa has been reduced to 4.0 kPa, reflecting the different live load factors in the two codes.
A loading of 4.0 kPa allows for a crowd of spectators standing close together on a walkway area. This
condition would be more critical than those created during a bicycle rally. The same equivalent load value
is specified in the British Standard (BSI 1978) and is close to the value specified for corridors in the National
Building Code (1977) and the 1974 edition of CSA S6.
For loaded lengths over 30 m, the loading is reduced progressively from 4.0 kPa to a minimum value of
1.6 kPa, to allow for the reduced probability of crowding along the full length.
In determining the total loaded length of the sidewalk, s, where two or more loaded segments of the
sidewalk are separated by unloaded segments, the loaded length is taken to be the sum of the lengths of
all the loaded segments. Each segment is loaded by the load intensity based on the loaded length so
determined. Figure C3.16 illustrates such cases.
The reduced value for pedestrian live load is used for structural components that support both
pedestrians and the highway live loads, because it is improbable that both loads would be at maximum
value at the same time.
The wheel load on sidewalk and pedestrian load are considered to be mutually exclusive.
p
1
Loaded length s = 1 + 2
2
p
1
p
2
3
4
Loaded length s = 1 + 3
Figure C3.16
Loaded length for pedestrian load
(See Clause C3.8.9.)
C3.8.10 Maintenance access loads
Where the width of a walkway and the geometry of its approaches are such that a front-end loader could
be used for snow removal, the local effect of its wheel loads may be critical. For pedestrian bridges
narrower than 3 m, the effect of the pedestrian load exceeds the effect of a small snow-removal vehicle
together with the snow on the bridge.
Maintenance access loads do not occur frequently enough to cause fatigue; however, for pedestrian
bridges, the possibility of kinking or cracking should be considered.
C3.8.12 Multiple-use structures
For bridges expected to carry rail transit in addition to the highway traffic, rail transit loads are required
and should be obtained from the appropriate transit authority.
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Such loads vary widely, depending on the transit system involved. Rail transit systems are classified
into light and heavy rail, according to their capacity in terms of number of passengers per direction
per day (ppdpd) (ACI-358 1993).
For instance, 30 000 ppdpd is considered the upper limit light-rail transit (LRT), whereas
70 000 ppdpd or more is classified as heavy rail (HRT). The range between the two is taken up by
intermediate transit systems (ICTS). The weight of a crush-loaded LRT vehicle (i.e., dead load and
maximum live load) ranges between 18 and 22 kN/m, and that of an HRT vehicle ranges between
22 and 26 kN/m.
It needs to be recognized that transit vehicles have unique load intensities, characteristics, and
combinations compared to those pertaining to highway vehicles. Furthermore, the load and resistance
factors of transit guideways are derived on the basis of a target reliability index of 4.0 compared to 3.5
for bridges. This yields a probability of failure of a guideway in the order of one-tenth of that of a
bridge.
C3.9 Superimposed deformations
C3.9.1 General
Traditionally, bridges have been designed to accommodate or resist only the overall longitudinal
movement arising from temperature strain. Expansion joints and bearings have been provided to allow
for movement. Bridges do, in fact, react in other ways to change in climatic conditions; instances of
damage have occurred when adequate provision for movement has not been made (Leonhardt
et al. 1970, Monier 1972).
Clause 3.9 provides detailed guidance for the calculation of overall longitudinal movements by
specifying a range of effective bridge temperatures, which depend on the location and the form of
construction. The specified range of effective temperatures represents the average range to be
considered in design. Factors such as altitude, exposure of the structure, and orientation to the sun
may result in localized effective temperatures that are beyond the specified range.
Temperature changes within a bridge superstructure are a function of the shade temperature,
intensity of incident solar radiation, the absorptivity of the superstructure materials, and the depth of
the superstructure (Emerson 1968a, b), as shown in Figure C3.17. During periods of hot, sunny
weather, the effective temperature of a bridge superstructure can exceed the maximum shade
temperature because of incident solar radiation. Similarly, during periods of cold weather, the effective
temperature of a bridge superstructure can be below the minimum shade temperature because of
re-radiation (Emerson 1976). The thermal conductivity of concrete is relatively poor and temperature
gradients can occur through the depth of concrete superstructures. Thermal gradients are discussed in
more detail in Clause C3.9.4.4.
The statement concerning wood structures is based on observations. Conventional short-span wood
structures appear to perform satisfactorily, even when there are a number of spans, with no particular
provision for temperature movement. However, restraints to movement that could cause forces for
which the structure is not designed should not be built into the structure.
C3.9.2 Movements and load effects
The plan geometry of a bridge superstructure should be considered when assessing the response of
the structure to changes in effective temperature. Bridges that are straight in plan generally exhibit
movements along their centreline when subjected to changes in effective temperature.
Bridges that are curved in plan will have two components of movement: a longitudinal component
along the centreline of the superstructure, and a transverse component perpendicular to the
longitudinal centreline. These movements are shown in Figure C3.18.
Bridge geometry will influence the design of expansion devices at abutments. With structures
curved in plan or with skew joints, the relative movement of the superstructure may or may not be
normal to the line of the expansion joint, as shown in Figure C3.19. This can lead to binding of
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expansion devices and to high transverse forces on joints, bearing, and abutments, with corresponding
reactions on intermediate piers. It is, therefore, important to assess this transverse movement and to
design the joints, bearings, and structure accordingly.
To determine the actual movement of a bridge superstructure, the position of the neutral or stationary
point needs to be established. The stationary point is that point about which a given set of movements
takes place. The position of the stationary point depends upon the geometry of the superstructure, the
location of the piers and bearings and their relative shear stiffnesses, and the type of dimensional change.
For straight structures, the stationary point is generally located on a longitudinal centreline of symmetry,
as shown in Figure C3.20. In curved structures, there are two components of movement; hence the
stationary point is generally not located on the longitudinal centreline and may lie outside the plan of the
superstructure. Movements are towards the stationary point for contraction as shown in Figure C3.21. For
a detailed explanation of procedures for determining the location of the stationary point, see Zederbaum
(1969).
The restraint of thermal movements will give rise to force effects in both the superstructure and
substructure. Even in unrestrained structures, loads will develop as a result of friction between bearing
plates or shear stiffness of elastomeric bearings. Clause 3.9.2 draws this to the attention of the designer.
Table C3.5 indicates the load effects that can develop in different structural forms as a result of restrained
thermal movements.
Normally, an elastic analysis is used to assess the forces due to movement. In some cases, it may be
necessary to consider inelastic action of the structure at the ultimate limit state in order to assess the forces
due to movement. When an inelastic distortion is calculated, the section assumed to rotate inelastically
must have sufficient rotational ductility to accommodate such movement without loss of strength.
C3.9.3 Superstructure types
The bridge types in Clause 3.9.3 are classified according to their thermal conductivity. In Type A structures,
the internal temperature of the superstructure is more or less uniform. In Types B and C structures,
temperature variation is nonlinearly distributed as a function of the depth of the system. In most cases,
however, a linear distribution may be assumed.
C3.9.4 Temperature effects
C3.9.4.1 Temperature range
The range of effective temperatures given in Clause 3.9.4.1 reflects the thermal properties of the
constituent materials of the bridge superstructure. Because of the relatively high conductivity of steel, steel
structures exhibit a larger range in effective temperature than concrete structures (Emerson 1976).
In Type C concrete structures that are deep, only the upper and lower surfaces of the bridge
superstructure are affected by rapid changes in climatic conditions. The central portion of deep concrete
structures is influenced by long-term variations in mean daily temperatures but not by diurnal heating
cycles (Radolli and Green 1975, Elbadry and Ghali 1983, Emmanuel and Hasley 1978). This permits
reductions to the effective temperature range with increasing depth. Permissible, depth-dependent
reductions are assumed to be similar for Type A and B structures.
These provisions are also applicable to bridges with an asphalt wearing surface.
Asphalt on a bridge deck increases solar radiation effects but also provides insulation.
C3.9.4.2 Effective construction temperature
The temperature given is an approximate average effective temperature. It is assumed that bridges are not
constructed in very cold conditions without protection.
When thick concrete members are cast-in-place, there is a considerable rise in temperature brought
about by the chemical processes involved in the setting and hardening of the cement. The heat liberated
is known as the heat of hydration. This heat dissipates over a period of a few days, depending on the size
of the concrete member. An idealized time-temperature graph is shown in Figure C3.22, which is based
on temperature readings taken during Construction of a number of bridges. During the casting of a bridge
superstructure, an initial set would occur before the maximum temperature is reached, but until concrete
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has begun to set around bearings there is still some freedom to expand. For this reason, the
temperature at the time the superstructure becomes effectively attached to the bearings or the
substructure is difficult to determine.
A further complication when elastomeric bearings without dowels are used, is that the bearings may
slide, up to the time of load transfer caused by falsework removal or prestressing. Observations at a
number of bridge sites, after casting and prior to post-tensioning, indicate that superstructures
contract and cause an amount of bearing movement or distortion consistent with the assumption that
initial hardening of the concrete occurs at a temperature between the ambient temperature and the
peak temperature. For the design of bearings and expansion joints, the subsequent contraction should
be considered and a temperature drop of 25 °C is recommended for the design of normal types of
structures, if a more precise prediction cannot be made.
Sun
Shade temperature
Radiation
Radiation
Reflected
radiation
Wind
Material
properties
Shade temperature
Wind
Figure C3.17
Factors affecting thermal response of superstructure
(See Clause C3.9.1.)
Unrestrained movement
of curved structure
Restrained movement
of curved structure
Figure C3.18
Response of curved structures
(See Clause C3.9.2.)
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Deck
movement
Normal
displacement
Transverse
displacement
Figure C3.19
Normal and transverse displacement across skew joint
(See Clause C3.9.2.)
Y
Y
A
A
L2
D BY = aD T (L2 – LAB)
LAB
LAB
D AY = aD T L2
L2
B
D CY = aD T (L1 – LDC)
B
D DY = aD T L1
X
X
Stationary
point
C
L1
LDC
D
C
LDC
L1
D
D T = Temperature change
D AY = Movement at A in direction Y
Figure C3.20
Stationary point in straight and skewed superstructure
(See Clause C3.9.2.)
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A
Y
B
LB
Stationary
point
*
C
DB
X axis
*
* Direction of
LD
DB = aDTLB
movement
Detail of movement at pier
for deck contraction
D
E
Figure C3.21
Stationary point in curved structure
(See Clause C3.9.2.)
Table C3.5
Load effects due to restraint of thermal movements
(See Clause C3.9.2.)
Structural form
Load effects
Column moments
Deck moments
Axial force in deck
Column moments
Axial force in columns
Deck moments
Axial force in deck
Column moments
Axial force in deck
Moments in deck and legs
Axial force in deck
C3.9.4.3 Positioning of bearings and expansion joints
This is a precautionary cross-reference.
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C3.9.4.4 Thermal gradient effects
Rapid temperature variations on the surface of a bridge superstructure will result in a non-uniform
temperature distribution through the depth of the superstructure. The magnitude of the temperature
gradient between any two points is a function of the thermal properties and the geometry of the bridge
superstructure.
Thermal gradients generally take two forms: linear or non-linear. Because of the high thermal
conductivity of steel, shallow Type A structures generally exhibit small linear gradients.
In deep Type A structures, non-linear gradients are present (Ostapenko 1976, Elbadry and Ghali 1983).
In composite superstructures Type B, there is generally a linear thermal gradient in the concrete deck
(Emerson 1968). The temperature of the steel portion of the superstructure can, however, be different
from that at the top of the concrete deck. The underside of the deck and the steel generally assume the
same temperature, corresponding to the local ambient temperature in the shade.
Because of the poor thermal conductivity of concrete, large gradients in concrete superstructures
Type C can occur (Bosshart 1970, Elbadry and Ghali 1983, Emanuel and Hulsay 1978). In shallow sections
less than 0.3 m deep, temperature gradients are nearly linear while in deeper sections gradients are
non-linear. Sectional curvature results from a linear gradient.
80
d > 1.0 m < 1.6 m
Temperature, ˚C
70
d > 0.5 m < 1.0 m
60
d = depth of concrete
superstructure
d > 0.3 m < 0.5 m
50
40
30
20
10
1
2
3
t, days
Initial set
4
5
6
Assumed construction temperature = 15 ˚C
Figure C3.22
Temperature during hydration and cooling
(See Clause C3.9.4.2.)
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Arbitrary solid
Temperature distribution
aDT
+
Axial strain
=
Self-compatibility
strain
Curvature strain
Figure C3.23
Components of thermal strain
(See Clause C3.9.4.4.)
L
(i) No temperature
gradient
dT
(ii) Induced curvature
d T = dP
P
(iii) Applied loading
(iv) Final moment
and reactions
dP
3EIf
2L
3EIf
L
Reaction:
3EIf
2L
Moment
3EIf
2
Figure C3.24
Induced moments and reactions
(See Clause C3.9.4.4.)
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CL
CL
Figure C3.25
Irregular support geometry
(See Clause C3.9.4.4.)
Nonlinear gradients cause, in addition to curvature, self-compatibility strains that produce no
displacements of the structure as a whole, but set up self-equilibrating stresses. If these strains are
neglected, an equivalent linear temperature gradient may be used in design, as indicated in Figure C3.23.
Curvature strain results in upward displacement of the superstructure for positive temperature differentials,
and a downward displacement for negative temperature differentials. These displacements, in the
presence of restraints, produce bending moments and associated reactions.
The equivalent linear temperature gradient causes an unrestrained curvature of φ .
The moments induced at supports in a continuous structure as a result of restraining the curvature,
shown for a simple, symmetrical example in Figure C3.24, are expressed by the following:
M = CEIφ
where
φ = unrestrained curvature due to linear temperature gradient
EI = longitudinal flexural rigidity, MPa mm4
C = a nondimensional coefficient
= 1.5 for the first interior supports
= 1.0 for remaining interior supports in multi-span bridges
For Type A and C structures, φ = αΔT / d
where
α = coefficient of thermal expansion
ΔT = temperature differential from Figure 3.6
d = section depth, mm
In the case of Type B structures, a nonlinear distribution of temperature takes place along the depth of
the section. However, the fibres in the section cannot deform independently of each other, resulting in a
linear deformation along the depth, and in plane sections remaining plane. Consequently, an internal
self-equilibrating state of stress occurs such that the sum of all forces and moments across the section are
equal to zero. These two relationships produce an equivalent linear thermal gradient that can be used in
the expression for M above.
Stresses induced in continuous structures as a result of restrained curvature have led to cracking in
Type C bridge superstructures (Leonhardt et al. 1970).
A temperature rise at the upper surface of a continuous bridge superstructure produces flexural
moments that induce tensile stress on the lower surface. In prestressed structures, areas may exist that,
under prestress and dead load, have a low compression stress reserve at the bottom surface. These zones
are normally near the interior supports. Cracking can result from the combination of low compressive
stress reserve and induced tensile stress.
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Of particular concern are T-sections, including those formed of precast I-beams with a composite
slab. The unfavourable position of the geometric centroid generally results in a relatively low
compression stress reserve under dead load and prestress at the underside, and the stress increase for
any given temperature gradient is greater than for an I-section or hollow box-section. The stresses
resulting from restrained curvature should therefore be added to those due to dead load and prestress
throughout the length of the structure. Sufficient non-prestressed reinforcement should be provided in
those areas where the allowable tensile stress is exceeded. In those cases where there is a low
compression stress reserve, typically T-sections, local prestressing may be provided.
The imposed curvature due to temperature gradients can induce torsional and transverse effects in
structures curved in plan or with support locations in an irregular pattern. For example, the structure
shown in plan in Figure C3.25 will be subjected to additional torsional forces as a result of an imposed
curvature and, depending upon the magnitude of the dead load reactions and curvature, uplift can
occur at the end supports.
C3.9.4.5 Thermal coefficient of linear expansion
The coefficient of linear thermal expansion for concrete varies due to the composite nature of normal
Portland cement concrete, and depends largely on the type and proportions of aggregate and cement
used, the moisture content of the hardened concrete, and the method of curing employed.
Table C8.1 shows the coefficient of linear thermal expansion of concrete made with various
aggregates and cured under different conditions.
In composite Type B structures, the linear coefficient of thermal expansion is a combination of the
thermal coefficients of the constituent materials.
The linear coefficient of expansion for a composite section is given by the following expression
(Emerson 1976):
a comp =
Ac Ec a c + AsE sa s
Ac Ec + AsE s
where
α comp = the thermal coefficient of expansion for composite section
αc
= the thermal coefficient of expansion for concrete
αs
= the thermal coefficient of expansion for steel
Ac
= the cross-sectional area of concrete, mm2
As
= the cross-sectional area of steel, mm2
Ec
= the modulus of elasticity of concrete, MPa
Es
= the modulus of elasticity of steel, MPa
C3.10 Wind loads
The scope and overall arrangement of Clause 3.10, and some prescriptive provisions, parallel the
AASHTO Standard Specifications for Highway Bridges and those for Structural Supports for Highway Signs,
Luminaires and Traffic Signals. The procedures and terminology used to specify the wind loads,
however, follow those of the National Building Code of Canada, referred to hereafter as the NBC (NBC
1977, 1990). Where the specific sources of prescribed aerodynamic data are not given, the data were
arrived at by comparisons with other wind loading codes and wind tunnel test data.
C3.10.1.1 General
The procedures prescribed are primarily intended for conventional highway bridges with spans not
exceeding 125 m and for various lighting standards, sign and traffic signal supports, various barriers
(including noise, visual and other types), and individual structural elements. Although the procedures
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provided also apply to lighter and more slender bridges such as pedestrian overpasses, the prescriptive
material is based on the assumption that the performance of the structure is not sensitive to wind action,
i.e., the structural design is not governed by wind loads.
For structures highly sensitive to wind loading, a more detailed analysis of dynamic wind effects based
on Approved methods is recommended. If significant uncertainties remain, representative wind tunnel
tests are appropriate. If wind loads are based on the results of wind tunnel tests, project-specific load
factors must be determined. The load factors for wind consider the accuracy of the wind tunnel test results
and the variability in site specific wind pressures. Bridge structures are required to resist wind-induced
horizontal drag and vertical lift loads applied as simultaneously acting equivalent static loads. Following
the procedures of the NBC, the magnitudes of these loads are based on a geographically varying hourly
mean reference wind pressure increased by a gust effect coefficient to allow for wind-induced dynamic
effects.
Lighting standards, sign and traffic signal supports, various types of barriers, and other slender structural
elements are required to withstand the wind-induced horizontal drag load, determined following
procedures similar to those used for bridge structures and assumed to act as an equivalent static load, as
well as the effects of vortex-shedding excitation. Vortices shed from these structures produce dynamically
acting lateral or across-wind loads. The dynamic magnification of these loads by the structure must be
allowed for. Although generally smaller than the drag forces, vortex-shedding induced forces may govern
the design of some slender, lightly damped structures. In view of their frequent occurrence, the possibility
of fatigue damage becomes an important consideration.
C3.10.1.2 Reference wind pressure
Annex CA3.1 gives a description of the hourly mean reference wind pressure, q, specified for a standard
open country exposure. The 20% increase in the reference wind pressure to account for funnelling is
generally conservative. Special consideration, however, is recommended for bridge sites in precipitous
terrain or in close proximity to very tall buildings.
C3.10.1.3 Gust effect coefficient
To allow for dynamic excitation due to buffeting by atmospheric turbulence or “gusting”, and a possible
dynamic magnification of the structural response due to resonant vibrations, the mean wind load, based
on the hourly mean reference wind pressure, q, for the design return period, is multiplied by the gust
effect coefficient, Cg . The load effects due to the static application of the resulting load correspond in
magnitude to the expected instantaneous peak load effects associated with the same return period.
Conventional highway bridges with spans not exceeding 125 m are unlikely to experience significant
wind-induced resonant vibrations and the use of Cg = 2 for such structures largely accounts for fluctuating
wind loads resulting from turbulent variations about the hourly mean wind speed used to establish q.
However, Cg = 2.5 is used for light slender structures and for individual structural elements in order to
allow for some increase in the effective loading due to possible wind-induced resonant vibrations.
Larger wind loads than those determined using the simplified gust factor approach may be appropriate
for structures found to be unusually sensitive to wind loading.
A detailed analysis of dynamic action is recommended for such structures. If Approved, such procedures
may follow methods similar to those outlined in the NBC (NBC 1990) (Davenport 1962, 1967, Davenport
and King 1984, Irwin 1987, Harris et al. 1976). Clause C3.10.4 provides some guidance to determine
whether a structure is deemed wind sensitive. In such cases, wind tunnel tests are advised to determine
suitable wind loads.
C3.10.1.4 Wind exposure coefficient
The definition of Ce is in accordance with the NBC “simple procedure”. Due to the uncertainty about the
vertical variation of the mean wind speed close to the ground, it is taken as unity for heights below 10 m.
Ce is not very sensitive to the height H, and a rough approximation is adequate. The “top of the structure”
may be the top of the vehicular barrier or the top chord of a through or half-through truss. Members and
appurtenances that contribute insignificantly to the exposed frontal area should not be considered to
affect the height of the structure. A more accurate determination of Ce is justified if the wind load
evaluation is based on more detailed methods.
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C3.10.1.5 Non-uniform loading
Wind loads exhibit significant spatial variations and unbalanced loads need to be examined in order to
determine critical load effects. The degree of load unbalance specified in Clause 3.10.1.5 is an estimate
based on the NBC. A more severe form of unbalance may be appropriate in situations where the
dynamic component of the wind-induced response is found to be pronounced. This would arise in
structures while under construction using balanced cantilever erection techniques.
C3.10.1.6 Overturning and overall stability
This is a precautionary provision. Clause 3.10.2 is broader in context.
C3.10.1.7 Alternative methods
The use of wind tunnel tests is recommended for structures and components of unusual geometry, as
well as structures found to be unusually sensitive to wind-induced effects evaluated on the basis of
normal design procedures; in other words, where structural design is found to be governed by wind
loads. Such tests may comprise measurements of mean load coefficients using rigid models or
measurements of the mean and dynamic wind-induced response using correctly scaled aeroelastic
models that simulate the aerodynamics of the structure as well as its mass, stiffness, and damping
properties. In both cases, it is important to simulate the mean and turbulent characteristics of natural
wind in the wind tunnel (Davenport and Isyumov 1967, Isyumov 1972). Proper allowances for
Reynolds number effects should be made, particularly for rounded shapes.
C3.10.2 Design of the superstructure
C3.10.2.1 General
Wind-induced loads for most highway bridges are largest for a wind direction perpendicular to the
longitudinal axis of the superstructure. In the case of a curved bridge structure, the longitudinal axis of
the superstructure is selected so that wind effects are maximized.
Drag-induced horizontal loads in Clause 3.10.2.2 and lift-induced vertical loads in Clause 3.10.2.3
specified for the design of the superstructure are thus prescribed only for this critical wind direction.
Overturning effects, resulting from wind-induced moments about the longitudinal axis, are accounted
for by applying the vertical load as an equivalent line load at the windward quarter point of the
superstructure width as described in Clause 3.10.2.3. For bridge types with continuity between the
deck structure and the supports, such as rigid frame structures, wind loads acting on the supports, as
prescribed in Clause 3.10.3, need to be included in the design of the structure. In this case, wind
directions other than perpendicular to the longitudinal axis of the superstructure should also be
examined. In assessments of wind action on the entire structure, the modification factors for the skew
angle of wind that are given in Table 3.9 apply.
C3.10.2.2 Horizontal drag load
Most highway bridge superstructures, typically slab, plate girder, and box girder configurations, act
aerodynamically as single bodies, i.e., there is no airflow through the superstructure. In such cases, the
prescribed horizontal wind load, taken to act on the exposed frontal area, accounts for the total
wind-induced drag load on the superstructure.
This assumption is not valid if there is significant flow through the superstructure, as in the case of
truss bridges. In such cases, the wind force on the leeward truss or trusses must be included in the
calculation of Fh . Due to shielding, the wind load on the leeward truss diminishes with reduced truss
spacing and increased solidity ratio, As /A. The effect of shielding is given in Table C3.6 (NBC 1990).
Shielding is taken into account by multiplying the reference wind pressure, q, by Kx for the first
leeward truss and all successive leeward trusses.
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Unpublished tests at the Boundary Layer Wind Tunnel Laboratory of the University of Western Ontario
indicate that Ch = 2, based on the entire exposed frontal area, is a conservative value for common slab,
plate girder, and box girder superstructures. For individual components of highway bridge superstructures
(e.g., truss elements), the approximate values of Ch given below can be used. For more exact values,
reference should be made to Table A3.2.2.
(a) For angular shapes, Ch = 2
(b) For circular shapes, Ch = 1.2
Table C3.6
Shielding factors, Kx, for trusses
(See Clauses C3.10.2.2 and CA3.2.2.)
As /A
X/h
0.1
0.2
0.3
0.4
0.5
0.6
0.8
0.5
1.0
2.0
4.0
6.0
0.93
0.99
1.00
1.00
1.00
0.75
0.81
0.87
0.90
0.93
0.56
0.65
0.73
0.78
0.83
0.38
0.48
0.59
0.65
0.72
0.19
0.32
0.44
0.52
0.61
0.00
0.15
0.30
0.40
0.50
0.00
0.15
0.30
0.40
0.50
Plane of
windward
truss
h
Plane of
leeward
truss
qx
q
qx = Kx q
x
Notes:
Kx = shielding factor
As = exposed frontal area of truss
A = gross area of truss in elevation
C3.10.2.3 Vertical load
The lift-induced vertical load is not uniformly distributed across the width of the deck. The requirement to
apply the total vertical load as an equivalent line load at the windward quarter point of the deck width
accounts for this eccentricity and the resulting torsional moment about the longitudinal axis. The
application of this load is along a line, or a curve in the case of curved structures, through the windward
quarter point of each cross-section of the deck.
For most superstructure types, the prescribed value of Cv = 1 leads to conservative values of both vertical
loads and torsional moments about the longitudinal axis. Cv is sensitive to the angle of attack of the wind.
This is defined as the angle of the wind in the vertical plane with respect to the horizontal. A higher value
of Cv may be appropriate if the angle of attack is significantly changed from zero by the local topography,
for example, in the case of bridges spanning a deep valley.
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C3.10.2.4 Wind load on live load
A minimal live load is expected to be present on the bridge during the 50- or 100-year return period
wind conditions. The factors specified in Clause 3.5.1 for the joint occurrence of wind loads on the
structure and on the live load reflect the improbability of the full loads being present simultaneously.
C3.10.3 Design of the substructure
C3.10.3.1 General
In all cases, the loads transferred from the superstructure are taken to act simultaneously with those
acting directly on the substructure. As noted in Clause C3.10.2.1, for some structural systems, the
loads on the substructure need to be taken into account in the design of the superstructure.
C3.10.3.2 Wind loads transmitted from the superstructure
The modification coefficients for arriving at the transverse and longitudinal components of the
horizontal load transferred from the superstructure, given in Table 3.9, are based on AASHTO.
The coefficients given for the horizontal transverse component also apply for the vertical load
prescribed in Clause 3.10.2.3.
Both vertical and horizontal loads are applied as equivalent line loads. The latter are applied at the
centroid of the exposed frontal area at each section of the superstructure. For a horizontal deck of
constant depth, and with solid barrier walls and railings, the horizontal loads are applied along a
horizontal line at the mid-height of the frontal area.
For normal girder and slab type highway bridges with spans of 50 m or less, Table C3.7, taken from
AASHTO, provides a conservative combination of prescribed horizontal loads.
Table C3.7
Conservative horizontal load combinations
(See Clause C3.10.3.2.)
Percentage of horizontal load applied
In transverse
direction
In longitudinal
direction
Forces transmitted from
superstructure, Clause 3.10.3.2
100
25
Forces on live load,
Clause 3.10.2.4
100
40
Type of horizontal load
C3.10.3.3 Loads applied directly to substructure
Appropriate values of Ch for circular piers and columns for which D qCe > 5.2, where the diameter, D,
is in metres and q is in Pa, are as follows:
(a) normal steel or concrete surface: Ch = 0.7;
(b) rough surfaces with protuberances of around 0.02D: Ch = 0.9;
(c) very rough ribbed surfaces with rib heights of 0.08D and higher: Ch = 1.2;
(d) circular shapes, with D qCe ≤ 5.2: Ch = 1.2; and
(e) rectangular and square shapes: Ch = 2. This value is conservative and is intended for sharp-edged
supporting elements.
The values of Ch for shapes with well-rounded corners may be reduced if justified by representative
experimental data.
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C3.10.4 Aeroelastic instability
C3.10.4.1 General
Because of the extensive technical literature necessary to examine the aeroelastic phenomena in depth,
Clause 3.10.4.1 is intentionally kept to a simple statement. Many bridges, decks, or separate structural
components have been shown to be aeroelastically sensitive if any of the following criteria are satisfied (in
this instance, studies by an expert in the field of wind engineering of bridges should be consulted):
(a) the ratio of the span length (or free cantilever length while under Construction) to deck width or
mean vertical depth of the deck structure (not including barriers), exceeds 30;
(b) the aerodynamic damping is significant, as measured by (i) a negative slope of either the lift or the
torsional force vs. angle of attack curve or (ii) the product of the mass damping parameter and the
reduced velocity:
⎛ rB 2 ⎞ ⎛ V ⎞
⎜
⎟⎜
⎟ > 0.01
⎝ m ⎠ ⎝ f0B ⎠
where ρ is the density of air (taken as 1.29 kg/m3); B and m are the width and mass per unit span
length of the bridge deck or structural component, respectively; V is the hourly mean wind speed
(m/s) and f0 is the natural frequency of the bridge deck or structural component;
(c) the dynamic response to turbulence is significant, as indicated by a matching of the reduced
frequency f0B/V of the structure and the dominant frequency of the fluctuations, which are due to the
large turbulent eddies in the wind:
fB
0.01 < 0 < 0.1 ; or
V
(d) the ratio of the fundamental torsional to vertical frequencies of vibration of the bridge deck is less
than 1.4, indicating a potential for flutter instability.
The motion of a structure due to the wind loads can cause aeroelastic forces that depend, in part, on the
velocity of the structure itself. These forces are called aerodynamic damping forces and can either oppose
or assist the motion. If they oppose the motion, they constitute positive aerodynamic damping; if they
assist the motion they constitute negative aerodynamic damping. The sum of the aerodynamic damping
and the structural damping constitutes the total effective damping. The total resonant response of the
structure is inversely related to the total effective damping.
If the aerodynamic damping is negative, the total damping available is reduced, in some cases to zero.
Under these circumstances, the amplitudes of vibration become extremely large and the motions are
described as unstable. The limitation of the amplitudes, if any, is defined by the “second order effects” of
the system and flow. Generally, these amplitudes are prohibitively large; under certain circumstances,
however, the limiting amplitudes may be acceptable provided that fatigue is taken into account.
Aerodynamic damping forces are generated whenever a structure is in motion through the flow.
Negative aerodynamic damping forces can arise under a variety of circumstances. One of these, described
as galloping, is associated with a “negative slope” to the force normal to the flow-angle of attack
relationship. The necessary characteristics are exhibited both by common structural shapes and iced
cables.
A typical aeroelastic effect is excitation due to vortex shedding. When the wind blows across a slender
prismatic or cylindrical body, vortices are shed alternately from one side and then the other giving rise to
fluctuating forces acting along the length of the body at right angles to the wind direction and the axis of
the body. There is, in addition, the tendency for the aerodynamic damping to become negative. The
critical wind speed, Vcr , when the frequency of vortex shedding equals the natural frequency, f0 , of the
structure or component is discussed in Clause A3.2.4. Negative aerodynamic damping characteristics are
also found at certain windspeeds in both lift and torsional motion of bridge decks. A particularly important
situation is produced by the negative aerodynamic damping forces set up at the critical wind speed at
which the vortex shedding frequency coincides with the natural frequency of the structure.
The forces are sometimes referred to as “locked-in” forces rather than negative aerodynamic damping
forces.
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Other forms of instability can occur involving the coupling of several modes of vibration. These are
described as “flutter”. They are only likely to affect exceptionally light, flexible structures such as
cable-supported bridges (Ostenfeld 1992). In all of these instances, the problem should be given
special treatment and an expert in the field should be consulted.
C3.10.4.2 Criterion for aeroelastic instability
The provision for design against aeroelastic instability is through coupling the design loads and
responses to a factored wind speed. A compatible level of safety against instability is achieved when
the square root of the load factor for wind is used, since wind load is generally proportional to the
square of wind velocity.
C3.10.5 Wind tunnel tests
C3.10.5.1 General
Flexible bridges, such as cable-supported or very long spans of any type may require special studies
based upon wind tunnel information. In general, appropriate wind tunnel tests involve the simulation
of the wind environment local to the bridge site. Wind tunnel testing of bridge and other structures is
a highly developed technology that can be used to study wind response characteristics of a structural
model or to verify the results of analysis. Details of this are part of the existing wind tunnel state of the
art and are beyond the scope of this Commentary.
C3.10.5.2 Load factors
If the horizontal and vertical forces acting on the bridge are determined using wind tunnel tests,
equations are presented in Clause 3.10.5.2 for computing a project-specific wind load factor. These
equations are necessary because the accuracy of wind tunnel tests and the definition of site-specific
wind pressures depend on the thoroughness of the investigation, which in practice varies to reflect the
trade-off between the cost of a more detailed analysis and the benefits of more accurate knowledge.
Generally, load factors for wind effects determined using wind tunnel tests exceed the values
specified in Table 3.1 because the conservatism of the specified loads and pressure coefficients for the
simplified procedure, presented in Clauses 3.10.1 to 3.10.3, is eliminated. It is envisaged that the
factored wind load effect obtained by wind tunnel testing will be roughly 70% of that obtained using
the simplified procedures on average. See Canadian Highway Bridge Design Code (CHBDC)
Calibration Task Force (2006).
The equation used to compute the wind load factor is based on conventional first-order second
moment reliability principles. The constant 3.5 represents the target reliability index, β t , for the
design life of the bridge. The constant 0.8 is intended to account for conservatism associated with the
current design practice of assuming a static failure mode while explicitly considering the dynamic
effect of the wind load.
The bias coefficient and coefficient of variation of the wind load effect can be determined following
the procedure given in Canadian Highway Bridge Design Code (CHBDC) Calibration Task Force
(2006). It is necessary to fit a lognormal distribution to the square of the velocity for the design
reference period to obtain the bias coefficient and coefficient of variation of the wind pressure.
The separation factor, k, should account for the presence of other force effects that add to (or
counteract) the wind load effect, and resistances. The value of 0.15 in the equation used to compute
the separation factor is intended to represent a conservative (that is, low) estimate of the overall
coefficient of variation due to these other effects.
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C3.11 Water loads
C3.11.4 Stream pressure
C3.11.4.2 Lateral effects
The formulas given in Clauses 3.11.4.2 and 3.11.4.1 are adapted from CAN/CSA-S6-88.
The more favourable drag coefficients from that specification for wedge-type pier nose angles of less
than 90° are not given because such pier noses are more prone to catching drift. If significant quantities of
drift are likely to collect at a pier nose, the area, A, for the drift should be estimated and the drift drag
force, P, computed and applied at an appropriate estimated level, which generally will be higher than that
of the drag force on the pier itself. The angle referred to in Clause 3.11.4.2 and the directions of Pp and P
are shown in Figure C3.26.
Pp
Direction of flow
P
Angle between
direction of flow
and longitudinal axis
Longitudinal axis
Figure C3.26
Plan view of pier showing direction of forces
(See Clause C3.11.4.2.)
C3.11.5 Wave action
Among the loads imposed on bridge substructure elements in maritime environments, the impact forces
induced by breaking waves are very intense in magnitude and complex in nature; they are difficult to
define by simple analytical models. The total impact force is a function of the shape of the structure front
exposed to wave action and the height of the wave. Hence, these forces may be reduced considerably by
providing the proper frontal shape of a support element. Most typical of the high impact forces are those
that occur over a large area of the exposed surface and at different elevations. The force history may be
defined by a sharp single peak load followed by a longer lasting quasi-static force. Existing formulas for
deriving the impact forces due to wave action on vertical surfaces are based on investigations of hydraulic
models in which caisson fronts are simulated by vertical plane surfaces; these forces cannot be defined
easily by a single formula. Thus, the expression given in the Code is only an approximate approach that
yields values of a dynamic loading induced by plunging breakers of moderate wave form impacting a flat
surface; it yields values of impact loading about twice as large as those obtained using static water pressure
expression. The resulting force may be considered to act at mid-height of the wave depth above the still
water level. For curved surfaces, the impact wave loading is equivalent to that of static water loading of
height equal to that of a plunging wave (Chau 1992, Oumeraci and Klommer 1993, Ramsden and
Raichlen 1990, and Camfield 1991).
C3.11.7 Debris torrents
A debris torrent is a type of mass movement that involves water-charged inorganic and organic material
flowing rapidly down a steep confined channel. The inorganic and organic materials that comprise the
debris can include rock fragments up to several metres in diameter, soil ranging from clay to gravel, and
wood ranging from mulch to logs. The debris is transported in a confined channel by high energy sediment
gravity flow. A debris torrent can be triggered by a landslide or rockfall from the following two scenarios:
(a) A creek is dammed by the landslide and creek flow consequently backs up until the dam fails, sending
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a large surgewave downstream. The surgewave carries the slide material and erodes the creek
bed material, producing a debris torrent.
(b) The slide enters the creek during high flow, possibly during a large rain event, and increases the
sediment load in the stream bed sufficiently to trigger a debris torrent.
Debris torrent hazards have been prominent during extreme rain events; they can also be triggered
by earthquakes.
C3.12 Ice loads
C3.12.1 General
The ice load provisions of OHBDC 1991 were based on those of the 1974 edition of CSA S6. Several
changes were introduced, largely based on the work of Neil (1976).
For the Code, the provisions have been updated fairly selectively.
C3.12.2 Dynamic ice forces
Dynamic forces result when a moving ice floe impacts a bridge pier. The forces imposed on a pier are
functions of the size of the floe, the strength and thickness of the ice and the pier geometry. The
following types of ice failures have been observed (Montgomery et al. 1980):
(a) Crushing: the ice fails by local crushing across the pier and is continuously cleared from around
the pier.
(b) Bending: in piers with inclined noses a vertical component of the impact force causes the floe to
rise against the nose and fail in flexure.
(c) Splitting: when a small floe impacts a pier, stress cracks tend to break up the floe.
(d) Buckling: this type of failure takes place when a relatively large floe hits a large pier surface.
(e) Impact: a small ice floe may fail as soon as it strikes a pier, before any of the above modes of
failures take place.
From normal size bridge piers in large bodies of water, crushing and bending failures control the
dynamic ice forces for design. In relatively small streams, impact failure dominates.
It is a significant improvement in the formulation of the horizontal load to recognize that the two
values, Fc and Fb are predicated upon two alternative and largely independent modes of failure in the
ice floes.
Minor changes have been made to the values of p, the crushing strength of ice, in some cases, to
give a better rounding off, and a better agreement with current estimates.
C3.12.2.1 Effective ice strength
As a guide, the 400 kPa stress applies at localities in which ice effects are minimal, and the 1500 kPa
stress is appropriate where ice loads are expected to be severe. The effective ice strength depends
primarily on the temperature and coarseness of the ice texture. However, the tensile strength is not
sensitive to temperature.
C3.12.2.2 Crushing and flexural strength
The limit of the ratio w/t of 6.0 is an estimate of the upper limit at which ice, having failed by bending,
tends to be washed around the pier. In the equation, the velocity term is absent, because it is expected
that the force on the pier is generated by the crushing or bending failure of the ice flow. The shape of
the nose of the pier has no effect of reducing the emanating ice loads. The thickness, t, of ice should
be derived from actual site measurement.
C3.12.2.3 Ice impact forces
As a realistic approach, a minimum lateral component of 15% of the longitudinal ice impact force is
specified. Figure C3.27 explains the idea further.
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The transverse force specified is for small angles of inclination to the stream flow. Large angles must be
avoided.
For pier shafts of conventional shape, an unmanageably large value of frontal width will be obtained if
the angle of inclination to the stream flow is large. In such cases, a different form of pier shaft should be
considered.
C3.12.2.4 Slender piers
The mass of the pier shaft plays a critical part in attenuating the impactive effects of ice flows. The
possibility of dynamic interaction is very real when the deflection of the pier shaft under ice action is
significant.
Resultant force
(normal)
Movement of
ice floe
Ft
(
b
+ qf)
2
F
2
qf Friction angle
90˚
b
2
Ice floe
Figure C3.27
Transverse ice load (floe flowing past a portion of a pier nose)
(See Clause C3.12.2.3.)
C3.12.3 Static ice forces
No prescriptive and definite recommendations can be made regarding ice pressure on piers frozen into
large sheets of ice. Large pressures can be generated in such circumstances due to thermally induced
dimensional changes in the ice sheet, changes in water level accompanied by the formation, filling and
refreezing of cracks, and wind and stream flow drag on the ice sheet. When bridge piers must be located
in a body of water likely to form a large unbroken sheet of thick ice, a study of the site should be carried
out by specialists to determine design requirements and investigate alternative solutions.
C3.12.4 Ice jams
The frazil accumulation in a hanging dam may exert a pressure as much as 10 times larger than that
exerted by ice jams, as it moves by the pier. This spread of pressure indicates that firm data is lacking in
this respect.
Ice jams and floating or hanging ice dams slowed down or held in place by friction against the river
bank or substructure element, are caused by a buildup of successive accumulation of ice cakes dipping
below the surface ice and causing the crest of the jam to rise in height. Frazil ice consists of masses of
loosely knitted needle-like ice spicules that move in suspension and form only in sediment-free open
flowing waters under clear skies. When present in great quantities, frazil produces a dense crystalline mass
known as slush ice.
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C3.12.5 Ice adhesion forces
When an ice sheet freezes onto a pier, it exerts a vertical force on the pier due to water level
fluctuations under the ice sheet. Thus, when the water level drops, the ice sheet hangs on the pier
exerting an additional dead load, and when it rises, it pushes on the ice sheet until the ice breaks
around the pier.
The equation for circular piers was derived by considering the failure of a semi-infinite,
wedge-shaped ice sheet on an elastic foundation under vertical load applied at its apex. For a single ice
wedge, the maximum vertical force, P, can be evaluated from the expression (Nevel 1972):
3
⎛ a ⎞ ⎫⎪
⎛a ⎞
⎛ d ⎞ ⎧⎪
P = s T t 2 tan ⎜ ⎟ ⎨1.05 + 2 ⎜ ⎟ + 0.5 ⎜ ⎟ ⎬ / 3
⎝ l ⎠ ⎭⎪
⎝l ⎠
⎝ 2 ⎠ ⎩⎪
in which
I
= (109Et3/12γ g)0.26
= 15.6t0.26
where
σT = tensile strength of ice, kN/m2
t
= maximum thickness of the ice, m
δ = angle of the truncated wedge, degrees
a = truncated distance, which is assumed equal to the radius of a circular pier, m
l
= characteristic length calculated from the expression, m
E = Young’s modulus for ice, MPa
v = unit density of water, kg/m3
g = acceleration due to gravity, m/s2
To obtain the equation for a circular pier, the vertical force is summed for the four wedges, each
with a truncated angle of 90°, and it is assumed that the tensile strength of ice is 0.84 times an
effective crushing strength of 1.1 MPa and that the ratio of the truncated distance to the characteristic
length, a/ l, is less than 0.6.
The equation for an oblong pier is the sum of two expressions:
(a) the equation for a circular pier that accounts for the vertical ice forces acting on the half circles at
the ends of an oblong pier; and
(b) an expression that calculates the vertical ice forces on the straight walls of the pier.
The expression for calculating the vertical ice forces on the long straight walls of the pier was
derived by considering a semi-infinite, rectangular ice sheet on an elastic foundation under a
uniformity distributed edge load. The forces required to fail the ice sheet, F, can be expressed as
2
t2
(Montgomery 1984).
sT
6
l
The equations for a circular pier and an oblong pier neglect creep and are, therefore, conservative
for water level fluctuations occurring over more than a few minutes, but they are also based on the
assumption that failure occurs on the formation of the first crack, which is nonconservative.
F=
C3.12.6 Ice accretion
Background information on the accretion of ice on exposed surfaces is provided in Annex CA3.1. The
design ice thicknesses, given in Annex A3.1, are provided for exposed objects that obstruct the air
flow. In such cases, greater ice accretion can occur during periods with significant wind speed. An
allowance for the action of wind has been included in the data.
For objects of relatively compact cross-section, ice accretion can occur around the entire perimeter.
The design ice thickness should therefore be applied around all surfaces of all exposed objects, with
the exception of plate-like shapes such as sign panels, bridge girders, or solid barriers, where ice
accretion is likely to occur only on one of the sides. Although the actual ice thickness is likely to vary
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around the perimeter of an exposed object, such a degree of refinement is difficult to include without
further information. The use of a uniformly distributed ice thickness is considered to be adequate for most
situations.
The unit weight of the accreted ice layer is taken to be somewhat greater than that of pure ice, in order
to allow for possible impurities.
C3.13 Earthquake effects
Since earthquake provisions are included in Section 4, the relevant clauses of this Commentary should be
consulted.
The clauses pertaining to seismic zones, seismic accelerations and velocities, load combinations, and
load factors are given in Section 3.
C3.14 Vessel collision
C3.14.1 General
The intent of the vessel collision provisions is to minimize the risk of catastrophic failure of superstructures
and piers for bridges crossing navigable waterways due to collisions with aberrant vessels. The collision
impact forces represent a probability-based worst-case head-on collision, with the vessel moving in a
forward direction at a relatively high speed. The requirements are applicable to steel-hulled merchant
ships larger than 1000 deadweight tonnage, DWT.
Any specification of vessel impact loadings and pier protection requirements involves balancing the risk
of the impact occurrence against the cost to society of designing structures to withstand the resulting
loading. Therefore, engineering judgement and experience, together with political wisdom, are as
necessary as scientific knowledge.
C3.14.2 Bridge classification
The bridge classification reflects the acceptable risk criteria to establish the design vessel to be used to
determine impact loadings for bridges. Hence, bridges are classified as Class I or Class II. Class I bridges are
those that must continue to function after impact from a design vessel whose probability of occurrence is
smaller than that for Class II bridges. The determination of the classification is necessarily subjective.
Consideration should be given to social, commercial, and security requirements.
C3.14.5 Design vessel
The selection of the design vessel is based on a probability analysis by which the predicted annual
frequency of bridge collapse is obtained by summation of annual frequencies of relevant bridge
components and is compared to an acceptance criterion, AFmax. The analysis is an iterative process in
which a trial design vessel is selected for a bridge component and a resulting AF is computed for that
component using the characteristics of waterway, bridge, and vessel fleet. The summation of the AFs is
compared with the acceptance criterion and revisions to the analysis variables are made as necessary to
achieve compliance. The primary variables that the designer can usually alter include
(a) the location of the bridge in the waterway;
(b) the location and clearances of bridge pier and span components;
(c) the strength of piers and spans; and
(d) the use of protection systems to either reduce or eliminate the collision forces applied to the bridge.
C3.14.6 Application of collision forces
Reference should be made to Annex CA3.3.
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C3.14.7 Protection of piers
The development of bridge protection alternatives for vessel collisions generally follows three
approaches:
(a) reduction in the annual frequency of collision events, e.g., by improving navigation aids near a
bridge;
(b) reducing the probability of collapse, e.g., by imposing vessel speed restrictions in the waterway;
and
(c) reducing the disruption costs of a collision, e.g., by physical protection and motorist warning
systems.
Since implementing modifications to navigation aids in the waterway and vessel operating
conditions are normally beyond the designer’s ability, the primary areas of bridge protection to be
considered by the designer are the physical means of protection and motorist warning systems.
The current practice in the design of protective structures is almost invariably based on energy
considerations. In these, it is assumed that the loss of kinetic energy of the vessel is transformed into an
equal amount of energy absorbed by the protective structure. The kinetic impact energy is dissipated
by the work done by bending, shear, torsion, and displacement of the members of the protective
structure.
Design of protective structures is usually an iterative process, in which a force vs. deflection diagram
is developed by analysis or physical testing and modelling as a first trial. The area under the diagram
yields the energy capacity of the protective system. The forces and energy capacity of the protective
structure is then compared with the impact force of the design vessel and energy to check if the vessel
loads have been safely withstood (see the AASHTO Guide Specification referenced in Annex CA3.3 for
examples and design of different bridge protection systems).
C3.15 Vehicle collision load
Barriers in current use may not be able to stop a heavy commercial vehicle from hitting a bridge pier.
Failure of the pier may cause a bridge to collapse with serious consequences. To prevent collapse,
highway bridge piers near the edge of the road surface must be designed to withstand the maximum
dynamic force due to such collisions. If the distance between the edge of the road and the pier is 10 m
or more, the probability of a severe collision is considered to be negligible.
Pedestrian bridge piers should be protected by vehicular barriers, and need not be designed for the
specified collision load. Their consequences of collapse could be minimized during critical periods.
The numerical value of the specified collision load is based on the loads used in the German
Standard DIN 1072 (1972). It was verified by considering the load and performance factors and
maximum lateral impact force due to a 450 kN vehicle. The numerical value is higher than the
OHBDC 1991 value, but the factored load value is unchanged.
C3.16 Construction loads and loads on temporary
structures
C3.16.1 General
Consideration is not given to the occurrence of an earthquake during normal Construction periods.
Although a 10-year return period for wind loads is excessive in many cases, reference wind pressures
for shorter return periods would not be much less (Annex A3.1). If fixed construction schedules justify
neglecting or reducing seasonal loads or neglecting them altogether, the assumptions made in design
should be indicated on the drawings.
C3.16.2 Dead loads
Bulk materials, although subject to movement, may be considered as temporary dead load, provided
that the addition and removal of such load are accomplished in small increments.
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C3.16.3 Live loads
Appropriate allowances should be made for dynamic effects in estimating live loads.
The weight of structural components will, in some cases, be considered as live load while being moved
into position; after installation, they should be considered as dead load.
The basic live load factor for ULS Combination 1 in Table 3.1 is 1.70, whereas the value in the
OHBDC (1991) is 1.40. The truck live load, however, has been reduced from 740 to 625 kN, and the
factored live loads in the OHBDC (1991) and the Code thus remain similar. For construction loads in the
OHBDC (1991), the basic live load factor of 1.40 has been applied satisfactorily, and as there is no defined
change in these loads, a basic value close to 1.40 should continue to be used. Thus, the live load factor
shown in Table 3.1 should be multiplied by 0.85 for construction conditions.
C3.16.4 Segmental construction
C3.16.4.1 Erection loads
The erection scheme used by the Constructor may differ in subtle but important respects from that
visualized by the designer. Therefore, the specified relevant information should be displayed on the Plans
to help reduce the risks inherent in possible modifications. This does not eliminate the need for a thorough
review of the proposed erection procedure by the Engineer. Overturning is addressed in Clauses 3.5.2.2
and C3.5.2.2.
C3.16.4.2 Construction live loads
The specified forces have been derived from experience gained in the design and construction of
segmental bridges, and assume a high level of co-operation between the Constructor and the Engineer
during all phases of the work.
C3.16.4.3 Incremental launching
The specified coefficient of friction is given to provide a basis for evaluating the erection loads in the
design of the substructure. The actual forces should be verified during erection, and additional restraints
provided where necessary.
C3.16.5 Falsework
It is not intended that loads from the Code should be used in designing to other specifications.
References for Clauses C3.4 to C3.16
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OHBDC. Ontario Highway Bridge Design Code, Second Edition, 1983 and Third Edition 1991. Vol. 1 & 2,
Ministry of Transportation of Ontario, Downsview, Ontario.
Ostapenko, A. 1976. “Rio-Niteroi Bridge: Thermal Field Studies.” TRB, Transportation Research Record
607.
Ostenfeld, K. 1992. “Aerodynamics of Large Bridges.” Structural Engineering International, IABSE, SEI
Vol. 2, No. 3, August, pp. 186–189.
Ottawa Citizen. 2000. “Pedestrian ‘Rhythm’ Made Bridge Sway: Experts.” July 8.
Oumeraci, H., Klammer, P., and Partenscky, H.W. 1993. “Classification of Breaking Wave Loads on Vertical
Structures.” Journal of Waterway, Port, Coastal and Ocean Engineering, ASCE, Vol. 119, #4, July–August, pp.
381–397.
Page, J. 1976. Dynamic Wheel Load Measurements on Motorway Bridges. Department of Environment,
Transport and Road Research Laboratory, TRRL Report LR 722, Crowthorne, England.
Radolli, M., and Green, R. 1975. “Thermal Stresses in Concrete Bridge Superstructures Under Summer
Conditions.” TRB, Transportation Research Record 547.
Ramsden, J.D., and Raichlen, F. 1990. “Forces on Vertical Wall Caused by Incident Bores.” Journal of
Waterway, Port, Coastal and Ocean Engineering, ASCE, Vol. 116, #5, Sep.–Oct., pp. 592–613.
Reiher, H., and Meister, F.J. 1946. The Effect of Vibration on People (in German), Translation: Report No.
F-TS-616-RE, Headquarters, Air Material Command, Wright Air Force Field, Ohio.
Rosler, M. 1994. “Dynamic Interaction Between Bridge and Vehicle.” TRB Record No. 1460, Structures,
pp. 81–86.
Shepherd, R., and Aves, R.J. 1973. “Impact Factors for Simple Concrete Bridges.” Proc. Inst. Civ. Eng.,
Vol. 55 Part 2, Research and Theory, paper 7548, March.
TAC. 1991. Memorandum of Understanding Respecting A Federal-Provincial-Territorial Agreement on Vehicle
Weights and Dimensions. Council of Ministers Responsible for Transportation and Highway Safety.
Tilly, G.P. 1977. “Analysis of the Dynamic Behaviour of Concrete Bridges.” Research Seminar, Cement and
Concrete Association, Slough, England, September 1977.
Wardlaw, R.L., and Cooper, K.R. 1974. “Mechanisms and Alleviation of Wind-Induced Structural
Vibrations.” Proc. of the 2nd Canadian Symposium on the Applications of Solid Mechanics, McMaster
University, June.
Wheeler, J.E. 1980. “Pedestrian Induced Vibrations in Footbridges.” 10th Australian Road Research Board
Conference, Sydney, Australia.
Whittemore, A.P., Wiley, J.R., Shultz, P.C., and Pollock, P.E. 1970. Dynamic Pavement Loads of Heavy
Highway Vehicles. National Co-operative Highway Research Program, Report 105.
Wright, D.T., and Green, R. 1964. Highway Bridge Vibration Part II. Ontario Test Programme, OJHRP Report
No. 5, Ontario Joint Highway Research Programme, Queen’s University, Kingston, Ontario.
Zederbaum, Joseph. 1969. “Factors Influencing the Longitudinal Movement of a Concrete Bridge System
with Special Reference to Deck Contraction.” First International Symposium on Concrete Bridge Design,
ACI Publ. SP-23, American Concrete Institute, Detroit, Michigan, pp. 75–95.
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Annex CA3.1
Commentary on Annex A3.1 — Climate and
environmental data
General
The climatic information included in this Annex, as well as its form of presentation, have been chosen
largely to suit the specific requirements of the Code. Some material has also been added for general
information.
The various climatic elements presented in chart or table form are briefly described below. The
charts present isolines or zones of equal intensity of the various parameters. The tabulation presents
reference design wind pressures and seismic zoning for the over 600 locations contained in Chapter 1
of the Supplement to the National Building Code of Canada (NBC 1990). These locations include
(a) incorporated cities and towns with populations in excess of 5000, unless they are close to other
larger cities;
(b) smaller towns and villages in sparsely populated areas; and
(c) in some cases, actual weather stations in preference to locations with somewhat larger
populations.
Although the values in both the charts and the tables are intended to provide an overall picture of
the climatic elements required for design, these may not accurately reflect the influence of the local
environment. The local topography and terrain, and the presence of bodies of water or other features,
may modify the local climate at the proposed bridge site. For example, winds are generally stronger in
open areas, near bodies of water, and near the tops of hills and escarpments. Similarly, air
temperatures and the relative humidity may be influenced by local bodies of water and local
topography. The weather data used in preparing the charts were, of necessity, recorded at inhabited
locations, and hence the charts apply only to populated areas. This is particularly significant in
mountainous areas where the lines on the charts apply only to the populated valleys and not to the
mountain slopes and high passes, where, in some cases, quite different conditions are known to exist.
The material in this Annex is based on data contained in Supplement No. 1 to the National Building
Code of Canada, with additional information supplied by the Atmospheric Environment Service,
Department of the Environment Canada, and the Boundary Layer Wind Tunnel Laboratory of the
University of Western Ontario.
Maximum and minimum mean daily air temperatures
Figures A3.1.1 and A3.1.2 present isotherms of recorded maximum and minimum mean daily air
temperatures measured at a height of 1.2 m above level grassy terrain and, where practicable, away
from the sheltering influence of trees and buildings. The mean temperature on a particular day has
been taken as the average of the highest and lowest temperatures recorded on that day.
In the drawings of the isotherms, emphasis has been placed on data from stations with record
length of 30 years and greater. The isotherms have been drawn as smooth curves to indicate overall
climatic trends, and thus do not necessarily reflect local departures. Detailed data may be found in
Environment Canada publications (Environment Canada 1975).
Relative humidity
Figure A3.1.3 presents isolines of annual average relative humidity used for estimating the shrinkage
and creep losses for prestressed concrete members, as specified in Section 8. Relative humidity is
defined as the vapour pressure of the air expressed as a percentage of the saturation vapour pressure
of the air at the same temperature. The annual average relative humidity is the arithmetic average of
the monthly average relative humidities for the decade of 1957 to 1966, inclusive.
The isolines of relative humidity presented in Figure A3.1.3 have been drawn as smooth curves to
indicate overall trends. These do not take into account departures from these trends due to local
topography, bodies of water, and other features. It is noteworthy that the relative humidity at a
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particular location generally exhibits a marked seasonal variation with a superimposed diurnal variation of
similar magnitude. Information on seasonal variations of relative humidity is contained in Canadian
Normals Volume 4 (Environment Canada 1968).
Ice accretion on exposed surfaces
Ice accretion on exposed surfaces is a common winter phenomenon. There are three main types of
ice-forming mechanisms. The most important of these is the formation of glaze or clear ice during periods
of freezing rain. During rainfall at or just below freezing temperatures, raindrops freeze when wetting the
surface and form a high-density clear ice. Ice thicknesses on exposed objects that disturb the airflow can
be significantly increased if freezing rain occurs during periods with significant wind speed. The other two
less important mechanisms are riming or cloud icing, which occurs during freezing drizzle or fog
conditions at or below freezing, and hoar frost, which is formed when water vapour comes in contact with
surfaces that are at below-freezing temperatures.
Ice accretion thicknesses on exposed surfaces for design are given in Figure A3.1.4. These values include
an allowance for the action of wind, which tends to increase the accumulation of ice on exposed objects
that obstruct the airflow. Ice accretion on nonobstructing surfaces, such as the roadway, are generally
lower than the values given in Figure A3.1.4. Nevertheless, exceptions to this trend can occur in relatively
sheltered areas, such as mountain valleys.
The ice thickness given for each zone is the anticipated freezing precipitation amount for a return period
of 20 years, averaged over the first order weather stations within the zone. Departures from these values
are possible depending on local topography and terrain, e.g., in mountainous regions; therefore, the
designer should exercise caution if ice accretion becomes an important consideration. In such cases, local
sources of information should be sought. Information is also available in Environment Canada publications
(Chaine et al. 1974, Chaine and Skeates 1974).
Permafrost
The lines on Figure A3.1.5 indicate the approximate southern limit of permafrost and the boundary
between the discontinuous and continuous permafrost zones in Canada. The distribution of permafrost
varies from continuous in the north to discontinuous in the south. In the continuous zone, permafrost
occurs everywhere under the ground surface and is generally hundreds of feet thick. Southward, the
continuous zone gives way gradually to the discontinuous zone where permafrost exists in combination
with some areas of unfrozen material. The discontinuous zone is one of broad transition between
continuous permafrost and ground having no permafrost.
In this zone, permafrost may vary from a widespread distribution with isolated patches of unfrozen
ground to predominantly thawed material containing islands of ground that remain frozen. In the southern
area of this discontinuous zone, permafrost occurs as scattered patches and is only a few feet thick.
It is emphasized that the lines on this map need to be considered as the approximate location of broad
transition bands many miles wide. Permafrost also exists at high altitudes in the mountains of Western
Canada, which are a great distance south of the southern limit shown on the map. Information on the
occurrence and distribution of permafrost in Canada has been compiled by the Division of Building
Research, National Research Council (Brown 1968, NRC 1969).
Seismic zones
The parameter used as the basis for establishing the seismic zones is the peak horizontal ground
acceleration or velocity having a 10% probability of being exceeded in 50 years (NBC 1990).
Figures A3.1.6 and A3.1.7 are based on the statistical analysis of past earthquakes throughout Canada for
this century (Milne and Davenport 1969). It is corroborated by the results from a larger but less reliable
seismic sample dating back to 1638.
The zones and the assigned horizontal design ground accelerations and velocities for each zone are
shown in the tables in Figures A3.1.6 and A3.1.7 respectively. In the Arctic Region and other parts of the
Northwest Territories, there are insufficient data for a thorough statistical study. The zone boundaries are
largely based on work by Milne and Davenport (1969) and have been drawn by the seismologists of the
Department of Energy, Mines and Resources.
For design applications, reference should be made to Section 4.
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Design and reference wind pressures
Table A3.1.1 provides design hourly mean reference wind pressures associated with return periods of
10, 25, 50, and 100 years for some 600 locations across Canada. These reference pressures are hourly
mean velocity pressures at the standard anemometer height of 10 m and are computed using the
mean hourly wind speed estimated for that return period and a constant air density. The relationship
between the reference pressure, q (in Pa), and the corresponding mean hourly wind speed, v (in km/h)
is
q = 0.05 v 2, Pa
The reference pressures for the return period of 10 years have been taken from Chapter 1 of the
Supplement to the National Building Code of Canada (NBC 1990). Reference pressures for return periods
of 25 and 50 years were obtained from the same source using the following interpolation procedure:
q(25) = 0.166 q(10) + 0.834 q(30)
and
q(50) = 0.576 q(30) + 0.424 q(100)
where q(10) , q(25) , q(30) , q(50) , and q(100) are the reference pressures corresponding to return periods
of 10, 25, 30, 50, and 100 years, respectively.
There are considerable geographic as well as regional differences in reference pressures indicated in
Table A3.1.1. Generally, wind speeds are higher near large bodies of water. For example, in Ontario
the highest design pressures occur along the north shore of Lake Ontario between Oshawa and
Cobourg. At the same time, very much lower values are quoted for extensively wooded portions of the
Muskoka and Western Georgian Bay areas. In addition, local variations are to be expected depending
on local topography; for example, higher design pressures are expected near hilltops and tops of
escarpments. For locations not listed in Table A3.1.1, the highest value for adjacent tabulated locations
should be used.
References
Other publications
Associate Committee on the National Building Code of Canada. 1990. Supplement to The National
Building Code of Canada, NRC No. 30629
Brown, R.J.E. 1968. “Permafrost Map of Canada.” Reprint from Canadian Geographical Journal,
February, pp. 56–63, NRC 10326.
Environment Canada. 1968. Climatic Normals Volume 4 — Humidity. 551.571.2 (71), Toronto, Ontario.
Environment Canada. 1975. Canadian Normals Volume 1Sl — Temperature 1941–1970. UDC 551.582
(71), Downsview, Ontario.
Chaine, P.M., and Skeates, P. 1974. Ice Accretion Handbook. Environment Canada, Atmospheric
Environment, Industrial Meteorology — Study VI, Toronto.
Chaine, P.M., Verge, R.W., Castonguay, G., and Gariepy, J. 1974. “Wind and Ice Loading in Canada.”
Environment Canada, Atmospheric Environment, Industrial Meteorology — Study II, Toronto.
Milne, W.G., and Davenport, A.G. 1969. “Distribution of Earthquake Risk in Canada.” Bulletin of
Seismological Society of America, Vol. 59, No. 2, pp. 729–754, April, also Fourth World Conference on
Earthquake Engineering, Santiago, Chile, January.
Permafrost Map of Canada, 1967 (a joint production of the Geological Survey of Canada and
DBR/NRC). August, National Research Council 6769.
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Annex CA3.2
Commentary on Annex A3.2 — Wind loads on
highway accessory supports and slender
structural elements
CA3.2.1 General
Only drag- and vortex shedding-induced loads are considered to be important for most support structures
and structural elements. Nevertheless, for some exceptionally slender and flexible prismatic elements, such
as ties and iced cables, galloping excitation due to negative aerodynamic damping may be important. This
excitation mechanism is described in Harris and Crede (1976). The load factors for wind effects on sign
support structures and structural elements are provided in Table 3.1. These load factors are less than those
for bridges as given in Table 3.1, reflecting the conservatism inherent in the pressure and gust coefficients
used in the design of sign support structures, as well as the less severe consequences of failure.
CA3.2.2 Horizontal drag load
Horizontal drag coefficients presented in Table A3.2.2 are adapted with some modification from AASHTO.
As indicated, the drag coefficient for rounded shapes depends on the Reynolds number. The onset of
0.5
critical flow conditions, leading to reduced values of Ch for cylindrical shapes, occurs from D (qCe ) = 3.6.
5
This corresponds to the Reynolds number of 3 x 10 .
The values of Ch provided for truss-type supports are most applicable for solidity ratios (defined as the
ratio of exposed frontal area to gross frontal area) from approximately 0.2 to 0.3. For higher solidity ratios,
these values are conservative. For solidity ratios of less than 0.2, use should be made of experimental data
(Cohen 1960) or, alternatively, the overall drag should be taken as the sum of the loads on individual
members. An allowance for shielding, as indicated in Table C3.6, is appropriate.
Horizontal drag coefficients for members, sign panels, barriers, and other shapes not included in
Table A3.2.2 may, in accordance with Clause 3.10.1.7, be established from representative wind tunnel
tests in which comparative tests are made on similar shapes included in this table. For free-swinging traffic
signals, wind loads calculated using the drag coefficient given in Table A3.2.2 may be modified on the
basis of experimental data.
CA3.2.3 Horizontal drag on highway accessory supports
The provisions of Clause A3.2.3 have been adapted from AASHTO. The wind loads Wa , Wh , Wp , and Wv
for components of the structure are obtained by multiplying Fh calculated in Clause 3.10.2.2 by the
exposed frontal area of the respective component. The ice accretion load to be used in combination with
that of wind is prescribed in Clause 3.12.6.
CA3.2.4 Across-wind loads
CA3.2.4.1 General
When the wind blows across a slender structural member, vortices are shed alternately from one side and
then the other, giving rise to a fluctuating force acting at right angles to the wind direction. This organized
pattern of vortices is referred to as the von Karman vortex street. A structural member may be considered
slender in this context if the aspect ratio exceeds 20. For lightly damped members, which are free to
oscillate, large amplitude vibrations in the plane normal to the wind may develop when the vortex
shedding is in resonance with one of the natural frequencies of vibration. Although this is most likely to
occur for the lower modes of vibration, vortex shedding induced effects for very flexible members may
also be important for higher modes. The character of the vortex shedding forces for circular cylinders
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depends on the Reynolds number, Re = VD/v, where v is the kinematic viscosity. The shedding tends to
be organized at subcritical and transcritical Reynolds numbers (Davenport et al., Harris and Crede
1976). In the critical range, namely for 3 x 105 ≤ Re ≤ 3 x 106, vortex shedding tends to be irregular
unless the structural motion is sufficiently large to organize the fluctuating flow around the body. This
phenomenon, referred to as “locking in”, becomes important for lightly damped members.
Although nearly periodic in a smooth airstream, vortex shedding in turbulent boundary layer flow
conditions that are characteristic of natural wind tends to become less regular, with energy distributed
over a band of frequencies around ne . The presence of turbulence effectively reduces the extent of the
member over which the vortex shedding forces remain correlated (Davenport et al., Harris and Crede
1976, Vickery 1968, 1972). A reduction of the aspect ratio has somewhat similar effects
(Vickery 1968).
Several measures may be considered should vortex shedding induced effects prove to be excessive.
These include
(a) strengthening and/or stiffening the member;
(b) increasing the mass;
(c) increasing the damping; and
(d) changing the aerodynamic characteristics by, e.g., increasing the taper or adding aerodynamic
spoilers.
Of these alternatives, increasing the damping of the member is the most desirable solution. The
effective damping can be increased using visco-elastic materials or special dynamic absorbers
(Harris and Crede 1976).
CA3.2.4.2 Vortex shedding excitation
The excitation due to vortex shedding is treated as a time-varying load of frequency ne = SV/D.
Resonant vibrations are assumed to occur when the frequency of vortex shedding coincides with a
natural frequency of the member. The evaluation of vortex shedding-induced effects requires a
dynamic analysis of the member to determine its natural frequencies and associated mode shapes of
vibration. All modes of vibration for which vortex shedding-induced resonant vibrations occur at wind
speeds equal to or less than that corresponding to the design mean hourly reference wind pressure,
namely, V ≤ 1.24 (qCe )0.5, must be considered. In the case of a member with a constant cross-section,
resonant vibrations for a particular mode of vibration with natural frequency, ni , occur at a specific or
critical wind speed, namely, Vcr = D n/S. In the case of a tapered member, the frequency of vortex
shedding at a particular wind speed varies over the length of the member. As the wind speed
increases, resonant excitation occurs first at the smaller diameter portion of the member and then
shifts to portions with larger diameter. Consequently, vortex shedding effects associated with a
particular mode of vibration with frequency, ni must be examined for a range of critical wind speeds.
Defining Dmin and Dmax as the minimum and maximum cross-sectional dimensions, respectively, this
range is expressed as
n D
n i Dmin
≤ Vcr ≤ i max
S
S
CA3.2.4.3 Structural response to vortex shedding excitation
For the harmonic sinusoidal model, the RMS (root-mean-square) time-varying vortex shedding
induced load acting at a particular location, x, along a member is expressed as
~
Fs ( x ,t ) = (1/ 2) rV 2 C L D ( x ) sin ⎡⎣2πne ( x ) t ⎤⎦
where
ρ
= air mass density, taken as 1.29 kg/m3
V
~
CL
= the mean wind speed at location x, m/sec
= RMS lift (across-wind) force coefficient for the cross-sectional geometry as specified in
Table A3.2.4
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x
= coordinate describing length along the member
D(x)
= the diameter or frontal width of a member at location x, m
© Canadian Standards Association
ne (x) = frequency at which vortex shedding occurs at location x, Hz
t
= time, s
For members of constant diameter or frontal width, the magnitude of the excitation is taken to be
invariant with x and proportional to the velocity pressure at the top of the member. This is a conservative
assumption since V approaches zero at ground level. It is also conservative to treat Fs (x,t) as a spatially
coherent excitation, that is, acting in phase along the entire length of the member (Figure CA3.2.1(a)). In
reality, this begins to occur only at large amplitudes of motion.
The variation of the wind speed with height, the turbulent flow functions normally experienced, and the
presence of signs and other accessories all tend to disrupt the spatial correlation of the excitation.
For structures with varying diameter or frontal width, the magnitude of the excitation will vary along
the length of the member. The vortex shedding excitation at location x 1 is taken to remain in phase over
the portion of the member for which the diameter or frontal width remains within ± Ω percent of D(x1)
and is taken to be zero over the remainder of the member (Figure CA3.2.1(b)). A default value of
Ω = ± 10% is prescribed in Clause A3.2.4.3.1, which is higher than the value of Ω = ± 5% prescribed in the
National Building Code of Canada (NBC 1980) for tapered chimney stacks, observation towers, and
buildings. This is because the majority of members covered by Clause A3.2.4 fall into the subcritical Re
range, which leads to a somewhat longer correlation length in comparison with that of members covered
by the NBC.
The value of Ω = ±10% is applicable for peak response amplitudes greater than 2% of D.
For a band limited random forcing model with a Gaussian load spectrum, the induced load is described
in references (Davenport et al., Harris and Crede 1976, Vickery and Clark 1972). The band limited random
forcing model differs from the sinusoidal model by
(a) allowing for a random (rather than harmonic) vortex lift force. This employs a different forcing
function than the sinusoidal model;
(b) allowing for the energy associated with the vortex shedding to be distributed about the dominant
frequency (rather than concentrated on the dominant frequency). This employs a bandwidth term, B,
which is a measure of the distribution of the energy;
(c) allowing for the three-dimensional nature of the flow — the loss of correlation of the lift forces along
the length of the member. This employs a term for the correlation length, L, which is a measure of the
length, in diameters, that the vortices remain correlated (in phase);
(d) allowing for the turbulence of natural wind (turbulence leads to a reduction in the vortex shedding
correlation length and leads to a small reduction in the strength of the shedding forces); and
(e) allowing for the variation of wind speed with height. This employs the power law wind-velocityprofile-exponent, α, to obtain an apparent taper between the wind and the member.
Treating vortex shedding as a sinusoidal process is an approximation leading to conservative estimates.
The variation of the wind speed with height, turbulence of the natural wind, and the presence of signs and
other accessories all tend to disrupt the spatial correlation of the excitation. It is generally accepted as
more accurate to treat the excitation as a band-limited random process and to assume that the forcing
tends to become harmonic only when the motion of the member is sufficiently large to organize the
shedding of vortices (Davenport et al., Harris and Crede 1976, Vickery and Clark 1972, Wootton 1969).
This tends to occur when the peak amplitude of the motion is of the order of 2.0% to 2.5% of the
diameter or the width of the cross-section, and greater.
For the evaluation of the vortex shedding-induced response in a particular mode of vibration, the
direction of the vortex shedding excitation at any location, x, is taken in the direction of the motion of the
member at that location. This is a simplification, as the direction of the vortex shedding force at large body
amplitudes is more likely to be in the direction of the local time derivative or velocity of the body motion.
For the purpose of evaluating the generalized force, GFi , associated with a particular mode of vibration,
both assumptions lead to the same RMS and peak values. Typical illustrations are presented in
Figure CA3.2.1.
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1st mode
2nd mode
2nd mode
Range over which D(x)
is within ± W% of D(x1)
H
x1
m1(x)
Arrows
indicate
direction
of force
Range over which D(x)
is within ± W% of D(x2)
Generalized force:
x1 + WD(x1)/p
H
GFi =
Fs (x)m i (x)dx
GFi (x1) =
0
x
Fs (x)m i (x)dx
x1 – WD(x1)/p
x2
(a) Constant diameter structure
(b) Structure with taper, p
Figure CA3.2.1
Typical vortex shedding-induced responses in two modes of vibration
The designer should follow a more rigorous analysis or consider representative wind tunnel model
tests in cases where vortex shedding effects, computed on the above prescribed basis, govern the
design.
CA3.2.4.3.1 Displacements
The maximum displacements of the member due to the excitation described in this Clause are
determined from a steady-state forced vibration analysis. This analysis is carried out by examining the
vortex shedding-induced response associated with the various modes of vibration of the member.
Following this approach, the peak displacement of a member at location x oscillating sinusoidally in its
i th mode of vibration is expressed as
yi (x) = ai μi (x)
where
ai
= modal coefficient of magnitude of the oscillatory displacement for mode of vibration, i, m
µ i (x) = amplitude of the member mode shape at location x for mode of vibration, i
The modal coefficient ai contains a peak factor of 2 for sinusoidal forcing and 3.5 for band limited
random forcing (Davenport et al.).
The peak factor is defined as the ratio of the peak response to the RMS response. For sinusoidal
forcing, the variability in the shedding of the vortices is caused by the unsteadiness of the wake of the
member and the movement of the structure itself. For band-limited random forcing, the variability in
the shedding of the vortices also includes the unsteadiness of the oncoming flow due to turbulence
and gusts in the wind.
For both constant diameter and tapered members, peak displacements are first calculated using the
band-limited random forcing model. If the peak displacements calculated are in excess of 2.5% of the
diameter at the location of vortex shedding excitation (a limit of 0.7% of the RMS displacements is
multiplied by a peak factor of 3.5 to obtain the 2.5% figure [Davenport et al.]), then the amplitudes
are sufficiently large to cause “locking-in” and the sinusoidal model should be used.
In the evaluation of ai for a member with a constant D, the integration of µi (x) is over the entire
length of the member. The absolute value of µi (x) is used, since the vortex shedding force at location x
is in the same direction as µ i (x).
In the case of a member with varying D, ai is no longer single valued but depends on the location
along the member at which the frequency of vortex shedding excitation for a certain wind speed
coincides with ni . Consequently, ai must be determined for all locations along the member at which
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vortex shedding excitation can occur as determined by Clause A3.2.4.2. The maximum value of ai will
produce the most severe force effects for the i th mode of vibration. In the case of a detailed fatigue
analysis, however, contributions to fatigue damage for the entire range of ai each associated with a
different wind speed, namely V = n i D(x)/S, must be considered.
For sinusoidal forcing, the integration required for the evaluation of ai at a particular location x = x 1 is
carried out over the part of the member for which D (x) is within ± Ω percent of D at x = x 1. In the case of
a member with a uniform taper, p, the indicated limits of integration become
x1 + b = x1 +
ΩD ( x 1 )
ΩD ( x 1 )
and x1 − b = x1 −
p
p
In the case of a nonuniformly tapered member, the local variation of D around x = x1 can be
approximated by a linear taper p.
A good approximation for tapered members is to neglect the variation of D over the limits of
integration. With this assumption the modal coefficient for a member with a taper p for the i th mode
becomes
~
2 2Ωr C L D 4 ( x1)
ai ( x 1 ) =
r ( 4πS ) z iGMi
2
m ave
where
H
GMi = ∫ m ( x ) mi2 ( x ) dx
0
and ⏐µ⏐ave is the average of the absolute values of the mode shape over the portion of the member
centred on x1, for which D(x) is within ± Ω percent of D(x1). Except near the node points, which do not
contribute to maximum values, ⏐µ⏐ave ∝ ⏐µ (x1)⏐.
The location along the member leading to the maximum value of a i ( x) for mode, i, can be found from
d
d
⎡D 4 ( x ) m ( x ) ⎤ = 0
ai ( x ) =
⎦
dx
dx ⎣
For a free-standing tapered member, the region of maximum excitation for the fundamental mode is at
approximately three-quarters of the height and moves downward for higher modes of vibration.
Although the evaluation of ai for a particular mode of vibration must be carried out over the entire
member, the response is normally governed by the excitation from its main components. For example, in
the case of lighting standards, the response in particular modes of vibration is dominated by shedding
from the pole, with the excitation on the luminaire bracket being of far lesser significance. As a good first
approximation, the evaluation of the various modal coefficients can thus be confined to locations along
the pole.
CA3.2.4.3.2 Stresses
Although smaller diameter components of the member, typically luminaire brackets, may be neglected in
the evaluation of the maximum value of the modal coefficient, ai , for a particular mode of vibration, such
components must be included in the evaluation of Fi ( x).
References
Other publications
Associate Committee on the National Building Code of Canada. 1980. Chapter 4 of the Supplement to the
National Building Code of Canada. NRC No. 17724.
104
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Cohen, E. 1960. “Wind Loads on Towers.” Meteorological Monographs, Vol. 4, No. 22.
Davenport, A.G. et al. “New Approaches to Design Against Wind Action.” Unpublished Text. Boundary
Layer Wind Tunnel Laboratory, University of Western Ontario, London, Ontario.
Harris, Cyril, M., and Crede, Charles, E. 1976. Shock and Vibration Handbook. Section 29, “Vibration of
Structures Induced by Wind,” Part II, 2nd Edition, McGraw-Hill Book Co.
Vickery, B.J. 1968. “Load Fluctuations in Turbulent Flow.” ASCE, Journal Eng. Mech. Div., Vol. 94,
February.
Vickery, B.J., and Clark, A.W. 1972. “Lift of Across Wind Response of Tapered Stacks.” ASCE, Journal
Struct. Div., Vol. 98, January.
Wootton, L.R. 1969. “The Oscillation of Large Circular Stacks in Wind.” Proceedings I.C.E., August.
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Annex CA3.3
Commentary on Annex A3.3 — Vessel collision
CA3.3.1 Vessel frequency
Sources for the vessel data and typical ship and barge characteristics are included in the AASHTO Guide
Specifications and Commentary for Vessel Collision Design of Highway Bridges (AASHTO 1991), referred to in
this Commentary as the “AASHTO Guide Specification”.
In developing the design vessel distribution, the designer should first establish the annual number, N,
and characteristics of the vessels using the navigable waterway or channel under the bridge. Since the
water depth limits the size of vessel that could strike a bridge component, the vessel frequency data can
then be modified on the basis of the water depth at each bridge component. This will be used to
determine the number and characteristics of the vessels that could strike the pier or span component
being analyzed. Thus, each component could have a different value of N.
In some cases, differentiation between the number and loading condition of vessels transiting the
waterway will also be necessary.
Vessel characteristics necessary to conduct the analysis include
(a) the vessel type, i.e., ship or barge;
(b) size based on the vessel’s deadweight tonnage, DWT;
(c) inbound and outbound operating characteristics;
(d) loading condition, i.e., fully loaded, partly loaded, ballasted, or empty;
(e) length overall, LOA;
(f) width or beam, B;
(g) draft associated with each loading condition;
(h) bow depth, DB ;
(i) bow shape;
(j) displacement tonnage, W;
(k) vertical clearances; and
(l) the number of transits under the bridge each year, N.
The designer should use judgement in developing a distribution of the vessel frequency data based on
discrete groupings or categories of vessel size by DWT. It is recommended that the DWT intervals used in
developing the vessel distribution not exceed 20 000 t for vessels smaller than 100 000 DWT, and not
exceed 50 000 t for ships larger than 100 000 DWT.
CA3.3.2 Design vessel selection
CA3.3.2.2 Method I
Method I can be used for the first estimation of the design vessel. Method I is a semi-deterministic
analytical procedure for selecting the vessel model for design. The intent of Method I is to provide a
simple, conservative procedure for determining the design impact loads, without having to deal with large
data collection and analysis required for Method II.
The framework of the Method I acceptance criteria was based on ship impact criteria for bridge design
stated in the Common Nordic Regulations (NREF 1980) currently in use in Scandinavian countries.
CA3.3.2.3 Method II
Method II procedure for selecting the vessel model for design is a probability based, risk analysis method.
Method II was developed to minimize the number of judgement calls that the designer must make during
the analysis. Consequently, various empirical relationships, based on experience and judgement, were
developed for the AASHTO Guide Specification, and adapted for the Code.
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Based on historical collision data, the primary area of concern for vessel impact is the central portion
of the bridge near the navigation channel. The limits of this area extend to a distance of three times
the vessel overall length on each side of the inbound and outbound vessel transit path centrelines. The
vessel transit path centrelines for most bridges coincide with the centreline of the navigable channel.
Where two-way vessel traffic exists under the bridge, the vessel transit path centreline of the inbound
and outbound vessels should be taken as the centreline of each half of the channel, respectively.
CA3.3.3 Annual frequency of collapse
CA3.3.3.1 General
Various types of risk assessment models have been developed for vessel collision with bridges by
researchers worldwide. Practically all of these are based on a similar form of equation that is used to
compute the annual frequency of bridge collapse, AF, associated with a particular bridge element.
Summation of AF for each element in the bridge results in the annual frequency for the entire bridge.
The inverse of the annual frequency for the entire bridge is equal to the return period, in years.
CA3.3.3.2 Probability of aberrancy
Since the determination of the probability of vessel aberrancy, PA, based on actual accident data in the
waterway, is often a difficult and time consuming process, an alternative method for estimating PA was
established. The equations in Clause A3.3.3.2 are empirical relationships based on historical accident
data. A comparison between the predicted PA value using these equations and values determined from
accident statistics is generally in fair agreement, although exceptions do occur.
It should be noted that the procedure for computing PA using the equation should not be
considered as being either rigorous or exhaustive.
Several influences, e.g., wind, visibility conditions, navigation aids, and pilotage, were not directly
included in the method, because their effects are difficult to quantify. Indirectly, these influences have
been included, however, since the empirical equations were developed from accident data in which
these factors had a part.
CA3.3.3.3.5 Geometric probability
The geometric probability, PG, is defined as the conditional probability that a vessel will hit a bridge
pier or span given that it has lost control (i.e., it is aberrant) in the vicinity of the bridge. The
probability of occurrence depends on a number of factors, e.g.,
(a) geometry of the waterway;
(b) depth of the water within the waterway;
(c) location of bridge piers;
(d) span clearances;
(e) sailing path of the vessel;
(f) manoeuvring characteristics and size of the vessel;
(g) location, heading, and velocity of the vessel;
(h) rudder angle at time of failure;
(i) environmental conditions;
(j) width, length, and shape of the vessel; and
(k) vessel draft (loaded or ballasted).
The methods used to determine PG vary significantly among researchers. The method used in the
Code is relatively simple and was developed by Knott (Knott and Bonyun 1983). The normal
distribution approach is detailed in the AASHTO Guide Specification.
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CA3.3.3.3.6 Probability of collapse
The probability, PC, that the bridge will collapse once it has been struck by an aberrant vessel is complex
and is a function of the vessel size, type, configuration, speed, direction and mass, and the nature of the
collision. It also depends on the stiffness and strength characteristic of the bridge pier and span in relation
to resisting the collision impact loads.
The methodology for estimating PC was adopted by Cowiconsult (Cowiconsult 1987), from studies
performed by Fujii (Fujii and Shiobara 1978) in Japan using historical damage data between vessels
colliding at sea. The damage to bridge piers is based on ship damage data, since accurate damage data for
collision with bridges is scarce.
Figure A3.3.2 is a plot of the probability of collapse relationships, from which the following results are
evident:
(a) In cases where the impact strength of the pier or span exceeds the vessel collision force of the design
vessel, the collapse probability of the bridge becomes zero.
(b) In cases where the impact strength of the pier or span is in the range of 10 to 100% of the collision
force of the design vessel, the collapse probability of the bridge varies linearly between zero and 0.10.
(c) In cases where the impact strength of the pier or span is below 10% of the collision force of the
design vessel, the collapse probability of the bridge varies linearly between 0.10 and 1.0.
CA3.3.4 Design collision velocity
A triangular distribution of the vessel collision velocity or speed across the length of the bridge and centred
on the centreline of the vessel transit path in the channel was based on historical accident data. This data
indicated that aberrant ships that collide with bridge piers farther away from the channel are moving at
reduced speeds compared to those hitting piers located closer to the navigable channel limits. Aberrant
vessels located at large distances from the channel are usually drifting with the current. Aberrant vessels,
located very near the channel, are moving at speeds approaching the speeds of ships in the main
navigation channel.
The exact distribution of the speed reduction is unknown. However, a triangular distribution was chosen
because of its simplicity, as well as its reasonableness in modelling the aberrant vessel speed situation. The
use of the distance 3 x LOA in Figure A3.3.3 to define the limits at which the design speed becomes equal
to the water current was based on the observation that very few accidents, other than drifting vessels,
have historically occurred beyond that boundary.
CA3.3.5 Ship collision force on pier
The determination of the impact load on a bridge structure during a ship collision is complex and depends
on many factors, e.g.,
(a) the structural type and shape of the ship’s bow;
(b) the degree of water ballast carried in the forepeak of the bow;
(c) the size and speed of the ship;
(d) the geometry of the collision; and
(e) the geometry and strength characteristics of the bridge pier.
The equation for the impact force on the pier was developed from research conducted by Woisin (1976)
in West Germany to generate collision data in order to protect the reactors of nuclear powered ships from
collisions with other ships. The ship collision data was derived from collision tests with physical ship
models at Scales 1:12 and 1:7.5. Woisin’s results have been found to be in good agreement with research
conducted by other ship collision investigators worldwide (IABSE 1983). Figure CA3.3.1 indicates typical
ship impact forces computed using the equation in Clause A3.3.5.
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350
T
0
Vessel collision force (MN)
300
DW
00
.
60
1
T
250
00
0
0.
10
200
DW
WT
D
00
.0
T
60
DW
0
0
0
40.
WT
00 D
0
.
0
2
T
0 DW
10.00
150
100
50
2.000 DWT
0
0
1
2
3
4
5
6
7
8
Collision speed (m/sec)
Figure CA3.3.1
Typical ship impact forces
CA3.3.6 Vessel collision energy
The equation for computing kinetic energy of the collision force is the standard energy expression of
mV 2/2, with conversion from mass to weight, conversion of units and incorporation of a
hydrodynamic mass coefficient, CH , to account for the influence of the surrounding water upon the
moving vessel. Recommendations for estimating CH for vessels moving in a forward direction were
based on studies by Saul and Svensson (1980) and data published by PIANC (1984). It should be
noted that these hydrodynamic mass coefficients are smaller than those normally used for ship
berthing computations, in which a relatively large mass of water moves with the vessel as it
approaches a dock from a lateral (broadside) direction. The calculation of the vessel collision energy is
usually required in the design of the protection system for the piers.
CA3.3.7 Ship collision force on superstructure
CA3.3.7.1 Collision with bow
Limited data exists on the collision forces between ship superstructure bows and bridge superstructure
elements.
CA3.3.7.2 Collision with deck house
Forces developed by Cowiconsult during the 1970 Great Belt Bridge Investigation in Denmark
(Cowiconsult 1987) for deckhouse collision with a bridge superstructure were
PDH = 5.4 MN for the deckhouse collision of a 1000 DWT freighter ship
PDH = 27 MN for the deckhouse collision of a 100 000 DWT tanker ship.
Based roughly on these values, the empirical relationship of these equations was developed for
selecting superstructure design impact values for deckhouse collision.
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CA3.3.7.3 Collision with mast
Very little data on mast impact forces exist in the published literature. The equation was developed by
estimating the impact forces based on bridge girder and superstructure damage from several historical
mast impact accidents.
CA3.3.8 Application of impact forces
CA3.3.8.1 Pier design
Two cases should be evaluated in designing the bridge pier for vessel impact loadings: (1) the overall
stability of the pier and foundation, assuming that the vessel impact acts as a concentrated force at the
waterline; and (2) the ability of each member of the pier to withstand any local collision force associated
with a vessel impact.
The need to apply local collision forces on bridge piers exposed to contact by overhanging portions of a
ship’s bow is well documented by accident case histories. The Sunshine Skyway Bridge in Tampa Bay,
Florida, collapsed in 1980 as a result of the ship’s bow impacting a pier column at a point 13 m above the
waterline. Ship bow rake lengths are often large enough that they can even extend over protective fender
systems and contact vulnerable bridge elements, as shown in Figures A3.3.4 and A3.3.5. Bow shapes and
dimensions vary widely, and the designer may need to perform special studies to establish vessel bow
geometry for a particular waterway location. Typical bow geometry data is provided in the AASHTO Guide
Specification.
CA3.3.8.2 Superstructure design
The ability of various portions of a ship to impact a span or superstructure element depends on the
available vertical clearance under the structure, the water depth, vessel type and characteristics and the
loading condition of the vessel.
References
Other publications
AASHTO. Guide Specification and Commentary for Vessel Collision, Design of Highway Bridges.
American Association of State Highway and Transportation Officials, Washington, DC.
Cowiconsult. 1987. “General Principles for Risk Evaluation of Ship Collisions, Standings, and Contact
Incidents.” Technical Note dated January (unpublished).
Fujii, Y., and Shiobara, R. 1978. “The Estimation of Losses Resulting from Marine Accidents.” Journal of
Navigation, Volume 31, No. 1.
IABSE. 1983. Colloquium, “Ship Collision with Bridges and Offshore Structures.” 3 Vols. (Introductory,
Preliminary and Final Reports). International Association for Bridge and Structural Engineering,
Copenhagen.
Knott, M., and Bonyun, D. 1983. “Ship Collision Against the Sunshine Skyway Bridge.” IABSE Colloquium,
Preliminary Report, pp. 153–162.
NREF. 1980. Load Regulations for Road Bridges. Nordic Road Engineering Federation, NVF Report No. 4,
1980 (in Norwegian).
PIANC. 1984. Report of the International Commission for Improving the Design of Fender Systems. Permanent
International Association of Navigation Congresses, Brussels.
Saul, R., and Svensson, H. 1980. “On the Theory of Ship Collision against Bridge Piers.” IABSE
Proceedings, pp. 51–82, February.
Woisin, G. 1976. “The Collision Tests of the GKSS.” Jahrbuch der Schiffautechnischen Gesellschaft,
Volume 70, pp. 465–487, Berlin.
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Annex CA3.4
Commentary on Annex A3.4 — CL-625-ONT live
loading
CA3.4.1 General
A live load factor of 1.70 generally produces a safety index equal to or above the target figure. The one
significant exception was for the Ontario trucks on simple spans of 25 m or less. To rectify this, Ontario
decided to modify the axle load distribution compared to the CL-625 Truck, but maintain the same
625 kN load and 1.70 load factor. The CL-625-ONT Truck and CL-625-ONT Lane Load are to be used
in Ontario for all span lengths.
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Section C4 — Seismic design
C4.1
Scope 115
C4.3
Abbreviations and symbols 115
C4.4
Earthquake effects 115
C4.4.1
General 115
C4.4.2
Importance categories 115
C4.4.3
Zonal acceleration ratio 116
C4.4.4
Seismic performance zones 116
C4.4.5
Analysis for earthquake loads 117
C4.4.5.2 Single-span bridges 117
C4.4.5.3 Multi-span bridges 117
C4.4.6
Site effects 118
C4.4.6.1 General 118
C4.4.7
Elastic seismic response coefficient 118
C4.4.7.1 General 118
C4.4.8
Response modification factors 119
C4.4.8.1 General 119
C4.4.8.2 Application 120
C4.4.9
Load factors and load combinations 120
C4.4.9.1 General 120
C4.4.9.2 Earthquake load cases 120
C4.4.10 Design forces and support lengths 120
C4.4.10.1 General 120
C4.4.10.2 Seismic Performance Zone 1 121
C4.4.10.3 Seismic Performance Zone 2 121
C4.4.10.4 Seismic Performance Zones 3 and 4 121
C4.4.10.5 Minimum support length requirements for displacements 122
C4.4.10.6 Longitudinal restrainers 122
C4.5
Analysis 122
C4.5.1
General 122
C4.5.3
Multi-span bridges 123
C4.5.3.1 Uniform-load method 123
C4.5.3.2 Single-mode spectral method 124
C4.5.3.3 Multi-mode spectral method 124
C4.5.3.4 Time-history method 125
C4.5.3.5 Static pushover analysis 125
C4.6
Foundations 125
C4.6.2
Liquefaction of foundation soils 125
C4.6.3
Stability of slopes 128
C4.6.4
Seismic forces on abutments and retaining walls 128
C4.6.5
Soil-structure interaction 130
C4.6.6
Fill settlement and approach slabs 133
C4.7
Concrete structures 133
C4.7.1
General 133
C4.7.2
Seismic Performance Zone 1 133
C4.7.3
Seismic Performance Zone 2 134
C4.7.4
Seismic Performance Zones 3 and 4 134
C4.7.4.2 Column requirements 134
C4.7.4.3 Wall-type piers 136
C4.7.4.4 Column connections 136
C4.8
Steel structures 137
C4.8.1
General 137
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C4.8.2
Materials 138
C4.8.3
Sway stability effects 138
C4.8.4
Steel substructures 138
C4.8.4.1
General 138
C4.8.4.3
Seismic Performance Zone 2 138
C4.8.4.4
Seismic Performance Zones 3 and 4 139
C4.8.5
Other systems 142
C4.10
Seismic base isolation 142
C4.10.1
General 142
C4.10.4
Site effects and site coefficient 144
C4.10.5
Response modification factors and design requirements for substructure 144
C4.10.6
Analysis procedures 144
C4.10.6.2 Uniform-load/single-mode spectral analysis 144
C4.10.6.3 Multi-mode spectral analysis 146
C4.10.6.4 Time-history analysis 146
C4.10.7
Clearance and design displacements for seismic and other loads 146
C4.10.8
Design forces for Seismic Performance Zone 1 147
C4.10.9
Design forces for Seismic Performance Zones 2, 3, and 4 147
C4.10.10 Other requirements 147
C4.10.10.1 Non-seismic lateral forces 147
C4.10.10.2 Lateral restoring force 147
C4.10.10.3 Vertical load stability 147
C4.10.11 Required tests of isolation system 147
C4.10.12 Elastomeric bearings — Design 147
C4.10.14 Sliding bearings — Design 148
C4.11
Seismic evaluation of existing bridges 152
C4.11.1
General 152
C4.11.2
Bridge classification 152
C4.11.3
Damage levels 153
C4.11.3.1 Moderate damage 153
C4.11.3.2 Significant damage 153
C4.11.4
Performance criteria 153
C4.11.5
Evaluation methods 153
C4.11.6
Load factors and load combinations for seismic evaluation 153
C4.11.8
Member capacities 153
C4.11.8.1 General 153
C4.11.8.4 Effects of deterioration 154
C4.11.9
Required response modification factor 154
C4.11.10 Response modification factor of existing substructure elements 154
C4.12
Seismic rehabilitation 155
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Section C4
Seismic design
C4.1 Scope
While many of the design provisions are based on AASHTO (1994), there are some significant
differences, as explained in this Commentary.
C4.3 Abbreviations and symbols
C’sm = seismic coefficient for isolation design
Fu = specified minimum tensile strength, MPa
kh = horizontal acceleration coefficient
kv = vertical acceleration coefficient
C4.4 Earthquake effects
C4.4.1 General
Section 4 establishes design and detailing provisions for bridges to minimize their susceptibility to
damage from earthquakes.
The design earthquake ground motions and forces specified in Section 4 are based on a low
probability of their being exceeded during the normal life expectancy of a bridge. Bridges that are
designed and detailed in accordance Section 4 may suffer damage, but should have low probability of
collapse due to seismically induced ground shaking.
A capacity-protected member is a member whose force level is limited by yielding of one or more
connecting members.
The following principles were used for the development of Section 4:
(a) Small to moderate earthquakes should be resisted with the structural components remaining
essentially elastic.
(b) Exposure to shaking from large earthquakes should not cause collapse of the bridge. Where
possible, damage that does occur should be readily detectable and accessible for inspection and
repair.
The capacity design procedures implicit in Section 4 may not apply directly for special bridges, e.g.,
arches, cable-supported bridges, and large trusses. Special studies are necessary to account properly
for the complex dynamic behaviour and nonlinear performance of these bridges during earthquakes.
C4.4.2 Importance categories
Table C4.1 summarizes the performance requirements of the three importance categories.
Section 4 is based on a single-level seismic design procedure. An analysis is performed for the design
earthquake (475-year return period event), and all forces and displacements are derived from this
analysis. This approach focuses on collapse prevention during the design earthquake, and, depending
upon the importance of the structure, different levels of damage are expected to occur as part of the
mechanism for resisting the event.
Section 4 does not require verification of the seismic performance criteria for bridges outlined in
Clause 4.4.2. Rather, it is implied that bridges designed in accordance with the response modification
factors listed in Table 4.5 will satisfy these performance criteria. For lifeline bridges that must be usable
by emergency vehicles immediately after a large earthquake, e.g., a 1000-year return period event, it
may be appropriate to evaluate the structure for this larger event separately rather than inferring the
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seismic performance of the bridge from the procedures of Section 4.
Table C4.1
Performance requirements
(See Clauses C4.4.2 and C4.4.7.1.)
Bridge
Return period
Lifeline
Emergency-route
Other
Small to moderate
earthquake
All traffic
Immediate use
All traffic
Immediate use
All traffic
Immediate use
Design earthquake
(475-year return period)
All traffic
Immediate use
Emergency vehicles
Immediate use
Repairable damage
Large earthquake
(1000-year return period)
Emergency vehicles
Immediate use
Repairable damage
No collapse
C4.4.3 Zonal acceleration ratio
The seismic zoning map provided in Figure A3.1.6 is based on a statistical analysis of historical earthquake
records as outlined in the National Building Code of Canada (1995). Figure A3.1.6 provides contours of
peak horizontal ground acceleration (PHA), in units of g (the acceleration due to gravity), having a
probability of exceedance of 10% in 50 years (which is equivalent to a 15% probability of exceedance
over the 75-year design life of the bridge). It can be shown that an event with the above probability of
exceedance has a return period of 475 years. Such an event is defined in Section 4 as the design
earthquake.
The range of the ratio of peak horizontal ground acceleration (PHA) to the acceleration due to gravity
(taken nominally as 10 m/s2) and the zonal acceleration ratio, A, values associated with each
acceleration-related seismic zone (Za ) are given in Figure A3.1.6 and Table A3.1.1.
C4.4.4 Seismic performance zones
Table C4.2 shows the relationship between the seismic performance zones of Section 4 with the
acceleration related seismic zones of the National Building Code of Canada (1995).
Table C4.2
Seismic performance zones
(See Clause C4.4.4.)
116
Accelerationrelated
Seismic zone
(Za) (NBCC)
Range of peak horizontal
ground acceleration (PHA),
g, for 10% probability of
exceedance in 50 years
Zonal
acceleration
ratio, A
0
1
2
3
4
5
6
0.00 ≤ PHA < 0.04
0.04 ≤ PHA < 0.08
0.08 ≤ PHA < 0.11
0.11 ≤ PHA < 0.16
0.16 ≤ PHA < 0.23
0.23 ≤ PHA < 0.32
0.32 or greater
0.00
0.05
0.10
0.15
0.20
0.30
0.40
Seismic
performance zone
Emergency-route
and other bridges
Lifeline
1
1
2
2
3
4
4
2
2
3
3
3
4
4
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Linear interpolation is not permitted in determining site specific zonal acceleration ratios for sites
located between contour lines in Figure A3.1.6 (i.e., within an acceleration-related seismic zone, Za).
The zonal acceleration ratio associated with each corresponding Za shall be used unless site specific
data is obtained. Site specific data may be obtained from the Geological Survey of Canada,
Department of Natural Resources, Ottawa, Ontario, or the Pacific Geoscience Centre, Sidney, B.C.
These seismic performance zones reflect the variation in seismic risk across the country and are used
to permit different requirements for methods of analysis, minimum support lengths, design
procedures, and details. The parameter used as the basis for establishing the seismic performance
zones is the zonal acceleration ratio. This parameter was used to correlate with the AASHTO seismic
design procedure (AASHTO 1994).
The higher levels of seismic performance zones for lifeline bridges for zonal acceleration ratios less
than 0.20 reflect the more stringent design and detailing requirements necessary to meet the
performance requirements.
C4.4.5 Analysis for earthquake loads
C4.4.5.2 Single-span bridges
For single-span bridges of construction other than a truss, and with a structurally continuous
reinforced concrete deck from abutment to abutment, a detailed analysis of earthquake effects on
superstructure components is not required. However, an assessment of end diaphragms between
girders at the abutments is required.
C4.4.5.3 Multi-span bridges
C4.4.5.3.1 Analysis requirements
The description of a regular bridge given in Table 4.2 is based on the results of an extensive parameter
study involving 27 case studies, in which the uniform load (UL) and single mode (SM) methods of
analysis were compared against the more rigorous multimode (MM) method (AASHTO 1994). A
regular bridge was defined as one for which either of the two approximate methods (UL or SM) could
be used without incurring an error greater than 10% in any force or displacement quantity. An
exception to this general rule is the transverse force at the abutments of “regular” bridges, which may
be overestimated by the UL method by as much as 100% as noted in Clause C4.5.3.1. As shown in
Table 4.2, as the number of spans increases, the permitted variation in pier-to-pier stiffness and
span-to-span length needs to decrease in order to allow the application of the simplified methods.
Whereas it may appear that wide variations in geometry are permitted for regular bridges, this is not
the case in reality. It is noted that the flexural stiffness of a column is inversely proportional to the cube
of its height, and a fourfold change in stiffness, for example, corresponds to only a 60% change in
height, assuming all the other dimensions remain constant. In addition, the weight per unit length is
relatively constant along the length of most bridges, which leads to a uniform mass distribution and
the satisfaction of one of the assumptions in the uniform load method. Higher mode effects play a
more dominant role as the number of spans increases and therefore the simpler analysis techniques
are limited to bridges with six or fewer spans.
An example of an irregular lifeline bridge that may be analyzed by the multimode elastic method is
a bridge with more than six essentially identical spans.
Seismic analysis of earthquake load effects on superstructure elements is required for multispan truss
bridges in Seismic Performance Zones 2, 3, and 4. The analysis should include an assessment of the
bracing, end diaphragms, and other seismic load path components where applicable. An assessment
of gravity load resisting truss members may not be required since these members, which support live
load, usually are found to have significant reserve capacity when the live load is removed and the load
factor for the earthquake load combination is applied.
For multi-span bridges of construction other than a truss, and with a structurally continuous
reinforced concrete deck from abutment to abutment, a detailed analysis of earthquake effects on
superstructure components is not required. However, an assessment of bracing or diaphragms
between girders at the abutments and piers is required.
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C4.4.6 Site effects
C4.4.6.1 General
Site effects on structural response are determined by assessing the soil conditions. Four soil profiles are
used in Section 4 to define a site coefficient that is used to modify the elastic seismic response coefficient
or spectrum of Clause 4.4.7.
These soil profiles are representative of different subsurface conditions that were selected on the basis of
a statistical study of spectral shapes developed on such soils close to seismic source zones in past
earthquakes.
C4.4.7 Elastic seismic response coefficient
C4.4.7.1 General
Earthquake loads are given as the product of the elastic seismic response coefficient Csm and the
equivalent weight of the bridge. The equivalent weight is automatically included in both the single-mode
and multimode methods of analysis specified in Clause 4.5.
The elastic seismic response coefficient is taken from the elastic response spectra outlined in AASHTO
(1994), except that the importance factor is explicitly included in the equation. The elastic seismic
response coefficient may be normalized using the zonal acceleration ratio A (as defined in Clause C4.4.3)
and the result plotted against the period of vibration. Such a plot, for the case of I = 1.0, is given in
Figure C4.1 for different soil profiles.
Csm
Normalized design coefficient
3
Soil profile type IV
Soil profile type III
Soil profile type II
Soil profile type I
2
1
0
0.0
0.5
1.0
1.5
Period — seconds
2.0
3.0
2.5
Note: Dotted line shows that the form of coefficient for soil type III and Ag is less than 0.3.
Figure C4.1
Seismic response coefficients for various soil profiles,
normalized with respect to zonal acceleration ratio A
(See Clause C4.4.7.1.)
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The elastic seismic response coefficient is consistent with the elastic response spectra outlined in
AASHTO (1994). The AASHTO spectra were developed from the National Earthquake Hazards
Reduction Program (NEHRP) document Recommended Provisions for the Development of Seismic
Regulations for Buildings (NEHRP 1988). The NEHRP document specified ground motions and design
spectra in terms of peak ground acceleration (PGA) and peak ground velocity (PGV). AASHTO decided
to simplify the NEHRP procedure by redefining the design spectra and ground motions in terms of an
acceleration coefficient only. The NEHRP Peak Ground Acceleration map was therefore adopted for
determining the acceleration coefficient of the AASHTO provisions.
To make use of the AASHTO design spectra and procedures outlined above, the peak horizontal
ground acceleration (PHA) from the National Building Code of Canada (NBCC) is used in these
provisions to define the zonal acceleration ratio. New methods for defining ground motion
(e.g., uniform hazard spectra) are being investigated for possible inclusion in future codes.
An earthquake may excite several modes of vibration in a bridge and, therefore, the elastic response
coefficient should be found for each relevant mode.
The discussion of the single-mode spectral method in Clause C4.5.3 is used to illustrate the relation
between period, Csm , and quasi-static seismic forces, pe (x). The structure is analyzed for these seismic
forces in the single-mode method. In the multimode method, also outlined in Clause 4.5.3, the
structure is analyzed for several seismic forces, each corresponding to the period and mode shape of
one of the fundamental modes of vibration, and the results are combined using acceptable methods.
The Importance Factors for the three different bridge classifications reflect their very different
performance expectations under different earthquake levels (see Table C4.1). It is noted that the
AASHTO LRFD Specifications (AASHTO 1994) combines the so-called “ductility” factor with the
importance factor, with the result that the importance factor, I, is not explicitly given. It is further noted
that use of the importance factor in Clause 4.4.7.1 together with the R-factor given in Table 4.5 gives
similar results to AASHTO (Mitchell et al. 1998). The CHBDC gives a larger range of R values for
emergency-route and lifeline bridges, which combined with the importance factors provides an
incentive for using more ductile systems.
C4.4.8 Response modification factors
C4.4.8.1 General
Section 4 recognizes that it is uneconomical to design a bridge to resist large earthquakes elastically.
Response modification factors (R-factors) make allowance for redundancy and ductility in a bridge
structure.
The column flexural forces (obtained from a linear elastic analysis) are reduced by dividing by the
R-factor to obtain the design forces. For a multicolumn bent, the R-factor is 5. This value reflects the
high degree of redundancy in a multicolumn bent, the inherent section ductility capacity of ductile
reinforced concrete and steel columns, and the low likelihood of total collapse. Single column bents
that are not redundant are assigned an R-factor of 3.
Section 4 generally only permits inelastic hinging at locations in columns, piers, walls, and pile bents
in regions where the damage can be readily inspected and/or repaired. For pile bents and buried
footings, this may not always be the case; however, the given R-factors should be acceptable for
inelastic hinges that form in reasonably accessible positions (less than 2 m below ground or mean
water or tide level). However, in some cases it may be suitable to permit limited yielding in the
foundations and allow the footings to “rock” on the soil or piles, thereby providing an acceptable
means of energy dissipation. This approach is considered to be outside the scope of Section 4. Suitable
rocking analyses need to be developed using seismic resistant principles providing a level of safety and
performance comparable to that intended by Section 4, and by Engineers knowledgeable in the field
of earthquake engineering.
The elastic displacements are not reduced by the R-factor to obtain the design displacements. The
displacements calculated from the elastic analysis are a reasonable estimate of the inelastic
displacements for structures with periods greater than about 0.7 seconds if the flexibility in the
foundations is included in the analysis. For structures with periods less than about 0.7 seconds,
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inelastic displacements may exceed elastic displacements and hence be more in agreement with the equal
energy approximation than the equal displacement approach. Better estimates of displacements may be
obtained if an inelastic time-history analysis is performed.
Section 4 provides maximum allowable values for response modification factors (R-factors) which are
qualitatively related to member ductility capacities of ductile substructure elements, but also account for
other factors, such as the degree of redundancy of the substructure.
It can be shown that continuous bridge decks spanning over irregular or steep sided valley profiles and
having piers of widely different height are subject to very severe concentrations of ductility demand at
shorter piers.
Due to the continuity of the deck, this phenomenon may also occur for bridges classified as Regular
(meeting the requirements outlined in Table 4.3). In these cases, the distribution of seismic forces may be
influenced by sequential, rather than simultaneous yielding of separate piers, particularly in the
longitudinal direction. For these cases, it is inappropriate to rely on design forces obtained from a linear
elastic dynamic analysis and the R-factor approach.
The R-factors used in Table 4.5 are taken conservatively and lower than expected member or sectional
ductility capacities, since the procedure is intended to apply to a wide variety of bridge geometries.
However, where possible, pier flexibilities should be adjusted to result in as uniform yield displacements
and ductility demands on individual piers as possible.
In cases where attempts to “regularize” the structure are impractical, suitable analyses need to be
developed to account for localized, rather than simultaneous, yielding of separate piers. In some cases, it
may be possible to use “stiff” piers with energy dissipating bearings to alleviate the problem.
C4.4.8.2 Application
For a wall-type pier, an R-factor of 2.0 is used in the direction of the larger dimension of the pier. An
R-factor of 3.0 may be used in the weak direction of the pier, provided that the provisions of
Clause 4.7.4.2 are satisfied.
C4.4.9 Load factors and load combinations
C4.4.9.1 General
In design, the minimum (0.8D) and maximum (1.25D) gravity loads are considered to account for, in an
indirect way, the occurrence of vertical accelerations. For bridge structures with long spans, outriggers, or
cantilever spans, response to vertical acceleration may be important. As a first approximation, vertical
ground motions may be represented by a design coefficient that is equal to two-thirds of the horizontal
coefficient, Csm .
C4.4.9.2 Earthquake load cases
The two perpendicular directions for earthquake load analysis are usually the longitudinal and transverse
axes of the bridge. In the case of a curved bridge, the longitudinal axis may be the chord joining the two
abutments.
C4.4.10 Design forces and support lengths
C4.4.10.1 General
Since rigorous analysis is not required for single-span bridges in any seismic performance zone, minimum
connection forces are specified in this Section for design purposes. These minimum values are based on
the assumption that these bridges have very short periods and that Csm will be given by the product of A
and S. This follows from the observation that single-span bridges on steel bearings or thin elastomeric
pads are almost rigid and respond to ground motion without period-dependent amplification. Soil effects
may be important here and are included in a somewhat conservative manner through the site
coefficient, S.
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C4.4.10.2 Seismic Performance Zone 1
Since rigorous analysis is not required for bridges in Seismic Performance Zone 1, minimum
connection forces are specified in this Section for design purposes. This minimum value is based on the
conservative assumption that the bridge period is short and that Csm will be given by 2.5 times PHA
values of 0.03 and 0.06 for the case when A equals 0.0 and 0.05, respectively (Clause 4.4.7.1). This
Csm is then multiplied by 1.25, which leads to the specified value after rounding. Soil effects do not
influence Csm in this period range. This value may be superseded by the results of rational analysis, if
available.
If each bearing supporting a continuous segment or simply supported span is an elastomeric
bearing, there are no restrained directions due to the flexibility of the bearings.
C4.4.10.3 Seismic Performance Zone 2
C4.4.10.3.2 Modified seismic design forces
For Seismic Performance Zone 2, the degree of capacity protection is slightly reduced from what is
required for Seismic Performance Zones 3 and 4. This would result in slightly less energy absorption,
somewhat earlier strength decay and slightly less ductility capacity. This is permitted in Seismic
Performance Zone 2 because of the smaller number of inelastic cycles expected.
C4.4.10.4 Seismic Performance Zones 3 and 4
C4.4.10.4.1 General
C4.4.10.4.2 Modified seismic design forces
Acceptable damage is restricted to ductile substructure elements that result from inelastic hinges such
as hinges in the columns or inelastic deformations in the braces. The capacity-protected elements such
as superstructures, cap beams, and foundations should, therefore, remain in their elastic range and
hence the value for the R-factor is taken as 1.0. However, in most cases, the maximum force effects on
the capacity- protected elements will be limited by inelastic actions in the ductile substructure
elements. In these circumstances, the use of a design force lower than the elastic seismic demand for
the capacity-protected elements is justified and should result in a more economic design.
Connectors are designed in their restrained directions for a maximum force effect equal to
1.25 times the elastic seismic force, but need not exceed the force that can be developed by the
ductile substructure elements attaining 1.25 times their probable resistances. The amplification factor
of 1.25 is intended to provide some reserve capacity for the connectors and hence to preserve the
integrity of the bridge under seismic loads.
C4.4.10.4.3 Yielding mechanisms and design forces in ductile
substructures
The purpose of the capacity design procedure adopted in Section 4 is to ensure that the desired
yielding mechanism will form in the bridge prior to any other undesirable failure mode. Yielding
should only occur at locations in the ductile substructure elements such as columns, piers, and braces
where the damage can be readily inspected and/or repaired. For pile bents, this may not be the case
and flexural hinging may occur below the ground. This is acceptable as long as these inelastic hinges
are at reasonably accessible locations, (e.g., less than 10 m below the ground). When
capacity-protected members such as superstructures, cap beams, and foundations are designed for
the maximum force effects that can be developed by the ductile substructure elements attaining their
probable resistances, the probable resistances of the ductile substructure elements need to be
determined from the final section dimensions and details of the members chosen. These resistances
are normally somewhat larger than those required from the design procedure.
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Multiplying the nominal flexural resistance of concrete sections by 1.30 and that of steel sections by
1.25 reflects probable material strengths (steel or reinforcement yield strengths and concrete compressive
strength) being greater than the minimum specified strengths, the effects of strain hardening, and
enhancement of concrete compressive strength as a result of confinement provided by transverse
reinforcement (for concrete sections designed in accordance with these provisions).
In calculating the column, pier, or pile bent shear force, consideration must be given to the potential
locations of inelastic hinges. Because of the consequences of shear failure, it is recommended that
conservatism be used in locating possible inelastic hinges such that the smallest potential column length
be used with the probable flexural capacity to calculate the largest potential shear force for design.
C4.4.10.5 Minimum support length requirements for displacements
The purpose of Clause 4.4.10.5 is to provide a minimum support length for the superstructure in order to
prevent loss of support.
The length of support provided at abutments, columns, and hinge seats needs to accommodate
displacements resulting from the overall inelastic response of the bridge structure, possible independent
movement of different parts of the substructure, and out-of-phase rotation of abutments and columns
resulting from travelling surface wave motions.
The minimum support length also provides for possible translation and rotation of the footings due to
ground failure and/or deformations due to liquefaction.
In summary, the current state of the art precludes a good estimate of the differential column and
abutment displacements to be expected when a bridge is subjected to an earthquake. It is therefore
prudent to specify minimum support lengths at abutments, piers, and hinge seats to provide for the
effects discussed in this Clause.
The minimum support lengths specified depend on the deck length between expansion joints and the
column height, since both dimensions influence one or more of the factors that cause the differential
displacements.
C4.4.10.6 Longitudinal restrainers
Determining the forces in restrainers is a complex analytical problem due to many factors, such as
out-of-phase motions of supports, impact force effects in slack restrainers, and the stiffness of the
restrainers. The prescribed force level is 20% greater than 2.5A (see Clause 4.4.7.1) to approximate the
influence of the above parameters.
C4.5 Analysis
C4.5.1 General
The weight should take into account structural elements and other relevant loads including, but not
limited to, pier caps, abutments, columns, and footings. Other loads such as live loads may be included.
(Generally, the inertial effects of live loads are not included in the analysis; however, the probability of a
large live load being on the bridge during an earthquake should be considered when designing bridges
with high live-to-dead load ratios that are located in metropolitan areas where traffic congestion is likely to
occur.) The effective weight is the dead load of the superstructure plus portions of substructure elements
that contribute to inertial mass. For example, in simplified analysis, the effective weight can be taken as the
pier cap beams plus one-third of the participating column weight lumped with the superstructure dead
load.
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C4.5.3 Multi-span bridges
C4.5.3.1 Uniform-load method
The uniform load method, described in the following steps, may be used for both transverse and
longitudinal earthquake motions. It is essentially an equivalent static method of analysis that uses a
uniform lateral load to approximate the effect of seismic loads. The method is suitable for regular
bridges that respond principally in their fundamental mode of vibration. Whereas all displacements
and most member forces are calculated with good accuracy, the method is known to overestimate the
transverse shears at the abutments by up to 100%. If such conservatism is undesirable, the
single-mode spectral analysis method is recommended.
Step 1
Calculate the static displacements Vs (x) due to an assumed uniform load po as shown in
Figure C4.2. The uniform loading po is applied over the length of the bridge; it has units of
force/unit length and may be arbitrarily set equal to 1.0. The static displacement Vs (x) has
units of length.
Vs
Vs(x)
Vs(x)
Po
x
Po
(a) Plan transverse
loading
(b) Elevation longitudinal
loading
Figure C4.2
Bridge deck subjected to assumed transverse and
longitudinal loading
(See Clauses C4.5.3.1 and C4.5.3.2.)
Step 2
Calculate the bridge lateral stiffness, K, and total weight, W, from the following expressions:
K =
po L
Vs ,max
W = ∫ w ( x ) dx
where
L
= total length of the bridge
Vs ,max = maximum value of Vs (x)
w (x)
Step 3
= dead load of the bridge superstructure and tributary substructure, expressed as
weight per unit length of the bridge.
Calculate the period of the bridge, T, using the expression
T = 2π
W
gK
where
g
Step 4
= acceleration of gravity (length/time2)
Calculate the equivalent static earthquake loading pe from the expression
pe =
C smW
L
where
Csm
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= the dimensionless elastic seismic response coefficient given in Clause 4.4.7.1.
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pe
Step 5
= equivalent uniform static seismic loading per unit length of bridge corresponding to
the primary mode of vibration.
Calculate the displacements and member forces for use in design either by applying pe to the
structure and performing a second static analysis or by scaling the results of Step 1 by the ratio
pe/po.
C4.5.3.2 Single-mode spectral method
The single-mode spectral analysis described in the following steps may be used for both transverse and
longitudinal earthquake motions. Examples illustrating its application are given by AASHTO (1992) and
ATC (1983).
Step 1
Calculate the static displacements Vs (x) due to an assumed uniform loading po as shown in
Figure C4.2.
Step 2
Calculate factors α, β, and γ as:
a = ∫ Vs ( x ) dx
b = ∫ w ( x )Vs ( x ) dx
g = ∫ w ( x )Vs2 ( x ) dx
where
po
= a uniform load arbitrarily set equal to 1.0, kN/m
Vs (x) = deformation corresponding to po , m
w (x) = dead load of the bridge superstructure and tributary substructure expressed as weight
per unit length of the bridge, kN/m
Step 3
Calculate the period of the bridge as
Tm = 2π
g
po ga
where
g
= acceleration due to gravity, m/sec2
Step 4
Using Tm and the equation in Clause 4.4.7.1, calculate Csm
Step 5
Calculate the equivalent static earthquake loading pe (x) as
pe ( x ) =
bC sm
w ( x )Vs ( x )
Y
where
Csm
= the dimensionless elastic seismic response coefficient
pe (x) = the intensity of the equivalent static seismic loading corresponding to the primary
mode of vibration, kN/m
Step 6
Apply loading pe (x) to the structure and determine the resulting member force effects.
C4.5.3.3 Multi-mode spectral method
Closely spaced modes are those within 10% of each other in terms of natural frequency. Complete
quadratic modal combination methods (CQC), or the absolute sum of modal quantities, should be more
suitable for closely spaced modes.
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C4.5.3.4 Time-history method
The time histories of input acceleration used to describe the earthquake loads shall be selected in
consultation with the Regulatory Authority. Unless otherwise directed, five spectrum compatible time
histories shall be used when site specific time histories are not available. The spectrum used to
generate these five time histories shall be the same as that used for the modal analysis method, as
specified in Clause 4.4.7, modified for the appropriate soil profile. However, time histories should
preferably be modified to match a target site specific spectrum, if available.
The sensitivity of the numerical solution to the size of the time-step used for the analysis should be
determined. A sensitivity study should also be carried out to investigate the effects of variations in
assumed hysteretic properties of the structural elements.
For the purpose of inelastic analysis, energy absorbed by inelastic deformations in a structural
component may be assumed to be concentrated in plastic hinges and yield lines. For these sections,
moment-rotation hysteresis curves may be determined by using verified analytical material models.
Inelastic time-history analysis may be required for lifeline bridges or bridges with energy dissipation
or base-isolation mechanisms.
C4.5.3.5 Static pushover analysis
Examples illustrating the application of this step-by-step force deformation analysis procedure are
provided in California Department of Transportation Memo-to-Designers (Caltrans 1992a) and
Priestley and Seible (1992). This procedure may be used to trace the force-deformation response of
bents and determine plastic rotations and local ductility demands at plastic hinge locations. The
analysis also includes provisions to account for inadequately anchored or lapped reinforcement, joint
shear deformations, and degrading concrete shear capacity at plastic hinges for higher flexural
ductility demands. The output of the analysis includes local (member) and global ductility demands
and capacities. This procedure may be used in conjunction with a dynamic analysis of sections of the
bridge or a suitable global model of the complete structure.
C4.6 Foundations
C4.6.2 Liquefaction of foundation soils
Liquefaction is the process by which sediments below the water table temporarily lose strength as a
result of the application of earthquake-induced oscillatory shear stresses and behave as a viscous liquid
rather than a solid. The types of sediments that are most susceptible to liquefaction are granular soils
such as silts, sands, and gravels. Dense or stiff soils or rock do not liquefy under earthquake shaking.
Liquefaction of sediments can lead to loss of bearing strength, flow failure of slopes, lateral spreading
of ground, settlement, and increased lateral soil pressures on deep foundations and on retaining
structures such as bridge abutments.
These effects have led to bridge and approach fill movements and failures during earthquakes:
(a) Triggering of soil liquefaction
To determine if liquefaction will be triggered in a saturated granular soil, a comparison can be
made between the available cyclic resistance ratio, or cyclic strength of the soil, to the cyclic stress
ratio caused by the design earthquake.
There are two basic methods of assessing the cyclic resistance ratio of soils:
(i) Empirical methods based on correlation of the cyclic resistance ratio of the soil with the
relative density of the soil expressed in terms of the normalized penetration resistance
(principally Standard Penetration Test N values or static cone tip resistance, Qc values), with
the fines content passing the USS#200 sieve and the magnitude of the earthquake, for sites
that have and have not liquefied in earthquakes. A state-of-practice chart proposed by Seed
et al. (1984) is shown on Figure C4.3.
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0.6
Percent fines = 35 15 <
–5
Cyclic stress ratio, Teq/so'
0.5
Liquefaction
0.4
0.3
No liquefaction
0.2
For M = 7.5
earthquake
0.1
0
0
10
20
30
40
50
(N1)60 (blows/0.3m)
Figure C4.3
Typical relationship between stress ratio triggering liquefaction
and (N1 )60 values for silty sand (Seed et al. 1984)
(See Clause C4.6.2.)
The chart shown in Figure C4.3 is applicable for generally level ground conditions, for
confining pressures less than or equal to 100 kPa and for an earthquake magnitude of M7.5.
Corrections should be applied for sloping ground conditions, confining pressures larger than
100 kPa and for different magnitudes of earthquakes (Seed et al. 1984, Seed and Idriss 1971,
Seed and Idriss 1985, Pillai and Byrne 1994).
(ii) Laboratory testing of soil samples under cyclic loading that is representative of the design
earthquake. In this case, the cyclic resistance ratio is determined as the cyclic stress ratio required
to induce a predetermined level of shear strain or excess pore pressure with respect to the initial
effective confining stress, resulting from the equivalent design earthquake loading.
The laboratory assessment of liquefaction resistance may be based on cyclic triaxial or simple
shear testing with appropriate corrections for the differences in the loading paths in the
laboratory and in-situ (Seed and Idriss 1971).
The cyclic stress ratio caused by the earthquake can be estimated by one of the following methods:
(i) The Seed and Idriss (1971) simplified procedure, where the cyclic stress ratio is related to the
peak ground surface acceleration, the ratio of total to effective overburden stress, and a stress
reduction factor, as follows:
(Teq)/ σ ’o = 0.65 rd (a max/g) (σ ô / σ’o)
where
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Teq
= equivalent cyclic shearing stress
a max
= maximum or effective peak acceleration at the ground surface
σô
σ ’o
= total overburden pressure on sand layer under consideration
= initial effective overburden pressure on sand layer under consideration
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rd
= stress reduction factor varying from a value of 1 at the ground surface to 0.9 at a
depth of about 9 m
g
= acceleration due to gravity
(N1) 60 = normalized standard penetration resistance.
(ii) Site-specific ground response analyses carried out using a dynamic wave propagation
analysis program such as SHAKE (Schnabel et al. 1972) or FLUSH (Lysmer et al. 1975).
A schematic comparison plot of the available cyclic resistance ratio and the required
penetration resistance with depth below ground surface is shown on Figure C4.4 with the
potentially liquefiable zone hatched (Seed et al. 1984, Robertson and Campanella 1985).
The liquefaction resistance of fine grained soils that contain more than 35% passing the
USS#200 sieve, e.g., silts and clays, depends on the plasticity of the fines and the amount of
clay size particles. The state-of-practice is to use the Chinese criteria (Marcuson et al. 1990),
given below, to evaluate the liquefaction potential of these soils:
— Percent finer than 0.005 mm size < 15%
— Liquid limit (wL) < 35%
— Water content > 0.9wL
If the soil meets the above criteria, it is potentially liquefiable.
The liquefaction potential of fine grained soils can also be evaluated by laboratory testing
of representative undisturbed soil samples.
0
Standard penetration or
static cone resistance
0
Depth, m
Zone of potential
liquefaction
Available resistance
Required resistance
Figure C4.4
Comparison of available and required resistance
in terms of SPT or static cone resistance
(See Clause C4.6.2.)
(b) Soil liquefaction-induced ground movements
Soil liquefaction may cause large lateral and vertical ground movements, particularly near bridge
abutments.
In areas with significant ground slopes (greater than 5%), soil liquefaction can result in flow
failures, causing very large lateral movements. The potential for such flow failures may be
evaluated using conventional static slope stability analysis techniques, where residual shear
strengths are assigned to the liquefied soils. The residual shear strength of liquefied soil may be
obtained from correlations proposed by Seed and Harder (1990) or appropriate laboratory tests.
In areas with gentle slopes (up to 5%), soil liquefaction at depth may result in lateral spreading of
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the surficial crust. Nonliquefiable crustal soils normally break into blocks because of the movement.
The lateral movements are caused by strain softening of liquefied soil and earthquake induced cyclic
inertia forces. The lateral movements may be estimated using the empirical method proposed by
Bartlett and Youd (1992). Liquefaction-induced lateral ground movements may be large even in areas
where a flow failure is not a possibility.
As well as lateral movements, vertical settlement of the ground surface may occur as a result of
dissipation of excess pore water pressures generated by an earthquake. These settlements are in
general proportional to the thickness of the liquefiable portion of the soil deposit and the relative
density of soil, and can be estimated using the empirical chart proposed by Tokimatsu and Seed
(1987). The presence of foundations that penetrate the liquefiable soils and zones of improved
ground may reduce the liquefaction-induced ground movements. The assessment of the impact of
foundations on liquefaction-induced bridge movements may be carried out using soil-structure
interaction techniques.
C4.6.3 Stability of slopes
The stability of natural and manmade slopes that do not pose a hazard with respect to soil liquefaction,
may be evaluated using conventional pseudo-static methods of slope stability analyses. If liquefaction is
predicted to occur, analyses may be carried out using appropriate reduced soil strength properties and
increased pore water pressures for the potentially liquefiable zones.
A calculated factor of safety of unity or less, under an earthquake-induced peak ground acceleration,
does not indicate full-scale failure of the slope. This is because the soil mass is subjected to the peak
acceleration in a given direction only for a very short period of time. In such instances, the design may be
based on displacements that occur during the period of shaking. Simplified Newmark sliding block or
equivalent models may be utilized to assess the approximate magnitude of ground movements (Newmark
1965, Houston et al. 1987). A more detailed analysis may be carried out using nonlinear pseudo-static or
dynamic finite element or finite difference methods.
C4.6.4 Seismic forces on abutments and retaining walls
Seismic shaking increases the pressure on the back of a retaining structure and can induce movement or
failure of bridge abutments during or following an earthquake. The increase in pressure may be allowed
for by the method suggested by Mononobe (1929) and Okabe (1926). Their expression for the combined
coefficient of static and seismic active earth pressure, KAE , on the back of a wall is as follows:
K AE =
cos2 (j − q − b )
y A cos q cos2 b cos (d + b + q )
where
ϕ = angle of friction of backfill soil
θ = arc tan (kh /1 – kv)
kh = horizontal acceleration coefficient
kv = vertical acceleration coefficient
2
ψA =
⎧⎪
sin (j + d ) sin (j − q − i ) ⎫⎪
⎨1+
⎬
cos (d + b + q ) cos ( i − b ) ⎪⎭
⎪⎩
δ = angle of friction between the soil and wall and β and i are defined in Figure C4.5
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i
b
Figure C4.5
Definition of β and i
(See Clause C4.6.4.)
The equivalent expression for the passive earth pressure coefficient if the abutment is being pushed
into the backfill is
K PE =
cos2 (j − q + b )
y P cos q cos2 b cos (d − b + q )
where
2
⎧⎪
sin (j + d ) sin (j − q + i ) ⎫⎪
y P = ⎨1+
⎬
cos (d − b + q ) cos (i − b ) ⎭⎪
⎩⎪
A graphical solution for the simple case of a vertical wall and horizontal backfill is given in Figure C4.6.
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Seismic active pressure coefficient, kAE
1.0
0.8
j = 20˚
25˚
0.6
30˚
35˚
40˚
0.4
45˚
b = i = Kv = 0
d = j/2
0.2
0.0
0.0
0.1
0.2
0.3
0.4
0.5
Horizontal seismic coefficient, kh
Figure C4.6
Effect of soil friction angle on seismic active pressure coefficient
(Elms and Martin 1979)
(See Clause C4.6.4.)
If peak ground accelerations are used in the Mononobe-Okabe expression, the size of retaining
structures may be excessive, and it has been suggested in AASHTO (1995) that it may be preferable to
design for a small tolerable displacement of the abutment or retaining structure in earthquake areas.
Elms and Martin (1979) have shown for several simplified examples that a value of kh = A /2 is adequate
for most design purposes, provided that allowance is made for an outward displacement of the abutment
of up to 250A mm, where A is the zonal acceleration ratio.
For nonyielding (i.e., virtually fixed and unable to move) abutments that are restrained against lateral
movement such as by tie-backs or batter piles, AASHTO (1995) suggests use of kh = 3/2A in the
Mononobe-Okabe equation.
A more detailed discussion of the above is given in AASHTO (1995), and Fang and Chen (1995).
C4.6.5 Soil-structure interaction
Soil-structure interaction analysis is normally required for lifeline and emergency-route bridges with Soil
Profiles III and IV in Seismic Performance Zone 2 and for all bridges in Seismic Performance Zones 3 and 4.
The interaction of soil-structure systems to earthquake loading is complex. Although the importance of
soil-structure interaction effects are recognized, the appropriate treatment of nonlinear effects resulting
from the nonlinear behaviour of the soil, soil-structure separation effects, and influence of neighbouring
structures that may be important in certain cases are often ignored due to this complexity.
In the analysis of bridge foundations, it is common to replace the soil-foundation system beneath the
footing or the pile cap by compliance springs. In the case of spread footings, the response of the
foundation may be represented by six compliance springs (for the six degrees-of-freedom) that are
uncoupled from each other.
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In the case of pile foundations, two methods can be followed:
(a) represent the complete soil-pile system by six uncoupled compliance springs at pile cap level; or
(b) represent the soil-reaction that develops as a result of the soil-pile interaction by a series of springs
distributed along the length of the pile. In this case, the pile itself may be modelled as a structural
member.
The compliance springs may be dependent on a number of variables including the shear modulus of
soil, elastic modulus of the structural elements, size, shape, and type of foundations, and group
interaction effects.
It is common to ignore the effects of frequency of excitation. The influence of some of the above
variables may not be significant, and may be eliminated by carrying out sensitivity analyses.
Soil-structure interaction analyses may require several iterations and considerable interaction
between the Structural and Geotechnical Engineers.
Shear modulus of soil
The shear modulus of soil is dependent on the type of soil, shear strain level, effective confining
pressure and void ratio. Typical variations in the shear moduli with shear strain for soils are shown in
Figures C4.7 and C4.8 (Seed et al. 1986, Sun et al. 1988, Zen and Higuchi 1984).
The earthquake loading induced pore water pressures reduce the shear modulus of the soil. In the
extreme case that liquefaction is triggered, a 500- to 1000-fold reduction in the shear modulus may
occur. Such reduced shear moduli coupled with soil movements may have a significant impact on the
performance of foundations.
Shear modulus of g = 10–4 percent
Shear modulus of shear strain g
1.0
0.8
0.6
0.4
Range of values
0.2
0
10–4
10–3
10–2
10–1
Shear strain, g = percent
Figure C4.7
Variation of shear modulus with shear strain for sands
(Seed et al. 1986)
(See Clause C4.6.5.)
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1.0
0.8
G/Gmax
0.6
Plasticity index
0.4
NP
10
20
30
50
70
0.2
0.0
10–4
10–3
10–2
10–1
1
10
Shear strain, percent
Figure C4.8
Variation of shear modulus with shear strain for clays
(Zen and Higuchi 1984)
(See Clause C4.6.5.)
Compliance springs for spread footings
Compliance springs that represent the load-deformation behaviour of bridge spread foundations may be
computed using the simplified procedures outlined by Gazetas (1983) and Dobry and Gazetas (1984). The
following variables may have an impact on the compliance springs:
(a) soil stratigraphy and properties of each layer;
(b) depth of embedment of foundation;
(c) proximity of the foundation to a stiff layer such as bedrock or glacial till or sloping ground; and
(d) shape of foundation.
A range of values for the compliance springs may be considered to take into consideration the
uncertainties and variations associated with estimating some or all of the above variables and the impact
of reduced soil shear modulus resulting from shear strains.
Compliance springs for pile foundations
Compliance springs that represent the load-deformation behaviour of pile foundations may be estimated
by first computing the response of a single pile and thereafter reducing the stiffness to take into
consideration the pile group interaction effects. The compliance springs may depend on the degree of
permissible pile-head rotation, extent of soil-pile separation at the interface, stiffness contrast between the
pile and soil, and the degree of interaction among piles, which in turn depends on the direction of
loading, mode of excitation, and the spacing of piles with respect to their diameter. Methods of
computing the compliance springs are outlined in Novak et al. (1981), El Sharnouby and Novak (1986),
Poulos and Davis (1974), and Poulos (1989).
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The nonlinear soil reaction that develops along the length of the pile is dependent on the soil type
and degradation of material behaviour under cyclic loading. The variation in soil-reaction with lateral
and vertical pile movement is commonly referred to as “p-y” and “t-z” curves.
These curves may be established following procedures outlined by API (1991) for a single soil-pile
system and thereafter modified for pile group interaction effects. In this method, the contrasting
properties of soil strata can be taken into consideration. The impact of superstructure inertia loads and
soil movement effects on the piles may be evaluated using a pseudo-static pile analysis program such
as LATPILE (Byrne and Janzen 1985, Reese and Sullivan 1980) or a dynamic pile analysis program, e.g.,
SPASM (Matlock et al. 1979).
C4.6.6 Fill settlement and approach slabs
Settlement (or approach) slabs are intended to provide continuity between the bridge deck and the
abutment fill in the case of approach fill settlement. Settlement slabs should be positively tied to the
abutment to prevent them from pulling away and becoming ineffective. They should be incorporated
in all bridges in Seismic Performance Zone 4. To minimize the discontinuity at the abutment following
an earthquake, settlement slabs should be provided with a minimum length of 3 m. Settlement slabs
should be designed as simple span reinforced concrete slabs spanning their full length.
C4.7 Concrete structures
C4.7.1 General
Clause 4.7 is based on the Ontario Highway Bridge Design Code (1991) and AASHTO (1992). The Loma
Prieta Earthquake of 1989 provided new insights into the behaviour of concrete details under seismic
loads and the results of a number of research projects that were initiated are currently producing
information that is useful for both the design of new structures and the retrofitting of existing
structures. Unfortunately, much of this information is still evolving and bridge designers working on
Seismic Performance Zones 3 and 4 should avail themselves of current research reports and other
literature to augment the requirements of Clause 4.7.
The Loma Prieta Earthquake confirmed the vulnerability of columns with inadequate core
confinement and inadequate anchorage of longitudinal reinforcement. In addition, new areas of
concern emerged, including
(a) lack of adequate reinforcement for positive moments that may occur in the superstructure over
monolithic supports when the structure is subjected to longitudinal dynamic loads;
(b) lack of adequate strength in joints between columns and bent caps under transverse dynamic
loads; and
(c) inadequate reinforcement for torsion, particularly in outrigger-type bent caps.
The purpose of the additional detailing requirements of Clause 4.7.1 is to increase the probability,
especially for bridges located in Seismic Performance Zones 3 and 4, such that the potential for failures
observed in past earthquakes is minimized. The column detailing requirements are such that a column
is provided with a reasonable ductility and forced to yield in flexure, and that the potential for a shear,
compression, or loss of anchorage mode of failure is minimized. The detailing requirements for
wall-type piers provide for some inelastic capacity; however, the response modification factors
specified for wall-type piers in Section 4 are such that the anticipated inelastic capacity is significantly
less than that of columns.
C4.7.2 Seismic Performance Zone 1
Clause 4.7.2 is intended to provide for connection of the superstructure to the substructure only. The
force specified in Clause 4.4.10.2 is not intended to be transferred to and resisted by the substructure.
The resistance is normally provided by bearing restrainers, shear friction action, or other methods.
Where the superstructure supports are cast integrally, the longitudinal reinforcing steel in the column
or pier should normally be adequate to satisfy this provision.
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C4.7.3 Seismic Performance Zone 2
Bridges in Seismic Performance Zone 2 have a reasonable probability of being subjected to seismic forces
that will cause yielding of the columns. Therefore the columns should have some ductility capacity,
although it is recognized that the ductility demand will not be as great as for columns of bridges in Seismic
Performance Zones 3 and 4. The most important requirement to ensure some level of ductility is the
transverse reinforcement requirement. This will prevent buckling of the longitudinal steel and provide
confinement for the core of the column.
C4.7.4 Seismic Performance Zones 3 and 4
C4.7.4.2 Column requirements
The definition of a column in Clause 4.7.4.2 is provided as a guideline to differentiate between the design
requirements for a wall-type pier and for a column. Where a column or wall-type pier is above or below
the recommended criterion, it can be considered either as a column or a wall-type pier, provided the
appropriate response modification factor of Section 4 and the appropriate requirements of Clause 4.7.4.2
or 4.7.4.3 are used. For columns with a clear height to maximum cross-section dimension ratio less than
2.5, the requirements resulting from plastic hinging generally exceed the elastic design forces and
consequently the requirements of Clause 4.7.4.2 would not be applicable.
A pier may be designed as a wall-type pier in its strong direction and a column in its weak direction.
C4.7.4.2.2 Longitudinal reinforcement
The lower limit on the column reinforcement reflects the traditional concern for the effect of
time-dependent deformations, as well as the desire to avoid a large difference between the flexural
cracking and yield moments. The 6% maximum ratio is to avoid congestion, extensive shrinkage cracking,
and to permit anchorage of the longitudinal steel. Wherever possible, the upper limit should be reduced
to 4%. The 200 mm maximum spacing is specified to help confine the column core.
C4.7.4.2.3 Flexural resistance
Columns are required to be designed biaxially and checked for both the minimum and maximum axial
loads.
C4.7.4.2.4 Column shear and transverse reinforcement
The requirements of Clause 4.7.4.2.4 are intended to minimize the potential for a column shear failure.
The shear force is specified as that capable of being developed by either flexural yielding of the columns or
the elastic shear force. This is because of the potential for superstructure collapse if a column fails in shear.
Particular attention needs to be given to flared columns and the effect the flares have on the stiffness of
the column. During the Northridge earthquake, some bridges exhibited shear failures (Mitchell et al.
1995) of columns flared for architectural purposes. The use of this type of column is not recommended
unless the column is properly designed and detailed.
A column may yield in the longitudinal or transverse direction; hence for noncircular columns, the shear
force corresponding to the maximum shear developed in either direction should be used for the
determination of the transverse reinforcement.
The concrete contribution to shear resistance is not reliable within the plastic hinge zone, particularly at
low axial load levels, because of full-section cracking under load reversals. As a result, the concrete shear
contribution should be neglected for axial load levels less than 0.10 f’c Ag.
C4.7.4.2.5 Transverse reinforcement for confinement at plastic hinge
regions
Plastic hinge regions are generally located at the top and bottom of columns and pile bents. The largest of
the requirements of Clause 4.7.4.2.5 or that of Clause 4.7.4.2.4 should govern the choice of the transverse
reinforcement.
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The main function of the transverse reinforcement specified in Clause 4.7.4.2.5 is to ensure that the
axial load carried by the column after spalling of the concrete cover will at least equal the load carried
before spalling. The spacing of the confining reinforcement is also important (see Clause C4.7.4.2.6).
The expression for ps in Clause 8.14.4.2 is based on the arbitrary concept that, under axial
compressive loading, the resistance of the spirally reinforced column before loss of cover concrete is
equal to that with the cover concrete destroyed and that the spiral reinforcement is stressed to its
useful limit.
Loss of concrete cover in the plastic hinge zone, as a result of spalling, requires careful detailing of
the confining steel. It is clearly inadequate simply to lap the spiral reinforcement. If the concrete cover
spalls, the spiral will lose its anchorage. Similarly, rectangular ties should be anchored by bending ends
back into the core.
Figure C4.9 illustrates column hoops and cross-tie details. The total area of the reinforcement should
be determined for both principal axes of a rectangular or oblong column and the greater value should
be used.
While Clause 4.7.4.2.5 allows the use of either spirals or ties for transverse column reinforcement,
the use of spirals is recommended as the more effective and economical solution.
135˚
< 150 mm
clear
< 150 mm
clear
< 150 mm
clear
Seismic hook
< 150 mm
clear
< 150 mm
clear
These ties need not extend full length in
the strong direction of wall-type piers
< 150 mm
clear
Figure C4.9
Hoops and cross-tie arrangements
(See Clause C4.7.4.2.5.)
C4.7.4.2.6 Spacing of transverse reinforcement for confinement
The spacing limit of “six times the diameter of the longitudinal bar” is aimed at preventing buckling of
the longitudinal bars between the spirals and hoops.
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Where more than one spiral cage is used to confine an oblong column core, the spirals should be
interlocked with longitudinal bars as shown in Figure C4.10.
Spiral
reinforcement
Minimum of 4
interlocking bars
200
max
Core
diameter,
Dc
<
– 0.75 Dc
Figure C4.10
Details of interlocking spirals in oblong columns
(See Clause C4.7.4.2.6.)
C4.7.4.2.7 Splices
It is often convenient to lap longitudinal reinforcement with dowels at the column base. This is undesirable
for seismic performance for two reasons:
(a) the splice occurs in a potential plastic hinge region where requirements for bond are critical; and
(b) lapping the main reinforcement tends to concentrate inelastic deformation close to the base and
reduce the effective plastic hinge length as a result of the increased strength of the column over the
lapping region. This may result in a severe local curvature demand.
C4.7.4.3 Wall-type piers
The requirements of Clause 4.7.4.3 are based on limited data available on the behaviour of wall-type piers
in the inelastic range. Consequently, the response modification factor in Section 4 for wall-type piers is
based on the assumption of minimal inelastic behaviour.
The requirement that pv > ph is intended to avoid the possibility of having inadequate web
reinforcement in piers that are short in comparison to their height. Splices are staggered in an effort to
avoid weak sections.
The requirement of horizontal and vertical reinforcement in each face of walls carrying substantial
shears is based on the premise that two layers of reinforcement will tend to “basket” the concrete and
retain the integrity of the wall after cracking of the concrete.
C4.7.4.4 Column connections
A column connection, as referred to in Clause 4.7.4.4, is the vertical extension of the column
reinforcement into the adjoining component.
The integrity of the column is important if the columns are to develop their flexural capacity and the
1.25 factor for the development length has therefore been specified. The transverse confining
reinforcement of the column should be continued a distance into the joint to avoid a plane of weakness at
the interface.
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The strength of the column connections in a column cap is relatively insensitive to the amount of
transverse reinforcement, provided that there is a minimum amount, and the shear resistance is
limited to the value specified.
C4.8 Steel structures
C4.8.1 General
The objective of Clause 4.8.1 is to provide details for establishing ductility consistent with the R-values
assumed in the analysis and design of steel structures.
Values of R greater than 1.0 can be justified only if the structure has the ability to undergo inelastic
deformations without significant loss of resistance. The degree of redundancy is also considered
because alternative load paths reduce the possibility of serious consequences arising from failure of a
member and enhance the energy dissipation. Hence a lower R-value is used for ductile single column
structures due to their inherently low redundancy.
Until recently, only a few steel bridges had been seriously damaged in earthquakes. One span of a
large steel truss bridge collapsed due to loss of support at its bearings during the 1989 Loma Prieta
earthquake, and another bridge suffered severe bearing damage (EERI 1990). The end diaphragms of
some steel bridges suffered damage in a subsequent earthquake in Northern California
(Roberts 1992). During the 1994 Northridge earthquake, some steel bridges, located very close to the
epicentre, sustained damage to either their reinforced concrete abutments, connections between
concrete substructures and steel superstructures, steel diaphragms, or structural components near the
diaphragms (Astaneh-Asl et al. 1994). However, a large number of steel bridges were damaged by the
1995 Hyogoken-Nanbu (Kobe) earthquake. The concentration of steel bridges in the area of severe
ground motion was considerably larger than for any previous earthquake and some steel bridges
collapsed. Many steel piers, bearings, seismic restrainers, and superstructure components suffered
significant damage (Bruneau et al. 1996). This experience emphasizes the importance of ductile
detailing in the critical elements of steel bridges.
In several instances during earthquakes, steel bridges have experienced failures in the foundations
and loss of support due to superstructure movements and lack of restraint (Kawashima 1992, Mitchell
and Tinawi 1992). The design requirements in Clauses 4.4.10.5 and 4.4.10.6 are intended to prevent
loss of support due to foundation deficiencies and soil liquefaction.
Research on the seismic behaviour of steel bridges (Astaneh-Asl et al. 1993, Dicleli and Bruneau
1995a, 1995, Seim et al. 1993) and findings from recent seismic evaluation and rehabilitation projects
(FHA/CALTRANS 1995 and 1997, Shirolé and Malik 1993) further confirm that seismically induced
damage is likely in steel bridges subjected to large earthquakes and that appropriate measures need to
be taken to ensure satisfactory seismic performance.
Care needs to be taken to ensure that load paths are provided for the entire structure. Applying the
concept of capacity design, the load effect arising from the inelastic deformations of part of the
structure needs to be considered in the design of other elements that are within its load path. Similarly,
the load redistribution following the yielding or buckling of components, such as braces, should also
be taken into account.
However, it is important to realize that many components of steel bridges are not expected to
behave in a cyclic inelastic manner during an earthquake. Hence, the provisions of Clause 4.8 are
intended to apply to a limited but key number of components in order to ensure satisfactory bridge
seismic performance. Although these new provisions are sometimes conceptually similar to the
seismic-resistant provisions applicable to buildings, a large number of differences exist to account for
the seismic behaviour germane to steel bridges.
The prevailing philosophy in the seismic resistant design of buildings is to force plastic hinging to
occur in the beams of frames to better distribute hysteretic energy distribution throughout all storeys
and avoid soft-storey type failure mechanisms. However, for steel bridges such a constraint is not
realistic, nor is it generally desirable. Steel bridges typically have deep beams that are not typically
Class 1 sections, and that are much stiffer and stronger flexurally than their supporting steel columns.
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Moreover, bridge structures in Canada are generally “single-storey” structures, and all the hysteretic
energy dissipated is concentrated in this single storey. It is understood that special care would be needed
to ensure the satisfactory ductile response of multilevel steel frame bents.
Because the behaviour of connections will often be critical for good performance under severe ground
motions, the Engineer needs not only to provide adequate connection design loads but needs to also
provide specifications for the type and details of the connections.
A number of welded beam-to-column connections exhibited unsatisfactorily brittle behaviour during
the Northridge earthquake. This is currently the subject of intensive research and it is prudent to take
special care to ensure the quality of welds near regions of expected inelastic action.
C4.8.2 Materials
The ductile substructure elements are the parts of the structure that are expected to absorb energy by
undergoing inelastic deformations. The steel grades listed represent some structural steels that possess the
following mechanical properties:
(a) Fy ≤ 0.8Fu ;
(b) longitudinal elongation in 50 mm ≥ 20%; and
(c) probable-to-nominal strength ratios are consistent with the overstrength factors chosen in
Clause 4.4.10.4.3.
Other steels, such as ASTM A 36 grade steel, that satisfy the requirements of Items (a) and (b) but may
have a probable strength substantially greater than the specified strength may only be used if the
overstrength factors are increased accordingly (AISC 1994).
Grades 350AT, 300WT, and 350WT have toughness properties suitable for ductile substructure elements
exposed to low temperatures.
C4.8.3 Sway stability effects
In the computation of second-order effects, the linear amplification procedure, as outlined in Appendix J
of the Supplement to the National Building Code of Canada (1995) may be used.
C4.8.4 Steel substructures
C4.8.4.1 General
Clause 4.8.4 does not apply to substructures with primary braces or beams framing into the intermediate
height of columns to form multi-tier frames or bents.
C4.8.4.3 Seismic Performance Zone 2
C4.8.4.3.1 General
In conformance with the general requirements outlined in Clause 4.4.10.3, the design requirements for
Zone 2 are somewhat less stringent than those stipulated for higher Zones. See Clause C4.8.4.4. The
nominal capacity of an element is equal to its resistance with φs = 1.0.
C4.8.4.3.2 Ductile moment-resisting frames and bents
The column axial load restriction for columns is less stringent than the requirement for Zones 3 and 4. See
Clause C4.8.4.4.2.2.
C4.8.4.3.3 Ductile single-column structures
See Clause C4.8.4.4.2.
C4.8.4.3.4 Ductile concentrically braced frames
See Clause C4.8.4.4.3.
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C4.8.4.3.5 Concentrically braced frames and bents with nominal
ductility
See Clause C4.8.4.4.4. The ductility measures required for chevron braces due to high ductility
demand for Zones 3 and 4 need not apply. Also, see Clause C4.8.4.4.4.6.
C4.8.4.4 Seismic Performance Zones 3 and 4
C4.8.4.4.1 General
Ductile substructure elements are the parts of the structure that are expected to absorb energy and
undergo significant inelastic deformations while maintaining their strength and stability. Applying the
concept of capacity design, an element is generally considered to be capacity-protected if the critical
element reaches its capacity before the capacity-protected element experiences the corresponding
load effect exceeding its resistance. The probable capacity of an element is equal to its nominal
capacity increased to account for overstrength due to higher yield than specified yield and
strain-hardening effects. The load combinations for design of capacity-protected elements in Clause
4.8.4.4.1 represent loads due to the extreme event earthquake combined with the permanent loads.
Alternatively, ductile substructure elements can be designed to resist the full elastic seismic load,
calculated using R = 1. However, this alternative usually results in higher loads.
C4.8.4.4.2 Ductile moment-resisting frames and single-column
structures
C4.8.4.4.2.1 General
Ductile moment-resisting frames are commonly used for building structures in regions of high seismic
risk. Properly detailed moment-resisting frames exhibit highly ductile behaviour and are highly
redundant.
Although beams, columns, and panel zones in their intersections can all be designed, detailed, and
braced to undergo severe inelastic straining and absorb energy (Redwood et al. 1990,
CAN/CSA-S16.1-94), Clause 4.8.4.4.2.1 concentrates on common bridge structures in which the
beams are not Class 1 sections and in which the system is therefore proportioned so that plastic hinges
form in the columns.
C4.8.4.4.2.2 Columns
At plastic hinge locations, members absorb energy by undergoing inelastic cyclic bending while
maintaining their resistances. Therefore, plastic design rules apply, namely, requirements for Class 1
sections, web-to-flange weld capacity, web shear resistance, lateral support, etc.
The axial load in the column is also restricted to avoid early deterioration of beam-column flexural
strengths and ductility when subject to high axial loads.
C4.8.4.4.2.3 Beams
Since plastic hinges are not expected to form in beams, beams need not conform to plastic design
requirements.
The requirement for beam resistance are consistent with the capacity-design procedure adopted in
Section 4. The beams should either resist the full elastic loads or be capacity-protected. In the extreme
load situation, the capacity-protected beams are required to have nominal resistances of not less than
the combined effects corresponding to the plastic hinges in the columns attaining their probable
capacity and the probable companion permanent load acting directly on the beams. The probable
capacity of a column should account for the overstrength due to higher yield than specified yield and
strain hardening effects. The amplifier of 1.25, in conjunction with the beams’ resistance factor of
0.95, gives an effective overstrength factor of 1.32 (i.e., 1.25/0.95). This is consistent with
CAN/CSA-S16.1-94 (i.e., 1.2/0.90 = 1.33). If column steels other than those listed in Clause 4.8.2 are
used, an appropriate overstrength factor needs to be established. (See also Clause C4.8.2.)
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C4.8.4.4.2.4 Seismic design forces for panel zones and connections
The panel zone should either resist the full elastic load or be capacity-protected.
Column base connections should also resist the full elastic loads or be capacity-protected, unless they
are designed and detailed to dissipate energy.
C4.8.4.4.2.5 Additional requirements for panel zones and connections
Clause 4.8.4.4.2.5 ensures that the beam-to-column connections either can resist the full elastic loads or
are capacity-protected by requiring the connections to resist what the beam is required to resist.
Field-welded connections that rely on unreinforced beam-flange-to-column welds to develop the
beam’s plastic moment capacity did not perform well in building frames (Engelhardt et al. 1995). Much
research is underway in this important area. Clause 4.8.4.4.2.5 requires that the beams and connections
resist full elastic loads or be capacity-protected and accordingly the high demand for connection rotation
does not apply. In addition, adequate weld quality and details need to be ensured and field welding
should be avoided if possible.
Column-to-beam connections should either resist the full elastic loads or be capacity-protected. Column
flange reinforcement may be required to shift the location of the plastic hinge in the column away from
the beam flange.
C4.8.4.4.3 Ductile concentrically braced frames
C4.8.4.4.3.1 General
Ductile concentrically braced frames are those in which the centrelines of diagonal braces, beams, and
columns are approximately concurrent with little or no joint eccentricity. Inelastic straining must take place
in bracing members subjected principally to axial loads.
Compression members can absorb considerable energy by inelastic bending after buckling and in
subsequent straightening after load reversal, but the amount of absorbed energy is small for slender
members. Local buckling or buckling of components of built-up members also limits energy absorption.
C4.8.4.4.3.2 Bracing systems
In any planar frame, this requirement ensures some redundancy and also similarity between the
load-deflection characteristics in the two opposite sway directions. A significant proportion of the
horizontal shear needs to be carried by tension braces so that compression brace buckling will not cause a
catastrophic loss in overall horizontal shear capacity. Clause 4.8.4.4.3.2 also excludes bracing systems that
have not exhibited the ductile behaviour expected for ductile concentrically braced frames.
C4.8.4.4.3.3 Bracing members
The member slenderness ratio is restricted because the energy absorbed by plastic bending of the braces
diminishes with increased slenderness. Early local buckling of braces prohibits the braced frames from
sustaining many cycles of load reversal. Both laboratory tests and real earthquake observations have
confirmed that premature local buckling significantly shortens the fracture life of HSS braces. The more
stringent requirement on the b / t ratio for rectangular tubular sections subjected to cyclic loading is based
on tests (Tang and Goel 1987, Uang and Bertero 1986).
The reduction factor on the factored compressive resistance takes into account the fact that, under
cyclic loading, the compressive resistance diminishes with slenderness ratio. This reduction stabilizes after
a few cycles. It is sufficient that the combined resistance of the tension and compression braces
(considering the reduced resistance) acting in the same plane exceeds the factored load effect.
C4.8.4.4.3.4 Brace connections
Connections need to be designed to ensure that the bracing member is capable of yielding the gross
section. However, their resistance need not exceed the combined effect due to full elastic seismic load and
permanent loads, if the member is grossly oversized.
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Eccentricities that are normally considered negligible (for example, at the ends of bolted or welded
angle members) may influence the failure mode of connections subjected to cyclic load (Astaneh et al.
1986).
A brace that buckles out-of-plane forms a plastic hinge at mid-length and hinges in the gusset plate
at each end. When braces attached to a single gusset plate buckle out-of-plane, there is a tendency for
the plate to tear if it is restrained by its attachment to the adjacent frame members (Astaneh et al.
1986). Provision of a clear distance, approximately twice the plate thickness, between the end of the
brace and the adjacent members allows the plastic hinge to form in the plate and eliminates the
restraint. When in-plane buckling of the brace may occur, ductile rotational behaviour should be
possible either in the brace or in the joint.
Buckling of double angle braces (legs back-to-back) about the axis of symmetry leads to transfer of
load from one angle to the other, thus imposing significant loading on the stitch fastener (Astaneh et
al. 1986).
C4.8.4.4.3.5 Columns, beams, and other connections
Columns, beams, beams-to-column connections and column splices that participate in the
lateral-load-resisting system also need to be designed to ensure that a continuous load path can be
maintained. The redistributed loads resulting from buckled compressive brace loads being transferred
to the tension brace need to be considered in beams and columns as well as in connections. The
reduced compressive brace resistance needs to be considered since it creates a more critical condition.
The unreduced resistance also needs to be considered because it may give a more critical loading
condition in the early loading cycles (Redwood and Channagiri 1991).
Other connections that participate in the lateral-load-resisting system also need to be designed to
ensure that a continuous load path can be maintained. Therefore,
(a) they need to resist the combined load effect corresponding to the bracing connection loads and
the permanent loads that they need to also transfer; and
(b) they need to also resist the load effect due to load redistribution following brace yielding or
buckling, unless they can resist the full elastic seismic load and the permanent loads.
C4.8.4.4.4 Concentrically braced frames with nominal ductility
C4.8.4.4.4.1 General
Ductile concentrically braced frames and bents with nominal ductility are required to resist higher
loads (R = 2.5) than ductile concentrically braced frames because they are not designed and detailed
to undergo the same level of inelastic deformations.
C4.8.4.4.4.2 Bracing systems
This category of bracing systems includes
(a) tension diagonal bracing;
(b) chevron bracing (or V-bracing); and
(c) direct tension-compression diagonal bracing systems that do not satisfy all the requirements for
ductile concentrically braced frames, except systems in which all braces are oriented in the same
direction and may be subjected to compression simultaneously should be avoided.
Analytical and experimental research, as well as observations following past earthquakes, have
demonstrated that K-bracing systems are poor dissipators of seismic energy. The members to which
such braces are connected can also be adversely affected by the lateral force introduced at the
connection point of both braces on that member due to the unequal compression buckling and
tension yielding capacities of the braces.
Knee-braced systems in which the columns are subjected to significant bending moments are
beyond the scope of Clause 4.8.4.4.4.2.
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C4.8.4.4.4.3 Bracing members
Braces in this category of braced systems are required to resist higher loads but less strict requirements
against local buckling, as compared to Clause 4.8.4.4.3.3.
C4.8.4.4.4.4 Brace connections
The additional factor of 1.10 for tension-only bracing systems is intended to ensure, for the slender
members used in this case, that the impact resulting when the slack of the buckled member is taken up
does not cause connection failure. Details leading to limited zones of yielding, such as those occurring at
partial joint penetration groove welds, should be avoided.
C4.8.4.4.4.5 Columns, beams, and connections
See Clause C4.8.4.4.3.5.
C4.8.4.4.4.6 Chevron-braced and V-braced systems
The beams intersected by the braces need to resist the load redistribution following brace yielding and
buckling either elastically or inelastically.
If the beam remains elastic, it needs to support the concentrated load at the brace intersecting point
due to the resulting difference in the vertical components of the brace forces. Lateral bracing may in this
case be required to resist some torsional load due to the buckling brace.
If the beam is a Class 1 section, a plastic hinge can be allowed to form at the brace intersection point. In
the chevron braced configuration, where the beam is supported from below, it needs to at least be able to
support the permanent loads without support from the braces. For this load case, the nominal resistance
may be used. Lateral bracing resistance is also required to be higher than the brace load for structures
analyzed elastically because of higher ductility demand on such a plastic hinge. The axial force in the beam
should be considered when determining the Class of section.
The braces need to be detailed as for braces of ductile concentrically braced frames because of the
potentially high ductility demand for Zones 3 and 4.
C4.8.5 Other systems
For many types of steel truss bridges, the distribution of mass is such that the seismically induced loads are
transferred to the substructures along a path that puts little strains on the structural members. Hence, even
using a response modification factor of 1.0 in the seismic-resistant design of those bridges may be of little
economical consequences. However, if a larger modification factor is used, the ductile detailing
requirements provided in Clause 4.8.4.4.3 or 4.8.4.4.4 need to be satisfied to ensure a satisfactory seismic
performance.
C4.10 Seismic base isolation
C4.10.1 General
This Section incorporates the generic requirements for seismic isolation design. The isolation of structures
from the damaging effects of earthquakes is not a new idea. The first patents for base isolation schemes
were obtained at the turn of the century, but until the past two decades, few structures were built using
these ideas. Early concerns were focused on the displacements at the isolation interface. These have been
largely overcome with the successful development of mechanical energy dissipators. When used in
combination with a flexible device such as an elastomeric bearing, an energy dissipator can control the
response of an isolated structure by limiting both the displacements and the forces. Interest in seismic
isolation as an effective means of protecting bridges from earthquakes has therefore been revived in recent
years. To date, there are several hundred bridges in New Zealand, Japan, Italy, and the United States that
use seismic isolation principles and technology for their seismic design.
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The basic intent of seismic isolation is to increase the fundamental period of vibration such that the
structure is subjected to lower earthquake forces. However, the reduction in force is accompanied by
an increase in displacement demand that needs to be accommodated within the flexible mount.
Furthermore, flexible bridges can be lively under service loads.
There are three basic elements in seismic isolation systems that have been used to date. These
elements include
(a) a flexible mounting so that the period of vibration of the total system is lengthened sufficiently to
reduce the force response;
(b) a damper or energy dissipater so that the relative deflections across the flexible mounting can be
limited to a practical design level; and
(c) a means of providing rigidity under low (service) load levels such as wind and braking forces.
Additional guidance on seismic isolation design of highway bridges is given in the Draft AASHTO
Guide Specification for isolation design (AASHTO 1996).
Flexibility
An elastomeric bearing is not the only means of introducing flexibility into a structure, but it certainly
appears to be the most practical and the one with the widest range of application. The idealized force
response with increasing period (flexibility) is shown schematically in the force response curve in
Figure C4.11. Reductions in base shear occur as the period of vibration of the structure is lengthened.
The extent to which these forces are reduced is primarily dependent on the nature of the earthquake
ground motion and the period of the fixed base structure. However, as noted above, the additional
flexibility needed to lengthen the period of the structure will give rise to relative displacements across
the flexible mount. Figure C4.12 shows an idealized displacement response curve from which
displacements are seen to increase with increasing period (flexibility).
Energy dissipation
Relative displacements can be controlled if additional damping is introduced into the structure at the
isolation level. This is shown schematically in Figure C4.13.
One of the most effective means of providing a substantial level of damping is through hysteretic
energy dissipation. The term hysteretic refers to the offset between the loading and unloading curves
under cyclic loading. Figure C4.14 shows an idealized force-displacement loop where the enclosed
area is a measure of the energy dissipated during one cycle of motion. By appropriate compounding
of the elastomer, energy dissipation can be provided in the flexible mount.
Rigidity under low lateral loads
While lateral flexibility is highly desirable for high seismic loads, it is clearly undesirable to have a
bridge that will vibrate perceptibly under frequently occurring loads such as wind loads or braking
loads. Mechanical energy dissipators and modified elastomers may be used to provide rigidity at these
service loads by virtue of their high initial elastic stiffness. Alternatively, some seismic isolation systems
require a separate elastic restraint device for this purpose — typically a rigid component that is
designed to fail at a given level of lateral load.
Design application
The design principles for seismic isolation are best illustrated by Figure C4.15. The dashed line is the
elastic ground response spectrum as recommended in Clause 4.4 for the highest seismic zone. This is
the spectrum that is used to determine actual forces and displacements for conventional design. The
solid line represents the composite spectrum for an isolated bridge. The period shift provided by the
flexibility of the isolation system is represented by Δ T. The isolation system’s increased damping is
represented by Δ B. The increased damping and flexibility combine to provide Δ F, the change in force
demand from conventional to isolated structure.
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C4.10.4 Site effects and site coefficient
The effect of the site soil conditions on the ground response spectra is discussed in Clause 4.4.6. It is noted
that in the constant velocity region (0.8–3.0 seconds) of the ground response spectra, there is a
1.0 to 1.5 to 2.7 relationship between the spectra for the different soil types. Because the design
displacement of the isolation system is determined from the ground response spectrum, the soil
coefficients for isolation design are consistent with the ground response spectra and different from those
used for conventional design, which are 1.0, 1.2, and 1.5.
C4.10.5 Response modification factors and design requirements for
substructure
There are two reasons for limiting the R-factors to 1.5 for isolated bridges. (This is considerably less than
that permitted for conventional nonisolated bridges.) The first is that the behaviour of a bridge
superstructure that is supported by yielding isolators that are in turn supported by yielding substructures is
uncertain at this time.
The second reason is that isolation can significantly improve bridge performance and reduce seismic
damage to the substructures to cosmetic levels, provided that the R-factors are about 1.5. If elastic
(i.e., damage-free) performance is to be assured, the R-factors should be even lower, say 1.0. Selecting
R-factors greater than 1.0 to 1.5 defeats the purpose of one of the principal attractions of isolation design,
that is, damage-free performance.
As a consequence of the expected elastic performance of the substructures, the detailing requirements
for bridges in Seismic Performance Zones 3 and 4 have been relaxed. Minimum levels of ductile detailing
are required to ensure adequate performance in the event of an earthquake larger than the design
earthquake.
C4.10.6 Analysis procedures
The basic premise of these seismic isolation design provisions (consistent with those for buildings and
hospitals) is twofold. First, the energy dissipation of the isolation system can be expressed in terms of
equivalent viscous damping; and second, the stiffness of the isolation system can be expressed as an
effective linear stiffness. These two basic assumptions permit both the single and multimodal methods of
analysis to be used for seismic isolation design.
For sliding systems without a self-centring mechanism or for pure elasto-plastic systems the equivalent
viscous damping concept is no longer valid. The equivalent viscous damping formula produces a value
that is independent of the coefficient of friction for sliding systems or the yield point for elasto-plastic
systems. Furthermore, because these systems lack a restoring force, the total design displacement may be
underestimated by Methods 1 and 2. Consequently, it is necessary to perform a nonlinear time-history
analysis for all seismic isolation systems that have no self-centring mechanism (Method 3).
C4.10.6.2 Uniform-load/single-mode spectral analysis
C4.10.6.2.1 Statically equivalent seismic force and coefficient
For the design of conventional bridges the form of the elastic seismic coefficient is
C sm =
1.2AIS
Tm2 / 3
with S values that range from 1.0 to 1.2 to 1.5 for different soil types. Although the ground response
spectrum decreases approximately as 1/T for longer periods, the form given above does not decrease as
rapidly as 1/T. In fact, at a period of 2.0 seconds, Csm will be approximately 50% greater than the ground
acceleration response spectra. The two major reasons for introducing this conservatism in the design of
longer period (tall columns, long spans) conventional bridges are as follows:
(a) In longer period conventional bridges, high ductility demands will be concentrated in a few columns;
and
(b) Instability of a conventional bridge is more of a problem as the period increases.
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For seismic isolation design, the elastic coefficient is directly related to the elastic ground response
spectra. This is because the intent of seismic isolation design is to introduce flexibility and damping in
specifically designed and tested elements with the goal of eliminating or significantly reducing the
ductility demand on the substructures. Consequently, the conservatism of the seismic coefficient
required for long period conventional bridges is not necessary for isolated structures. The form of the
seismic coefficient is therefore slightly different from that for a conventional design and, for 5%
damping, is given by
′ =
C sm
ASi
Te
In this equation, A is the acceleration ratio, Si is the site coefficient for seismic isolation (Table 4.7)
discussed in Clause C4.10.4, and the 1/Te factor accounts for the decrease in the ground response
spectra ordinates as Te increases. The specific Si values reflect the fact that above a period of
1.0 second, there is a 1.0 to 1.5 to 2.0 to 2.7 relationship for the spectral accelerations for Soil Types I,
II, III, and IV, respectively. Once again, C’sm should not exceed a value of 2.5A.
The equation for C’sm does not include an importance factor, since the design philosophy for
isolated bridges already assures a level of performance for all bridges that is comparable to that
required for conventional lifeline and emergency-route bridges for the design earthquake.
If the effects of damping are included, the elastic seismic coefficient is given by
′ =
C sm
ASi
TeB
where B is the damping term given in Table 4.8. Note that for 5% damping, B = 1.0.
The quantity C’sm is a dimensionless design coefficient, which when multiplied by g produces the
spectral acceleration. This spectral acceleration (SA) is related to the spectral displacement (SD) by the
relationship
SA = w 2SD
where ω is the circular natural frequency and is given by 2π / Te . Therefore, since SA = Cs g,
SA =
ASi
g
TeB
and
1 ASi
g
w 2 TeB
SD =
Te2 ASi
mm ⎞
⎛
⎜ 9810
⎟
sec2 ⎠
( 2π ) TeB ⎝
=
2
248ASiTe
mm
B
Denoting SD as di , which is the displacement across the elastomeric bearings, we approximate the
above by
=
di =
250ASiTe
mm
B
An alternative form for C’sm is possible. The quantity C’sm is defined by the relationship
F = C’smW
where F is the earthquake design force and W is the weight of the structure. Therefore,
′ =
C sm
S k × di
F
= eff
W
W
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where
Σ keff is the sum of the effective linear springs of all bearings supporting the superstructure segment. The
equivalence of this form to the previous form is evident by recalling that Σ keff = ω 2W / g, from which
W d i ( 2π )
1
248ASiTe
× =
×
×
2
g W
B
9810
Te
2
′
= w2
C sm
=
ASi
BTe
C4.10.6.2.2 Application of uniform-load/single-mode method of
analysis
The simplified methods of analysis given in Clauses 4.5.3.1 and 4.5.3.2 are appropriate for seismic
isolation design. In fact, these methods are simplified with seismic isolation. Steps 1, 2, and 3 are not
necessary since the use of an isolation system will ensure a simple rigid body deformation pattern of the
superstructure. However, the calculation of the period Te may require iteration since the displacement, di ,
is not known until the analysis is complete. It will therefore need to be estimated in order to start the
analysis.
In Step 4, the value of pe (x), the intensity of the equivalent static seismic loading, is determined as
pe (x) = w ( x)C’sm
where w (x) is the dead load per unit length of the bridge superstructure.
In Step 5, this loading pe (x) is applied to the superstructure to determine the resulting member forces
and displacements.
C4.10.6.3 Multi-mode spectral analysis
The guidelines given in Clause 4.5.3.3 are appropriate for the response spectrum analysis of an isolated
structure with the following modifications:
(a) The isolation bearings are modelled by use of their effective stiffness properties determined at the
design displacement di (Figure C4.14);
(b) The ground response spectrum is modified to incorporate the damping of the isolation system
(Figure C4.15).
The response spectrum required for the analysis needs to be modified to incorporate the higher
damping value of the isolation system. This modified portion of the response spectrum should only be
used for the isolated modes of the bridge and will then have the form shown in Figure C4.15.
C4.10.6.4 Time-history analysis
When a time-history analysis is required, it is necessary for the time histories to be frequency scaled so that
they closely match the appropriate ground response spectra for the site. In addition, the analytical model
should incorporate the nonlinear deformational characteristics of the isolation system.
C4.10.7 Clearance and design displacements for seismic and other loads
Adequate clearance for the seismic displacement needs to be provided between the girders and the
abutment. Adequate clearance needs to be provided for the displacements resulting from the seismic
isolation analysis of Clause 4.10.6.2, 4.10.6.3, or 4.10.6.4 in either of the two orthogonal directions. As a
design alternative in the longitudinal direction, a knock-off abutment detail may be provided for the
seismic displacements between the abutment and deck slab.
In order to account for the possibility of earthquakes larger than the design earthquakes, an increase of
25% in the clearance requirements for emergency-route and lifeline bridges has been provided.
The horizontal deflections in the isolators resulting from longitudinal forces, wind loads, and centrifugal
forces will be a function of the force-deflection characteristics of the isolators. Adequate clearance at all
expansion joints needs to be provided for these movements.
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C4.10.8 Design forces for Seismic Performance Zone 1
Clause 4.10.8 permits use of the real elastic force reduction provided by seismic isolation. It should be
noted, however, that the acceleration ratio, which has a maximum value of 0.05 for Seismic
Performance Zone 1 bridges, is specified to have a minimum value of 0.10 if seismic isolation is used.
This conservatism ensures, for most areas designated Seismic Performance Zone 1, that the isolation
bearings are capable of resisting force levels associated with twice the design earthquake.
C4.10.9 Design forces for Seismic Performance Zones 2, 3, and 4
Design forces for a seismically isolated bridge are obtained using the same load combinations as for a
conventionally designed bridge.
C4.10.10 Other requirements
C4.10.10.1 Non-seismic lateral forces
Since an element of flexibility is an essential part of an isolation system (Clause 4.10.1), it is important
that the isolation system also provide sufficient rigidity to resist more frequently occurring wind and
braking loads. This requires an elastic restraint system with higher initial stiffness than the element of
flexibility (see Figure C4.14). Limits on displacements resulting from nonseismic loads need to be
satisfactory to the Design Engineer.
C4.10.10.2 Lateral restoring force
The basic premise of these seismic isolation design provisions is that the energy dissipation of the
system can be expressed in terms of equivalent viscous damping and the stiffness by an effective linear
stiffness. The requirements of Clause 4.10.10.2 provide the basis for which these criteria are met.
C4.10.10.3 Vertical load stability
Clause 4.10.10.3 provides minimum requirements for the design of the isolation system. The detailed
design requirements of the system will be dependent on the type of system. The multipliers of
1.5 and 3.0 on the total design displacement are based on a design response spectra corresponding to
a 475-year return period event. If a maximum credible response spectra is used for the design of the
isolation, these multipliers are reduced to 1.1 and 2.2, respectively. In some of the low seismic risk
areas (A < 0.25) of Canada, a multiplier of 2.0 and 4.0 may be appropriate since a longer return period
event (2400 years) may be up to two times greater than the 475-year event.
It must be noted that the properties of some isolation systems may change considerably under cold
temperatures.
C4.10.11 Required tests of isolation system
The Code requirements are predicated on the fact that the isolation system design is based on tested
properties of prototype isolators. Clause 4.10.11 provides a comprehensive set of tests to both
establish the design properties of the system and then determine the adequacy of the tested
properties. Systems that have been previously tested with this specific set of tests on similar type and
size of isolator units do not need to have these tests repeated. Design proprieties must therefore be
based on manufacturers’ pre-Approved or certified test data. Extrapolation of design properties from
tests of similar type and size of isolator units is permissible.
C4.10.12 Elastomeric bearings — Design
Elastomeric bearings that are used for seismic isolation will be subjected to earthquake-induced
displacements, di , and must therefore be designed to safely carry the vertical loads at these
displacements. Since earthquakes are infrequently occurring events, the factors of safety required
under these circumstances will be different from those required for more frequently occurring loads.
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Since the primary design parameter for earthquake loading is the displacement, di , of the bearing, the
design procedures need to be capable of incorporating this displacement in a logical consistent manner.
The requirements of Section 14.2 of AASHTO (1996) limit vertical loads by use of a limiting compressive
stress and therefore do not have a mechanism for including the simultaneous effects of seismic
displacements. The British Specifications BE 1/76 and BS 5400 recognize that shear strains are induced in
reinforced bearings by both compression and shear deformation. In these codes, the sum of these shear
strains is limited to a proportion of the elongation-at-break of the rubber. The proportion (1/2 or 1/3 for
service load combinations and 3/4 for seismic load combinations) is a function of the loading type.
Since the approach used in BE 1/76 and BS 5400 incorporates shear deformation as part of the criteria,
it can be readily modified for seismic isolation bearings. The design requirements given are based on the
appropriate modifications to BE 1/76 and BS 5400. It is assumed that the displacements, di , due to
earthquake loads have been determined by the provisions of Clause 4.10.6.
The more conservative aspects of BE 1/76 and BS 5400 have been used. For example, BS 5400 requires
the summation of compression, thermal, and rotational shear strains and requires it to be less than 5.0.
BE 1/76 requires the summation of only the compression and thermal shear strains and requires it to be
less than ε µ /2. These requirements require the summation of the three different shear strains with a limit of
ε µ /2, where ε µ /2 may not exceed 5.0.
C4.10.14 Sliding bearings — Design
Guidance for design and construction of sliding isolators is given in the draft AASHTO Guide Specifications
for seismic isolation design (AASHTO 1996).
Acceleration
Period shift
Period
Figure C4.11
Idealized force response curve
(See Clause C4.10.1.)
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Displacement
Period shift
Period
Figure C4.12
Idealized displacement response
(See Clause C4.10.1.)
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Acceleration
Increasing damping
Period
Displacement
Increasing damping
Period
Figure C4.13
Response curves for increasing damping
(See Clause C4.10.1.)
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Force
F max
Kd
Fy
K eff
Qd
Ku
Ku
Dm
Displacement
Legend:
Q d = Characteristic strength
F y = Yield force
F max = Maximum force
K d = Post-elastic stiffness
K u = Elastic (unloading) stiffness
K eff = Effective stiffness
D m = Maximum bearing displacement
Figure C4.14
Characteristics of bilinear isolation bearings
(See Clauses C4.10.1, C4.10.6.3, and C4.10.10.1.)
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Acceleration
coefficient
Structure modes Isolated (fundamental) modes
1.0
5% damping
damping of isolation system
0.8
DF
0.6
0.4g S2 ATC spectrum
0.4
5% Composite
spectrum
DB
0.2
DT
Ti
1.0
0.8Ti
2.0
3.0
Period
(seconds)
Figure C4.15
Modified input response spectrum
(See Clauses C4.10.1 and C4.10.6.3.)
C4.11 Seismic evaluation of existing bridges
C4.11.1 General
Clause 4.11 is applicable only to the seismic evaluation of existing bridges and cannot be used for the
design of new bridges. For this purpose, an existing bridge is any bridge designed using a code or
standard that has earthquake-resistant design requirements less stringent than those mandated by the
Code.
For an inventory of existing bridges, preliminary screening is recommended to identify and prioritize
those bridges that are seismically deficient and need a detailed evaluation of their seismic capacities. There
exists a large number of preliminary screening methodologies that can be used for this task, taking into
account the relative effect of structural, economical, and societal factors on this ranking
(CALTRANS 1992(b), Filiatrault et al. 1994, Maffei 1995, Dicleli and Bruneau 1996).
C4.11.2 Bridge classification
The provisions of Clause 4.11 are minimum evaluation requirements for existing bridges classified as
emergency-route or other bridges. Lifeline bridges are not addressed since they need to remain open to
traffic after a major earthquake; hence, more stringent and more detailed evaluation is typically required.
For example, a 1000-year return period seismic event may be appropriate for evaluation of lifeline bridges,
instead of the 475-year return period event specified in this Section.
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C4.11.3 Damage levels
C4.11.3.1 Moderate damage
Moderate damage is primarily defined by the functional availability of the bridge. Limited access may
mean a reduced number of lanes, reduced lane width, reduced speed, or weight restriction.
C4.11.3.2 Significant damage
Collapse of the bridge includes collapse of any part of the deck, such as happened to the San
Francisco–Oakland Bay Bridge during the 1989 Loma Prieta earthquake. To meet the requirements of
avoiding significant damage, it must be possible to drive a vehicle across the bridge on the deck with
the assistance, if necessary, of ramps over rubble or across small gaps.
C4.11.4 Performance criteria
It is implied that bridges that can withstand a major earthquake with significant damage can also
withstand a moderate earthquake with reduced damage and therefore need not be evaluated for a
moderate earthquake separately.
C4.11.5 Evaluation methods
The minimum analysis requirements for evaluation, and particularly the limited evaluation procedure,
does not waive the Engineer’s responsibility to identify structural details that could be most vulnerable
during earthquake and to correct these potentially dangerous deficiencies.
C4.11.6 Load factors and load combinations for seismic evaluation
Due to the large cost incurred when a bridge needs to be seismically rehabilitated, the Regulatory
Authority can reasonably be expected to tolerate higher risks for existing bridges than for new bridges.
Hence, Clause 4.11.6 permits that existing structures be evaluated to a lower earthquake requirement
than new structures unless instructed otherwise by the Regulatory Authority. Furthermore, it may be
possible to reduce the earthquake load effect for cases such as older bridges with low expected
remaining service life, provided that permission is obtained from the Regulatory Authority.
This approach is consistent with the philosophy that has been adopted for existing buildings
throughout North America (NRC 1992, ATC 1987).
The design of new bridges requires the consideration of minimum (0.8D) and maximum (1.25D)
gravity loads (see Clause C4.4.9). In the evaluation of existing bridges, only one combination with
1.0D is required.
C4.11.8 Member capacities
C4.11.8.1 General
The nominal resistance of members not detailed as per the requirements of Clause 4.11.8 may not be
able to maintain their resistance when undergoing reversed cyclic inelastic deformations. However, if
these members are not expected to be stressed into the inelastic range during the major earthquake,
their maximum resistance to noncyclic loading can be considered in the evaluation. Alternatively,
when supported by research, rational evaluation of the reliable resistance at the level of reversed cyclic
inelastic deformations expected during the major earthquake can be conducted.
Steel compression members in older bridges may have elements whose width/thickness (b/t) ratios
exceed those specified for Class 3 sections in the Code. These slender compression elements will
buckle elastically before the yield strength of the material is attained. Therefore, local elastic buckling
governs the strength of these members. The effect of local buckling can be accounted for by using a
reduced effective, Fy , or a reduced effective element width b in the calculation of member compressive
strength. A more refined procedure to consider local buckling effect is given in Appendix B of
AISC (1994) and in CSA S136-94.
Steel members with slenderness ratios exceeding those allowed by the Code should be modelled as
tension-only members in the computer model to estimate seismic demands.
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Inadequately anchored or spliced bars are common in reinforced concrete components of older bridges.
Premature bond failure may occur before steel bars develop their yield strength. The assessment of
strength for such details is difficult, since current design methods do not represent actual performance of
these details. Priestley et al. (1992) provides some guidelines on the assessment of flexural strength for
members with inadequately anchored or spliced bars.
Guidance on the performance of columns with lap-spliced dowels at their base, with significant lap
lengths, is given by Griezic et al. (1996).
In design of new reinforced concrete members, the concrete shear resistance, Vc , is assumed to be zero
in plastic hinge regions unless axial compression force exceeds a certain value. This assumption would be
too conservative for the evaluation of existing members. Vc is a function of the confinement reinforcement
and the flexural ductility level in plastic hinge regions. Vc should decrease as flexural plastic deformation
(ductility) increases. Priestley et al. (1992) provide a procedure to account for the degradation of concrete
shear strength with increasing flexural ductility.
Damage observations following recent major earthquakes (e.g., the 1989 Loma Prieta earthquake)
indicate that severe bridge damage and possible collapse may result from poorly detailed cap
beam/column joints. Therefore, joints should be assessed to determine their capacity to sustain expected
actions from columns and cap beams framing into the joint. A procedure to check joint shear strength is
given in Priestley et al. (1992).
Further research is needed to determine the reliable cyclic inelastic deformation capability of many types
of nonductile details, how much of this capacity can be relied on during major earthquakes, and the
extent of the corresponding damage resulting from reliance on such partly deficient details.
C4.11.8.4 Effects of deterioration
Careful inspection of existing bridges needs to be carried out to determine if any defects or deterioration is
present. Detrimental effects of defects and deterioration need to be accounted for in determining the
capacity of members as well as their ability to undergo reversed cyclic deformations. Guidance on the
influence of corrosion on the ductility of steel members subjected to reversed cyclic loading is given by
Zahrai and Bruneau (1997).
C4.11.9 Required response modification factor
The most commonly used method for detailed assessment of seismic performance is based on a
comparison between seismic demand and existing capacity for each element. This procedure is thus based
on an element-by-element evaluation rather than on the performance of a bridge as a single structural
system.
Seismic evaluation considers the load combination of dead plus seismic loads. A portion of the member
capacity is usually required to resist the dead load effect, and therefore only the reserve capacity, C, above
that required for dead load effects needs to be considered in this demand versus capacity comparison.
Seismic effects should be obtained from elastic spectral methods. If plastic hinging in other members
limit this seismic effect (e.g., bending moment demand on a cap beam is limited by plastic hinging in bent
columns), it may be taken as the reduced effect resulting from plastic hinging in the other members.
However, probable moment capacities (instead of nominal capacities) should be used in plastic hinge
zones to calculate this reduced effect.
A calculated Rreq of greater than 1.0 indicates that the member is likely to be damaged during the
design earthquake. The acceptable level of response modification factor depends on the actual detailing of
the member, the redundancy of the structural system, and the consequence of failure of the member on
the overall seismic performance of the bridge, as discussed in Clauses 4.11.10 and 4.11.11.
C4.11.10 Response modification factor of existing substructure
elements
It is recognized that ductile substructure elements are key to the seismic survival of bridges (Mitchell et al.
1995, Anderson et al. 1966, Bruneau et al. 1996). The ability of members and joints to resist, in a stable
manner, large reversed cyclic inelastic deformation is generally unknown when they are not detailed in
accordance with the requirements of the Code. A significant amount of research is underway to enhance
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the current state of knowledge on this topic, particularly for existing Canadian bridges (Mitchell et al.
1994, Sexsmith 1994, Sexsmith and Williams 1995, Williams and Sexsmith 1995, Dicleli and Bruneau
1995a, 1995b and 1995, Griezic et al. 1995 and 1996, Finn et al. 1995 and 1996, Ventura et al. 1995
and 1996, Villemure et al. 1995, Gauvreau 1995).
Extreme care needs to be taken when using experimental results from existing details typical of
non-Canadian bridges. Existing bridges in Canada have a number of unique seismic vulnerabilities.
In absence of knowledge on the reliable reversed cyclic inelastic seismic performance of a particular
type of detail, the Engineer needs to follow one of the two procedures specified in Clause 4.11.10, or
limit seismic response to the elastic range. For large bridges, or an inventory of bridges having a
frequently repeated detail identified as seismically vulnerable, a carefully designed and executed
program of reversed cyclic inelastic tests on structural components built with this detail may prove to
be the economical and more reliable solution.
C4.12 Seismic rehabilitation
Examples of different methods for the design of seismic retrofits for concrete bridges are given by
Priestley et al. (1992) and (1996). Examples of different retrofit techniques used for concrete bridges
damaged in the Loma Prieta earthquake and used on some Canadian bridges are given by Mitchell
et al. (1994). Results of reversed cyclic loading tests on the retrofitting of deficiencies in existing
Canadian concrete bridge structures are given below:
(a) retrofitting of reinforced concrete two-column frames (Sexsmith et al. 1993, Anderson
et al. 1995, and Jennings et al. 1995);
(b) retrofitting of a column with lap-spliced dowel bars (Griezic et al. 1996); and
(c) retrofitting techniques for reinforced concrete columns with concrete hinges at their bases
(Griezic et al. 1995).
The seismic retrofit of steel bridges is a relatively new area of research and practice. Examples of
retrofit techniques in recent projects are given by FHA/CALTRANS (1995, 1997). In certain cases,
passive energy dissipators added to the steel superstructure may be used to provide compliance with
the stated performance objectives (Bruneau and Sarraf 1997, Zahrai and Bruneau 1997).
Seismic retrofit should be considered whenever nonseismic rehabilitation of a bridge is planned
(e.g., replacement of existing deficient bearings). It is considerably more cost-effective to perform
seismic retrofit at the same time as other nonseismic rehabilitation.
Retrofit measures should be designed to limit damage to easily accessible areas. In this way, bridges
can be readily repaired following an earthquake, if necessary, and restored to their intended use.
Maintenance and inspection of retrofitted components should be considered during the retrofit
design stage. The retrofit measures should be designed so that they can be properly maintained to
function as originally planned when and if an earthquake does occur.
If seismic retrofit of a bridge is a phased operation, retrofit items should be prioritized based on a
cost-benefit analysis. Components that impose high seismic risk and are cost-effective to retrofit
should be given high priority. The effects of retrofit measures in each phase on the overall seismic
performance of the bridge should be evaluated before the start of the phased retrofit program.
References
CSA (Canadian Standards Association)
CAN/CSA-S16.1-94 (withdrawn)
Limit states design of steel structures
S136-94 (withdrawn)
Cold formed steel structural members
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Short-Span Reinforced Concrete Bridges.” Proceedings, 11th World Conf. on Earthquake Eng., Acapulco,
Mexico, Paper No. 921, 8 pp.
Ventura, C.E., Finn, W.D.L., and Felber, A.J. 1995. “Ambient Vibration Study of the Painter Street
Overpass.” Proc., 7th Canadian Conf. on Earthquake Eng., Montréal, pp. 787–794.
Villemure, I., Ventura, C., and Sexsmith, R. 1995. “Impact Testing to Quantify Structural Damage in
Reinforced Concrete Frames.” Proceedings, 7th Canadian Conference on Earthquake Engineering,
Montréal, pp. 649–656.
Williams, M., and Sexsmith, R. 1995. “Seismic Damage Indices for Concrete Structures: A State-of-the-Art
Review.” Earthquake Spectra, Vol. 11, No 2, pp. 319–349.
Williams, M., Villemure, I., and Sexsmith, R. 1997. “Evaluation of Damage Indices for Concrete Elements
loaded in Combined bending and Shear.” American Concrete Institute Structural Journal, Vol. 94, No. 3,
pp. 315–321.
Zahrai, S.M., and Bruneau, M. 1996. “Substructure Protection by Ductile-End Diaphragms in Steel
Bridges.” Proc. Fourth National Workshop of Bridge Research in Progress, National Center for Earthquake
Engineering Research, Buffalo, pp. 275–280.
Zahrai, S.M., and Bruneau, M. 1997. “Capacity Design Principles and Ductile End-Diaphragms to
Seismically Retrofit Slab-on-Girder Steel Bridges.” 25th Canadian Society for Civil Engineering, Annual
Conference, Sherbrooke, Québec.
Zen, K., and Higuchi Y. 1984. “Prediction of Vibratory Shear Modulus and Damping Ratio for Cohesive
Soils.” Proceedings, Eighth International Conference on Earthquake Engineering, San Francisco, July,
Vol. 3, pp. 23–30.
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Section C5 — Methods of analysis
C5.1
Scope 163
C5.3
Abbreviations and symbols 163
C5.4
General requirements 163
C5.4.2
Analysis for limit states 163
C5.4.4
Structural responses 163
C5.4.5
Factors affecting structural responses 165
C5.4.6
Deformations 167
C5.4.6.1 General 167
C5.4.6.2 Dead load deflections 167
C5.4.6.3 Live load deflections 167
C5.4.7
Diaphragms and bracing systems 168
C5.4.8
Analysis of deck slabs 168
C5.4.9
Analysis for redistribution of force effects 168
C5.4.10 Analysis for accumulation of force effects due to construction sequence 168
C5.4.11 Analysis for effects of prestress 168
C5.4.12 Analysis for thermal effects 168
C5.5
Requirements for specific bridge types 169
C5.5.1
General 169
C5.5.2
Voided slab — Limitation on size of voids 169
C5.5.4
Truss and arch 169
C5.5.5
Rigid frame and integral abutment types 169
C5.5.5.1 Rigid frame 169
C5.5.5.2 Integral abutment 170
C5.5.7
Box girder 170
C5.5.8
Single-spine bridges 171
C5.6
Dead load 171
C5.6.1
Simplified methods of analysis (beam analogy method) 171
C5.6.1.1 Conditions for use 171
C5.7
Live load 172
C5.7.1
Simplified methods of analysis 172
C5.7.1.1 Conditions for use 172
C5.7.1.2 Longitudinal bending moments in shallow superstructures 173
C5.7.1.3 Longitudinal bending moments in multi-spine bridges 185
C5.7.1.4 Longitudinal vertical shear in shallow superstructures 186
C5.7.1.5 Longitudinal vertical shear in multi-spine bridges 186
C5.7.1.6 Deck slab moments due to loads on the cantilever overhang 186
C5.7.1.7 Transverse bending moments in decks 189
C5.7.1.8 Transverse vertical shear 189
C5.7.1.9 Analysis of stringers in truss and arch bridges 189
C5.7.1.11 Analysis of orthotropic steel decks 190
C5.8
Idealization of structure and interpretation of results 190
C5.8.1
General 190
C5.8.2
Effective flange widths for bending 190
C5.8.2.1 Concrete slab-on-girders 190
C5.8.2.2 Orthotropic steel decks 190
C5.8.3
Idealization for analysis 191
C5.9
Refined methods of analysis for short- and medium-span bridges 191
C5.9.1
Selection of methods of analysis 191
C5.9.2
Specific applications 191
C5.9.3
Model analysis 192
C5.10
Long-span bridges 192
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C5.10.1
C5.10.2
C5.10.3
C5.11
C5.11.1
C5.11.1.1
C5.11.1.2
C5.11.1.4
C5.11.2
C5.11.2.1
C5.11.2.2
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General 192
Cable-stayed bridges 192
Suspension bridges 192
Dynamic analysis 193
General requirements of structural analysis 193
General 193
Distribution of masses 193
Damping 193
Elastic dynamic responses 193
Vehicle-induced vibrations 193
Wind-induced vibrations 194
Annex
CA5.1 — Factors affecting structural response 199
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Section C5
Methods of analysis
C5.1 Scope
The bridge types concerned have been selected with a view to associating each type with one or more
acceptable methods of analysis. These bridge types cover most cases of bridge construction.
Figure C5.1 illustrates the bridge types referred to.
C5.3 Abbreviations and symbols
The explanations given in this Commentary involve, in some cases, symbols not defined in the Section
itself. These are defined in this Commentary at the places where they occur, except for the following:
D = when a bridge superstructure is analyzed in accordance with earlier simplified methods
specified in this Commentary, the corrected width of a longitudinal strip over which one-half of
a lane load, one-half of a truck load, or one line of wheels is distributed, m
Wc = bridge deck width, m
C5.4 General requirements
C5.4.2 Analysis for limit states
For many types of bridges, the pattern of load distribution at the ultimate limit state may differ from
the pattern of load distribution in the elastic state. It is sometimes an advantage to the designer to be
aware of this difference and to utilize nonlinear methods of analysis. Since, in the present state of the
art, some nonlinear methods of analysis are not yet fully proven, the Code requires the use of linear
analysis for design unless the designer secures Approval for a nonlinear method.
C5.4.4 Structural responses
The number of diaphragms or internal cross-frames for box girder bridges were determined for
bridges meeting the requirements of the simplified methods of analysis. Bridges that do not meet the
requirements of Clause 5.7.1.1 may require additional cross-frames or diaphragms in order for the
warping and distortional effects to be negligible.
The structural responses that are referred to in Clause 5.4.4 are illustrated in Figure C5.2.
Table 5.1 indicates that transverse moment is one of the structural responses to be considered for
slab type bridges. The requirements of Clause 8.18.7 are often used to determine the amount of
distribution reinforcement for slabs analyzed by elastic methods if the slabs are supported on girders,
stringers, or floor beams as specified in Clause 8.18.1. For slabs supported on transverse floor beams,
and with the main reinforcement parallel to traffic, the determination of the relevant structural
responses in the floor beams coupled with the provision of distribution reinforcement in accordance
with Clause 8.18.7 will satisfy the requirements specified in Clause 5.4.4 for analysis for transverse
moment response.
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(a)
(b)
Shear key
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
Figure C5.1
Representative cross-sections and elevations of bridge types
(See Clause C5.1.)
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Longitudinal
moment
Transverse
moment
Transverse
shear
Longitudinal
shear
Transverse
torsion
Longitudinal
torsion
Deformation
due to distortional
warping
Deformation due to
warping of
an open section
Interface
shear
Figure C5.2
Illustration of certain structural responses
(See Clause C5.4.4.)
C5.4.5 Factors affecting structural responses
For the bridge types given in Clause 5.1, some of the structural responses given in Clause 5.4.4 always
need to be considered. Certain factors are sometimes present in bridges of the type concerned and
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sometimes not. These factors, when present, either give rise to structural responses not given in
Clause 5.4.4 or cause changes in the relative importance of the structural responses, or both. Some of
these factors are listed in Clause 5.4.5, and are described below. Appropriate analysis considerations are
given in Annex A5.1.
Continuity of spans
Continuity of spans always needs to be considered. The manner in which multispan bridges may be
treated similarly to single-span bridges for transverse load distribution is given in Clause A5.1.2.
Plan geometry (including skewness and curvature)
Simple methods of analysis are based on the assumption of a simply supported single-span bridge whose
plan form is rectangular. When the plan form is other than rectangular, relatively large torsional effects are
usually introduced; the provisions of Clause A5.1.3 then apply.
Edge stiffening
Edge stiffening introduces a local increase in the flexural rigidity per unit width of the deck slab near to the
edges. Hence, a relatively large share of the total longitudinal bending moment is taken along the edges of
the deck slab. The simplified method given in Bakht and Jaeger (1985) can be used to account for the
effects of edge stiffening.
Longitudinal variation of transverse cross-section
In calculating transverse distribution effects in continuous bridges with haunches over the supports,
assuming constant depth in the longitudinal direction equal to the depth at midspan results in
overestimation of the degree of transverse load distribution over the supports. However, the distribution of
moments and shears in the middle region of this span may be taken to remain unaffected by such an
assumption. The continuity of spans affects the total longitudinal moment and shear at a given
cross-section if the transverse cross-section is not constant. Suitable methods must be used to account for
this variation.
Transverse variation of longitudinal cross-section
With the limitation on the extent of the tapered zones of the slab given in Clause A5.1.4, the replacement
of the tapered zones by reduced width portions of full slab depth is found by rigorous analysis to be closely
correct.
Diaphragms and cross-frames
The presence of transverse diaphragms or cross-frames in the superstructure of slab-on-girder bridges does
not significantly affect load distribution characteristics when the governing load cases require the
simultaneous loading of all the bridge lanes. In the case of eccentric loading, the diaphragms or
cross-frames mainly have the effect of reducing the stresses due to longitudinal moments and shears.
In box girder bridges, the transverse diaphragms or cross-frames, by preventing the distortion of the
transverse cross-section, can considerably reduce the stresses that would otherwise result from such
distortion. The presence of adequate diaphragms or cross-frames can also enable the designer to use the
simplified methods of analysis, which were developed for shallow superstructures, for the analysis of box
girders. In steel and steel-composite box girders, where the stresses due to distortion can be substantial,
the provision of a sufficient number of transverse diaphragms or cross-frames can significantly improve the
efficiency of the structure. However, for every structure, the increase of either the number or the stiffness
of the diaphragms or cross-frames beyond a certain limit has little effect on further improving its
distributional properties.
Barrier and parapet walls
If barrier and parapet walls are structurally integral with the bridge superstructure, they will have the effect
of attracting load, and the bridge should be analyzed for the resulting distribution of longitudinal bending
effects. Conversely, if such a wall ceases to be structurally integral with the bridge structure, for example as
a result of collision by a vehicle, the distribution of longitudinal bending moment becomes changed.
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Hence, the requirements of the first paragraph of Clause A5.1.8 apply with respect to various limit
states. By contrast, for deck slab design only, the beneficial effect of barrier walls can be relied upon
with confidence; hence, the inclusion of the second paragraph. The effective positioning of the neutral
axis of the barrier wall acting as an edge stiffener of the cross-section is something that cannot be
closely defined; engineering judgement is needed here. Bakht and Jaeger (1985) provides some
guidance on this matter.
Support boundary conditions
Many of the simplified methods of analysis are based on the assumption of the continuity of support
all along the support lines for the full width of the bridge. Departure from this condition should be
taken into account.
Creep and shrinkage
Although creep and shrinkage frequently do not affect the ultimate load-carrying capacity of a
structure significantly, they can influence the behaviour of a concrete structure in its serviceability limit
states. Excessive cracking problems can occur due to stresses caused by creep and shrinkage. It is
especially advisable to analyze these effects in composite construction where differential shrinkage can
cause severe stresses. Similar considerations apply to the redistribution of load effects due to creep and
shrinkage in segmental bridges.
The relevant portions of Section C3 should also be referred to.
C5.4.6 Deformations
C5.4.6.1 General
In view of the approximate nature of the deformation analysis, it is not appropriate to introduce the
added complication of using dynamic properties of materials. Thus, in calculating deflections for the
purposes of Section 3, it suffices to use relevant static material properties as defined in other sections
of the Code.
C5.4.6.2 Dead load deflections
Retaining the simplicity of existing methods, it is sufficiently accurate to calculate dead load deflection
by ignoring the effects of transverse curvature and considering only beam type deflections due to
flexure in the vertical longitudinal plane. With a similar simplification in mind, it is also permissible, for
example, to assume that the total dead load of a slab-on-girder bridge is divided equally between the
girders and to calculate the deflections of the girders accordingly, provided that the girders all have
equal flexural rigidity and are equally spaced, and that the transverse cross-section of the bridge is
symmetrical with respect to the longitudinal centerline. Similar simplifications apply to the other types
of bridge, based on a uniform transverse spread of dead load.
C5.4.6.3 Live load deflections
(a) In calculating the average deflection due to live load, it is permissible to use the same basic
approach as outlined in Clause C5.4.6.2 and treat the entire bridge as a beam undergoing flexure
in the vertical longitudinal plane only.
(b) In calculating the maximum deflection due to live load in compliance with the deflection
limitations of Clause 3.4.4, it is necessary to take into account transverse distribution effects. The
simplified method given in this clause uses the same approach as that given in Clause 5.7.1.2.2. It
will be appreciated that transverse variation of longitudinal bending moments is accompanied by
substantially the same pattern of variation of vertical deflections.
The treatment of multispine box girder bridges of steel-concrete composite construction has the
same general formulation — a load fraction is obtained from Clause 5.7.1.3 and this load is applied to
a single spine treated as a beam.
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C5.4.7 Diaphragms and bracing systems
For slab-on-girder bridges, rigorous analysis shows that, in practical cases, two intermediate diaphragms
per span provide almost all of the benefit that is available, with very little further beneficial effect
becoming available with an increase in the number of diaphragms beyond this. Jaeger et al. (1989) may
be found helpful.
C5.4.8 Analysis of deck slabs
When the deck slab is designed by the empirical method of Clause 8.18.4, the analysis of load effects in
the slab becomes redundant for the reasons given in Clause C8.18.4.
C5.4.9 Analysis for redistribution of force effects
Among the principal causes of redistribution of force effects are cracking, creep, and shrinkage. For
example, long-term creep may significantly affect the negative moment at an interior support position of a
continuous span bridge.
The effects of cracking are dealt with in the Code mainly by the provision for serviceability limit states.
Clause 5.4.9 requires examination of the effects of creep and shrinkage. It is noted that in simply
supported single spans, redistribution of internal stresses can occur without any change in total force
effect, such as total longitudinal vertical shear force or bending moment, since these are statically
determinate for a given loading. An example of this is the single-span, simply supported bridge of
composite construction. Here, as the section deforms because of creep, the girder portion of the
composite section tends to accept a higher and higher fraction of the total load. However, Clause 5.4.9
does not require attention to be given to such cases. In other words, only cases in which the statically
indeterminate force effect, such as longitudinal vertical shear force and moments in a continuous-span
bridge, is itself altered need be considered.
C5.4.10 Analysis for accumulation of force effects due to construction
sequence
It is noted that Section 3 requires that bridge components be proportioned for all critical load stages
during the life of the structure, including Construction. Good engineering practice calls for the
anticipation, by the designer, of the probable construction sequence. When the bridge is fully built, and if
it then constitutes a statically indeterminate system, the values due to dead load of force effects such as
support reactions and negative moments at interior supports depend on the construction sequence and
on the effects of creep. In addition, the overall state of cracking in a concrete deck depend on the pour
sequence employed, and this affects the statically indeterminate forces and moments. These will also be
subject to further changes due to creep.
The designer is required to follow the anticipated construction sequence stage by stage. At each stage,
a linear elastic analysis is performed using the structural properties appropriate to that stage, and any
locked-in force effects that occur at that stage are accumulated, along with those of preceding stages, in a
progressive manner. Once again, the effect of creep on this progressive accumulation should be borne in
mind.
C5.4.11 Analysis for effects of prestress
Standard text books on prestressed concrete structures provide methods of dealing with the requirements
of Clause 5.4.11.
C5.4.12 Analysis for thermal effects
Thermal stresses depend upon the thermal gradient and the support restraints of the bridge structure. It
has been shown by Fu et al. (1990) and Dilger et al. (1981) that thermal stresses increase when the
thermal gradient increases. Dilger et al. (1983) and Priestly (1978) have found that, for continuous box
girder bridges, thermal stresses can be in the same order of magnitude as those of live load. Ghali and
Favre (1994) may also be found helpful on this topic.
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C5.5 Requirements for specific bridge types
C5.5.1 General
In order to be satisfactory in service, a bridge needs to be designed so that it can adequately resist the
effects of longitudinal moment, transverse moment, longitudinal torsion, longitudinal vertical shear,
transverse vertical shear, and in-plane forces. Methods of analysis exist that are capable of giving the
effects of all of these, and such methods are quoted in Section 5. Some of these methods, for example,
folded plate and finite strip methods, are such that they give all of the required information directly,
without calculating explicitly the overall magnitude of any structural response such as longitudinal
moment.
For certain types of bridges, it is frequently possible to use more simplified methods of analysis that
do not take account of all of the structural responses just mentioned. Such simplified methods are
embodied, for example, in the AASHTO Specifications. In these specifications, it is only necessary to
cater directly for longitudinal moment and longitudinal vertical shear, the remaining structural
responses being looked after by the specification of minimum thicknesses of material, minimum
percentages of reinforcement, and the like. In particular, for bridges with shallow superstructures, a
design that is satisfactory for some of the structural responses will be found to satisfy other
requirements automatically, provided that the bridges are free of complicating aspects such as heavy
skew. As an example, one may consider, for a slab bridge without skew, a slab that is designed on the
basis of transverse bending moment. Such a slab is invariably found to be more than adequate to
accept any longitudinal torsion that arises. Again, if the slab of a slab-on-girder bridge is designed by
the empirical method of Section 8, it is found that such a slab can accommodate both transverse
moments and transverse vertical shears without the need to calculate these.
C5.5.2 Voided slab — Limitation on size of voids
Structural responses
It is noted that the requirement to analyze for transverse moments is retained. This is because even
though, under dead load, such moments are frequently very small, there are some cases in which they
must be considered. Examples are cantilevered overhang portions of decks and decks in the vicinity of
isolated supports.
In the case of voided slab bridges, there is a limit to the size of voids that can be accepted if warping
of the cross-section is to be negligible. The limitations for circular voids and rectangular voids from this
point of view are given in Clause 5.5.2. Designers should bear in mind that minimum thickness
requirements for proportioning are given in Section 8.
C5.5.4 Truss and arch
The forces in the members of a truss are calculated by linear analysis; nevertheless, stability of
individual members and overall stability of the truss should be considered. The AASHTO LRFD Bridge
Design Specifications may be found useful for simplified moment magnification methods for the
analysis of short to medium span arches.
C5.5.5 Rigid frame and integral abutment types
C5.5.5.1 Rigid frame
The work of Robbins and Green (1978) is recommended for information on the behaviour of such
bridges; this work may be found helpful in complying with the requirements of Clause 5.5.5.1.
The effects of axial force and bending moments induced from frame action, restrained moment and
applied loads need to be included in the analysis, together with the stability effects resulting from the
application of axial forces.
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C5.5.5.2 Integral abutment
Because this type of structure eliminates the expansion joints at the abutments, the effects of structural
continuity need to be taken into account.
Integral abutment bridges need to be designed to resist all of the vertical and lateral loads acting on
them individually and in combination. The combined load effects on the structure at various stages of
Construction also need to be considered in the design.
The analysis of structural response at the stages at which the structure is simply supported, then later
made integral with the abutments and backfilled, are of primary importance. Consideration should be
given to the rigidity of the entire frame and the connection detail of superstructure and abutment in
establishing the degree of fixity at the abutment corners. It is conservative to design the girders for positive
moments by treating them as simply supported but to allow for full continuity in establishing the design
requirements for the abutment wall, the piles, and the negative moment region of the girders. In some
cases, it may be economical to take advantage of frame action in the design of the girders by assuming
partial fixity. The degree of fixity assumed should be consistent with the abutment connection detail.
Husian and Bagnariol (1996) may be consulted for further information.
C5.5.7 Box girder
In box girder bridges, torsional warping effects are often considerable and cannot be ignored, especially in
bridges of steel or steel/concrete composite construction. Maisel (1982), Kollbrunner and Basler (1990),
and Haaijeer (1981) will be found helpful in calculating such effects.
Distortional warping is a very important aspect of behaviour of box girder bridges; its effects can be
considerably reduced by the provision of adequate diaphragms or cross-frames. Richmond (1966) and
Haaijer (1981) provide guidance on these effects.
The Engineer needs to clearly distinguish between the distortional and warping effects present in box
girder bridges. In the case of torsion on a box section in which distortion is prevented by means of internal
diaphragms or cross-frames, the section will experience torsional warping if the section is free to warp
longitudinally or it will develop warping stresses if it is not free to do so. Figures C5.3 and C5.4 illustrate
the behaviour of box girders under bending and torsional moments. In the case of a section with internal
diaphragms or cross-frames that possess insufficient number or inadequate stiffness, the section will
experience distortional warping (deformation of the section in its own plane) that will also create
longitudinal displacement or stresses depending upon the restraint of the longitudinal movement. Usually,
if internal diaphragms or cross-frames are not adequately provided in terms of number and stiffness, the
warping displacements or stresses due to distortional warping are greater than those due to torsional
warping. Normandin and Massicotte (1995) or Rybarova and Massicotte (1996) may be found useful.
The provision of adequate diaphragms or cross-frames, and the consequent diminution of distortional
effects, enables simplified methods of analysis to be used without the need to calculate these effects due to
live loading.
2P
2P
4P
Bending
2P
2P
General
loading
Torsion
Figure C5.3
Behaviour of box girder — Bending and torsional decomposition
(See Clause C5.5.7.)
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P(b/h)
P
2P
P
P(b/h)
St-Venant
2P
Rotation
Axial stresses
or warping
displacements
Shear flow
Sectional
distortion
Axial stresses
or warping
displacements
Transverse
bending
moments
h
P(b/h)
Torsion
b
P
P
P(b/h)
Distortion
Figure C5.4
Behaviour of box girder — Torsional components
(See Clause C5.5.7.)
C5.5.8 Single-spine bridges
Where transverse distortion of a superstucture is small in comparison with longitudinal deformation,
the former does not significantly effect load distribution; hence an equivalent beam idealization is
appropriate. The relative transverse distortion is a function of the ratio between structural width and
height, with the latter, in turn, being a function of the length. Thus, the criterion is presented as the
length-to-width ratio.
The appropriate torsional and flexural moments, shear and reaction forces, and the resulting stresses
are superimposed as appropriate. The equivalent beam idealization does not alleviate the need for
investigation of warping effects in steel structures. In all equivalent beam idealizations, the eccentricity
of load with respect to the beam centre-of-gravity needs to be accounted for. With symmetrical
cross-sections that are curved in plan, the centre of gravity of the permanent loads falls outside of the
centre of gravity and shear centre of the cross-section, and the resulting eccentricity needs to be
investigated.
C5.6 Dead load
C5.6.1 Simplified methods of analysis (beam analogy method)
In the case of dead load, the simplified method of analysis that treats the bridge superstructure as a
beam is permissible provided that transverse effects are small. This means that such aspects as heavy
skew and pronounced curvature-in-plan are not acceptable. Analysis as a beam is permissible,
generally speaking, whenever the applied loading results closely in single curvature rather than double
curvature.
C5.6.1.1 Conditions for use
The restrictions that are applied to the analysis of live load effects are also imposed for the dead load
analysis of skew bridges in which the concrete deck is cast when the girders are shored. The rationale
to the restrictions is discussed in Clause C5.7.1.
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C5.7 Live load
C5.7.1 Simplified methods of analysis
C5.7.1.1 Conditions for use
Simplified methods of analysis for live load for the Code are based on the analysis results from many
bridge structures using grillage, semi-continuum, and finite element methods, for which the idealized
structure was essentially an orthotropic plate. The conditions for the use of simplified methods of analysis
are consistent with those that were present in the Ontario Highway Bridge Design Code. The analysis for the
OHBDC was based upon regarding the bridge superstructure as a rectangular orthotropic plate that was
simply supported at two opposite ends on unyielding line supports that were continuous across the width
of the plate and did not impose moment restraint. The restrictions on the use of this method of analysis
are the same as those that were present in CAN/CSA-S6-88. For consistency, these same restrictions were
used as a basis for establishing the limitations for the simplified analysis methods of the Code. The
restrictions are given in Clause 5.7.1.1 and the bridge must not depart significantly from these conditions
if the simplified methods of analysis are to be valid.
Shear-connected beam bridges are analyzed by the methods applicable to shallow superstructures,
provided that continuity of transverse flexural rigidity across the cross-section is present. If not, the analysis
for longitudinal moments and shears is by the same method as for multispine box girders.
When the skew angle of a bridge is less than 20°, it usually has been considered safe to ignore the skew
angle and analyze the bridge as a right bridge whose span is equal to the skew span. The implication of
this practice is that the angle of skew is considered to be the only necessary measure of the “skewness” of
the bridge with respect to its load distribution characteristics.
Consistent with prevalent practice, the OHBDC in its first two editions specified that bridges having
skew angle, ψ , smaller than 20° could be analyzed as equivalent right bridges. After extensive
comparative analyses of skew and equivalent right bridges, it has been shown by Jaeger and Bakht (1989)
that the angle of skew of the bridge is, indeed, not the only necessary measure of its skewness, which is
also affected by its span, width, and girder spacing, if present. In particular, it has been shown that a
dimensionless parameter characterizing the skewness of a slab-on-girder bridge is S tan ψ / L, and for a slab
bridge is B tan ψ /L, where B is the bridge width and the other notation is as defined in the Code. For
permitting the analysis of a skew bridge as an equivalent right bridge, the Code has imposed the upper
limits of 1/18 and 1/6, respectively, for these parameters. These limits ensure that the shear values in
particular are not in unsafe error by more than 5%. It is to be noted that the force effects in skewed,
slab-on-girder type bridges may be analyzed by the simplified methods presented in Annex CA5.1, if the
other provisions of Clause 5.7.1.1 are met. The simplified methods presented in Annex CA5.1 enable the
designer to calculate the increased shear effects that occur with increasing skew.
The two limitations pertaining to an overhanging deck slab, as given in Clause 5.7.1.1(h) and adopted
from previous bridge design codes, relate to the need to have the structure remain such that the
orthotropic plate approximation is closely applicable. For a deck-on-girder bridge with equally spaced
girders a distance S apart, a cantilever overhang of S / 2 on either side is the desired condition, since each
longitudinal girder can then be associated in a width S /2 of deck on either side of its centerline; a
uniformly distributed load over the entire deck area would then result in the girders sharing equally in
accepting the total longitudinal responses. If the overhang is permitted to be a maximum of 0.6S, the
outer girders then accept rather more bending moment and shear force than the interior ones, but the
departure from uniformity is still acceptable.
So far as the limitation on the deck overhang of 1.80 m is concerned, when due allowance is made for
barrier walls, curbs, etc., this limitation means that when a vehicle is travelling as far over in the outside
lane as possible, its centre of gravity will not be significantly outside the centerline of the outermost girder.
This limitation is necessary if the orthotropic plate representation is to be realistic.
The bridges selected for establishing analysis results for the simplified methods in the Code had the
same limitations for the deck slab overhang, being equal to or less than 60% of the girder spacing, S, with
a maximum overhang equal to 1.8 m.
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C5.7.1.2 Longitudinal bending moments in shallow superstructures
C5.7.1.2.1 Longitudinal bending moments for ultimate and
serviceability limit states
The concept of analyzing the bridge as a single beam line, by applying the total number of lanes on
the bridge that are to be contained within the curb-to-curb width, as specified in Section 3, is easily
comprehensible.
The total load applied to the bridge will be n lanes, reduced by the multiple presence factor, RL , as
stipulated in Section 3. If the effects were averaged over the width of the bridge, the average effect
across the width would be uniform, as shown in Figure C5.5.
If MT is the total moment of one lane, the average moment intensity per metre of width is
mavg =
nMT RL
B
Envelope of mx
mx
mavg
S
B
Figure C5.5
Transverse variation of maximum longitudinal moment
intensity in the idealized orthotropic plate
(See Clause C5.7.1.2.1.)
For girder-type bridges, the total moment on the cross-section at any point along the span can be
averaged by sharing the total moment equally among all girders, such that Mg avg = nMT RL /N.
The actual variation in maximum force intensity across the width of the bridge depends on the
transverse position of the lane loads, the torsional stiffness of the cross-section, the span length, and
the transverse and longitudinal stiffnesses Dy and Dx , respectively. The actual intensity of force effects
will be greater than, or at best, equal to, the average intensity. This transverse variation in force effect
can best be visualized by the introduction of an amplification factor, Fm , which represents the ratio of
the true intensity to the average intensity. In the example presented for moment intensity, the
transverse distribution factor for moment, Fm , will be
Fm =
mx
mavg
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In Figure C5.5, the value mx represents the envelope of maximum longitudinal moment intensities
across the width of the bridge, which is derived by analyzing the bridge for cases of one, two, three, or
four lanes loaded, if appropriate, for ultimate and serviceability limit states.
In the Code, Fm is expressed as follows:
Fm =
SN
mCf ⎞
⎛
F ⎜ 1+
⎟
100
⎝
⎠
For girder-type bridges with girders at equal spacings and exterior deck overhangs of one-half of the
girder spacing, the term SN in the numerator, represents the bridge width B; consequently the equation
takes the same form as the expression for slab and voided slab type of bridges. The denominator of the
equation represents a width, in metres, that always needs to be less than the actual bridge width, or SN,
with the result that Fm always needs to be greater than 1.00.
It will readily be appreciated that such a ratio may be different for external girders of a cross-section
than for internal ones, because of the extremely nonuniform distribution of moments and shears that
result from eccentric loads. Because of this, internal and external girders are treated separately. Designers
may sometimes wish to take the highest value of this ratio and use it for designing both internal and
external girders.
For slabs and voided-slab bridges, a similar approach is used, except that the relevant formulae are for a
one metre width of slab rather than for S metres spacing between girders.
It is recalled that, in earlier codes, the transverse distribution of live load was commonly represented by
a width D, having the units of length that, when related to the spacing S between girders, gave the
fraction S/D of one line of wheels which was to be carried by one girder and the associated portion of the
deck of a slab-on-girder bridge. In the AASHTO and CSA S6 specifications, a value of D was given for each
type of bridge, and was taken to be constant for all bridges of that type.
The first two editions of the OHBDC provided methods of obtaining D from charts, using a
nondimensional bending parameter, θ , and a nondimensional torsional parameter, α ; this approach was
based upon orthotropic plate theory. The third edition of the OHBDC provided methods of obtaining D
using equations that account for the variables of bridge type, span length, bridge width, and lane width.
Bakht and Jaeger (1988, 1990, and 1991) may be consulted for further information. These methods were
derived from the results of the orthotropic analyses from the first and second editions. D was defined as
the uncorrected width, in metres, of a longitudinal strip over which a line of truck wheels should be
distributed.
It can be shown that F in Clause 5.7.1.2.1 for distribution of highway live load at ULS and SLS is
conceptually related to D as it appeared in the OHBDC by the following expression:
F = 2nRLD
In the Code, selected structures in the shallow superstructure group were analyzed including slabs,
voided slabs, slab-on-girders, wood deck-on-girders, and steel grid deck-on-girders. The analysis results,
presented in a series of reports by Smith (1996, 1997), were used to reformulate the distribution
characteristics using the same variables as in the third edition of the OHBDC but utilizing the amplification
factor format explained above. In addition, Aly (1996) analyzed numerous slab-on-girder bridges with
practical ranges of α and θ and constant girder spacings equal to 1.80 m. The results of these analyses
were in agreement with the corresponding analyses by Smith (1996).
The magnitudes of F have been derived, accounting for a known range of stiffness parameters for North
American bridges.
For slab-on-girder bridge types, it is recognized that bridges constructed with girders possessing a high
longitudinal flexural stiffness will attract more load than those composed of shallow flexible girders. A
comprehensive sample of composite steel and prestressed concrete bridges from the Province of New
Brunswick were examined and an average stiffness parameter, Dx , was determined to be represented by
the following equation:
Dx = 3350L2 + 66 000L
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where Dx is the flexural stiffness per metre of width in kN-m2/m and L is the characteristic span length
in metres as determined from Annex A5.1. It is noted that the values of Dx thus obtained are about
25% larger than those given by the upper-bound representation by Bakht and Moses (1988) that were
used in the development of the OHBDC simplified methods. Consequently, greater live load responses
are attracted to the longitudinal girders of slab-on-girder types as a result of the increased stiffness
used for the establishment of the Code’s simplified methods.
Approximately 550 slab-on-girder bridges were analyzed for varying span lengths, girder spacings,
lane widths, bridge widths, and deck slab overhangs (Smith 1996, 1997). A sample of the analysis
results for the internal girders of a narrow 3-lane bridge with Wc = 10.0 m, We = 3.33 m, and deck slab
overhang = 0.5S, is shown in Table C5.1. The results are compared with the values determined from
the equations presented in the Code. The equations for F were derived using a format that excluded
the variable S, the girder spacing, for simplicity, as was also done in the third edition of the OHBDC.
Examination of the results reveals that F at ULS and SLS may vary by up to 10% for different girder
spacings, S, if the span length is held constant.
The equations for F were selected to safely satisfy most cases for the various cross-section
configurations that were analyzed. Only the analysis results for bridges that were considered to be of
realistic configurations were considered for the final selection of the equations for F.
Table C5.1
Analysis results for flexure — 3-lane slab-on-girder
at ULS and SLS, B = 10.92 m
(See Clause C5.7.1.2.1.)
Summary of F value for 3-lane bridges
Internal girders
Class A bridges
B = 10.92 m
Narrow
Slab-on-girder
0.5S overhang
No. of girders in cross-section and girder spacing, m
Span
3
4
5
6
7
9
F min
F CHBDC
Code
% increase
3.66
2.73
2.18
1.82
1.56
1.21
3
7.73
7.54
7.45
7.97
6.72
6.65
6.646
6.93
–4.12%
5
7.35
7.51
7.66
7.89
7.13
7.18
7.128
7.10
0.39%
10
7.46
7.86
7.73
8.20
7.66
7.68
7.459
7.52
–0.81%
15
7.83
8.40
8.15
8.67
8.17
8.20
7.834
8.21
–4.58%
20
8.47
8.97
8.72
9.09
8.75
8.79
8.472
8.56
–1.00%
30
9.88
9.86
9.60
9.47
9.37
9.33
9.325
8.91
4.72%
50
10.36
10.27
10.01
9.61
9.40
9.13
9.130
9.18
–0.57%
80
10.54
10.43
10.13
9.67
9.40
9.07
9.070
9.34
–2.89%
Slab and voided slab types with geometrical configurations conforming to Clauses 5.5.2 and 5.7.1.1
and Section 8 were selected for performing refined analysis for the purpose of establishing the
equations for F. Solid slabs were used for span lengths of 15 m or less, with a span-to-depth ratio of 20.
For spans greater than 15 m, rectangular voided slabs with span-to-depth ratios of 20 and 25 were
used for determining F for flexure at ULS and SLS.
For design purposes, recognizing that some degree of lack of uniformity always exists, a lower limit
of 1.05 is imposed upon Fm . The numerical value of Fm is indicative of the ability of the bridge to
transfer loads across the width of the structure. Bridges with good transverse load distribution
characteristics, such as narrow voided-slab types, will have Fm in the range of 1.05 to 1.10. A graphical
representation of Fm versus L for slab and voided slab bridges with narrow lane widths equal to 3.33 m,
given in Figure C5.6, confirms these observations. As shown in Figure C5.7, wide bridges of the
deck-on-girder type have Fm in a higher range of approximately 1.2 to 1.5. Figure C5.7 is a graphical
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representation of Fm versus L for slab-on-girder types with narrow lane widths equal to 3.33 m and a deck
slab overhang equal to 0.5S. Wider bridges will obviously have a greater departure from the average
moment intensity condition; this is the reason for the larger Fm for this type of bridge. In general, Fm will
increase as the bridge width B increases, for slab-on-girder bridge types.
When using Tables 5.3 to 5.5, the term L for continuous spans is as specified in Clause A5.1.4.
The analysis results for the external girders of slab-on-girder types indicate that Fm increases significantly
when the deck slab overhang exceeds 0.5S. Therefore, the equations for F were formulated for bridges
with the deck overhang equal to or less than 0.5S. An increase of 5% in Fm was found to be sufficient to
represent most bridges with an overhang between 0.5S and 0.6S.
The F values presented in Table 5.3 are for bridges comprising four design lanes or less. The equations
provided for the calculation of F for bridges comprising five design lanes or more are derived in such a
manner that the distribution factors are equal to those of a 4-lane bridge.
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Fm for internal portion
ULS and SLS — slab and voided slab bridge types narrow lane widths
1.6
1.5
1.4
Fm
2 Lane
3 Lane
4 Lane
1.3
1.2
1.1
1.0
0
20
40
60
80
100
120
Span L, m
Fm for external portion
ULS and SLS — slab and voided slab bridge types narrow lane widths
1.6
1.5
1.4
Fm
2 Lane
3 Lane
4 Lane
1.3
1.2
1.1
1.0
0
20
40
60
80
100
120
Span L, m
Figure C5.6
Fm curves for slab and voided slab type — Narrow lane width
(See Clause C5.7.1.2.1.)
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Fm for internal girders
ULS and SLS — slab-on-girder
Narrow lane width — 0.5S deck slab overhang
1.8
1.7
1.6
Fm
2 Lane
3 Lane
4 Lane
1.5
1.4
1.3
1.2
1.1
1.0
0
20
40
60
80
100
120
Span L, m
Fm for external girders
ULS and SLS — slab-on-girder
Narrow lane width — 0.5S deck slab overhang
1.8
2 Lane
3 Lane
4 Lane
1.7
1.6
Fm
1.5
1.4
1.3
1.2
1.1
1.0
0
20
40
60
80
100
120
Span L, m
Figure C5.7
Fm curves for slab-on-girder type — Narrow lane width
(See Clause C5.7.1.2.1.)
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C5.7.1.2.2 Longitudinal bending moments and associated deflections
for fatigue limit state and superstructure vibration
Simplified methods of analysis at the fatigue and vibration limit states are treated in a similar fashion to
that of ULS and SLS with the exception that only one vehicle is placed on the bridge for the
computation of the average force effects. Consequently, Fm at FLS will be larger than Fm at ULS due to
the greater lack of uniformity in moment and shear distribution transversely across the bridge.
Figure C5.8 illustrates the variation of Fm at the fatigue limit state for the internal girders of 2, 3, and
4 lane slab-on-girder bridges with narrow design lane widths equal to 3.33 m and a deck slab
overhang of 0.5S. The values of Fm shown in Figure C5.8 are those for selected minimum practical
girder spacings, since Fm varies with the girder spacing and the span. The curves for the internal
girders are derived by using selected girder spacings corresponding to various span length ranges. In
the span range up to approximately 40 m, a spacing S greater than 1.2 m was used. In the 50 m span
length range, a spacing S greater than 1.7 m was selected. For spans greater than 50 m, values of S
greater than 2.0 m were used for selecting Fm. Again, the trend is for Fm to increase as the deck width
B increases. Also, for internal girders, Fm generally decreases as the span length L increases. This trend
may or may not be true for external girders and depends on the vehicle edge distance, DVE , and the
bridge width.
Fm for fatigue limit state
Slab-on-girder — internal girders
Narrow lane width — 0.5S deck slab overhang
4.5
B = 7.6 2 Lane
B = 10.9 3 Lane
B = 14.4 4 Lane
4.0
3.5
3.0
Fm
2.5
2.0
1.5
1.0
0.5
0
0
20
40
60
80
100
120
Span L, m
Figure C5.8
Fm curves for internal girders of slab-on-girder type at FLS
(See Clause C5.7.1.2.2.)
The influence of vehicle edge distance upon the selection of Fm for the design of a slab-on-girder
bridge for fatigue and vibration limit states is exemplified by comparing curves of Fm for the internal
and external girders. If DVE = 1.00 m, Fm for the external girder will be larger than Fm for the internal
girders when spans are approximately 15 m in length or longer, as is also the case for live loading at
ULS and SLS. When the vehicle is placed in the centre of the travelled lane, DVE increases, thereby
reducing Fm for the external girder such that it is comparable to that of the internal girders in the
longer span range.
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Figure C5.9 illustrates the variation of Fm at the fatigue limit state for the external girders of 2, 3, and 4
lane slab-on-girder bridges with narrow design lane widths equal to 3.3 m and a deck slab overhang of
0.5S. Two charts are shown, one with DVE equal to 1.00 m and another with DVE equal to 1.50 m. For
small values of DVE , the trend of diminishing Fm with a corresponding increase in span length L is present
for narrow bridges. However, as the bridge width increases and DVE increases, this trend actually reverses
as illustrated in Figure C5.10. This figure illustrates the effect of vehicle edge distance upon the value of Fm
for a 3-lane slab-on-girder type of bridge with narrow design lane width equal to 3.33 m.
For consistency in the selection of a format for the equation for the distribution factor F for this Code,
the girder spacing S was omitted as a variable, as it had been in the third edition of the OHBDC, for
presentation of the equations in Table 5.4. This is the same format as that used for F at ULS and SLS, where
F depends on the bridge type and width, lane width, and span length L. Smith (1996) presents the results
of the analysis for approximately 600 slab-on-girder bridges on which the equations in Table 5.4 are
based. The analysis results revealed that, for internal girders, the distribution characteristic F depends
much more on the girder spacing, S, for the one-lane-loaded condition. For internal girders, the variation
of F with the girder spacing S for a particular bridge width and span length may be as low as 10% for very
short spans and as large as 80% for very long spans. In general, F increases as S increases, if the span
length, bridge type, bridge width, and stiffness parameters are held constant. The equations for the
internal girders are derived by using the minimum values of F that were determined from the analysis
results, which coincidentally usually represent the analysis results for bridges with minimal girder spacing.
A further modification factor is presented for internal girders of slab-on-girder type bridges to account for
the influence of girder spacing for the one-lane-loaded case, since this influence is substantial. In the
longer span range, the variance between the modified equation for F for internal girders and the analysis
results for large girder spacings and long spans was effectively reduced to between 0% and 20% by using
the modification equation that accounts for girder spacing.
Fm for fatigue limit state
External girders — slab-on-girder - 3 lane
Narrow lane width — 0.5S deck slab overhang, B = 10.92
3.0
2.5
2.0
Fm
1.5
DVE = 1.00
DVE = 1.50
DVE = 2.00
DVE = 2.50
DVE = 3.00
1.0
0.5
0
0
20
40
60
80
100
120
Span L, m
Figure C5.9
Fm curves for external girders of 3-lane narrow
slab-on-girder type at FLS
(See Clause C5.7.1.2.2.)
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Fm for fatigue
Slab-on-girder — DVE = 1.00 m
Narrow lane width — 0.5S deck slab overhang
4.0
3.5
3.0
Fm
2.5
2.0
1.5
B = 7.6 2 Lane
B = 10.9 3 Lane
B = 14.4 4 Lane
1.0
0.5
0
0
20
40
60
80
100
120
Span L, m
Fm for fatigue
Slab-on-girder — DVE = 1.50 m
Narrow lane width — 0.5S deck slab overhang
4.0
3.5
3.0
Fm
2.5
2.0
1.5
B = 7.6 2 Lane
B = 10.9 3 Lane
B = 14.4 4 Lane
1.0
0.5
0
0
20
40
60
80
100
120
Span L, m
Figure C5.10
Fm curves for external girders of slab-on-girder type at FLS
(See Clause C5.7.1.2.2.)
Table C5.2 gives a sample of the comparison of analysis results with the equations for distribution
characteristics for bridges with closely spaced girders as presented in Tables 5.4 and 5.5. Table C5.3
presents the values for F as determined using the equations for modifying F for the effect of girder
spacing S. This comparison reveals a very good agreement, but may indicate where an Engineer may
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wish to perform a more refined analysis for some bridges with widely spaced girders in order to improve
upon the distribution factor. However, it should be noted that the external girder may take precedence
over the internal girders in those situations, since the variance in F with girder spacing is not as significant
for external girders.
Table C5.2
Analysis results for internal girders of 3-lane
slab-on-girder with narrow lanes
(See Clause C5.7.1.2.2.)
Summary of F value for 3-lane narrow, 0.5S overhang
Internal girders — slab-on-girder
No. of girders and spacing in m
Span L, m 3
3.660
4
2.730
5
2.180
6
1.820
7
1.560
9
1.210
F min
3
4.270
3.583
5
4.256
3.646
10
4.413
15
Analysis
results
F Code
%
increase
F min
3.364
3.459
3.088
3.088
3.160
–2.28%
3.464
3.474
3.562
3.524
3.464
3.400
–1.88%
4.087
4.033
4.079
4.100
4.020
4.020
4.000
0.49%
4.748
4.700
4.684
4.674
4.507
4.248
4.248
4.267
–0.44%
20
5.250
5.330
5.259
5.108
4.760
4.434
4.434
4.400
0.77%
30
6.523
6.524
6.195
5.518
5.090
4.704
4.704
4.533
3.76%
50
8.042
7.316
6.280
5.560
5.172
4.776
4.776
4.640
2.94%
80
8.781
7.511
6.229
5.567
5.204
4.826
4.826
4.700
2.68%
100
8.951
7.545
6.219
5.567
5.211
4.841
4.841
4.720
2.57%
120
9.076
7.573
6.214
5.567
5.214
4.853
4.853
4.736
2.48%
Note: Shaded areas = F less than the Code.
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Table C5.3
Code equations for internal girders of 3-lane
slab-on-girder bridges with narrow lanes
(See Clause C5.7.1.2.2.)
Summary of F for three lane narrow, 0.5S overhang, Code equations
Internal girders; slab-on girder
Number of girders/Spacing in m
3
4
5
6
7
9
Span L
m
3.660
2.730
2.180
1.820
1.560
1.210
Analysis
results
Fmin
Code
Fmin
Increase
%
3
3.160
3.160
3.160
3.160
3.160
3.160
3.088
3.160
–2.28%
F adjusted for girder spacing
5
3.400
3.400
3.400
3.400
3.400
3.400
3.464
3.400
1.88%
10
4.000
4.000
4.000
4.000
4.000
4.000
4.020
4.000
0.49%
15
4.646
4.502
4.417
4.361
4.321
4.267
4.248
4.267
–0.44%
20
5.183
4.886
4.710
4.596
4.513
4.401
4.434
4.400
0.77%
30
6.146
5.535
5.173
4.936
4.765
4.535
4.704
4.533
3.76%
50
7.941
6.689
5.947
5.465
5.115
4.644
4.776
4.640
2.94%
80
8.044
6.776
6.026
5.536
5.181
4.704
4.826
4.700
2.68%
100
8.078
6.805
6.052
5.559
5.203
4.724
4.841
4.720
2.57%
125
8.105
6.828
6.072
5.578
5.221
4.740
4.853
4.736
2.48%
It is prudent to note that the relationship between F and D from the previous Code format for
fatigue limit state is expressed by F = 2D, since neither lane load reduction factors nor multiple lane
loading are involved.
The effect of the vehicle edge distance, DVE , on the correction factor Ce can be seen in Figure C5.11
for a 3-lane slab-on-girder bridge.
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Equations for DVE correction
1 + Ce / 100
Slab-on-girder — 3 Lane
2.5
DVE = 1.00
DVE = 1.50
DVE = 2.00
DVE = 2.50
DVE = 3.00
2.0
1+
Ce
1.5
100
1.0
0.5
0
0
20
40
60
80
100
120
Span L, m
Figure C5.11
Vehicle edge distance correction — 3-lane slab-on-girders
(See Clause C5.7.1.2.2.)
Approximately 100 slab and voided slab type of structures were analyzed by refined methods for
establishing the equations for F for the fatigue and vibration limit state. A graphical representation of Fm for
3-lane bridges with narrow design lane widths equal to 3.33 m is given in Figure C5.12 for both internal
and external portions. These curves again reveal the better distribution characteristics for the voided slab
type as compared to the slab-on-girder type, since Fm is significantly less for the slab and voided slab type
for any selected span length.
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Fm for fatigue limit state
Slab and voided slab
3 Lane — narrow lane width
3.0
2.5
External portion
Internal portion
2.0
Fm
1.5
1.0
0.5
0
0
20
40
60
80
100
120
Span L, m
Figure C5.12
Fm for 3-lane narrow slab and voided slab bridge at the
fatigue and vibration limit state
(See Clause C5.7.1.2.2.)
The values of F for the external and internal portions of slab and voided slab types were determined
using a minimum DVE equal to 1.20 m for the bridges with narrow design lane widths equal to
3.33 m, while DVE equal to 1.50 m was used for bridges with design lane widths equal to 3.9 m. No
correction factor for vehicle edge distance was derived for this type of structure, since it is not as
influential as it is in the case with slab-on-girder types.
Approximately 120 wood deck-on-girder bridges were analyzed for determining F for the fatigue
and vibration limit state. Again, no correction factors were determined for the effects of vehicle edge
distance. The equations for F for the external girders were selected using a minimum value of
DVE = 1.20 m.
C5.7.1.3 Longitudinal bending moments in multi-spine bridges
When the transverse flexural rigidity, Dy , of a structure is very small compared to its longitudinal
rigidity, as it is in multi-spine bridges, the influence of the actual magnitude of Dy on distribution
properties becomes very small. These distribution properties are then capable of being represented by
the single parameter β defined in Clause 5.7.1.3, as discussed in Bakht and Jaeger (1985). The
expressions for F that are given in Table 5.6 were derived from the results of the analysis of several
multi-spine bridges by the finite element, grillage, and folded plate methods. Normandin and
Massicotte (1995) and Rybarova and Massicotte (1996) will be found useful for further details. It needs
to be noted that the simplified analysis method is based on the assumption that the boxes contain
sufficient internal bracing to prevent them from distorting. External diaphragms, or cross-frames,
between the girders do not substantially improve the distribution of live load at ULS and SLS. However,
at FLS, the distribution characteristics may improve by as much as 20%. The expressions for F in this
clause were derived without the presence of cross-frames between the girders in order to be consistent
with Clause A5.1(d) and other parts of the Code.
In the calculation of β , it is noted that for multi-spine girder types, Dx = SiL and Dxy = SjL , where iL
and jL are as defined in Annex A5.2.
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C5.7.1.4 Longitudinal vertical shear in shallow superstructures
Bakht and Jaeger (1985), among others, have shown that the D values for longitudinal moments, and
hence F, when applied to longitudinal vertical shears, as is done in some bridge codes, can lead to large
errors.
C5.7.1.4.1 Longitudinal vertical shear for ultimate and serviceability
limit states
The methods specified in Clauses 5.7.1.4.1 and 5.7.1.4.2 were developed by a systematic analysis of a
large number of structures using the semi-continuum, grillage, and finite element methods. The
procedure for calculating Fv is similar to that for longitudinal moments.
C5.7.1.4.2 Longitudinal vertical shear for fatigue limit state
The distribution factors for F presented in Clause 5.7.1.4.2 for slabs and voided slabs are DVE = 1.20 m for
bridges with narrow design lane widths of 3.3 m, and DVE = 1.50 m for bridges with design lane widths of
3.9 m. For the case of one-lane-loaded at ULS with DVE = 1.00 m, the shear may be found by increasing
those obtained from Clause 5.7.1.4.2 at FLS by 6% for solid slabs and 10% for voided slabs.
C5.7.1.5 Longitudinal vertical shear in multi-spine bridges
Clause 5.7.1.5 is based on considerations similar to those outlined in Clause C5.7.1.3.
The analyses results presented in Normandin and Massicotte (1995) and Rybarova and
Massicotte (1996) reveal that the distribution factor F for shear does not vary as a function of the
parameter β , as is applicable for bending moment. Also, it is noted that the analyses results reveal that the
case of one-lane-loaded often governs for the distribution of shear at ULS and SLS and, if not, is
comparable to the multiple-lanes-loaded condition.
C5.7.1.6 Deck slab moments due to loads on the cantilever overhang
C5.7.1.6.1 Transverse moments due to wheel loads on the cantilever
overhang
C5.7.1.6.1.1 Transverse moments in the cantilever overhang
In the second edition of the OHBDC, My was obtained from
My =
PA ′
p
1
⎡ A ′x ⎤
cosh ⎢
⎥
⎣C − y ⎦
It has been shown by Jaeger and Bakht (1990) that the above equation is closely equivalent to the
algebraic equation given in Clause 5.7.1.6.1.1, in which the old A’ has been replaced by 2A to be
consistent with the notation used in Jaeger and Bakht (1990) and other publications.
The moments provided in Table 5.10 address the case of a cantilever slab with infinite rotational stiffness
at the root of the cantilever. The moment intensity decreases as the ratio S / Sc increases, thereby
decreasing the rotational stiffness at the root of the cantilever. A more refined method of analysis is
presented in Mufti et al. (1993), which accounts for cases in which the rotational restraint at the root of
the cantilever is finite. The designer must be aware that the case of infinite rotational restraint may be
more appropriate, and conservative, for the determination of cantilever moment intensity in some bridges
due to the presence of stiff transverse diaphragms in the first panel adjacent to the cantilever.
The designer should account for the possibility of full wheel loads being placed on the cantilever deck
slab during Construction, prior to the casting of the barrier, when selecting a value of A for the design of
the cantilever deck slab, unless other provisions are made. The case of the unstiffened edge should be used
to evaluate this situation. Also, the continuity of longitudinal reinforcement in the barrier should be
assured before using the stiffened edge case for design.
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For the stiffened edge case, the stiffness used to evaluate A was equivalent to that of a standard
New Jersey Barrier. Tadros et al. (1994) may be consulted for more information.
Table 5.10 has been prepared for the CL-625 Truck. If a slab is designed for any other CL-W loading,
the design moments should be obtained by multiplying the moments given in the table by a fraction
equal to W / 625.
C5.7.1.6.1.2 Transverse moments in the interior panel next to the
cantilever overhang
A more refined method of analysis for transverse moments in the first interior panel, as the result of
wheel loads applied to the cantilever overhang, has been published by Mufti et al. (1993). In this
reference, it is shown that the transverse moments diminish more rapidly as one moves away from the
exterior girder than the linear decrease that is permitted to be assumed in Clause 5.7.1.6.1.2.
Employing the method presented in Mufti et al. (1993) will result in some saving of reinforcement
compared with an approach using the linear decrease assumption.
C5.7.1.6.3 Transverse moments in cantilever slabs due to railing
loads
The magnitudes of the unfactored loads that are to be applied to various performance level barrier
and/or railing systems to determine the force effects in the deck slab and barrier anchorage are
specified in Clause 3.8.8.1. The length of load application on the barrier and the location or height of
load application above the roadway are specified in Clause 12.4.3.5. Horizontal loads in the transverse
and longitudinal directions are specified to be applied simultaneously with vertical loading on the
barrier or rail.
The force effects in the deck due to horizontal loads alone can be determined and superimposed on
the analysis results of the deck slab for vertical loads applied to the barrier. Simplified methods of
analysis were presented in the OHBDC and CAN/CSA-S6-88 for the determination of moments in the
deck slab due to concentrated horizontal railing loads. A constant length of slab at the exterior edge or
face of barrier equal to 1.50 m was used for determining moment intensity resulting from horizontal
concentrated loads on barriers. This length was increased by a linear dispersion equal to 0.8 times the
distance between the longitudinal line of deck section being analyzed and the face of the barrier,
representing an angle of dispersal equal to 21° for an inner portion of deck. This angle of dispersal was
probably conservative for most cases. However, the magnitudes of the design loads in previous codes
were much lower than the present load requirements for performance level barriers. This necessitates
the use of more refined methods of analysis to determine the dispersal of combined horizontal and
vertical loads that are applied over specified lengths on performance level barriers and rails.
The results of finite element analysis for horizontal loading on selected PL-3 and PL-2 barriers used in
some Canadian provinces are shown in Table C5.4. The factored loads are shown with the length of
the load application at the point of loading on the barrier. Transverse moment intensity (kN-m/m) at
the face of barrier and transverse tensile load intensity (kN/m) in the deck at the barrier-deck
intersection are shown for both inner and end portions of the deck. The end portion of the deck is
located at the discontinuous end of a deck or barrier, such as found at a transverse expansion joint.
The width of an end portion in the longitudinal direction of the bridge deck is approximately equal to
1.5 to 2.0 times the height of load application above the deck. Additional transverse deck
reinforcement is usually placed in this region to resist the increased moment intensity.
The analysis results show lines of dispersion for distribution of moment and tensile load intensities.
This is the classic concept used for load dispersion in previous codes and is only shown here to indicate
the approximate nature of moment and load dispersal. The actual dispersal depends on the stiffness
and geometry of the barrier and deck elements and the load location relative to the supporting
elements. Also, as shown in Table C5.4, the actual lines of dispersion are not linear but vary from
element to element. The results of this analysis would be superimposed on the separate analysis for the
effects of vertical loading on the barrier as specified in Clause 12.4.3.5. This combined analysis would
be used for determining the length and size of cantilever deck reinforcement that may be required to
resist barrier or railing loads. These requirements are independent of the case required to resist vertical
wheel loads as specified in Clause 5.7.1.6.1 and are considered separately. The loading case that
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determines the maximum amount of reinforcement will then govern. The magnitude and distribution of
force effects resulting from vertical barrier loading depend greatly on the location of beam lines in the
deck cross-section. However, the magnitude of maximum moment intensity resulting from horizontal
barrier loading is not as sensitive to this geometrical feature. Regardless, this geometrical feature has an
influence on the dispersal of moment intensity in the deck resulting from horizontal load on the barrier.
Table C5.4
Transverse moments in cantilever slabs due to horizontal
railing loads in selected PL-3 and PL-2 barriers
(See Clause C5.7.1.6.3.)
Horizontal load or moment
dispersion at inner portion of deck
Transverse
moment
per m
Performance Level 3 barrier
405
55
430
80
Pt
170
q
q
Transverse
tensile load
per m
Performance Level 2
barrier with rail
180
170
800
575
1025
Inner
End
portion portion
800
250
250
90
250
min
90
Factored horizontal load Pt
(Clause 3.8.8.1)
357 kN
170 kN
Length of load application
(Clause 12.5.2.4)
2400 mm
1050 mm
Height of load application
above deck (Clause 12.5.2.4)
900 mm
700 mm
Moment in inner portions of deck
per metre at face of barrier
83 kN-m/m
38 kN-m/m
Dispersal angle
for barrier
θ = 42°
q
q
Dispersal angle
for deck
Tensile force in inner portion of
deck at deck edge
144 kN/m
Dispersal angle
for barrier
θ = 3°
Dispersal angle
for deck
Moment in end portion of deck
per metre at face of barrier
102 kN-m/m
Dispersal angle
for barrier
θ = 48°
Dispersal angle
for deck
Tensile force in end portion of deck
at deck edge
161 kN/m
Dispersal angle
for barrier
θ = 0°
188
180
Dispersal angle
for deck
225
θ = 47°
θ = 56°
θ = 55°
100 kN/m
θ = 10°
θ = 25°
θ = 20°
52 kN-m/m
θ = 45°
θ = 55°
θ = 55°
142 kN/m
θ = 0°
θ = 8°
θ = 8°
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C5.7.1.7 Transverse bending moments in decks
C5.7.1.7.1 Concrete deck slabs supported on longitudinal girders
Clause 5.7.1.7.1 is adapted from CAN/CSA-S6-88 after the confirmation of the validity by recent
analyses by Jaeger and Smith (1997). From these analyses, it was found that the transverse moments
are governed by the wheel loads of Axle No. 4 of the Code’s CL-W Truck. The classical expression for
transverse moment, using Axle No. 4, was found to represent the actual transverse moment from the
CL-W Truck sufficiently closely to warrant adapting this equation for the Code, which is desirable since
it is currently familiar to designers.
C5.7.1.7.2 Steel grid decks
Clause 5.7.1.7.2 is adapted from CAN/CSA-S6-88 and the AASHTO Guide Specifications for Distribution
of Loads for Highway Bridges (1994).
C5.7.1.7.3 Transverse laminated wood decking on sawn timber
stringers
Maximum transverse moment intensity, My , due to live loads in the transversely laminated wood
decking of bridges with sawn timber stringers, is the same as the “global” transverse moment. It
depends upon the characterizing parameters α and θ , discussed in Jaeger and Bakht (1985). By
assigning α a small, representative value, and thus eliminating it from explicit consideration, Bakht
(1988) has provided charts for My in bridges with sawn timber stringers for different values of L and θ .
These charts, which correspond to the AASHTO HS-20 vehicle, were obtained by analyzing the bridges
by the well-tested orthotropic plate method. Bakht (1988) has also provided a simple method in
which the charts can be converted to any other design loading.
Using a technique similar to that described in Clause C5.7.1.2, it was found that for a given span
length and bridge width, the value of θ for a sawn timber stringer bridge, and hence the value of My ,
lies within a fairly narrow margin. It was a relatively simple matter to convert the charts of Bakht
(1988) to correspond to the Code’s truck, and present the intensities of My plotted directly against L.
C5.7.1.7.4 Transverse stress-laminated wood deck-on-girders
Prestressed wood decks (with transverse laminates and longitudinal post-tensioning) are provided in
those stringer or girder bridges in which the stringer or girder spacing is relatively large. In these
bridges, My is caused by “local” bending of the deck between stringers, or girders, rather than by
“global” bending which is discussed in Clause C5.7.1.7.3. Bakht (1988) has shown that in these
bridges, My can be determined by assuming the stringers or girders to be nondeflecting; this reference
has also developed, through orthotropic plate analysis, charts for the value of Dt plotted against S. It
was found that these charts could be represented with good accuracy by the simple expression given
in Clause 5.7.1.7.4.
C5.7.1.8 Transverse vertical shear
The development of the method which gave rise to Figure 5.4 will be found in Bakht et al. (1983).
C5.7.1.9 Analysis of stringers in truss and arch bridges
For the purpose of determining the lateral distribution of load, the panel between floor beams may be
regarded similarly to a bridge between nondeflecting supports. The fact that the supports (in this case,
the floor beams) do in fact deflect, improves the load distribution, but the effect is marginal. Hence,
the assumption of nondeflecting supports is slightly conservative. If the stringers are continuous over
the floor beams, the consideration of Clause A5.1.2 may be applied.
The longitudinal distribution of moment may be significantly affected by the flexibility of the
supports, and therefore the requirement for this consideration is presented.
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C5.7.1.11 Analysis of orthotropic steel decks
C5.7.1.11.1 General
Clause 5.7.1.11 briefly outlines the basic requirements for the analysis of orthotropic decks. The methods
presented in Wolchuk (1963) and Troitsky (1987) are considered acceptable methods.
C5.7.1.11.2 Wheel load distribution
The 45° distribution is a conservative assumption.
C5.7.1.11.5 Approximate analysis of decks with closed ribs
The Pelikan-Esslinger method, presented in Wolchuk (1963) and Troitsky (1987), is a well established
semi-empirical method that may be employed.
C5.8 Idealization of structure and interpretation of results
C5.8.1 General
The requirements for idealization contained in Clause 5.8 and in Annex A5.2 are based on many published
papers and reports, of which Goodall (1971), Holowka (1973), and Massonnet and Gandolfi (1967) are
representative, and may be found useful. In the particular case of wind bracing and its interrelationship
with the remainder of the superstructure, the work of Kollbrunner (1990) is recommended.
C5.8.2 Effective flange widths for bending
C5.8.2.1 Concrete slab-on-girders
Clause 5.8.2.1 provides the information necessary to obtain reduced values, Be , of overhang. The total
effective flange width of the cross-section, per girder or per spine, is then obtained by the following:
(left-hand overhang plus central portion plus right-hand overhang), where the central portion may be
noted from Figure 5.5 for various types of superstructure. It is noted that the left-hand value of Be and the
right-hand value of Be may be different, so that an asymmetrical effective section results. This will be the
case when an outermost girder has an overhang B that is not equal to one-half of the clear spacing
between girders.
The formula given in Clause 5.8.2.1 is an accommodation between two different curves as given in
Cheung and Chan (1978). The formula refers to effective flange width for bending.
C5.8.2.2 Orthotropic steel decks
C5.8.2.2.1 Longitudinal ribs
The effective width of deck plate, ao , acting with one rib is defined as the width of strip that will have the
same contraction, when uniformly compressed by longitudinal shearing forces, as the actual plate at the
junction of the rib. The effective width depends on the type and distribution of loading, the span length,
and rib spacing.
Assumption of the effective width equal to the actual rib spacing is permissible for calculations of the
relative rigidity ratio by the Pelikan-Esslinger method and the flexural effects of uniformly distributed load.
Effective width of deck plate for flexural effects due to wheel loads is based on unequal loads on individual
ribs. The stipulated values are based upon more exact computations.
If the ribs are closely spaced and the loading of adjoining ribs varies considerably, as in the case of an
orthotropic bridge deck, the exact computation of effective width becomes rather involved. However,
for practical purposes, it is sufficient to use the approximate methods presented in this section, since the
effect of small variations in the effective width, ao , on the magnitude of the moments obtained from
the orthotropic plate computation and the stresses in the bottom fibre of the ribs is insignificant
(Wolchuk 1963).
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C5.8.2.2.2 Longitudinal girders and transverse beams
The development of this Section is explained in Moffatt and Dowling (1975). This particular
adaptation is taken from Wolchuk (1979).
C5.8.3 Idealization for analysis
The designer is reminded that the questions of “composite or noncomposite” and “cracked and
uncracked” are distinct from one another.
For the purposes of analysis for determining moments and shears, it is common practice to use
uncracked section properties for continuous reinforced concrete superstructures, although the true
behaviour with respect to cracking is load dependent. The variation of stiffness parameters between
positive and negative moment regions will not significantly affect the distribution of moments and
shears. It is particularly to be noted, however, that the provisions of Clause 5.8.3 do not apply in
calculating the strength of the section, which is assumed to be cracked, or the requirements for
interface shear transfer. Also, the effective stiffness as specified in Section 8 needs to be used when
calculating deflections of concrete structures.
C5.9 Refined methods of analysis for short- and
medium-span bridges
Refined methods with general applications are by now well reported in the technical literature. The
references given in Table C5.5 are representative of a large number of published papers.
Table C5.5
Refined methods of analysis for short- and medium-span bridges
(See Clause C5.9.)
(i) Grillage analogy
Jaeger and Bakht (1982), West (1973), Hambly (1991), Sawko and
Mosley (1969), Keogh and O’Brien (1996)
(ii) Orthotropic plate
Cusens and Pama (1969), Cusens and Pama (1975), Chu and
Krishnamoorthy (1968), Heins and Loney (1968), Bakht and Jaeger (1985),
Bakht and Jaeger (1991), Cheung et al. (1982)
(iii) Finite element
Zeinkiewicz and Taylor (1989), Davies et al. (1971), Moore and Can (1976),
Jategaonkar et al. (1985)
(iv) Finite strip
Cheung et al. (1970), Loo and Cusens (1971), Cheung and Cheung (1971),
Cheung et al. (1996), Cheung and Li (1989), Cheung et al. (1990)
(v) Folded plate
Evans and Rockey (1971), Scordelis (1960), Scordelis (1967)
(vi) Semi-continuum
Jaeger and Bakht (1989), Bakht et al. (1997)
C5.9.1 Selection of methods of analysis
The methods listed in Table 5.12 are capable of analyzing the relevant structural responses for the
bridge types shown.
In selecting a method or methods of analysis, Table 5.1 may be found useful. It indicates, in
summary form, the structural responses for which analysis is needed. It is to be noted that Table 5.1
does not list “deformation”, which is one of the required structural responses of Clause 5.4.4. Analysis
for deformation should also be included.
C5.9.2 Specific applications
Pucher (1964) and Rusch and Hergenroeder are representative of a large body of published work on
influence surfaces, and may be found useful.
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C5.9.3 Model analysis
To be valid, model analysis needs to be carried out by individual(s) of wide experience who are capable of
designing the model or models so as to reproduce properly all relevant behaviours of the bridge and
capable of interpreting the model behaviour in terms of bridge behaviour. Mehmel and Weise (1963),
Batchelor and Hewitt (1976), and Zia et al. (1970) give explanations of the approach.
In Approval of model analysis, a relevant criterion is that the resulting design ensure a level of safety and
performance at least equivalent to that provided for, or implicit in, other methods of analysis.
C5.10 Long-span bridges
C5.10.1 General
The analysis and design of long span bridges needs to be performed by knowledgeable Engineers with
experience in the type of bridge being considered. Because of this requirement, the analytical
requirements are given in general terms only and acceptable methods are not prescribed.
C5.10.2 Cable-stayed bridges
Cable sag may be investigated using an equivalent member modelled as a chord with modified modulus
of elasticity, Emod , given by Equation C5.10.2-1 for instantaneous stiffness, and Equation C5.10.2-2,
applied iteratively, for changing cable loads.
⎡ EAW 2 ( cosa )5 ⎤
Emod = E ⎢1+
⎥
12H 3
⎢⎣
⎥⎦
−1
⎡ (H + H2 ) EAW 2 ( cosa )5 ⎤
Emod = E ⎢1+ 1
⎥
24H12H22
⎢⎣
⎥⎦
Equation C5.10.2-1
−1
Equation C5.10.2-2
where
E
W
A
= modulus of elasticity of the cable, MPa
= total weight of the cable, Newtons
= cross-sectional area of the cable, mm2
α
= angle between cable and horizontal, °
H, H1 , H2 = horizontal component of cable force (Newtons), where H1 and H2 are iterative loads
Multiple stay cable systems are desirable in order to meet the requirements for the case of the loss of a
stay cable. All stay cables should be designed for replaceability in service.
Troitsky (1988), Cheung et al. (1990), and AASHTO Standard Specifications for Highway Bridges: Fifteenth
Edition (1992) may be found useful for the analysis methods for cable-stayed bridge types.
C5.10.3 Suspension bridges
If the suspension type is used for a bridge below the long span category, it should also be analyzed by
large deflection theory.
Buckland et al. (1979), Gimsing (1983), and Pugsly (1968) may be found useful for the methods of
analysis for suspension bridge types.
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C5.11 Dynamic analysis
C5.11.1 General requirements of structural analysis
C5.11.1.1 General
If the number of degrees-of-freedom in the model exceeds the number of dynamic
degrees-of-freedom used, a standard condensation procedure may be employed. Condensation
procedures may be used to reduce the number of degrees-of-freedom prior to the dynamic analysis.
Accuracy of the higher modes can be compromised by condensation; thus, if higher modes are
required, such procedures shall be used with caution.
The number of frequencies and mode shapes necessary to complete a dynamic analysis should be
estimated in advance or determined as an early step in a multi-step approach. Having determined that
number, the model should be developed to have a larger number of applicable degrees-of-freedom.
Sufficient degrees-of-freedom should be included to represent the mode shapes relevant to the
response sought. One rule-of-thumb is that there should be twice as many degrees-of-freedom as
required frequencies. The number of degrees-of-freedom and the associated masses should be
selected in a manner that approximates the actual distribution of mass. The number of required
frequencies also depends on the frequency content of the forcing function.
C5.11.1.2 Distribution of masses
The distribution of stiffnesses and masses should be modelled in a dynamic analysis. The discretization
of the model should account for geometric and material variation in stiffness and mass.
The selection of the consistent or lump-mass formulation is a function of the system and the
response sought, and is difficult to generalize. For distributive mass systems modelled with polynomial
shape functions where the mass is associated with distributive stiffness, such as a beam, a
consistent-mass formulation is recommended, e.g., Paz (1985). In lieu of a consistent formulation,
lumped masses may be associated at the translational degrees-of-freedom, a manner that
approximates the distributive nature of the mass; Clough and Penzian (1975) is recommended for
reference.
For systems with distributive mass associated with larger stiffness, such as in-plane stiffness of a
bridge deck, the mass may be properly modelled as lumped. The rotational inertia effects should be
included where significant.
In seismic analysis, nonlinear effects, such as inelastic deformation and cracking, that lead to
decrease in stiffness, should be considered.
C5.11.1.4 Damping
Damping may be neglected in the calculation of natural frequencies and associated nodal
displacements. The effects of damping should be considered where a transient response is sought.
Suitable damping values may be obtained from field measurement of induced free vibration or by
forced vibration tests. In lieu of measurements, as percentages of critical damping, the following values
may be used:
(a) concrete construction: 2%;
(b) welded and bolted steel construction: 1%; and
(c) timber: 5%.
C5.11.2 Elastic dynamic responses
C5.11.2.1 Vehicle-induced vibrations
The dynamic load provisions of Clause 3.8.4.5 are well established. Methods of static analysis are
frequently capable of being extended to cover dynamic analysis by the introduction of suitable
dynamic allowances. This is an acceptable approach, provided that it is carried out in a manner
consistent with the provisions of Section 3.
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C5.11.2.2 Wind-induced vibrations
Additional information on design for wind may be found in references Scanlan (1975), Simiu and Scanlan
(1978), Basu and Chi (1981a & b), and ASCE (1961).
References for Clauses C5.4 to C5.11
CSA (Canadian Standards Association)
CAN/CSA-S6-88 (withdrawn)
Design of highway bridges
Other publications
ACI. 1970. Models for Concrete Structures. ACI Publication No. SP-24, American Concrete Institute, Detroit.
ASCE. 1961. “Wind Forces on Structures.” ASCE Transactions. New York.
Aly, A. 1996. “Study of Live Load Distribution Factors for Longitudinal Moment in Selected Slab-on-Girder
Bridges.” Report for Ontario Ministry of Transportation and Communications, Structural Research Branch.
American Association of State of Highway and Transportation Officials (AASHTO). 1994. LRFD Bridge Design
Specification. Washington, DC.
American Association of State of Highway and Transportation Officials (AASHTO). 1994. Guide
Specifications for the Distribution of Loads on Highway Bridges. Washington, DC.
American Association of State of Highway and Transportation Officials (AASHTO). 1992. Standard
Specifications for Highway Bridges. Washington, DC.
Bakht, B. 1988. “Load Distribution in Laminated Timber Decks.” ASCE Journal of Structural Engineering,
114(7), pp.151–157.
Bakht, B., Aly, A., and Smith, D. 1997. “Semi-Continuum versus Grillage Methods of Analysis.” CJCE,
Vol. 24, No. 1, pp. 157–160.
Bakht, B., and Jaeger, L.G. 1985. Bridge Analysis Simplified. McGraw-Hill Book Company, New York.
Bakht, B., and Jaeger, L.G. 1990. “Bridge Evaluation for Multi-Presence of Vehicles.” ASCE Journal of
Structural Engineering, 116(3), pp. 603–618.
Bakht, B., and Jaeger, L.G. 1991. “Simplified Methods of Bridge Analysis for the Third Edition of OHBDC.”
Proceedings of the Annual Meeting of the Canadian Society for Civil Engineering held in Vancouver.
Bakht, B., and Moses, F. 1988 “Lateral Distribution Factors for Highway Bridges.” ASCE Journal of Structural
Engineering, Vol. 114, No. 8.
Bakht, B., Jaeger L.G., and Cheung, M.S. 1981. “Cellular and Voided Slab Bridges.” ASCE Journal of the
Structural Division, June.
Bakht, B., Jaeger, L.G., and Cheung, M.S. 1983. “Transverse Shear in Multi-beam Bridges.” ASCE Journal of
the Structural Division, April.
Basu, S., and Chi, M. 1981b. Design Manual for Bridge Structural Members Under Wind-Induced Excitation.
Report No. FHWA TS-81-206, FHWA, U.S. Department of Transportation, Washington, DC.
Basu, S., and Chi, M. 1981a. Analytic Study for Fatigue of Highway Bridge Cables. Report No.
FHWA-RD-81-090, FHWA, U.S. Department of Transportation, Washington, DC.
Batchelor, B. de V., and Hewitt, B.E. 1976. “Test of Model Composite Bridge Decks.” Journal of the
American Concrete Institute, Vol. 73, No. 6, January.
Buckland, P.G., Hooley R., Morgenstern, B.D.M., Rainer, J.H., and van Selst, A.M. 1979. “Suspension
Bridge Vibrations: Computed and Measured.” Journal of Structural Division, American Society of Civil
Engineers, Vol. 105, No. ST5, May, pp. 859–874.
194
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Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
Cheung, M.S., Bakht, B., and Jaeger, L.G. 1982. “Analysis of Box Girder Bridges by Grillage and
Orthotropic Plate Methods.” Canadian Journal of Civil Engineering, Vol. 9, No. 4, December,
pp. 595–601.
Cheung, M.S., and Chan, M.Y.T. 1978. “Finite Strip Evaluation of Effective Flange Width of Bridge
Girders.” Canadian Journal of Civil Engineering, Vol. 5, No. 2, June.
Cheung, M.S., and Cheung, Y.K., 1971. Analysis of Curved Box Girder Bridges by Finite Strip Method.
IABSE Publications, Vol. 31–1, June, Zurich.
Cheung, M.S., Cheung, Y.K., and Ghali, A. 1970. “Analysis of Slab and Girder Bridges by the Finite
Strip Method.” Building Science, 5, p. 95.
Cheung, M.S., and Li, W. 1989. “Analysis of Continuous Haunched Box-girder Bridges by Finite
Strips.” ASCE Journal of Structural Engineering, Vol. 115, No. 5, pp. 1076–1087.
Cheung, M.S., Li, W., and Chidiac, S. 1996. Finite Strip Analysis of Bridges. E & FN Spon/Chapman Hall.
Cheung, M.S., Li, W., and Jaeger, L.G. 1990 “Improved Finite-Strip Method for Nonlinear Analysis of
Long-Span Cable-Stayed Bridges.“ Canadian Journal of Civil Engineering, Vol. 17, pp. 87–93.
Chu, Kuang-Han, and Krishnamoorthy, C. 1968. “Bridge Analysis Using Orthotropic Plate Theory.”
Journal of the Structural Division, ASCE, February.
Clough, R.W., and Penzian, J. 1975. Dynamics of Structures. McGraw-Hill, New York.
Cusens, A.R., and Pama, R.P. 1969. “Distribution of Concentrated Loads on Orthotropic Bridge
Decks.” The Structural Engineer, September.
Cusens, A.R., and Pama, R.P. 1975. Bridge Deck Analysis. John Wiley and Sons, London.
Davies, J.D., Somerville, I.J., and Zienkiewicz, O.C. 1971. “Analysis of Various Types of Bridges by the
Finite Element Method.” Proc. Conference on Developments in Bridge Design and Construction,
Cardiff, March-April, Crossby Lockwood, London.
Dilger, W.H., Beauchamp, J.C., Cheung, M.S., and Ghali, A. 1981. “Field Measurements of the Muskwa
River Bridge.” ASCE Journal of Structural Engineering, Vol. 107, No. 11, November, pp. 2147–2161.
Dilger, W.H., Ghali, A., Chan, M., Cheung, M.S., and Maes, M. 1983. “Temperature Stresses in
Composite Box Girder Bridges.” ASCE Journal of Structural Engineering, Vol. 109, No. 6, June, pp. 1460–
1478.
Evans, H.R., and Rockey, K.C. 1971. “A Folded Plate Approach to the Analysis of Box Girders.” Proc.
Conference on Developments in Bridge Design and Construction, Cardiff, Crossby Lockwood, London.
Fu, H.C., Ng, S.F., and Cheung, M.S. 1990. “Thermal Behaviour of Composite Bridges.” ASCE Journal
of Structural Engineering, Vol 116, No. 12, December, pp. 3302–3323.
Ghali, A., and Favre, R. 1994. Concrete Structures: Stresses and Deformations, 2nd ed. E & FN Spon.
Gimsing, N.J. 1983. Cable Supported Bridges: Concept and Design. John Wiley and Sons, Chichester,
England.
Goodall, J.K. 1971. “Torsional Stiffness of Multi-Cellular Box-Sections.” Proc. Conference on
Developments of Bridge Design and Construction, Cardiff, Crossby Lockwood, London.
Haaijer, Geerhard. 1981. “Simple Modelling Technique for Distortion Analysis of Steel Box Girders.”
The Proceedings of the MSC/Nastran Conference on Finite Element Methods and Technology”,
March, Pasadena.
Hambly, E.C. 1991. Bridge Deck Behaviour. E & FN Spon.
Heins, C.P., and Loney, C.T.C. 1968. “Bridge Analysis Using Orthotropic Plate Theory.” Journal of the
Structural Division, ASCE, February.
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Holowka, M. 1973. Prestressing Effects in a Straight Voided Slab Bridge. M.A.Sc. thesis, University of
Waterloo, Waterloo, Ontario.
Husain, I., and Bagnariol, D. 1996. Integral Abutment Bridges. Report SO-96-01, Ministry of Transportation
and Communications, July, Downsview, Ontario.
Jaeger, L.G., and Bakht, B. 1982. “The Grillage Analogy in Bridge Analysis.” Canadian Journal of Civil
Engineering, Vol. 9, No. 3.
Jaeger, L.G., and Bakht, B. 1989. Bridge Analysis by Microcomputer. McGraw-Hill Book Company, New York.
Jaeger, L.G., and Bakht, B. 1990. “Rationalization of Simplified Methods of Analysing Cantilever Slabs.”
Canadian Journal of Civil Engineering, 17(5), pp. 865–867.
Jaeger, L.G., Jategaonkar, R., and Cheung, M.S. 1989. “Effectiveness of Intermediate Diaphragms in
Distributing Live Loads in Beam-and-Slab Bridge,” CSCE, Monographs: Desktop Series No. 1, May.
Jaeger, L.G., and Smith, D.S. 1997. Simplified Elastic Analysis of Concrete Deck Slabs for CHBDC CL-W Live
Load.
Jategaonkar, R., Jaeger, L.G., and Cheung, M.S. 1985. Bridge Analysis Using Finite Element. Canadian
Society of Civil Engineering, 148 pp.
Keogh, K.L., and O’Brien, E.L. 1996. “Recommendations on the Use of a 3-D Grillage for Bridge Deck
Analysis”, Structural Engineering Review, Vol. 8, No. 4, pp 357–366.
Kollbrunner, C.F., and Basler, K. 1990. Torsion in Structures, an Engineering Approach, Springer-Verlag,
New York.
Loo, Y.C., and Cusens, A.R. 1971. “Development of the Finite Strip Method in the Analysis of Bridge
Decks.” Proc. Conference on Developments in Bridge Design and Construction, Cardiff, Crossby
Lockwood, London.
Maisel, B.I. 1982. “Structural Analysis of Concrete Box Beams Using Small Computer Capacity.
Proceedings, International Conference on Short and Medium Span Bridges.” Canadian Society for Civil
Engineering, Vol. 2 pp. 17–30.
Massonnet, C., and Gandolfi, A. 1967. “Some Exceptional Cases in the Theory of Multi-girder Bridges.”
Publications, IABSE, 27, pp. 73–94.
Mehmel, A., and Weise, H. 1963. Model Investigation on Skew Slabs on Elastically Yielding Point Supports.
C & CA translation.
Moffat and Dowling. 1975. “Shear Lag in Steel Box Girder Bridges.” The Structural Engineer, October.
Moore, T.A., and Can, A.G. 1976. “Finite Element Analysis of Box and Plate Girder Bridges.” Proc. of the
International Conference of Finite Element Methods in Engineering, December 6–8.
MTO. 1977. Ontario Highway Bridge Design Code and Commentary. Ministry of Transportation and
Communications, Downsview, Ontario.
MTO. 1983. Ontario Highway Bridge Design Code and Commentary, 2nd ed. Ministry of Transportation and
Communications, Downsview, Ontario.
MTO. 1992. Ontario Highway Bridge Design Code and Commentary, 3rd ed. Ministry of Transportation and
Communications, Downsview, Ontario.
Mufti, A., Bakht, B., and Jaeger, L.G. 1993. “Moments in Deck Slabs Due to Cantilever Loads.” Journal of
Structural Engineering, Vol. 119, No. 6, June.
Normandin, P., and Massicotte, B. 1995. Étude du comportement des ponts à poutrais-caissons mixtes
acier-béton. Rapport EPM/GCS-1995-06, Department de Génie Civil, École Polytechnique de Montréal.
Paz, M. 1985. Structural Dynamics. Van Nostrand Reinhold Company, New York, 2nd ed.
196
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Priestly, M.J.N. 1978. “Design of Concrete Bridges for Temperature Gradients.” Journal of American
Concrete Institute, Vol. 75, No. 5, pp. 209–217.
Pucher, A. 1964. Influence Surfaces of Elastic Plates. Springer-Verlag, Wien, New York.
Pugsley, A. 1968. Theory of Suspension Bridges. Edward Arnold (Publishers) Ltd., London, England.
Richmond, B., April 1966. “Twisting of Thin-Walled Box Girders.” Proceedings of the Institution of Civil
Engineers.
Robbins, S., and Green, R. 1978. The Portal Frame Bridge, Structural and Soil Interaction Behaviour. Parts
1 and 2, University of Waterloo reports for the Ontario Ministry of Transportation and
Communications.
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EPM/GCS-1996-09, Department de Génie Civil, École Polytechnique de Montréal.
Rusch, H., and Hergenroeder, A. Influence Surfaces for Moments in Skew Slabs. C & CA translation,
London, England.
Sawko, F., and Mosley, W.H. 1969. “Grillage Analysis of Composite Box Girder Bridge Decks.” Civil
Engineering (London) Vol. 64, No. 759, October.
Scanlan, R.H. 1975. Recent Methods in the Application of Test Results to the Wind Design of Long
Suspended-Span Bridges. Report No. FHWA-RD-75-115, FHWA, U.S. Department of Transportation,
Washington, DC.
Scordelis, A.C. 1960. “A Matrix Formulation of the Folded Plate Equations.” Journal of the Structural
Division, ASCE, ST-10, October.
Scordelis, A.C. 1967. “Analysis of Continuous Box Girder Bridges.” University of California, Berkeley,
Structural Engineering and Structural Mechanics, No. SESM 6.7-5, November.
Simiu, E., and Scanlan, R.H. 1978. Wind Effects on Structures. Wiley-Interscience, New York.
Smith, D.S. 1996. Force Effects in Slab-on-Girder Bridge Types at ULS and SLS and Recommendations for
Live Load Distribution Factors for the Canadian Highway Bridge Design Code. Report for New Brunswick
Department of Transportation.
Smith, D.S. 1997. Force Effects in Slab-on-Girder Bridge Types at FLS and Recommendations for Live Load
Distribution Factors for the Canadian Highway Bridge Design Code. Report for New Brunswick
Department of Transportation.
Smith, D.S. 1996. Force Effects in Slab and Voided Slab Bridge Types at ULS and SLS and Recommendations
for Live Load Distribution Factors for the Canadian Highway Bridge Design Code. Report for New
Brunswick Department of Transportation.
Smith, D.S. 1997. Force Effects in Slab and Voided Slab Bridge Types at FLS and Recommendations for Live
Load Distribution Factors for the Canadian Highway Bridge Design Code. Report for New Brunswick
Department of Transportation.
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Distribution Factors for the Canadian Highway Bridge Design Code. Report for New Brunswick
Department of Transportation.
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Proceedings, 5th Colloquium on Concrete In Developing Countries, Cairo, Egypt — CSCE.
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Report 21, Cement and Concrete Association, London, England.
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Wolchuk, R. 1963. The Design Manual for Orthotropic Steel Plate Deck Bridges. AISC.
Wolchuk, R. 1979. Steel-Plate-Deck Bridges, Structural Engineering Handbook. McGraw-Hill Book Company,
New York.
Zia, P., White, R.N., and Vanhorn, D.A. 1970. Principle of Model Analysis. ACI Publication No. SP.24, Detroit.
Zienkiewicz, O.C., and Taylor, R.L. 1989. The Finite Element Method, 4th ed. McGraw-Hill.
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Annex CA5.1
Commentary on Annex A5.1 — Factors
affecting structural response
CA5.1.3 Plan geometry
CA5.1.3.1 Shallow superstructures on skew spans
In skew span bridges, the reactions over supports do not follow the same pattern as their right span
counterparts, and the reaction at bearings in obtuse-angled corners of skew slab bridges can be several
times larger than those in comparable rectangular bridges. The analysis of support reactions should be
based upon a realistic modelling of the support conditions.
For the calculation of longitudinal vertical shear in slab-on-girder bridges with skew, Jaeger and
Smith (1997), in an as-yet unpublished report, have proposed the following method:
The corresponding bridge without skew, using the skewed span length, needs to be analyzed for
longitudinal vertical shear in accordance with Clauses 5.7.1.4.1 and 5.7.1.4.2. The shear force found
in the skewless bridge shall be multiplied by Cv , where
ε
=
S tany
L
η
=
⎛ Dy ⎞ ⎛ L ⎞4
0 .5 ⎜
⎟⎜ ⎟
⎝ Dx ⎠ ⎝ S ⎠
Dy
= transverse bending stiffness of the bridge superstructure per unit length = Ect 3/12 for a
structure without diaphragms
Dx
= longitudinal bending stiffness per unit width = total longitudinal bending stiffness of the
cross-section divided by the total width of the bridge
and Cv is obtained from Table CA5.1 for the values of ε and η concerned:
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Table CA5.1
Values of Cv
(See Clause CA5.1.3.)
Skew parameter, ε
η
0.05
0.10
0.15
0.20
0.25
0.30
10
20
40
60
80
100
120
140
200
300
400
500
1.023
1.045
1.056
1.067
1.078
1.089
1.093
1.103
1.119
1.148
1.177
1.198
1.056
1.082
1.116
1.128
1.140
1.170
1.184
1.198
1.239
1.273
1.307
1.326
1.079
1.118
1.157
1.170
1.183
1.235
1.252
1.269
1.310
1.342
1.374
1.390
1.102
1.150
1.201
1.238
1.274
1.300
1.326
1.339
1.381
1.410
1.440
1.454
1.126
1.165
1.237
1.275
1.312
1.338
1.363
1.385
1.421
1.454
1.485
1.501
1.157
1.196
1.274
1.312
1.350
1.375
1.399
1.430
1.460
1.498
1.529
1.547
Note: The values of Cv were derived in a sequence of steps as follows:
(a) Initially, very simple frameworks comprising small numbers of torsionless
longitudinal girders and transverse beams were analyzed for the
distribution of responses such as moments, shears, etc. under the action of
concentrated loads; in such cases explicit formulae can be obtained for the
responses, and the dimensionless parameters η and ε are found to appear
in these formulae.
(b) Progressively more complicated structures were then considered, in which
the numbers of longitudinal and transverse members were increased and
torsional effects were included; this treatment involved finite element
analysis from a fairly early stage of complication.
(c) Finally, the ranges of values of η and ε were established for practical
designs, and a number of existing bridges were chosen as representative of
various combinations of η and ε, and were analyzed by finite element
methods. Good agreement was found in all cases with the values given in
the table.
CA5.1.3.2 Bridges curved in plan
These parameters for establishing the limits for the applicability of simplified methods were in the second
and third editions of the OHBDC. Simplified methods have been developed for predicting the response of
selected horizontally curved composite box girders that lie outside of the limits specified in
Clause A5.1.3.2. Cheung and Foo (1995) should be consulted for further information.
References
Other publications
Cheung, M.S., and Foo, S.H.C. 1995. “Design of Horizontally Curved Composite Box Girder Bridges; A
Simplified Approach.” Canadian Journal of Civil Engineering, Vol. 22, No. 1, February.
Jaeger, L.G., and Smith, D.S. 1997. Simplified Analysis Methods for Skewed Slab-on-Girder Bridge Types.
MTO. 1983. Ontario Highway Bridge Design Code and Commentary, 2nd Edition. Ministry of Transportation
and Communications, Downsview, Ontario.
MTO. 1992. Ontario Highway Bridge Design Code and Commentary, 3rd Edition. Ministry of Transportation
and Communications, Downsview, Ontario.
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Section C6 — Foundations
C6.1
C6.3
C6.3.2
C6.4
C6.4.1
C6.4.1.1
C6.4.1.2
C6.4.1.3
C6.4.2
C6.4.3
C6.4.4
C6.4.5
C6.4.6
C6.5
C6.5.1
C6.5.2
C6.5.3
C6.5.4
C6.5.5
C6.5.6
C6.6
C6.6.1
C6.6.2
C6.6.2.1
C6.6.2.2
C6.6.2.3
C6.6.2.4
C6.6.3
C6.6.3.1
C6.6.3.3
C6.6.3.6
C6.7
C6.7.1
C6.7.2
C6.7.3
C6.7.3.1
C6.7.3.2
C6.7.3.3
C6.7.3.4
C6.7.4
C6.7.5
C6.8
C6.8.1
C6.8.2
C6.8.3
C6.8.4
C6.8.5
C6.8.5.1
C6.8.5.2
C6.8.5.3
C6.8.5.4
Scope 204
Abbreviations and symbols 205
Symbols 205
Design requirements 206
Limit states 206
General 206
Ultimate limit state 206
Serviceability limit state 206
Effects on surroundings 206
Effects on structure 207
Components 208
Consultation 208
Inspection and quality control 208
Geotechnical investigation 209
General 209
Investigation procedures 209
Geotechnical parameters 210
Shallow foundations 210
Deep foundations 210
Report 211
Resistance and deformation 212
General 212
Ultimate limit state 215
Procedures 215
Geotechnical formulas 215
In-situ tests 216
Assessed value 216
Serviceability limit state 217
General 217
Tests 219
Calculation considerations 219
Shallow foundations 223
General 223
Calculated geotechnical resistance at ULS 225
Pressure distribution 227
Effective area 227
Pressure distribution at the ULS for structural design 227
Pressure distribution at the SLS 229
Eccentricity limit 230
Effect of load inclination 230
Factored geotechnical horizontal resistance 231
Deep foundations 232
General 232
Selection of deep foundation units 232
Vertical load transfer 233
Downdrag 233
Factored geotechnical axial resistance 235
General 235
Static analysis 235
Static pile load tests 236
Dynamic analysis and tests 237
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C6.8.5.5
C6.8.5.6
C6.8.6
C6.8.6.1
C6.8.6.2
C6.8.7
C6.8.7.1
C6.8.7.2
C6.8.7.3
C6.8.8
C6.8.8.2
C6.8.8.3
C6.8.8.5
C6.8.9
C6.8.9.2
C6.8.10
C6.8.10.1
C6.8.10.2
C6.9
C6.9.1
C6.9.2
C6.9.2.1
C6.9.2.2
C6.9.2.3
C6.9.3
C6.9.4
C6.9.5
C6.10
C6.10.1
C6.10.2
C6.10.2.1
C6.10.2.2
C6.10.2.3
C6.10.3
C6.10.4
C6.10.4.1
C6.10.4.2
C6.11
C6.11.1
C6.11.2
C6.11.3
C6.11.3.1
C6.11.3.3
C6.11.3.4
C6.11.4
C6.12
C6.12.1
C6.12.2
C6.12.2.1
C6.12.2.2
C6.12.2.3
C6.12.3
C6.13
C6.13.1
202
© Canadian Standards Association
Limitation for tension piles 237
Relaxation of driven piles 237
Group effects — Vertical loads 237
Load distribution 237
Group resistance 238
Factored geotechnical lateral resistance 238
General 238
Static analysis 240
Lateral deflection 241
Structural resistance 241
Unsupported length 241
Structural instability 241
Factored structural resistance 241
Embedment and spacing 241
Pile spacing 241
Pile shoes and splices 242
Pile shoes or points 242
Splices 242
Lateral and vertical pressures 242
General 242
Lateral pressures 247
General 247
Calculated pressures 248
Equivalent fluid pressures 249
Compaction surcharge 249
Effects of loads 249
Surcharge 250
Ground anchors 250
Application 250
Design 252
General 252
Factored geotechnical resistance at the ULS and geotechnical reaction at the SLS 252
Spacing, bond length, and free-stressing length 252
Materials and installation 253
Anchor testing 253
General 253
Acceptance criteria 253
Sheet pile structures 253
Application 253
Design 254
Ties and anchors 254
Deadman anchors 254
Tie load 255
Sagging of tie rods 255
Cellular sheet pile structures 255
MSE structures 255
Application 255
Design 255
General 255
Calibration 255
Factors for consideration 256
Backfill 256
Pole foundations 256
Application 256
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C6.13.2 Design 256
C6.13.2.1 General 256
C6.13.2.2 Assumptions 256
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Section C6
Foundations
C6.1 Scope
Section 6 is a further evolution of earlier limit states bridge design codes (OHBDC 1979, 1983, 1991).
Limit states design philosophy has been accepted in structural design for some time.
In contrast, the application of limit states to geotechnical design is more recent. Previously, substructure
design was based on allowable stress, even though much of geotechnical engineering has been based on
concepts of limiting equilibrium — an ultimate limit state. The use of two design philosophies — one, a
limit states design philosophy for superstructures; the second, an allowable stress design philosophy for
substructures — led to complications. It became evident that a limit state approach was required for
foundation design.
This evolution has not been without difficulties. Initially (OHBDC 1979, 1983), the partial factor format
was adopted following Danish practice (DGI 1985 and earlier). Soil strength factors were applied to soil
cohesion and angle of internal friction to account for uncertainties in material properties. However, the
partial strength factor approach did not lead to design consistency with the allowable stress approach and
the use of partial strength factors was not readily accepted by many Geotechnical Engineers. When
strength factors were applied to cohesion and friction, well-proven empirical relationships for geotechnical
design no longer applied. For example, many of the empirical relationships for bearing resistance of
shallow and deep foundations are based on limiting vertical deflection. Thus, it was difficult for the
Geotechnical Engineer to utilize earlier predictive methods and sources of data.
To address these concerns, the approach was modified in the third edition of the OHBDC (1991).
Resistance factors were applied to the various ultimate limit states of geotechnical resistance rather than
using partial strength factors applied to the soil strength parameters of friction and cohesion. The
resistance factors were chosen to give a level of safety generally comparable to that obtained by the earlier
allowable stress design procedures. Thus, traditional design aids were applicable, with some modifications.
This total resistance factor approach has been carried on in the Code. It is emphasized that no other
factors are required in strength formulations and that representative values of soil strength parameters
should be used.
Some key elements of the Code are as follows:
(a) The terminology has been modified. Foundation design considers structural “loads” applied against
geotechnical “resistances” or “reactions”.
(b) In the Code, “resistance” is the term used for strength, capacity, or resistance of a structure or
foundation at the ultimate limit state (ULS). A number of general papers discussing limit states design
in geotechnical engineering are available, for example, Baikie (1985), Bolton (1981), Krebs Ovesen
(1981), Green (1991), Barker (1991), Lumb (1970), Becker (1996), and Christopher (1990).
Resistances at the ULS are factored to provide a safety margin. Resistance factors are the inverse of the
margin of safety implied by the appropriate load factors.
(c) In the Code, “reaction” is the term used for strength, capacity, or resistance of a structure or
foundation at the serviceability limit state (SLS). Attention is drawn to serviceability limit states and
the variability in the prediction of actual deformation.
(d) In order to ensure the quality of geotechnical engineering, minimum requirements are given for site
investigation and reporting. Communication between the Structural Engineer and the Geotechnical
Engineer is required throughout all phases of the project in order to ensure clear interpretation and
application of the geotechnical information used in design. Specific reference is made to
requirements for inspection and quality assurance.
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C6.3 Abbreviations and symbols
C6.3.2 Symbols
The symbols listed below are those used in this Commentary. These are additional to the Code. The
units given are those generally used; however, care should be taken to check the consistency of units
in any equation.
Cc
representative compression index from test results
recompression index
Cr
coefficient of secondary compression defined as change in void ratio per log cycle of time
Cα
coefficient of consolidation
cν
E
in-situ soil modulus, kPa
E’
in-situ drained deformation modulus of soil representing the case when all excess pore water
pressures have been dissipated, kPa
H
horizontal resistance, kN
h
height, m; or height of earth retaining structure, m
I
influence coefficient, a function of footing geometry
Ka
active earth pressure coefficient
at-rest earth pressure coefficient
Ko
passive earth pressure coefficient
Kp
l
span length, m
mν
coefficient of compressibility
N
Standard Penetration Test (SPT) blow count; or number of piles in the group
Nt
bearing toe coefficient
force applied by the pile cap to a single pile or cluster of piles at point x,y
Px,y
factored resistance as specified by the Geotechnical Engineer, kPa
qr
ultimate bearing resistance, kPa
qu
R
reduction factor
Rs
shaft resistance, kN
toe resistance, kN
Rt
secondary consolidation or creep, m
screep
immediate settlement, m
si
primary consolidation settlement, or change in thickness of compressible stratum, m
sp
settlement at time t, m
st
total settlement, m
sT
t
time at which it is desired to determine the amount of secondary compression, years
V
vertical resistance, kN
x
distance to the pile from the centroid of the pile group, taken positive or negative in the x
direction, m; or ratio of horizontal to vertical load
y
distance to the pile from the centroid of the pile group, taken positive or negative in the y
direction
β
coefficient for shaft resistance
Δ
initial or final settlement or displacement, m
θ
relative rotation, radians; or footing rotation, radians
σ ‘p
preconsolidation pressure, kPa
ν
Poisson’s ratio, which equals 0.5 for undrained or no volume change conditions
ν′
Poisson’s ratio for drained conditions
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C6.4 Design requirements
The provisions of Clause 6.4 apply to the design of foundations for piers, abutments, retaining walls, and
sheet pile walls, as well as appurtenances, which include mast lighting, sign supports, and sound barriers.
For proprietary structures, such as mechanically stabilized earth walls (MSE), the design of the
reinforcement and backfill to ensure internal stability is normally the responsibility of the supplier.
Deviations from the Code occurring as part of the design for internal stability require Approval. Typical
details of design and construction are provided by Christopher et al. (1990). The supplier should verify
that the design and installation does not create external instability.
C6.4.1 Limit states
C6.4.1.1 General
The intent of Clause 6.4.1.1 is to draw attention to the various ways that structures and the supporting soil
or rock may interact. For example, while the tie rod force for a sheet pile wall provides resistance to forces
acting on the wall, it also imposes a force on the anchor block embedded in the soil. The anchor rod serves
as both a resisting component and a loading component.
When a footing slides or rotates sufficiently to mobilize the shear resistance within the backfill, the earth
pressures acting on the wall tend to an active condition. When no sliding or rotation of the base occurs
during installation of the backfill, the stem of the wall should be designed to resist pressures due to fill,
compaction of the fill, and superimposed loads. The soil pressures associated with various limit states
should be considered for structural proportioning.
C6.4.1.2 Ultimate limit state
The first definition of ULS refers to a limit equilibrium analysis in the soil or rock.
The second definition of ULS refers to cases where the movement of the foundation could be sufficient
to cause a structural failure without the foundation reaching a limit equilibrium state.
Reference is made to the overall stability of a foundation and of an adjacent slope. The overall stability of
the slope upon which a foundation might be founded should be considered even though that topic is not
covered by this Section.
C6.4.1.3 Serviceability limit state
A SLS condition implies deformation associated with a geotechnical reaction value selected on the basis of
past experience and existing data or on the basis of an iterative analysis of soil and structure resulting in
movements that do not damage the structure.
Stresses in the soil or rock for an SLS condition are selected to limit long-term deformation in the soil.
C6.4.2 Effects on surroundings
Evaluation of the effects of Construction in the immediate vicinity of the structure, in terms of existing
structures and soil conditions, is part of the design process. Examples of the effects of Construction on
existing structures and services are provided. Each site needs to be considered.
(a) New construction may influence the safety of existing foundations. For example, if a new shallow
foundation is placed below an existing unit, the existing footing may lose resistance unless the
excavation is supported, Figure C6.7. Soil movement may also occur when adjacent soil is removed,
Figure C6.8. If a new footing is installed at a lower level than an existing footing or service, the
geometry given in Figure C6.9 should be considered.
(b) The risk of unfavourable water levels caused by changes in water catchment or reduced drainage
should be considered. It is often necessary to assume that the groundwater could rise to ground level
in extreme cases. This action could be considered as an accidental action, with less than lifetime load
factors. Direct observations are normally made of groundwater conditions if these greatly affect either
the method of construction or the performance of the structure. The effect of groundwater changes
on the strength and volumetric deformations of soil or weak rock should be considered.
(c) Blasting may give rise to ground-induced vibration, the motion of which may be perceptible.
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(d) Observations indicate that the additional pressures due to compaction of fill depend upon the
applied energy, the thickness of the compacted layers, and the travel pattern of the compaction
equipment. Compaction in an underlying layer is reduced when the next layer is placed and
compacted. Normally, excess lateral pressure acts on the upper part of the structure.
(e) Pressure changes from single applications of surface load can be calculated using elastic analysis
(Poulos and Davis 1974). In the case of repeated surcharge loading, care is needed as the
pressures, after several cycles, can be significantly different from those due to initial loading.
C6.4.3 Effects on structure
Section 3 specifies where maximum and minimum values of load factors should be used. For
foundations, a maximum or a minimum factored horizontal load should be combined with a
maximum or a minimum factored vertical load. The combination that yields the largest dimension for
either the structure, structure cross-section, or the base width should apply. Various combinations are
shown in Figure C6.1 in the absence of surcharge effects. The toe dimension required for load case b is
larger than that required for case a as the inclination of Qf is larger than for case b and governs the
design shown.
(a) The original and changes in ground water conditions should be monitored. Changes to
groundwater conditions may lead to overload of structures due to lateral water pressure or loss of
resistance in the foundation due to changes in water content, buoyancy, or removal of bearing
material.
(b) Lateral and vertical soil pressures are present with and without movement and should be
considered in design. If the soil movement is more than the extreme value assumed in design, the
consequences of this additional movement should be considered.
(c) The effects of earthquake on design are specified in Section 4. Liquefaction of granular soils may
reduce or eliminate the resistance of foundations. Blasting may cause similar dynamic effects.
(d) Frost penetration is damaging if water is present in the material being penetrated by frost and the
material is frost susceptible. For coarser-grained material, the penetration of the frost will be
greater than for the fine-grained material.
(e) Variability of natural soil or natural rock across the site and also at the location of any shallow or
piled foundations should be considered. Major variations will be revealed by inspection. Ground
that is treated to improve its properties may be either natural ground or fill. Fill is frequently used
beneath foundations or ground slabs, as backfill to excavations, and approaches. The
geotechnical parameters associated with these various fills should be verified against design
values.
(f) Provisions for scour are provided in Section 1. Future dredging or excavation may lead to
undermining and result in the failure or excessive deformation of an existing structure. Such
modes of loss of serviceability are similar to those shown in Figures C6.7 to C6.9. Loss of lateral
support for a pile foundation may lead to loss of resistance of the piles as loss of lateral support
will influence the shaft resistance of the pile. Care needs to be taken to ensure that shoring
maintains lateral support.
(g) Backfill compaction pressures achieved by the field equipment should be similar to those
considered in design. If compaction pressures are excessive, damage may result. Compaction
pressures of 30 kPa are possible without site control and the effects may extend vertically for
approximately 5 to 6 m below the surface being compacted during and following compaction.
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1
Vf (aD = 1.25)
Vf (aD = 1.00)
48*
Qf
Qf
Hf (aE = 1.25)
Hf (aE = 1.25)
Stress, qf , = Vf /A, but
less than the Rb • qr limit
Stress, qf , = Vf /A, but
less than the Ra • qr limit
Note: The reduction factor Rb
is less than the reduction factor Ra
* Typical front
face inclination
(a) Forces with maximum
vertical load
(b) Forces with minimum
vertical load
Figure C6.1
Various load cases
(See Clause C6.4.3.)
C6.4.4 Components
Foundation components that are structural in nature such as connectors, tendons, and liners should meet
the requirements of the appropriate material sections of the Code.
C6.4.5 Consultation
Consultation between the Structural Engineer and the Geotechnical Engineer needs to take place during
planning, design, and construction for activities including, but not limited to, evaluating alternatives and
ensuring that the foundation aspects of the project have been incorporated as intended. When
unanticipated subsurface conditions are encountered, or for any foundation-related construction problem
requiring modification of the foundation design, consultation needs to take place between the
Geotechnical Engineer and the Structural Engineer. The Geotechnical Engineer needs to review the
geotechnical aspects of the Plans prior to construction. Inspection of construction of critical foundation
elements by qualified personnel is necessary.
C6.4.6 Inspection and quality control
The inspection and quality control associated with geotechnical work are usually covered by specifications
together with special provisions developed specifically for a given site covered by a given contract.
Clause 6.4.6 stipulates minimum requirements for inspection of a project that should be carried out under
the direction of an Engineer with geotechnical expertise who is familiar with the geotechnical design. This
requirement is included to ensure that this Engineer has the opportunity to verify that the actual site
conditions are similar to those documented in the geotechnical reports and on which the design was
based. The provisions of Section 6 require that this professional Engineer maintains responsibility for
geotechnical site work and inspection.
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C6.5 Geotechnical investigation
C6.5.1 General
Clause 6.5 does not provide specific procedures for dealing with possible environmental problems
associated with the previous use of a proposed site. For a given site, the possible presence of
contaminants (such as organic material or heavy metals) in the ground or a river bed should be the
subject of a special investigation. Although geotechnical investigations may include preliminary tests
to identify gaseous, solid, or liquid pollutants, a separate environmental investigation should be carried
out where environmental contaminants are discovered or anticipated.
A geotechnical investigation for a structure having sufficient scope to develop foundation design
recommendations should be conducted. Adequate subsurface information should be gathered to
permit the construction of foundation elements and to address related concerns of a geotechnical
nature. The intent of a geotechnical investigation is to present a three-dimensional model of
subsurface conditions through interpolation of borehole data. This is normally accomplished by
(a) evaluating the available geological and other pertinent subsurface information, including the
nature of the terrain and the performance of existing structures — such as previous reports,
maps, air photos and water well records;
(b) obtaining subsurface data from boreholes or test pits, by retrieving soil, rock, and groundwater
samples, and by performing in-situ testing and geophysical explorations. The material may be
accessed by diamond drill, continuous flight auger, or by other suitable techniques. The number,
location, and depth of borings are functions of a number of factors, including the subsurface
conditions at the site and the proposed bridge geometry and loading; and
(c) carrying out laboratory tests on recovered samples.
The data obtained from sampling and testing should be adequate to determine
(a) the vertical and horizontal extent of subsurface materials (including both soil and rock) and their
pertinent engineering properties; and
(b) groundwater conditions including groundwater levels, perched or otherwise, the location of
aquifers, the location and characteristics of artesian groundwater if any, the quantity of flow, and
the presence or otherwise of natural gas or chemicals dissolved in groundwater or surface water
that might prove harmful to structures and/or to personnel engaged in Construction of the
project. For chemical analysis of the groundwater, samples should not be taken from a borehole
in which bentonite slurry, any other contaminant, or runoff has collected.
The value of a site investigation may be limited if potential problems such as ease of access,
permission to enter property, presence of utilities, and subsurface variability are not considered.
Interpretation of the data obtained from the subsurface investigation requires judgement and
experience.
In some cases, especially for bridges to be built over major watercourses, it may be necessary to
carry out a site investigation in two phases. The first phase is to carry out a general assessment of the
conditions at the site, such as the presence of soft layers of soil or irregular rock surfaces. The second
phase is to derive detailed data for subsurface conditions and for foundation design and typically
includes borings at structure foundation locations and approaches to the structure.
No site investigation can reveal all aspects of the soil or rock. Thus, Clause 6.4.6 provides a
minimum requirement for inspection to ensure that new data of geotechnical importance revealed
during the work at the site are not ignored. Design revisions may be required as a consequence of new
data, e.g., changes in groundwater conditions or an increase in the frequency of boulders that may
not have been detected during the geotechnical investigation.
C6.5.2 Investigation procedures
Site investigations and field and laboratory testing should be carried out using the appropriate
CSA standard or the ASTM equivalent as given in ASTM Volume 04.08 (1997). Information and
recommendations on the extent of site investigation, both depth and number of borings details are
given in the Canadian Foundation Engineering Manual (CFEM), 3rd Edition, Chapter 4, pp. 40–65.
Deviations from a standard, due to local subsurface conditions, should be recorded as part of the
overall documentation for the site investigation.
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The abandonment of boreholes should comply with guidelines set out by the governing jurisdiction.
Site investigations should be planned to obtain the maximum possible information at a reasonable cost.
Many techniques are available for exploring subsurface site conditions. Details are given, for example, in
CFEM (1992), FHWA (1985), Devata and Selby (1987), Hvorslev (1948), Robertson (1986), Tavenas
(1986), and AASHTO (1988). The use and limitations of in-situ tests are given in CFEM (1992), Hvorslev
(1948), and Robertson (1986).
Following completion of field work, selected samples should be subjected to laboratory testing. Soil and
rock properties should be determined for classification and analysis purposes. These can include the
following:
(a) nature of soil or rock;
(b) organic content;
(c) Atterberg limits;
(d) bulk density;
(e) water content;
(f) grain size distribution;
(g) shear strength parameters based on total or effective stress considerations;
(h) consolidation characteristics;
(i) swelling or collapse characteristics;
(j) sulphate content;
(k) rock mass classification; and
(l) permeability.
The results from such testing should be included in the geotechnical report. Soils should be classified in
accordance with an accepted classification system, preferably the extended Casagrande Soil Classification
System (Transport and Road Research Laboratory 1973).
C6.5.3 Geotechnical parameters
The type of test chosen should be compatible with the soil or rock at the site and the expected behaviour
during and following Construction. For example, a number of different types of laboratory and in-situ tests
can be used to assess the resistance and reaction of a soil. A range of values for a geotechnical parameter
should be documented where sufficient data exist. Supplemental tests may be required for slope stability
analysis or for temporary wall design, among other applications.
C6.5.4 Shallow foundations
See Clause C6.5.5.
C6.5.5 Deep foundations
Once the initial investigation has been completed and a possible structure selected for the bridge,
consultation between the Structural and Geotechnical Engineers should lead to an agreement concerning
the SLS conditions. These conditions relate to settlement, horizontal movements, and rotation; their
magnitude will depend on the structure type chosen. In some cases, the initial site investigation may be
inconclusive and further investigation may become necessary.
Acceptable deformation of the foundations at SLS can often be predetermined by the Structural
Engineer. In the past, a total settlement of 25 mm has often been found acceptable for spans of less than
about 25 to 35 m. This normally gives a differential settlement of 10 to 15 mm. Where estimates of SLS
loads are not available, SLS reactions for a range of deformations that include 25 mm and 50 mm should
be provided.
In cases when an angular rotation of 1/1000 between supports is acceptable, settlements of more than
25 mm may be found acceptable for spans of 25 m or more. A rotation limit of 0.004 has been suggested
(Barker et al. 1991). Much larger deformations may be acceptable depending upon span, type of
structure, and ride quality limitations.
The problem of acceptable deformation at SLS may be resolved using the following analysis procedure:
(a) The vertical, horizontal, and rotational stiffness of footings or pile groups and associated soil or rock
should be assessed and used in an interactive analysis of structure and foundation that considers the
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construction sequence (Hambly 1991). The constraints that apply are those of SLS for
superstructures.
(b) The bearing resistance for footings of various widths and embedment should be assessed using
deformation criteria acceptable for the class of structure and type of construction.
Bearing resistances depend on a number of items, including soil/rock and geotechnical parameters,
the layering of soil, embedment depth, shape, and width of footing. Frequently, Geotechnical
Engineers derive a bearing resistance by assuming a width for a footing and choosing a depth based
on frost penetration or embedment to firm strata. If the inclination of the applied load is large, as may
be the case for portal frame structures, bearing resistances may be reduced to as little as 20% of the
resistance for vertical load, and revisions to footing embedment or the design procedure may be
necessary.
For deep foundations, factored resistance of individual piles or caissons should be included in the
geotechnical report. Generally, factored resistances of individual piles for axial load are required at ULS.
Group effects should be provided where applicable.
Structural and Geotechnical Engineers should also agree on an axial stress limitation at SLS. The
deformation of a group of piles should also be considered, and SLS and ULS limitations appropriate to
this group should be given.
In the absence of analysis, for piles where passive resistance to horizontal forces is of concern, the
reaction at the SLS may be taken as corresponding to a horizontal deformation of 10 mm. Structural
resistances rather than geotechnical resistances will often control at the ULS for piles loaded both
axially and laterally.
C6.5.6 Report
The geotechnical report should include a factual portion presenting details of subsurface conditions
that will ultimately become part of the Plans, providing the Constructor with details of the subsurface
conditions.
The design portion of the report should present discussion and recommendations for design. The
Geotechnical Engineer should analyze field data and test results and make recommendations
pertaining to permanent conditions and, where appropriate, to temporary conditions.
Clause 6.5.6 provides minimum requirements for a geotechnical report and is based on Krebs
Ovesen (1981), CFEM (1992), and NAVFAC DM-7.1 (1982). It is important that the geotechnical
report identify those factors favouring one type of design over another. The report should also identify
subsurface conditions or seasonal effects that could have a significant influence on the difficulty of
Construction. For example, slope stability, the presence of large boulders that would make pile driving
difficult, or an artesian groundwater condition that would cause problems during excavation or pile
driving should be clearly identified.
Two aspects related to design that the Geotechnical Engineer should address and resolve
satisfactorily in concert with the Structural Engineer are
(a) whether the design of the proposed foundations and structure is compatible with the
geotechnical conditions at the site; and
(b) whether the substructure can be constructed without unreasonable difficulty using available
construction technology.
The report should also discuss and provide recommendations for stability and settlement aspects of
the approaches, including dewatering requirements of approach cuts where basal heave of the
roadway is a concern and the stability of excavations for various stages of Construction.
The geotechnical report should define all terms and symbols used in the report.
The geotechnical report is valid only for the design assumptions on which it is based. A change in
project scope may require additional subsurface investigation.
Since site conditions may change over time, the existing surface and subsurface conditions should
be verified to be consistent with those described in the geotechnical report, particularly if Construction
of the structure has been delayed for an extended period of time.
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C6.6 Resistance and deformation
C6.6.1 General
The purpose of a foundation is to support a structure. An essential feature of the foundation design
process is to determine relationships between stress and strain for the soil or rock supporting the
foundations at the site. When a load is applied to a foundation, stresses are induced in the ground in both
horizontal and vertical directions. The primary objectives of foundation design are to ensure that these
stresses do not
(a) exceed the ultimate resistance of the foundation soil or rock; or
(b) cause deformations that will adversely affect the function of, or exceed, a SLS in the structure.
In working stress design, the allowable bearing capacity was chosen as the lesser of the ultimate bearing
capacity of a footing or pile divided by a factor of safety (Bowles 1988, NAVFAC DM-7.1 1982, Meyerhof
1956 and 1963, Peck, Hansen, Thornburn 1974, Tomlinson 1986, Winterkorn and Fang 1986, Terzaghi
and Peck 1967, Al-Khafaji and Andersland 1992), or a capacity causing a prescribed deformation. In
practice, especially for cohesive soils, the deformation corresponding to the load or pressure satisfying the
first criterion was calculated. If this was found to be equal to or less than the prescribed deformation, the
allowable capacity quoted by the Geotechnical Engineer would be the value related to rupture
considerations. For the case of footings on granular soil, deformations usually govern and the
Geotechnical Engineer could employ design methods that would provide the allowable capacity
corresponding to the prescribed deformation. In any event, a single value of allowable capacity was
provided by the Geotechnical Engineer as part of the geotechnical report.
There can be variations in stratigraphy and in geotechnical properties within individual strata at a site.
The introduction of limit states concepts in design separated the uncertainty associated with the
imposed loads from that of the resistance of the soil or rock. This separation caused a change in
methodology for the evaluation of resistance and reaction. In limit states design, the geotechnical
resistance of soil or rock is considered at the ULS, while strain or deformation of soil or rock (geotechnical
reaction) is considered at the SLS. Rather than providing a single design recommendation for resistance,
the Geotechnical Engineer provides two values: one (the factored geotechnical resistance at ULS) that
satisfies the strength or resistance aspect at the ULS, and the other (geotechnical reaction at SLS) that
satisfies the criteria associated with the tolerance of either the soil or the structure to deformation at the
SLS. In practice, the structural designer also analyzes both conditions.
The condition that yields the foundation element governed by the lower of the values for factored
geotechnical resistance at ULS or geotechnical reaction at SLS controls design. These concepts are
illustrated in Figures C6.2 and C6.3. Stress-strain curves for typical soil/rock (Types A and B) are shown in
Figure C6.2. The ascending portion of the stress-strain curve may or may not be linear. With a knowledge
of the site and the material, the Geotechnical Engineer is able to choose an ultimate resistance for the soil
or rock. This may be based on a limiting strain or a maximum resistance.
With a knowledge of the depth and width of a shallow foundation, a schematic load-deformation curve,
Figure C6.3, can be developed from the stress-strain curve of Figure C6.2, assuming that the pore water
pressure conditions in the soil are identical. Figure C6.4 illustrates various values of geotechnical resistance
and reaction that can be derived from (a) and (b) for any particular footing. These are
A = ultimate geotechnical resistance at ULS;
B = factored geotechnical resistance at ULS with resistance factor of 0.5;
C = factored geotechnical resistance B with a horizontal to vertical load ratio of 0.4;
D = geotechnical reaction at SLS for 25 mm deformation; and
E = geotechnical reaction at SLS for 50 mm deformation.
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Maximum
resistance
Stress
Resistance for
limiting strain
value chosen
at “a”
Type A
Type B
Strain
a
Figure C6.2
Typical stress-strain curves for soil/rock
(See Clause C6.6.1.)
Paths may vary
Load
Range of possible
deformation
2550
Deformation, mm
Figure C6.3
Load-deformation curve for footing
(See Clause C6.6.1.)
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Stress
qu
qu/2
qu/3
Resistances based on ULS
Based on SLS
B
C
A
D
Factored
Factored
Ultimate
Resistance
resistance
resistance
bearing
for 25 mm
resistance with resistance (B) with
deformation
factor of 0.5 inclination
of 0.4 and
reduction factor,
R, of 0.29
E
Resistance
for 50 mm
deformation
Figure C6.4
Typical resistance and reaction values
(See Clause C6.6.1.)
It is important to recognize that the ultimate geotechnical resistance is not a simple multiple of the SLS
reaction. In fact, the simple comparison of Figures C6.2 and C6.3 is often not relevant in practice because
of duration of loading effects and the related response of the soil. Most soils in the ground contain water
within the pores of the soil structure. As load from a foundation element is applied, the pore water
pressure within the soil tends to increase. If, for example, the loading is applied gradually during the
construction process, and the soil is a granular material with a relatively high permeability, the pore
pressure buildup may be considered negligible because the pore water can drain away from the zone of
loading (pressure bulb). This is denoted as a drained condition of loading. If, however, the loading is
applied relatively quickly to a fine-grained cohesive soil having a low permeability, the pore water
pressures will increase and drainage from the zone of loading will be negligible in the short-term. This is
denoted as the undrained condition of loading.
For any foundation-soil system, the Geotechnical Engineer must decide whether to design for
undrained, partially drained, or drained conditions, and must employ soil testing procedures and methods
of analysis that are appropriate for the assumed condition of drainage. To illustrate, the factored
geotechnical ULS resistance for a particular foundation may be based on short-term undrained conditions,
while the geotechnical SLS reaction may be governed mainly by long-term drained conditions. The
consideration of pore water pressure effects is a fundamental aspect of soil mechanics and foundation
design, and must be considered by the Geotechnical Engineer in practical problems. In the wetter climatic
zones of Canada, saturated soil conditions may be assumed in design; however, in arid and semi-arid
portions of the country, the soils at some depths may never become fully saturated. In this case, soil
suction and pore air pressures should also be considered in design.
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C6.6.2 Ultimate limit state
The ultimate geotechnical ULS resistance of the foundation is the limit at which a failure mechanism
forms in the soil. Values of geotechnical ULS resistance may be obtained directly or indirectly. One of
the following may be used to determine ULS values:
(a) field and laboratory tests in which geotechnical parameters such as vane shear resistances and
triaxial shear strength, or indicators such as SPT N-values, are measured and correlated to actual
site conditions;
(b) in-situ load tests, e.g., a pile load test in which geotechnical ULS resistance is measured directly.
When geotechnical parameters are obtained from in-situ testing, geotechnical resistances at ULS are
frequently obtained from empirical equations or design graphs, e.g., correlations with standard
penetration test results. It is important to realize that design graphs developed for working stress
concepts require modification for use with limit states design.
The calculated geotechnical ULS resistance for both cohesive and non-cohesive soils is a function of
the method of analysis, as well as the following geotechnical parameters or geometric features:
(a) density;
(b) angle of internal friction;
(c) apparent cohesion;
(d) undrained shear strength;
(e) groundwater level and vertical and horizontal hydraulic gradients;
(f) shape of footing, i.e., length, width;
(g) depth of footing;
(h) length, type and size of pile; and
(i) load inclination.
Resistances at ULS for the structural components forming a foundation are discussed elsewhere in
the Code.
C6.6.2.1 Procedures
The selection of the procedure used to determine factored geotechnical ULS resistances is influenced
by the scope of the site investigation and the complexity of subsurface conditions at the site. For a
major structure, for example, a long-span bridge, a comprehensive site investigation may be able to
provide sufficient data to enable the geotechnical parameters for strata at various depths to be
described in terms of a mean and standard deviation. If sufficient data are available to adequately
describe both loads and resistances, a complete probabilistic method may be used for design.
The variability of a soil or rock is site-dependent, and as such differs from the variability of steel or
concrete. The selection of geotechnical parameters for design varies with local state-of-practice and
with the training, intuition, background, and experience of the Geotechnical Engineer. Thus, the
concept of using statistics and frequency distribution curves is not commonly applied in a formal
manner in standard geotechnical engineering practice.
The Geotechnical Engineer selects “representative” geotechnical parameters based on the results of
appropriate investigations, field and laboratory. “Representative” in this sense refers to the
Geotechnical Engineer’s “best estimate” of the likely values of parameters required for design. The
Geotechnical Engineer should consider the above described interrelationship between resistance and
load factors and characteristic value when selecting the “representative” geotechnical parameters
referred to in Clause 6.5.6. Details of the calculation of factored resistance are given in MacGregor
(1976), Nowak (1993), Nguyen and Chowdhury (1985), and Becker (1996).
C6.6.2.2 Geotechnical formulas
The selection of a geotechnical formula or formulas needs to be based on a decision by the
Geotechnical Engineer as to whether drained, partially drained, or undrained conditions govern the
design. In marginal cases both the undrained and drained analyses may be evaluated, with the one
giving the smallest geotechnical ULS resistance being chosen. For each design situation, there may be
a number of possible design equations that could be used. A Geotechnical Engineer usually favours
one or two equations for shallow or deep foundation design based on experience, local practice, and
the known conditions at the site. Rigorous methods may be inappropriate for a site where the
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subsurface conditions are variable, layered, or the geotechnical data are limited in scope and quantity. In
these cases, a conservative choice of geotechnical parameters is advisable. A variety of geotechnical texts
and handbooks provide so-called presumed values of geotechnical resistance. These are generally based
on working stress design and, as such, are an incomplete characterization of the required geotechnical
ULS resistance and the SLS geotechnical reaction.
Presumed values may, however, be used for preliminary proportioning of the foundations. Additional
information is given in Clause C6.7.2.
Partial coefficients or soil strength factors used in other codes and standards do not apply in the Code.
C6.6.2.3 In-situ tests
The geotechnical ULS resistance of foundations can be determined from small-scale or full-scale in-situ
loading tests. For shallow foundations, the field test may consist of a plate bearing test or a screw plate
bearing test (Selvadurai 1980). For driven and cast-in place piles, the field test may consist of static load
tests on one or more piles at the site. Driven piles can be subjected to dynamic tests. Static pile load tests
and/or dynamic tests may be conducted at the design stage, or during Construction for quality assurance
purposes.
Plate bearing tests should be carried out until failure of the supporting soil has been reached. The failure
value should be determined from the shape of the load-deformation curve. A plate bearing test is normally
carried out on a plate that is small in relation to the size of the footing considered. Therefore, the stress at
failure cannot be taken as directly representative of the ultimate geotechnical resistance of the footing.
Instead, the failure stress found in the test is used in a calibration of the bearing resistance equation
discussed in Clause C6.6.2.2 to the conditions of the tested soil layer.
Pile loading tests are normally performed at full-scale. At the design stage, tests on single piles are
usually carried out to failure, or to a prescribed deformation, and the results taken as representative of the
actual geotechnical resistance at ULS of similar piles at the site. Clause C6.8.5.3 gives details of pile load
tests. The applicable standards are given in ASTM Volume 04.08 (1997). Proof load testing is discussed in
Clause C6.8.5.3.
C6.6.2.4 Assessed value
Situations may occur where there are sites with existing structures that are similar in stratigraphy, and have
similar soil or rock properties to the site of the structure to be built. The design and construction
experience from the existing site or sites may be used with caution to determine an assessed geotechnical
ULS resistance for the structure at the new site. For this evaluation to be valid, the characteristics of the
foundation design should be similar. It is imperative that a subsurface investigation be done to confirm
that the ground conditions are similar at the existing and new sites.
For shallow foundations, assessed values for geotechnical ULS resistance and SLS deformations or
reactions may be used when suitable geotechnical data, including detailed stratigraphy, have been
obtained from the site. Such values should be based on a knowledge of the locality and the results of
observations obtained from sites having similar stratigraphy. In the absence of more precise site-specific
values, assessed values for factored vertical ULS geotechnical resistance ULS for sound level bedrock and
nonyielding soil may be determined by reference to an appropriate publication, e.g., CFEM (1992). Higher
values may be used when substantiated by tests or experience. Lower values should be used when the
rock is weakened by joint fissures or other planes of weakness, or if it is weakly cemented.
In the case of pile foundations, a static analysis may give an inaccurate estimate of the geotechnical
resistance. Sometimes, depending on the size and remoteness of the project, it may be too costly to
perform either static or dynamic tests to confirm the design pile capacity. In such cases, experience from
other nearby sites with similar geotechnical conditions and similar types, sizes, and methods of installation
of piles may be used to assess the geotechnical resistance at ULS. If any discrepancies, such as major
changes in penetration resistance or driven length are observed during installation and restriking, the
situation must be analyzed and reported, and the necessary revisions made.
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C6.6.3 Serviceability limit state
C6.6.3.1 General
When serviceability limit states are dealt with in design, the movement of the approaches to the
structure, the type of bridge structure, and the presence of adjacent structures or adjacent
construction operations should be considered. Any differential movement of the riding surface due to
settlement of the supports of a structure warrants consideration.
Design for serviceability implies eliminating the loss of function of the structure and its approaches,
and requires consideration of the following initial or short-term and long-term movements within the
supporting soil or rock:
(a) settlement or heave;
(b) horizontal movement; and
(c) rotation about a longitudinal or a transverse axis.
Both total movement and differential movement are important.
Figure C6.5 shows an example of the vertical movements to which a series of footings might be
subjected, under the action of specified dead loads, other permanent loads and live loads, when
settlement of the supporting soil occurs. The approach to the left of the first abutment settles Δ 0 , the
abutment, pier 1 and pier 2 settle Δ 1 to Δ 3, respectively, and both the second abutment and the
associated approach fill do not settle. The settlement at the first abutment is assumed to be caused by
two effects. The first is due to the dead and live loads acting on the superstructure. The second is an
additional settlement beneath the footing caused by the surcharge load due to the approach fill.
Approach
Zero line
D0
Approach,
with
settlement
Approach
Structure
Top of riding surface,
superstructure not shown
D3
Typical
D1
q3
D2 displacement
Approach,
with no
settlement
q2
Typical
rotation
q1
Pier 3
Pier 1
abutment
l1
Pier 4
abutment
Pier 2
l2
l3
Figure C6.5
Total and differential settlement
(See Clause C6.6.3.1.)
If the superstructure is composed of a series of simple spans, moderate vertical deformation of any
one of the piers does not usually lead to structural serviceability problems other than effects on
bearings or joints. The relative rotation between various spans, θ 1 to θ 3 , may affect ride quality. In
cases where large movements are predicted, jacking of the supports at various times or the use of
alternative foundations should be considered. When the structure is continuous, additional moments
and shear forces are induced in the superstructure after continuity is developed. These additional
forces and moments are not necessarily large. For voided-slab bridges having spans of approximately
25 to 30 m, support settlements of 25 mm, for example, would lead to changes in support moments
of about 10% of the dead load moment. These moments vary with the geometry of the structure and
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may be significantly larger for structures stiffer than voided slabs. Each case should be checked through
analysis using the loads specified in Section 3 and, where necessary, considering the construction
sequence.
Rotation at the base of a pier that is assumed to be founded on soil or supported by piles can lead to
other serviceability problems. Potential deformation problems caused by rotation, horizontal movement,
or uneven settlement are illustrated in Figure C6.6.
The example in Figure C6.6(a) relates to rotation away from backfill due to backfill pressure or
shortening of the superstructure. The former can lead to jamming of expansion joints. If the footing tilts as
shown in Figure C6.6(b), the expansion joints may open more than intended.
Length changes due to temperature effects or horizontal forces due to braking could lead to horizontal
or rotational movements of a footing as shown in Figure C6.6(d).
Dh = qh
Dh = qh
Rotation due to
settlement at
rear of footing
Rotation due h
to backfill or
superstructure
shortening
q
h
q
(a)
(b)
Force due to
shortening of
structure
Rotation due
to uneven
settlement
Horizontal
movement
of footing
q
Soft
Firm
Variable
thickness
strata
(c)
(d)
Figure C6.6
Movements of components
(See Clause C6.6.3.1.)
When a superstructure is continuous, interaction between the foundations and the superstructure
should be considered. In the calculations, the sequence of Construction and a range of deformation
characteristics of the supporting soil or rock should be considered. The approximate effects of initial or
final differential settlement due to footing loads can be calculated if the spring stiffness characteristics of
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the soil or rock supporting a footing are known (Hambly 1991). These stiffness characteristics should
take into account, either directly or indirectly, the width, length, and embedment of the footing, the
soil type, and the number of piles, if any.
C6.6.3.3 Tests
The use of the plate bearing test to determine the geotechnical SLS reactions or deformations is
problematic. Firstly, the test is normally done over a short time frame, while the settlement problem
can be a long-term one. Secondly, the small size of the loading plate means that the pressure bulb
within the soil below the plate is considerably smaller than it would be under the actual structure.
Nevertheless, the test may be useful to measure a soil modulus of deformation if the supporting soil is
consistent with depth, for example, a dense, mixed-grained glacial till extending to bedrock. If the site
of the structure has an underlying compressible layer, then the results of the plate bearing tests would
be virtually meaningless. Static cone penetration tests and pressuremeter tests have an important
advantage in that tests can be done at intervals of depth in a test hole.
Pile loading tests may on occasion be useful in estimating settlement as long as there are no
underlying compressible layers that would undergo long-term consolidation. The pile test should be
carried out a sufficient time after driving that induced pore water pressures have dissipated. The test
would not be meaningful in estimating long-term settlements of pile groups in the case of friction piles
driven into soft to firm clay.
C6.6.3.6 Calculation considerations
(a) Cases may exist where it is possible to construct approach embankments in stages, or to employ
vertical foundation drains to take advantage of the resulting beneficial changes in soil parameters.
For example, drains accelerate pore pressure dissipation and rate of settlement. Staged
Construction allows for some pore pressure dissipation, possible strength gain, and some
settlement to occur before the next stage of loading is applied.
(b) In most of the wetter parts of Canada, the primary problem causing vertical movement of
structures is settlement. In arid and semi-arid regions, swelling of the soil may be a more
significant problem. Collapsible soils are relatively rare in Canada and usually consist of very loose,
sandy or silty soils, e.g., loess, with a weakly cemented bond between particles. When these
materials are saturated and loaded, the soil structure collapses causing compression of the soil.
Some shales, through swelling, e.g., in the Ottawa area, can undergo a complex biochemical
weathering, whereby pyrite in the presence of sulphite reducing bacteria and oxygen produces
sulphuric acid, which reacts with carbonate in the shale to produce a gypsum. The formation of
gypsum and other by-products of the reaction produces large pressures within the shale that can
heave overlying structures. Backfill composed of this shale may also exert significant pressures on
retaining walls and its use should therefore be avoided.
The total settlement of soil, sT , consists of three main components:
(a) immediate settlement, si ;
(b) primary consolidation settlement, sp ; and
(c) secondary consolidation or creep, screep .
Estimates of total settlement of shallow foundations and approach embankments on soil can be
based on the following equation:
sT = si + sp + screep
Equation C6.6.3.6 (1)
With the exception of highly compressible soils, such as organic silts and marine clays, creep
settlement is usually small and in most cases can be ignored.
Settlement calculations based on the approaches described below are usually reasonable estimates
of deformation. Problems or uncertainties that can occur with settlement analysis include
(a) the lack of reliable methods to assess in-situ values of deformation moduli;
(b) the sequence of loads applied to the footing may not be well-known;
(c) uncertainties in the soils profile; and
(d) uncertainties in determining stress and strain profiles throughout the soil mass.
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In most cases, the geometry associated with footings on soil is two-and three-dimensional in nature.
Therefore, it is appropriate and consistent to base estimates of settlement using theory that incorporates
two-and three-dimensional considerations. An example of this is the elastic displacement theory.
Immediate settlement below a footing or embankment is calculated using the following elastic
displacement equation which relates settlement to bearing stress, footing or embankment geometry, and
undrained deformation modulus:
si = IqB (1 – ν 2) / E
Equation C6.6.3.6 (2)
The immediate settlement component represents undrained or no volume change conditions in the
loaded soil. It is concomitant with the applied loading, i.e., during Construction, it is not time-dependent.
For most situations, immediate settlement seldom poses significant consequence, as the settlement is
complete by the end of loading.
The value for E can be determined from consolidated triaxial compression tests. It is preferable that the
triaxial specimen be consolidated under in-situ mean effective stress prior to shearing. Accordingly, the
value of Ko should be measured or estimated based on many available empirical correlations. However, in
most cases the use of Ko equal to unity will suffice.
Typical values for E are presented in textbooks. Often E can be approximated, based on elasticity
considerations, as
E = 1/ m v
Equation C6.6.3.6 (3)
where mv is the coefficient of compressibility measured in oedometer tests at the appropriate field stress
range. For clays, E is frequently estimated from undrained shear strength, with its value ranging from 200
to 1000 times the undrained shear strength. Typically a value of 300 to 500 times the undrained shear
strength is a reasonable approximation.
The value of E can also be determined from field plate load tests that are carried out in such a way as to
reflect undrained conditions. The plate bearing test, however, has limitations as described in CFEM (1992).
The value of I is given in many textbooks, for example, Perloff and Baron (1976) and CFEM (1992).
Equations similar to Equation C6.6.3.6 (2) also exist for the calculation of horizontal displacement and
footing rotation in terms of load and modulus (Poulos and Davis 1974).
Consolidation settlement is a time-dependent process that is governed by the rate of dissipation of
excess pore water pressures that are induced by the footing or embankment loads. It relates to volume
change taking place in the soil. The rate of excess pore water pressure dissipation is controlled by hydraulic
conductivity and other factors. In sands where hydraulic conductivity is high, consolidation settlement
usually occurs simultaneously with applied loading. By contrast, clays and other fine-grained soils have low
hydraulic conductivity and it takes time for excess pore water pressures to dissipate. Consolidation
settlement, if its magnitude is relatively large, can pose a significant problem because it will occur after
Construction. This post-Construction settlement needs to be taken into account in design.
Elastic displacement theory can be used to calculate the total settlement of soil in those cases where the
creep component is negligible and, for all practical purposes, can be ignored in the settlement analysis. In
this case, the equation becomes
sT = si + sp = IqB (I – ν 2) / E’
Equation C6.6.3.6 (4)
The value of E' is less than E. It can be determined from consolidated drained triaxial compression tests
in a manner similar to that described above for undrained tests. The value of E’ can range from being only
slightly less than E to about 30% smaller. Often, E’ is approximated as
E′ =
(1+ n ′) (1− 2n ′)
(1− n ′) mn
or as
E′ =
2E (1+ n ′)
3
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The value of E’ can also be determined from field plate load tests that are carried out slowly enough
to ensure drained conditions. The plate bearing test, however, has limitations as outlined in
CFEM (1992).
The value of Poisson’s ratio for drained conditions, ν’, depends on soil type, but typically is about
0.3. The range for Poisson’s ratio is from 0.5 for undrained conditions to about 0.2 for drained
conditions. The effect of Poisson’s ratio on settlement is usually small because its value is squared in the
Equation C6.6.3.6 (4).
Equations C6.6.3.6 (2) and C6.6.3.6 (4) represent the change in deformation characteristics that a
soil undergoes when loaded. Immediately upon load application, undrained conditions exist, defined
by E and ν = 0.5 if the soil has low hydraulic conductivity. Excess pore water pressures induced by the
footing pressure then dissipate at a rate controlled primarily by hydraulic conductivity. As excess pore
water pressure dissipates, a volume change occurs resulting in settlement.
Upon complete dissipation of excess pore water pressure, the soil deformation properties are
represented by a drained modulus of deformation, E’, and a drained Poisson’s ratio, ν’.
Based on the above, it can be appreciated that in sandy soils, the total settlement (si + sp) essentially
occurs immediately. The settlement in sands, therefore, is given by drained parameters. The value of E’
for sands has been correlated to in-situ tests such as SPT and CPT. The following simple correlations
with SPT N-value often provide reasonable estimates of E’ in sands.
Soil
E'/ n (MPa)
Silt and silty sand
0.5
Compact sand
1.0
Dense sand
1.5
Sand and gravel
4.0
The following table provides typical values for E’ for various soils:
Soil
E' (MPa)
Loose sand
10 – 20
Compact sand
20 – 50
Dense sand
50 – 100
Dense sand and gravel, till
100 – 300
Silt
2 – 20
Soft clay
2–5
Stiff clay
10 – 20
Very stiff clay
20 – 50
Hard clay
50 – 100
For clays, there is a distinct time dependency of settlement, and two direct components of si and sp
can be observed. Equation C6.6.3.6 (4) can be rewritten as follows to obtain consolidation settlement:
sp = sT – si
The settlement at time t may then be computed as
st = si + U (sp) = si + U (sT – si)
Equation C6.6.3.6 (5)
where
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= average degree of consolidation (0 ≤ U ≤ 1.0).
From Equation C6.6.3.6 (5), it is seen that when U = 0 (i.e., no consolidation) st = si and when U = 1.0
(complete consolidation), st = sT. The value of U is a function of time, nature of loading, and coefficient of
consolidation, cn. In most cases, Terzaghi’s one-dimensional theory is used to evaluate U, even though
shallow foundations are typically two- to three-dimensional in nature. Solution for U under two- and
three-dimensional conditions are available (Davis and Poulos 1972). The use of Terzaghi theory is generally
conservative because the rate of consolidation is faster for two- and three-dimensional conditions than it is
for one-dimensional conditions.
When a footing or embankment is founded on layered soils, the immediate and consolidation
settlement components can be estimated by calculating the settlement of each layer and then adding
them together to obtain the settlement for the soil mass. In the calculation procedure, settlements are
calculated using a vertical strain summation approach as described by Davis and Poulos (1968) and Becker
and Lo (1981). The stresses induced in the soil are used with values of E, E’, ν , and ν’ to compute the
various components of settlement.
One-dimensional consolidation settlement theory is commonly used to compute the time dependent
consolidation settlement component. The basis of the theory and calculation are well known and
described in textbooks. The parameters needed in the calculations are obtained from consolidation tests in
oedometers. The basic test procedures and analysis of results are described in ASTM Volume 04.08, and
Terzaghi and Peck (1967).
By definition, one-dimensional conditions are represented by a loaded area that is very large compared
to the thickness of the compressible soil layer. In many situations, the geometry associated with footings is
not one-dimensional and the use of one-dimensional theory to predict settlements of footings will
generally overestimate values of actual settlement. The use of the elastic displacement theory as described
above is consistent in that it appropriately models the two- and three-dimensional nature of most footings.
In general, embankments tend to approximate one-dimensional loading more closely than footings. If
consolidation settlement is calculated using one-dimensional theory, the amount of settlement predicted
will be greater than that observed. Corrections to the one-dimensional calculated consolidation settlement
have been proposed by Skempton and Bjerrum (1957) so as to better represent two- and
three-dimensional characteristics.
The magnitude of the preconsolidation pressure, σ ’p , relative to the final stress state imposed by the
footing or embankment is a key consideration in the calculation. If the final stress is less than σ ’p , the
settlement will usually be small and can be given by the recompression index, Cr . However, if the final
stress is greater than σ ’p , both Cr and the compression index, Cc , need to be used appropriately in the
calculation. The calculation procedure is outlined in textbooks (Perloff and Baron 1976) and in
CFEM (1992).
For highly compressible soils, such as organic silts and marine clays, secondary consolidation or creep
settlement that occurs at little or no excess pore water pressure can be significant in magnitude. The
magnitude of secondary consolidation settlement may be estimated according to well-known procedures
using Cα , the coefficient of secondary compression, which is defined as the change in void ratio per log
cycle of time. Mesri and Godlewski (1977) and Mesri (1973) give comprehensive discussions on the
selection of parameters and analysis of secondary compression.
For coarse-grained soils such as sands, empirical correlations have been developed to estimate total
settlements. These correlations have usually been based on observations of actual settlements of
foundations. However, the different approaches, although well-defined and well-recognized, often
produce different estimates of settlement. For example, the methods of Terzaghi and Peck (1996),
D’Appolonia et al. (1970), Burland and Burbidge (1985), Schmertmann (1970), and Janbu (1985) yield
different results for settlement given the same data set.
The Terzaghi and Peck data design charts are based on SPT values and maximum values of observed
settlement data; they will tend to provide larger estimates of settlement than actually occur. Other
correlations are intended to predict average settlement, or make use of statistical estimates. The basis of
the correlations should be understood so that the Engineer appreciates whether maximum (upper limit) or
average values are being predicted. Tan and Duncan (1991) suggest adjustments that could be made to
various settlement predictions to bring them to a common level of reliability.
U
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C6.7 Shallow foundations
C6.7.1 General
Although the requirements of Clause 6.7 generally apply to isolated footings that support a single
column or wall, they are also applicable to combined footings and mats that support two or more
columns or walls. Information concerning the design of combined footings and mats can be found in
the following references: Danish Geotechnical Institute (1985), Bowles (1988), ACI Journal, Volume 63,
No. 10 (1966), and Meyerhof (1982).
Some general design considerations are as follows:
(a) For relatively homogeneous soil conditions, bearing resistance will generally increase with
increase in size of footing and depth of embedment. In the case of layered soils or soils whose
shear strength varies with depth, this is not necessarily the case and calculations for various sizes
and embedment depths are advisable.
(b) The Geotechnical Engineer should specify factored geotechnical resistance at ULS and
geotechnical SLS deformation and indicate the range of footing width, depth of embedment, and
footing elevations over which the recommendations apply. Consideration should be given to the
magnitude, direction, and point of application of external forces.
(c) The tolerance of the structure to deformation, and the possible consequences of excessive
deformation during the design life should be considered.
(d) The depth of embedment of the footing should be considered.
(e) Risk of major ground movements that may result from sinkholes or man-made installations such
as underground mines, or soils having an internal structure that collapses in the presence of
water, should be considered.
(f) When placing a new shallow footing lower than an adjacent existing unit, there is a possibility
that the soil may displace laterally or flow out from beneath the existing footing, thereby causing
movements of the existing structure. In some cases, the problem may be minimized by
constructing a shoring wall to retain the soil with limited movement, as illustrated in Figure C6.7.
Removal of overburden adjacent to an existing footing can sometimes result in a ground
movement causing settlement of the existing unit, and an upward movement of the soil in the
vicinity of the new footing. It is difficult to predict without careful evaluation just how close an
excavation can be carried out without causing distress. This distress depends on the subsoil
conditions and the type of Construction; it is illustrated in Figure C6.8.
Generally, when a shallow footing is placed adjacent to an existing footing that is at a lower
elevation, it should be located so that a 45° line from the bottom edge of the new footing does
not intersect any portion of the underside of the existing footing, as shown in Figure C6.9.
Otherwise, shoring may be required. This is to avoid the possibility of imposing additional loads
on the existing footing or causing damaging settlement.
A new footing can impose additional loads on an underground conduit, depending on the
nature of the founding soil and the location of the buried conduit relative to the new footing. As
a precaution, the new footing should be located as shown in Figure C6.9. Otherwise, shoring
may be required. A Geotechnical Engineer should be consulted when problems of this nature
arise.
(g) The effects of actual and potential changes to groundwater conditions, including any dewatering,
on the properties of the soil supporting the footing, and also on the soil supporting any nearby
facilities, should be considered. Consideration should be given to the effect of increase of natural
water content on cohesive soils, the effect of submergence on the effective weight of
non-cohesive soils, and changes in bearing resistance due to dewatering.
(h) Scour, dredging, or excavation adjacent to a shallow footing can lead to undermining, resulting
in failure, settlement, or tilting of a structure. Accordingly, when determining the depth of the
footing, the possibility of future ground elevation change should be considered and the assumed
minimum depth of the footing should be indicated. In some cases, a change from shallow
foundation to deep foundation may be required. Future placement of fill or a heavy load adjacent
to a footing should also be evaluated, as this could lead to footing settlement or tilting.
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Ground line
Excavation line or
shoring wall
Existing footing
Soil tends to flow out
due to loss of lateral
support in the absence
of either native soil or
shoring wall
New footing
Figure C6.7
Influence of an excavation for a new footing on an existing footing
(See Clauses C6.4.2, C6.4.3, and C6.7.1.)
Location of new footing
Potential soil “bulge”
Excavation line
Existing footing
Settlement caused
by adjacent soil
movement
Figure C6.8
Settlement caused by an adjacent excavation
(See Clauses C6.4.2, C6.4.3, and C6.7.1.)
New footing
New footing
45˚
45˚
Buried
conduit
Existing footing
Figure C6.9
Recommended locations for a new footing
(See Clauses C6.4.2, C6.4.3, and C6.7.1.)
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(i)
Seasonal volume changes may result from the effects of changes in water content, the presence
of groundwater, and varying temperature.
(j) Volume changes in cohesive soils depend mainly on the seasonal variation in water content of the
soil. The change could result in settlement or expansion of the soil, and hence, deformation of the
structure. Similarly, soil can dry out from excavation and the resulting change in volume can
cause settlement of a shallow footing. Where collapsible or expansive soils are present, special
measures including site remediation or deep foundations should be considered.
The presence or loss of vegetation may cause the following types of damage, each of which
may affect footing performance:
(i) uplift by roots;
(ii) increased erosion, if vegetation is lost on slopes;
(iii) changes to groundwater elevation; and
(iv) changes to the water content of the soil.
(k) Seismic considerations and earthquake effects, as discussed in Section C4, should be considered.
(l) For frost action to occur, it is generally accepted that three basic conditions must exist:
(i) frost-susceptible soil;
(ii) water; and
(iii) cooling conditions that cause either water in the soil or free water to freeze.
The depth of frost penetration varies throughout Canada and, in some instances, within a
specific locality. The bottom of a footing, in a frost susceptible soil, should be located below the
lowest depth of frost penetration that is likely to occur during the life of the structure (CFEM
(1992)). Where frost protection is marginal or becomes deficient, for example, in the case where
a roadway grade adjacent to an existing structure is lowered, consideration should be given to
the use of insulation to improve the amount of frost protection.
(m) When a shallow footing is located on or adjacent to a slope, the lack of soil on the down-slope
side of the footing tends to reduce its stability and hence resistance. NAVFAC DM-7.1 (1982),
Meyerhof (1956), Meyerhof (1963), Winterkorn and Fang (1986), Brinch Hansen (1970), Vesic
(1973, 1975), and Meyerhof (1953, 1957) provide useful information in such cases.
(n) It is often advantageous, and sometimes necessary, to place shallow footing units on
well-compacted granular fills, using controlled methods of construction and materials. Such fills
often provide a better footing base than the original subsoil underlying the fill.
The bearing resistance and settlement of the footing units placed on compacted fills depend
on the type of fill material, inspection and quality control, and the proximity of the footing to the
sloping surface of the fill. These aspects should be considered by a Geotechnical Engineer.
C6.7.2 Calculated geotechnical resistance at ULS
Calculation procedures and appropriate resistance factors are given in Clauses 6.6.2 and C6.6.2.
The geotechnical ULS resistance of a foundation may be calculated by a variety of techniques, which
include evaluating the shear strength of the soil, and applying the results of in-situ tests.
The resistance of a foundation is derived from the geotechnical parameters, the depth of
embedment of the foundation, and the weight of the soil within the failure zone. Direct and simple
shear tests and conventional triaxial tests, with or without pore pressure measurements, of relatively
undisturbed soil samples can be used to obtain strength parameters. Alternatively, the strength
parameter can be obtained from the results of in-situ tests such as field vane shear, static cone
penetration (CPT/CPTU), and pressuremeter tests. These in-situ tests offer the advantage of
minimizing the detrimental effects associated with disturbance caused by the drilling and sampling
operations. The field vane test is commonly used in soft to stiff clays. However, as described by
Bjerrum (1972), Holtz and Wennerstrand (1972), Aas (1986), and ASTM (1988), corrections to the
measured shear strength may be required. Such corrections need to be applied with caution and
calibrated against local experience using engineering judgement. The complete development of a
mathematical model for bearing resistance is available in Terzaghi and Peck (1967), Sokolovski (1965),
Harr (1966), Chen (1975), Meyerhof (1951), Brinch Hansen (1970), Vesic (1973, 1975), and Meyerhof
(1953, 1957). Models should include the influence of footing geometry, footing embedment,
proximity to slopes, and load inclination.
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The bearing coefficients, Nc , Nq , and Nγ , are dimensionless and depend only on the value of the
internal friction angle. Nc and Nq were developed for weightless soils as early as 1921 by Prandl (1921).
The factor Nγ includes the effect of the soil weight. The expressions were derived by Terzaghi (1943) and
by Lundgren and Mortensen (1953). Several others have also proposed expressions for these factors. The
following expressions have been taken from the CFEM (1992) and were proposed by Terzaghi (1943) and
the Danish Geotechnical Institute (1985):
Nq =
(e
π tan f ′
sin f ′ ⎞
) ⎜⎝⎛ 11+− sin
⎟
f′ ⎠
Nc = (Nq – 1) cot φ ’
Nγ = 3/2 ( Nq – 1) tan φ ’
It is noted that these bearing resistance coefficients involve exponentials that are functions of φ ‘,
making the calculation of the bearing resistance sensitive to small variations in φ ‘, as shown in Figure 6.3.
The determination of the friction angle is difficult, and engineering experience and judgement must be
used in its selection.
The resistance equation, as given in the Code, is intended for use in an effective stress analysis. The
values c’, γ ’, and φ ’ are effective values. When evaluating the ULS resistance of soils, both the short-term
(undrained or total) and long-term (drained or effective) conditions should be checked. The ultimate
bearing resistance is the lesser of the two values. For soft to stiff clays, the short-term condition generally
governs.
For the short-term or undrained condition in clay, φ’ is zero and the value c’ corresponds to shear
strength, c. For undrained conditions, in terms of total stresses, when φ’ = 0, then Nc = 5.14, Nq = 1.00,
and Nγ = 0.00. For this case, the ultimate bearing resistance equation for clay becomes
qu = 5.14 c sc i c + γ ’ D f s q i q
where Df is the minimum depth of footing below the ground surface. The term γ ‘Df corresponds to the
total overburden pressure at the base of the footing, i.e., it represents q’Nq.
Because the pore pressure above the groundwater table is assumed to be zero, the total stress is the
effective stress. When the distance of the groundwater table to the base of the footing is less than the
footing width, B, the value of γ ’ may have to be proportioned to account for the effect on unit weight.
Above the water table, the effective weight is the total unit weight, while below the water table it is the
submerged unit weight. The value used for γ ’ must also reflect the presence of any hydraulic gradient in
the soil. When an artesian pore pressure exists below the footing or the eccentricity is large, the expression
for ultimate resistance, qu , may become unreliable (DGI 1985).
Typically, the geotechnical resistance at ULS of a footing is calculated by assuming that the foundation is
located on uniform ground with a level surface in which the depth of the supporting stratum is sufficient
to develop the failure mechanism assumed in the calculation. Otherwise, the bearing resistance may
require modification to account for the influence of sloping ground, and non-uniform or layered soils
(NAVFAC DM-7.1 1982, Winterkorn and Fang 1986, Brinch Hansen 1970, Vesic 1973 and 1975, and
Meyerhof 1953, 1957).
Where retrieval of soil samples is expected to introduce significant sampling disturbance, the shear
strength and bearing resistance of the soils can be calculated from the results of in-situ tests, which include
the standard penetration test (SPT), static cone penetration test (CPT), and pressuremeter test.
Standard penetration test (SPT)
Results obtained from SPT are subject to variability as the equipment, procedures, and operator
characteristics used for the test are not fully standardized. The limitations on the use of SPT test results for
calculating bearing resistances are given in the CFEM (1992), Wroth (1988), Mitchell (1988), and ISUPT
(1988). Nevertheless, many correlations have been developed between SPT value (N) and various
geotechnical parameters. Correlation between N-values and vertical settlement is established for a known
stratigraphy and forms the basis for design charts relating bearing resistance, N, and width for a vertical
settlement of 25 mm as shown in NAVFAC DM-7.1(1982), Peck, Hansen and Thornburn (1974), and
Terzaghi and Peck (1967).
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Static cone penetration test (CPT/CPTU)
A static cone penetrometer test is carried out by pushing the point of a cone into the soil, while
recording the cone point stress and the side resistance along a short length of the straight portion of
the cone immediately behind the cone point. The pore pressure induced by the cone penetration is
measured by a piezo-cone. The static cone results, and in particular the piezo-cone data, are useful in
determining the soil profile and variations in its density and strength. Theoretical and empirical
functions have been proposed for relating the results of other in-situ tests. The use of the static cone
results in design remains largely empirical.
The advantages and limitations on the use of results derived from static cone penetration tests for
the calculation of various bearing resistances are discussed in the CFEM (1992), Robertson and
Campanella (1984), Schmertmann (1970, 1977), ISUPT (1988), and Lunne et al. (1997).
Pressuremeter test
A procedure for estimating the bearing resistance of a foundation from results of a pressuremeter test
was proposed by Menard (1975). The limitations on the use of results derived from pressuremeter
tests for the calculation of geotechnical resistance at ULS are discussed in the CFEM (1992), Menard
(1975), and Baguelin, Jezequel, and Shields (1978).
C6.7.3 Pressure distribution
C6.7.3.1 Effective area
For spread footings subjected to eccentric loading, a uniform distribution of soil pressure acting over
the effective area of the footing should be assumed for the geotechnical analysis of the foundation.
For eccentricity in two directions, the effective area can be determined in such a way that the
resultant of the factored load passes through the centroid of the effective area. Clause 6.7.3.1 based
on the centroid of pressure does not uniquely define the shape of the contact pressure, and this is
acceptable for footing proportioning.
C6.7.3.2 Pressure distribution at the ULS for structural design
In the structural design of a footing, the designer needs to consider two cases of contact pressure
distribution at the ULS. The first case assumes a contact pressure distribution due to a yielding soil,
Clause 6.7.3.2(a), which approximates a uniform pressure distribution over the effective area, A,
Figure C6.10. The second case, Clause 6.7.3.2(b), assumes a contact pressure distribution due to an
elastic, non-yielding soil. This is a linear pressure distribution, assuming a linear elastic soil response
and a nearly rigid footing, Figure C6.11. The pressure distribution for the yielding soil is shown in plan
in Figure C6.11 for double eccentricity.
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Centroid of factored loads
Plan
Contact area
Centroid of
bearing pressure
Elevation
Factored loads
Centroid of bearing pressure
Figure C6.10
Shallow foundation, effective contact area — Uniform
pressure distribution
(See Clause C6.7.3.2.)
Centroid of factored loads
Plan
Centroid of
resistance
Elevation
Bearing resistance
acting over bearing area
Resultant
Figure C6.11
Shallow foundation, effective contact area — Linear
pressure distribution
(See Clause C6.7.3.2.)
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The computed value, Rqr , represents a minimum resistance expected from the soil based on the
factored bearing resistance, including the effects of load inclination, R. The uniform pressure
distribution is appropriate for geotechnical analysis in the determination of bearing area. It is also
applicable for structural analysis at the ULS (Figure C6.12(a)).
However, structural design should also include the case of loading where resistance of the soil
exceeds that of the calculated minimum, Rqr . For this case, elastic response to factored load is
probable, as shown in Figure C6.12(b), where a linearly varying pressure distribution results. For
footings on rock or dense glacial till, the contact pressure at the ultimate limit state is more closely
represented by a linear distribution, where the maximum calculated pressure for structural design is
not limited.
(a) Yielding soil
(b) Linear elastic non-yielding soil
CL Resistance
CL Resistance
Factored load, Qf
Factored load, Qf
Factored stress
R • qr limit, R less than 1.0
R • qr limit, R equal to 1.0
Applied over
effective area, A
Maximum applied stress at the
toe may be greater than R • qr
Figure C6.12
Pressure distributions, ULS structural design
(See Clause C6.7.3.2.)
C6.7.3.3 Pressure distribution at the SLS
Under the SLS, materials are assumed to respond elastically to load. Hence, a linear distribution of
stress is used in analysis. Figure C6.13 indicates the vertical contact pressure distribution that can be
assumed for bearing resistance at the SLS. For those cases where the rotation and horizontal
movements are to be calculated, Bowles (1988), Barker et al. (1991), and Poulos and Davis (1974)
provide design data.
Normally, shallow footings on sound bedrock or nonyielding soil need not be checked for
settlement. The loads required to produce detrimental settlement of the structure for such cases will
be larger than the factored bearing resistance at the ULS. However, when bedrock contains, for
example, either compressible clay seams at shallow depth or solution cavities, a settlement analysis
should be carried out.
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CL Resistance
Specified load, Q
Applied stress
qs limit
Maximum applied stress
at the toe should not be
greater than qs
R always equal to 1.0, with
no reduction for inclination
Figure C6.13
Reaction at the SLS
(See Clause C6.7.3.3.)
C6.7.3.4 Eccentricity limit
The 30% eccentricity for geotechnical proportioning was chosen in order to limit local bearing stresses in
either the concrete footing or the soil or rock so as to avoid the possibility of a bearing failure towards the
rear of the footing or overturning. The limit is not related to the middle-third rule employed in elastic
analysis, where an eccentricity in the direction of the load of more than 1/6 results in tension at the heel.
Corrections should be made to the calculated bearing resistances for eccentricity values greater than
0.30 B (DGI 1985). For a footing with a non-rectangular geometry, the 0.30 rule will also apply. However,
checks of bearing resistance of the soil should be carried out to ensure that failure does not occur in a
direction opposite to the line of action of the load.
The eccentricity limitation given in Clause 6.7.3.4 applies to static loading. For seismic loading, an
eccentricity limitation of 0.4 B applies in design.
C6.7.4 Effect of load inclination
The preferred method for considering the effect of inclined load on geotechnical ULS resistance is through
the general bearing resistance equations given in Clause 6.7.2. In the absence of such detailed
calculations, or where the bearing ULS resistance under vertical load has been developed using an assessed
value or empirical design relationships, and where geotechnical parameters may not be known, the
reduction factors given in Clause 6.7.4 may be used as default values. Where values of factored bearing
resistance are calculated using known geotechnical parameters, the provisions of Clause 6.7.2 should be
used in the interests of economy.
The values specified in Clause 6.7.4 do not include consideration of factored horizontal resistance, and a
separate analysis is required for sliding at the interface of the soil-foundation surface or within the soil. The
curves given in Clause 6.7.4 may be represented by the equations given in Table C6.1, as a convenience
for calculation purposes. The data in Clause 6.7.4 and Table C6.1 are based on Meyerhof’s bearing
resistance equations (Meyerhof 1951 and 1953) and various depths of cover, and the angle of internal
friction of the supporting soil is taken as 30°. The equations given in Table C6.1 are provided for the
convenience of the designer to avoid the necessity to recalculate the curves given in the Code.
Prescriptive reduction factors cannot be developed for rock because of the variations in weak seams and
their shear resistance. A site-specific analysis is required.
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Table C6.1
Reduction factors, R, to account for the effects of inclined loads
(See Clause C6.7.4.)
Material type
Reduction factor equation
Cohesive soil
Noncohesive soil
Noncohesive soil
Noncohesive soil
Noncohesive soil
Noncohesive soil
R = 1.00 – 1.30 x + 0.57 x
R = 1.00 – 2.76 x + 2.22 x2
R = 1.00 – 2.50 x + 1.80 x2
R = 1.00 – 2.20 x + 1.50 x2
R = 1.00 – 1.92 x + 1.22 x2
R = 1.00 – 1.63 x + 0.94 x2
2
D/B′ = 0.125
D/B′ = 0.25
D/B′ = 0.50
D/B′ = 1.00
D/B′ = 2.00
Notes:
(1) x = the ratio of factored horizontal load, Hf , to factored vertical
load, Vf , applied to the shallow foundation, and is taken as
positive when the vertical component of the load compresses
the soil or rock.
(2) D = the embedment depth of the footing from the surface; note
that more values of D may apply at a site.
(3) B′ = the effective width of the equivalent shallow foundation, not
to exceed the footing width, B, as shown in Figure 6.5.
C6.7.5 Factored geotechnical horizontal resistance
Shear resistance should be checked using a separate calculation from bearing resistance. The
surcharge at the toe of the footing may not be affected by frost penetration for consideration of
bearing resistance. However, the zone in front of the footing may not contribute to sliding resistance,
due either to frost action or lack of compaction of fill during Construction. Caution is advised in the
calculation of passive resistance sliding due to sliding. The resistance factors for passive resistance
include an allowance for the movement necessary to provide the resistance. For example, a horizontal
movement of more than 25 mm is necessary to generate full passive resistance for an undisturbed soil
having a height of 1.0 m.
Failure at the interface between the structure and the foundation or through various layers within
the resisting soil or rock below the footing should be considered. The interface friction between the
foundation and the soil or rock depends on the method of construction of the structural footing. If the
footing is cast-in-place, shear failure takes place within the soil just below the surface of the footing. If
the footing is precast concrete or steel with a surface that is relatively friction-force, with a relatively
friction free surface, the failure surface is usually at the interface of the supporting soil and the footing.
The horizontal shear resistance of the soil or rock can be supplemented by consideration of passive
resistance at the toe, shear keys, dowels, or anchors preloading the footing to the bearing material.
Shear keys are useful when shear resistance is required. The keys may require special construction
considerations and these should be taken into account in design. If special considerations are required
during Construction, these should be clearly identified on the Plans, e.g., protection of shale against
deterioration through exposure.
Reference is made in Clause 6.7.5 to a detailed analysis. This applies to cases in which the
equilibrium equations are not used or where the soils are variable and an important structure is being
founded. A finite element analysis is an example of such a detailed procedure. An example of such an
analysis in which the lateral load was due to ship impact is given in Ministeriet für offentlige
arbejder (1979).
The horizontal resistance consists of two components. The first is the factored resistance due to
cohesion (0.8 A’c’); for overconsolidated clays, this value of cohesion should take into account the
effects of remoulding. The second is the frictional resistance due to the normal force caused by the
dead load of cast-in-place concrete and of backfill. The density of the backfill appears on both sides of
the sliding resistance equation as part of the action and of the resistance. With Vf and Hf correlated, a
load factor of 1.25 is applied to the horizontal force, and a load factor of 1.0 to the vertical force.
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C6.8 Deep foundations
C6.8.1 General
Deep foundation units comprising driven or bored piles, caissons, or drilled shafts are used in a variety of
conditions (Fellenius, Samson and Tavenas 1989), which include the following:
(a) where a competent soil or rock level can be found only at depth;
(b) where a foundation at a shallow depth may be subject to scour;
(c) where the use of shallow foundations would result in unacceptable settlements; and
(d) where conditions are adverse below the surface, e.g., high groundwater levels or artesian conditions.
Piles are vertical or inclined structural members having a small cross-section relative to their length. Piles
may be wood, concrete, or steel. Wood piles are generally restricted to 10 to 15 m in length.
Concrete piles may be precast or cast-in-place. Commonly adopted sections are circular, square,
hexagonal, or octagonal. Reinforcement or prestressing in precast piles is normally provided to resist
handling and driving stresses. The larger diameter precast piles (600 mm or greater) may have a hollow
core.
Steel piles are usually H-piles or pipe piles. Steel piles have some advantages over the other types,
especially during handling and installation. However, H-piles are prone to bending or twisting during
installation.
Caissons or drilled shafts are generally constructed by placing concrete in an excavated hole. This hole
may be formed by boring, using a casing, or by the continuous bentonite circulation method. The main
feature of bored piles is that displacement of adjacent soil during installation is minimized. Caisson
excavations may be lined or unlined.
A pile foundation, including the pile cap, is generally statically indeterminate. Uncertainty can be
associated with the horizontal and vertical response of a pile bearing against the supporting soil or rock.
The distribution of forces transferred through the pile cap to the individual piles is a function of the
stiffness of the pile cap, the geometry and stiffness of the individual piles, and the soil.
A quality assurance program is required to verify that the construction procedures and site conditions
agree with the design assumptions. Clause 6.4.6 covers inspection and quality control.
C6.8.2 Selection of deep foundation units
(a) Depending on the site conditions, various combinations of factors influence the selection of the type
of pile. It is not practical to formulate or to give general rules for pile selection.
A technical and economic feasibility analysis should be used. The type, size, and depth of the
foundation unit selected depend on the amount of vertical and horizontal deformation that can be
tolerated by the structure.
Piles installed in soil develop their geotechnical resistance from a combination of shaft and toe
resistance. If the piles bear, either directly or at shallow depth, on a hard bearing stratum such as
strong bedrock, a high proportion of their geotechnical resistance is obtained from toe resistance.
Except for such piles, the geotechnical resistance is usually less than the structural resistance of the
pile.
When deep foundation units are driven adjacent to existing structures or services, precautions
should be taken to avoid damage to the existing installations from heave, compaction due to
vibration, or ground displacements. This type of damage can be minimized by the use of
nondisplacement types of piles and selective pre-augering.
Construction difficulties resulting from the presence of groundwater should be considered,
particularly in the case of cast-in-place concrete caissons and pile caps.
A driven pile should be adequately proportioned to satisfy both the static and dynamic stresses
imposed during installation and driving. The wave equation, combined with dynamic measurements,
is generally used to calculate driving stresses. There is some diversity of opinion as to what the
maximum permissible driving stress should be. Usually driving stress should be limited to 50% to
60% of the specified compressive strength of concrete piles, and to 60 to 70% of the ultimate
strength of wood piles in order to avoid splits and other damage during driving. Driving stresses for
steel piles should be limited to about 90% of the specified yield strength. Tensile stresses for concrete
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piles should be based on the area of reinforcing steel only, and be limited to 70% of the yield
strength of the reinforcement.
When a pile is driven through soil containing boulders, the pile may drift and bend in the soil
or twist and deviate from its intended location at the cutoff level.
Caissons or drilled shafts founded on rock or socketed into bedrock are common. They form
effective foundations for large piers or abutments. Shafts larger than about 1 m in diameter
permit visual inspection and testing of the rock socket; such inspections and their associated
safety requirements may be complicated by water conditions, wall stability, and air quality. The
bottom of the excavation should be properly cleaned, since otherwise the bearing resistance may
not be fully mobilized, and settlement may occur due to the compression of mud or debris
remaining at the bottom of the socket. The socket shaft resistance is controlled by the interface
strength between the concrete and the rock socket.
The durability of the pile material in contact with the soil or water needs to be evaluated; for
example, in the case of concrete piles, it may be necessary to use sulphate-resisting cement where
high sulphate soils or water are present.
Changes in ground loading through the removal or addition of soil in the vicinity of a structure
can induce additional vertical or lateral load on a deep foundation unit. When deep foundation
units are driven in granular soils, an alteration of the soil structure may result in a subsidence of
the adjacent area. Piles that are already in place may be affected by this alteration. Pile driving
may induce heave in saturated fine-grained cohesive materials and the piles already installed may
be subject to uplift. Voids created near to the ground surface by pile driving should be filled with
compacted granular material.
Deep foundation units for bridge abutments and piers installed adjacent to or in flowing water
should be carried to such a depth as to ensure both adequate geotechnical and structural
resistance after scour.
Where future dredging or excavation is anticipated, deep foundation units should be carried to
such a depth that they can continue to support the imposed loads after removal of material
surrounding the units. In addition, stability of the unit should be considered, as stipulated in
Clauses 6.8.8.2 and 6.8.8.3.
Factors to consider here include the problems associated with installing bored piles or caissons
below the groundwater level, or the possibility of reduced pile capacity for driven piles installed in
situations where artesian water pressures occur.
The presence of obstructions to pile installation, such as boulders or construction debris, may
influence the type of pile selected. For example, an open-ended steel pipe pile provides the
possibility of churn drilling through obstructions, whereas a closed-ended pipe pile or a solid
precast concrete pile does not. If steeply sloping bedrock is present at a bridge site, driven piles
may slide down the slope and not provide adequate support. In such cases, special pile tips may
be required to secure the pile toe on the rock.
Shaking induced by earthquakes results in complex soil-pile-structure interaction. Special
methods of analysis may be required under the guidance of an expert in this field. The pile
ductility is important in such situations, as brittle pile materials break more readily than ductile
materials.
C6.8.3 Vertical load transfer
Load sharing between a pile cap and deep foundation units depends on a number of factors, such as
the rigidity of the pile cap, pile spacing, and the soil immediately below the pile cap, and is not to be
taken into account. The soil below the pile cap may settle under its own weight or the weight of the
approach embankment and lose contact with the pile cap.
C6.8.4 Downdrag
Downdrag on a pile occurs when the soil surrounding the pile shaft moves downward relative to the
pile shaft. The following cases may be cited in which downdrag may develop:
(a) where piles are installed through a soft compressible stratum that consolidates due to a
surcharge, such as an approach embankment; or
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(b) where the groundwater is lowered resulting in an increase in effective stress in a soft, compressible
clay layer.
In the structural design of a pile, the factored downdrag load should be added to the factored
permanent loads. In geotechnical analysis of downdrag, live load effects should not be considered.
Approach embankment fill may contribute to the load on an adjacent footing, supported on piles.
The location of the neutral plane for a pile or groups of piles should be determined by using unfactored
loads and unfactored geotechnical parameters. An analysis procedure, based on unfactored material
characteristics for both soil and structure, is usual in limit states design.
The method of deriving the neutral plane is shown in Figure C6.14. With a knowledge of the location of
the neutral plane, forces can be calculated. The load factor for downdrag of 1.25 accounts for
uncertainties regarding analysis and geotechnical parameters.
Dead load
Ultimate resistance
Downdrag
Axial
load
Negative
shaft
friction
Structural
section of
interest
Neutral plane
Positive
shaft
resistance
Transition zone from
positive to negative
Toe
resistance
Positive
shaft
resistance
Depth
Figure C6.14
Downdrag and the neutral plane
(See Clause C6.8.4.)
Downdrag effects may include the following:
(a) additional axial load present in the pile as the adjacent material settles. The changes in the vertical
deflection with time may require that additional SLS checks be carried out; and
(b) additional axial load developed by downdrag acting on the pile could lead to structural failure of the
pile. Factored dead and downdrag load should not exceed the factored structural resistance of the
pile. This is an ULS consideration for the pile. If the pile is end bearing, there is unlikely to be
significant additional vertical deflection of the structure.
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Table C6.2
Downdrag calculations
(See Clause C6.8.4.)
Type
Structural resistances, kN
Geotechnical resistances, kN
Ultimate unfactored
Factored for structural design
Factored for below-ground design
Allowable stress design
3350
3000
2250†
1900*
2800
2800
1600
1000
Loads, kN
Allowable stress design, kN
Load factors
Limit states design, kN
Specified dead load
Downdrag load
Forces to be resisted by the
pile as a structural unit
800
1000
1800*
1.2
1.25
1000
1250
2250†
*In allowable stress design, where a factor of safety for structural design of 1.7 to 1.8 is common, the design resistance
of the pile is greater than the applied forces.
†The basic design equation, Section 2, is satisfied when the factored below grade structural resistance equals or
exceeds the factored load.
Table C6.2 illustrates computational procedures applicable to the assessment of downdrag effects in
piles. Two cases are shown in the table: one is for allowable stress design, while the second is for
ultimate limit states design. ULS procedures are permitted by Section 6; the SLS procedure is shown
for interest only. The values given in Table C6.2 are for a hypothetical section and site location.
C6.8.5 Factored geotechnical axial resistance
C6.8.5.1 General
There are a number of empirical methods that can be used to determine the axial resistance of deep
foundation units. Experience suggests that these methods yield results that for given site conditions
may be considered acceptable for design purposes.
A static analysis should always be performed to estimate the axial resistance of a pile or group of
piles. In the case of driven piles, in addition to the static analysis, a dynamic analysis is recommended
in order to calculate the axial resistance and driving stresses, as well as to select or verify the
appropriate driving system. When conditions warrant, the design and Construction may include either
static or dynamic pile tests or both. If properly documented experience and data from other sites with
similar geotechnical conditions are available, these may be used for comparison with the results of the
analysis in assessing the axial resistance. Resistance factors based on reliability of each method of
estimation are given in Table 6.1.
In the case of driven piles, the maximum stress may occur at the pile toe during driving to a hard
stratum. The damage to a pile toe cannot be readily monitored, except in the case of a closed-ended
steel pipe pile. Dynamic analysis should be used to assess the capability of the driving system chosen
to drive the pile to the design depth with the minimum of damage.
C6.8.5.2 Static analysis
Piles and caissons derive their ultimate resistance, Ru , from shaft resistance Rs , toe resistance, Rt , or a
combination thereof. As noted above, several empirical methods are available to estimate the values of
shaft and toe resistance. Some of these are discussed in CFEM (1992).
Table C6.3 gives typical values of φ , β , and Nt for use in computation.
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Table C6.3
Ranges of φ, β, and Nt values
(See Clause C6.8.5.2.)
Soil type
φ, degrees
β
Nt
Clay
Silt
Sand
Gravel
25–30
28–34
32–40
35–45
0.25–0.35
0.27–0.50
0.30–0.60
0.35–0.80
3–30
20–40
30–150
60–300
In selecting a β value for piles in compression or tension, it is important to consider the pile material as
well as whether the pile shaft is tapered or straight and whether the pile toe is flush with the pile shaft.
It has been suggested that the static analysis of ultimate resistance using these empirical formulae ceases
to be valid at a certain critical depth equal to about 10 to 20 pile diameters. Below the critical depth, the
unit shaft resistance would be constant and equal to the value at the critical depth. However, the concept
of critical depth is unproven and in question. It should therefore be applied with caution, if at all.
For cohesive soils, the shaft resistance becomes
Ru = Σα c As’
where
α = a proportionality coefficient, less than 1.0 (Tomlinson 1957)
Shaft resistance may be a function of both friction and cohesion in cemented soils and for some
cast-in-place piles. The expression for the unit shaft resistance in these cases then changes to
rs
= c’ + β σ ’
Table C6.3 and the CFEM (1992) suggest ranges of the toe bearing coefficient, Nt . The ranges shown
are broad and approximate.
The movement of the pile toe to mobilize the ultimate toe resistance is considerably larger than that
necessary for mobilizing the maximum shaft resistance. The magnitude of vertical movement required for
piles of large diameter is larger than for small diameter piles. Driven piles will densify or preload the natural
soil below the pile toe and require smaller movements to mobilize resistance compared to bored or
cast-in-place piles. These latter piles do not densify the soil below the pile toe, but instead may have
disturbed and loosened the soil during installation.
Several methods, based on the theory of plasticity or derived empirically, are available to estimate the
geotechnical resistance using soil or rock parameters. The method selected should be appropriate to both
the site and the method of installation (CFEM 1992, Tomlinson 1957, 1977, and 1986, Bozozuk 1972,
Burland 1973, Bjerrum et al. 1969, O’Neill et al. 1982, and Vesic 1967).
C6.8.5.3 Static pile load tests
The most reliable method for determining the geotechnical resistance of a pile is a static test. Static testing
can be performed as either a proof test or for investigative purposes. A proof test is usually carried out to a
predetermined load that is some multiple of the factored resistance of the pile in question. For production
piles, the multiple should be limited to approximately 1.5 times the factored resistance to avoid
permanent damage to the pile. Tests for investigative purposes are usually carried out to either the failure
load of the pile or to at least the calculated ultimate resistance of the pile.
Load tests should be carried out in general conformity with ASTM D 1143. The measurement of pile
compression and toe movement by a telltale or a sensor attached to the pile toe will enhance the value of
a static test (CFEM 1992, Brinch Hansen 1963, Chin 1970, Davisson 1972, Fellenius 1990, and Kondner
1963). A load cell may be required for an accuracy of 2%.
When evaluating the test results for limit states design, the ultimate load or plunging failure as
determined from the shape of the load-displacement curve should be used. If failure has not been reached
in a test, extrapolation of the load-displacement curve beyond observed values is not recommended.
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C6.8.5.4 Dynamic analysis and tests
There are commercially available computer programs for the dynamic analysis of pile driving. These
programs provide the user with a functional relationship between both bearing resistance and pile
stress, and blow count. The traditional wave equation approach provides a prediction of driving
behaviour and aids the selection of an efficient and effective driving system. A bearing graph
representing the expected pile resistance as a function of the penetration resistance or blow count can
be obtained. It is advisable to produce several bearing graphs to derive a range of possible driving
system performances and installation depths.
Dynamic testing of a pile consists of measuring acceleration and strain induced in the pile by the
hammer. The analysis of the measurements provides the amount of energy transferred to the pile as
well as the force induced in the pile at impact. The analysis of the test data is used to determine the
resistance of the pile as activated by the hammer, using methods based on wave propagation theories.
The performance of the driving system can then be evaluated.
One of the advantages of dynamic measurement and analysis is that several piles can be tested for
the same cost as that of one static pile test, thereby permitting an assessment of any variations within
the project site (Fellenius et al. 1989, Hannigan and Webster 1988, Rausche, Moses and Goble 1972,
Rausche and Goble 1978, and Rausche, Goble, and Likins 1985).
A number of empirical pile driving formulae are in use. These were established on the assumption
that energy delivered by the hammer at impact is transmitted to the toe of the pile. These formulae
are fundamentally incorrect and their use is discouraged.
C6.8.5.5 Limitation for tension piles
The consequence of failure of a pile in tension can be more severe than that in compression. Generally,
a pile in tension has less ductility than a pile in compression when the shear resistance of the soil
reaches ULS. Therefore, to account for possible adverse consequences of failure in tension, the
resistance factor given in Table 6.1 for piles in tension is lower than for piles in compression.
C6.8.5.6 Relaxation of driven piles
Pile penetration resistance usually increases after driving as a result of soil set-up. For some sites,
however, resistance may decrease due to soil relaxation. When a pile is restruck and the penetration
resistance decreases for the same driving energy as used for the original driving, relaxation is assumed
to be present.
C6.8.6 Group effects — Vertical loads
C6.8.6.1 Load distribution
Clause 6.8.6.1 recognizes that the soil or rock supporting the piles may provide either the
lower-bound resistance as estimated by the Geotechnical Engineer or a larger resistance if conditions
are better than those anticipated. Both possibilities should be considered in the structural design of the
footing and structure.
The forces in the individual piles may be calculated using linear methods or nonlinear methods for
geotechnical resistance at the ULS. This calculation relates to determining the number of piles required
and ensuring that the factored geotechnical resistance is not exceeded. Nonlinear methods permit the
consideration of the redistribution of axial forces between adjacent rows of piles and can only apply
where more than two rows of piles are present. If a nonlinear method is used to determine loads
acting on individual piles, it frequently results in higher forces for some piles than those given by an
elastic analysis used for the structural design of the footing.
Moment, axial load, and horizontal load applied to a footing should not be treated as separate and
independent actions.
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C6.8.6.2 Group resistance
For end bearing piles, grouping has little effect on resistance. The resistance of a group of friction piles is a
function of pile spacing; when spacing is less than a critical distance, resistance decreases as the spacing
decreases. For piles that derive their resistance from both the shaft and the toe, the group effect applies
only to the shaft friction portion (Poulos and Davis 1980 and Chellis 1962).
C6.8.7 Factored geotechnical lateral resistance
C6.8.7.1 General
A single vertical pile or a group of piles will resist lateral loads at the pile cap by deflecting until the
necessary passive resistance in the surrounding soil is mobilized. This lateral load response of a single pile is
illustrated in Figure C6.15, together with the vertical response. The passive resistance developed for lateral
deformations typical of bridge foundations is generally much less than the passive pressure associated with
a full passive resistance. This full passive resistance is calculated from earth pressure theories assuming
unlimited deformation of the soil. Figure C6.15, which was developed from a combination of calculation
and test data, also shows that in some cases the lateral resistance may be limited by the factored structural
flexural resistance of the pile rather than the resistance of the soil.
2000
ULS
D
H
P
200
1000
U LS
D
SL
S
Load (kN)
300
SLS
ULS (structural) for pile
(varies with axial load
and soil conditions)
100
0
0
10
20
30
Vertical displacement (mm)
0
10
20
30
40
Horizontal displacement (mm)
Figure C6.15
Idealized load vs. displacement relationships
(See Clause C6.8.7.1.)
The behaviour of the foundation depends essentially on the relative stiffness of the pile and the soil. The
lateral resistances of deep foundation units may be limited by horizontal movements that may be
unexpectedly large.
For some loading cases, a Design Engineer may neglect the lateral resistance provided by the soil.
For single piles, usually used to support lighting poles or masts, the resistance of the passive wedge
within the zone of frost penetration should not be included in calculations of factored passive resistance,
unless calculation or construction procedures permit.
Static analysis
Many of the methods available for the design of pile foundations subjected to horizontal loads need to be
regarded as empirical. Where pile load test data or the results of a detailed analysis are not available, the
unfactored lateral passive resistance of a single pile in noncohesive soils may be estimated by calculating
passive earth pressure over an equivalent wall area having a depth from the ground surface equal to six
times the pile diameter, and a width equal to three times the pile diameter. The pile diameter is the
diameter of round piles or the average face-to-face distance of octagonal, hexagonal, and square piles.
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For piles in cohesive soils, the passive earth resistance should be limited to 2c at the surface and
increase linearly to 9c at a depth of three pile diameters and beyond. This pressure should be
converted into a passive resistance by using a bearing width equal to the pile diameter.
Similarly, the lateral resistance of a pile group may be approximated by the soil resistance on the
group calculated as the passive earth pressure over an equivalent wall area with a height equal to
6 times the pile diameter and a width equal to the width of the pile group in plan, perpendicular to
the direction of movement. The shear resistance on the sides of the block may also be considered. It is
necessary for the lateral passive resistance of the pile group not to exceed the sum of the lateral passive
resistances of the individual piles (CFEM 1992, Broms 1964, ASTM D 3966, Kishida and Meyerhof
1965, Poulos 1971). Additional methods of static analysis are discussed in Clause C6.8.7.2.
Static tests
The most reliable method of assessing the horizontal resistance of piles subjected to lateral loads is by
means of a load test. Lateral tests indicate the overall load-deflection behaviour of a pile. Tests should
be designed and carried out in accordance with ASTM D 3966. The results should include assessment
of the structural resistance of such piles in the presence of axial load.
The SLS resistance should be taken as that corresponding to a horizontal deflection of 10 mm at the
underside of the pile cap for units supporting abutments, piers or retaining walls. The SLS resistance
will normally be greater than the ULS resistance for piles embedded in very stiff clays. This 10 mm
limitation of horizontal movement does not apply where an analysis of the structure including the
foundation indicates that a horizontal movement of more than 10 mm can be accommodated by both
the foundation and the structure at SLS. In many cases, integral abutment bridges will have total
lengths that result in SLS horizontal deflections that are greater than 10 mm.
Values of the subgrade reaction modulus or the elastic modulus of the soil at various depths may
also be calculated from a test. These values may be used to assist predictions of movements of piles of
other dimensions or of groups of laterally loaded piles and should include consideration of the ULS in
the soil (CFEM 1992, Alizadeh and Davisson 1970, Poulos and Davis 1980).
Assessment
Assessed values of lateral resistance may be obtained from experience from other projects at sites
having a similar stratigraphy near the surface or Table C6.4.
The values given in Table C6.4 assume
(a) an embedment length that is greater than 5 m;
(b) an inclination that is less than 15°;
(c) uniform soils with the consistencies shown in Table C6.5;
(d) a horizontal deformation of 10 mm at ground surface for SLS condition; and
(e) no allowance for the horizontal component of axial force when inclination is present.
A minimum value of undrained shear strength, for a given consistency, was used to model the
passive resistance of the soil in the analysis. For the calculation of the structural resistance of the pile, a
specified yield strength of 300 MPa was assumed. Extrapolation to higher values is not permitted.
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Table C6.4
Assessed horizontal passive resistance and geotechnical reaction at SLS
(See Clause C6.8.7.1.)
Soil and pile type
ULS, kN
SLS, kN*
Steel H-pile, 360 × 108, in cohesive material:
Firm
Stiff
Very stiff
Hard
120
160
240
320
50
80
140
240
Steel H-pile, 310 × 79, in cohesive material:
Firm
Stiff
Very stiff
Hard
120
160
200
260
35
65
110
200
Steel H-pile, 360 × 108 in noncohesive material, φ′ =
25°
30°
35°
130
150
170
40
50
70
Steel H-pile, 310 × 79 in noncohesive material, φ′ =
25°
30°
35°
100
110
120
25
40
50
*For a lateral movement of 10 mm.
Table C6.5
Assumed strength of cohesive soils (CFEM 1992)
(See Clause C6.8.7.1.)
Consistency
Undrained shear strength,
kPa
Firm
Stiff
Very stiff
Hard
25 to 50
50 to 100
100 to 200
> 200
C6.8.7.2 Static analysis
Clause 6.8.7.2 is based on the assumption that both vertical and inclined piles can deflect until the
necessary passive resistance is mobilized. In this case, reference is not made to the full passive resistance,
but rather to some fraction of this resistance occurring at relatively small horizontal displacements.
The horizontal resistance of an inclined pile has two contributions. The first is due to the inclination of
the pile and is equal to the horizontal component of the axial force present in the pile; this component will
change from loading condition to loading condition as the axial force in the pile changes. The second
component of horizontal force is the passive resistance generated when the inclined pile moves laterally
into the soil. For most pile footings, this horizontal passive resistance of the soil will be nearly the same for
both vertical and inclined piles when the footing moves laterally. This should be recognized in calculation.
Design approximations are available that suggest that piles with inclinations greater than some arbitrary
value, say 1 horizontal to 8 vertical, will resist all external horizontal forces if combined with vertical piles.
For a pile group consisting of both, this approximation may provide a first estimate of the number of piles
required for the footing; however, it will not provide a satisfactory method of calculating the moments and
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shear forces in a footing or supporting piles. A combination of inclined and vertical piles will provide
more resistance to lateral load than vertical piles alone. However, field data are available to show that
for a group of eight piles with both inclined (20°) and vertical piles, in all cases, more than 60% of the
horizontal load was resisted by the combined passive resistance of the inclined and vertical piles
(McNulty 1956). For vertical pile groups, this combined resistance will normally be less than the sum
of the factored horizontal resistances of the individual piles in the group.
C6.8.7.3 Lateral deflection
Clause 6.8.7.3 permits the analysis of individual piles or groups of piles using a variety of methods.
The lateral resistance for a given horizontal displacement may be modelled using the procedures
documented by Reese (1986) and Ochoa and O’Neill (1989). A resistance factor is applied to values
of passive resistance that are calculated from unfactored values of geotechnical parameters.
The methods of Reese (1986) and Ochoa and O’Neill (1989) allow soils providing passive
resistances occurring at less than the maximum passive value to be modelled. These analyses apply
to single piles or groups. For a group of piles, the axial load deformation characteristics should be
included in the analysis so that compatibility of deformation between the pile cap and three or more
rows of piles is maintained in analysis.
If an elastic analysis using a constant subgrade reaction modulus is used, care should be taken to
consider the range of deformation and soil resistances over which this modulus applies. The limited
resistance and limited range of elastic response of soils near the surface should be considered.
For closely spaced piles, interaction between adjacent piles, and between leading and trailing piles,
should be considered (Poulos and Davis 1980, Reese 1986).
C6.8.8 Structural resistance
C6.8.8.2 Unsupported length
Lateral soil support may not be present if deep foundation units adjacent to or located in flowing
water are subject to scour or founded in an area where future dredging or excavation is expected. Very
soft soils such as extremely loose silts and sands, organic soils, or unconsolidated soils may also not
provide sufficient lateral support. If the undrained shear strength of the supporting soil is less than
10 kPa, a pile should be considered to be unsupported.
C6.8.8.3 Structural instability
The instability of individual piles, as well as the pile group as a whole, should be considered where
lateral support is absent (Fellenius 1972). Pile or pile groups and the structure supported by piles
should be considered as a single system in any stability analysis.
C6.8.8.5 Factored structural resistance
The reduction factor 0.75 is applied to account for uncertainties in subsurface conditions, quality and
consistency of cast-in-place concrete, adequacy of installation procedures, effectiveness of quality
control, and the type and geometry of the deep foundation units being used. It can be increased if the
design, construction, and inspection conditions warrant.
C6.8.9 Embedment and spacing
C6.8.9.2 Pile spacing
Clause 6.8.9.2 provides the minimum spacing of piles in terms of width and diameter of the pile that
will minimize the possibility of interference with adjacent piles and ensure an adequate connection to
the pile cap. Close spacing reduces the cost of the pile cap and is also advantageous with loose sands
because it becomes compacted after driving. Driving piles in dense sands and saturated plastic soil can
cause heave or lateral ground displacement that may damage or cause misalignment of previously
driven piles.
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C6.8.10 Pile shoes and splices
C6.8.10.1 Pile shoes or points
When piles are driven through bouldery soils or gravels, damage to the pile toe can be minimized by
means of a suitable protection. For closed-ended steel pipe piles, a flat steel plate is considered to be
sufficient protection. Some pipe piles have a plate that is somewhat wider than the pile. In noncohesive
soil, the wider plate may result in loss of contact and significant reduction in shaft resistance. For steel
H-piles and open-ended piles, a separate shoe made of cast steel or ductile iron is used. In the case of piles
driven to rock, rock points should be used to provide proper grip when driven to a hard sloping bedrock
surface through weak soil.
C6.8.10.2 Splices
The pile splice should be such as to maintain continuity and alignment, and its structural resistance as
defined in Clause 6.8.8.5 should not be less than that of the pile section. It is possible to splice wood piles;
however, this should be avoided.
C6.9 Lateral and vertical pressures
C6.9.1 General
Earth pressure should be calculated using representative values of geotechnical parameters (Bowles 1988,
Barker 1991, CFEM 1992, NAVFAC DM-7.1 1982, Clayton and Militsky 1986). The uncertainty associated
with the density of the backfill, earth pressure theories, and the position of the centroid of the earth
pressure is accounted for through the use of load factors based on pressures and loads calculated using
unfactored geotechnical parameters. The procedures used in CAN/CSA-S6-88, where soil strength
parameters and load factors are applied together, do not apply to the Code.
In the calculation of earth pressure forces, distinctions must be made between overall stability, bearing
resistance, overturning and sliding resistance, and the forces acting in the design of the individual
components of the retaining structure. Different pressures are specified for design, depending on the
deformation of the structure. There are also forces within the earth resulting from compaction pressures,
and dead load and live load effects. In the computation of earth pressure, the nature and drainage
properties of the backfill material should be carefully determined. Frost pressures, swelling pressures, or
hydrostatic pressure can develop in the backfill material. These pressures act on the retaining structure and
cannot be reliably determined; because of this, the use of free-draining granular backfill is preferred.
The following comments are relevant to Clause 6.9.1:
(a) When computing earth pressures, moist density of the backfill should be assumed above the
groundwater table, and submerged or saturated density below the water table.
(b) For free-draining granular soil or backfill, the same strength parameters can be assumed for
short-term and long-term conditions. For fine-grained cohesive soil or backfill, earth pressures tend to
increase with time due to softening or swelling and for this reason cohesive backfill is normally
avoided. If cohesive soil is used as fill, the design should employ conservative effective stress strength
parameters assuming c’ equal to zero and using an appropriate angle of internal friction φ ’. Pore
pressure effects in the soil must also be considered as should expansion due to frost.
(c) The magnitude of earth pressure of retained earth during placement depends on the displacement
characteristics of the structure relative to the supporting soil or rock. Accordingly, earth pressure due
to fill may range from an active pressure to a passive pressure. Active earth pressure is the minimum
value of lateral earth pressure that a soil mass can exert against an unrestrained structure. Passive
pressure is the maximum value of lateral earth pressure and occurs when the structure moves into or
against the soil mass.
If the movement of the structure during placement of the backfill is minimal, the pressures
developed correspond to an at-rest earth pressure condition, and will include residual stresses due to
compaction effects (Clayton and Militsky 1986, Ingold 1979). The active, at-rest, and passive pressure
conditions are used as a design convenience to describe backfill pressures. During the compaction of
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each lift in the lower part of the backfill, the wall will move away from the previously compacted
fill to yield a pressure that increases linearly with depth and has a magnitude that is generally
between active and at-rest. In the upper backfill, the compaction effects are relieved by wall
movement to a lesser extent than at depth and the pressure diagram at depth tends to be
trapezoidal.
Figure C6.16 and Table C6.6 indicate the relative movements between a wall and the adjacent
soil that produce the active and passive earth pressure conditions in granular soils. Full passive
pressure requires considerably greater movement than active pressure.
At-rest
Passive
Active
K
Dense sand
D
8.0
Medium dense sand
h
4.0
Loose sand
D
2.0
h
D
D
1.0
Active movement
h
h
0.5
Ko
Loose sand
Passive movement
0.25
Medium dense sand
Dense sand
0.12
0.049
0.025
0.009
0.001
0
0.001
Movement toward retained soil
0.009
0.025
Movement away from retained soil
Ratio of wall movement to wall height, D/h
Figure C6.16
Various earth pressures
(See Clause C6.9.1.)
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Table C6.6
Movements required to mobilize various conditions (Ovesen 1981,
Barker 1991, NAVFAC DM-7.1 1982, Clayton and Militsky 1986)
(See Clauses C6.9.1, C6.9.2.2, and C6.9.4.)
Movement to mobilize
Active pressure
Passive pressure
Displacement, Δ
Rotation, Δ/h
Displacement, Δ
Rotation, Δ/h
0.001h
0.002 (about bottom
of wall)
0.050h
0.100 (about bottom of
wall)
0.020 (about top of wall)
Notes:
(1) Displacements take place in the absence of rotation.
(2) h is the height of the retaining wall.
(3) Rotation is assumed to take place about a fixed point at either the top or the bottom of the wall.
(d) There can be friction between the retaining wall and the backfill. The earth pressure resultant may act
at an angle with respect to the horizontal. The direction of the resultant is a function of the relative
movement between the structure and the backfill. In most practical cases, wall friction may be
neglected. The neglect of wall friction under active conditions leads to larger lateral force on the wall.
Wall friction should be considered where a high gravity wall is founded on bedrock. Wall friction
contributes to bin action. Data concerning the angle of wall friction for various surfaces and backfill
can be obtained from NAVFAC DM-7.2 (1982).
(e) Figures C6.17 and C6.18 indicate how the slope of the backfill behind a retaining structure affects the
magnitude of the active and passive earth pressure coefficients, respectively. Both the active pressure,
Ka , and the passive pressure, Kp , increase nonlinearly with increase in slope angle i. Where the ground
surface slopes down behind the wall, Ka and Kp decrease with increasing downward slope. Where the
slope has a value greater than 10°, the computation of earth pressure should be carried out by a
Geotechnical Engineer.
(f) Compaction of the retained soil will exert pressures on the structure as shown in Figure C6.19. This
additional pressure due to compaction should be taken into account in the design of a retaining
structure. Typical compaction pressures due to different types of compaction equipment are given by
Broms (1971) for cohesionless soils as noted in Clause C6.9.2. Lateral movement of the wall away
from the retained soil will tend to reduce the effects of compaction. The effects of compaction tend
to zero if the movement of the wall causes an active state in the backfill. Use of heavy compactors
adjacent to a retaining structure will cause large horizontal stresses to develop and these may cause
damage to the structure. Construction specifications should limit the maximum mass of compactor
allowed next to a retaining structure.
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C
Pa = Ka
Pa
B
g H2
2
i
Pa
d
H
b
g H
Pah = Kah
2
2
Weight of
wedge ABC
Soil: f ; g
A
cosec b sin( b – f )
Ka =
sin( b + d ) +
2
if:
sin ( d + f ) sin( f – i )
sin( b – i )
d=0
i = 0 b = 90
1 – sin f
K a = K ah =
1 + sin f
K ah = K a sin( b + d )
Figure C6.17
Effect of ground slope — Active earth pressure
(See Clauses C6.9.1 and C6.9.2.2.)
B
i
Pp
Pp = Kp
g H2
d P
p
H
b
2
g H2
W
P ph = K ph
d=0
i = 0 b = 90
2
Soil: f ; g
A
cosec b sin( b + f )
Kp =
sin( b – d ) –
sin( d + f ) sin( f + i )
2
if:
sin( b – i )
K p = K ph =
1 + sin f
1 – sinf
K ph = K p sin( b + d )
Figure C6.18
Effect of ground slope — Passive earth pressure
(See Clauses C6.9.1 and C6.9.2.2.)
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Lateral earth pressure, kN/m2
0
0
10
20
30
s h = Kpg h
40
50
zc
Depth, m
0.5
hc
1.0
Compaction
pressure
1.5
2.0
s h = Kag h
Horizontal earth pressure
due to weight of backfill
Figure C6.19
Backfill pressure after Broms and Ingold
(See Clause C6.9.1.)
(g) The surcharge loading in Clause 6.9.1 provides for the effect of dead load, such as loads from other
footings or structures, and the effect of live load, such as those from wheels adjacent to the retaining
structure.
(h) A drainage system behind a retaining structure should ensure that a groundwater table does not exist
above the footing level. Preferably, the ground water level is controlled by the use of free-draining
granular backfill and a collection system such as weep holes or perforated drains at the footing level.
These weep holes and drains should be inspected and maintained to ensure that they do not become
blocked. If free-draining, granular backfill is not employed, the permeability of the backfill and the
hydrostatic head will control the extent to which the groundwater table can be depressed locally by
seepage towards a footing drain. In practice, design for frost protection mitigates against the use of
other than free-draining backfill.
The design should also consider the risk of unusually large inflows of water creating a temporary
hydrostatic head of water behind the wall. An example is the overtopping of a retaining wall,
adjoining a large body of water, by storm waves. Measures such as the use of quarried rock backfill,
design for full hydrostatic pressure, or provision of a sloped impermeable surface layer should be
considered.
(i) Measurements have shown that earth pressures can vary seasonally, but the effects have normally
been neglected in design, except for winter frost pressures. These latter can be very large if the
backfill is frost susceptible and for this reason free-draining granular backfill is recommended.
(j) Earth pressures for seismic analyses are specified in Section 4. The Geotechnical Engineer should refer
to available guidelines for design, such as the Federal Highway Administration publication on Seismic
Design of Bridges, FHWA-SA-97-006 through -012, October 1996.
(k) Figure C6.20 shows examples of minimum backfill requirements.
The distance, x, should be equal to or greater than the estimated vertical frost penetration. This
distance may be reduced if the wall abuts a vertical face of bedrock that is not susceptible to frost.
The frost penetration may be reduced by the use of suitable insulation, in which case a thermal
analysis should be performed by a Geotechnical Engineer.
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If rock fill is used as a backfill material, consideration should be given to the possible
deterioration of the rockfill with time, which could result in the reduction or even the total loss of
free-draining properties and, hence, increased frost susceptibility.
Granular backfill
Granular backfill
<1
>X
X
X
1
X
(b) Unrestrained wall
(a) Restrained wall
Figure C6.20
Backfill for frost protection
(See Clause C6.9.1.)
C6.9.2 Lateral pressures
C6.9.2.1 General
Earth pressure acting on a structure depends on the relative movement of the structure, the backfill,
the type of soil adjacent to the backfill, and the soil below the footing or supporting piles. Appropriate
geotechnical parameters should be chosen for the calculation of lateral pressures based on recognized
geotechnical theories as specified in Clause 6.9.2.2 for the backfill behind the wall. Geotechnical
parameters frequently used in allowable stress design methods are applicable in limit states design
pressure calculation. Where the possibility exists, hydrostatic pressure needs to be considered, e.g., in
situations where walls are partially submerged or where non-free-draining backfill is used.
Clause 6.9.2.1 includes the specification of four lateral pressure conditions for design. The first two
cases apply to unrestrained structures, with Item (a) applying to the sizing of the base or pile
arrangement with respect to external stability, and Item (b) to the sizing of the structural sections with
respect to internal stability. Such sections could be of structural concrete, structural steel, or a
proprietary product.
An unrestrained structure is one in which active pressure is mobilized in the backfill due to
movement in the supporting structure. This movement corresponds to a rotation of approximately
0.002 about the base of a vertical wall, a horizontal translation of 0.001 times the height of the wall, or
a combination of these movements. The lateral pressure applied to the wall for the condition
described is an active pressure.
The supporting material will generally be more robust than what is assumed by the Geotechnical
Engineer for factored conditions in design. Hence, following installation of the backfill, movement
sufficient to cause active condition will generally not have taken place. Horizontal or rotational
movement of the base will occur during the installation of each lift of the backfill. Wall deflection
during each application and compaction of the backfill will add to the existing deformations. For such
a post placement of the fill condition, Item (b) applies, the forces acting on the retaining structure
being a function of the compacting equipment and the flexural stiffness of the wall. The residual
horizontal pressures due to compaction are largest at the top of the wall, and this is reflected in
Clause 6.9.3.
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For a restrained structure where the rotational or horizontal movement is not sufficient to mobilize an
active earth pressure condition, an at-rest pressure plus any compaction surcharge should be used for
design. The connection between the structure and the supporting soil should be designed for the forces
assumed to be created by an at-rest pressure condition.
Restrained structures are typically culverts or rigid frame bridges. Unbalanced forces may act on these
structures during Construction. Such forces may be controlled through specifications, inspection and
quality assurance. Short cantilever walls may also act in a restrained manner because of the lack of wall
deflection during compaction of the backfill.
C6.9.2.2 Calculated pressures
The coefficient of active earth pressure can be calculated from the relationship illustrated in Figure C6.17.
For cohesionless soil, a vertical wall, level ground surface, and no wall friction,
Ka =
1− sin f ′
1+ sin f ′
Similarly, the coefficient of passive earth pressure can be calculated from the relationship in
Figure C6.18, which for δ = 0, i = 0 and β = 0 becomes
Kp =
1+ sin f ′
1− sin f ′
As an approximation, the coefficient of at-rest earth pressure Ko soil at both the ULS and the SLS can be
estimated from the following empirical formula:
Ko = (1 – sin φ′ )
and for sloping ground,
Ko = (1 – sin φ′ )(1 + sin i)
In these formulae, φ′ is the effective angle of internal friction of the natural granular soil or granular
backfill.
Active and passive earth pressures may be evaluated by considering the limiting equilibrium of the soil
or rock. Methods acceptable for earth pressure computations include the Coulomb and the Rankine earth
pressure theories (Coulomb 1773, Rankine 1857), solutions by Caquot and Kerisel (1948), and the trial
wedge method of Bowles (1988). Although Coulomb’s method is approximate in that it assumes a planar
sliding surface and may not satisfy all the equilibrium conditions, it does allow the designer to take into
account the effects of surcharge, sloping ground surface, wall friction, and layered soil profiles. Moreover,
the value of active earth pressure obtained by Coulomb’s solution for cohesionless soil does not differ
appreciably from those obtained by more refined and rigorous methods. When passive earth pressures or
resistances are calculated, Barker (1991), NAVFAC DM-7.1 (1982), and Clayton and Militsky (1986) may
be used.
As illustrated in Table C6.6, the movements required to fully mobilize passive pressure or resistance are
much larger than those required to mobilize active pressure. In practice, movements may not be sufficient
to mobilize full passive pressure or resistance, and consequently conservative values should be used in
design. The resistance factor for passive pressure includes an allowance for limiting movement, and hence
force.
Where a relatively narrow zone of granular backfill is placed between a retaining structure and a rock
face, bin action may occur. In this case, the lateral earth pressures are reduced, but downward vertical
forces are transferred to the wall through arching. Structural design should be based on the worst force
effects calculated from bin action or conventional earth pressure theories. The same type of bin action can
occur in earth pressures from fill contained within cellular walls such as timber or concrete cribs.
The design of the earth retaining structure should also take into account any uplift forces that may act at
the underside of the foundation due to groundwater and associated seepage. High concrete gravity walls
on strong soils or bedrock may act as restrained structures and the backfill pressure condition along with
wall friction should be assumed in design.
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C6.9.2.3 Equivalent fluid pressures
The earth pressure theories of Rankine, Coulomb, and others provide the magnitude and direction of
the force due to earth pressure. While some theories are silent as to the distribution of pressure over
the height of the wall, a triangular distribution is commonly assumed.
For design purposes an equivalent fluid pressure on a wall is assumed for a wall up to a height of
approximately 6 m. The 6 m value is a judgement decision to ensure that, for high walls, an analysis of
the pressure distribution is completed by the Geotechnical Engineer. The geometric limitations on the
well-drained granular fill are an attempt to ensure that the rupture plane associated with active
pressure conditions is within the granular fill and not in the native material abutting the fill. If the
failure plane were to be located in the native material, the equivalent fluid pressures would be greater
than those due to a failure plane within the engineered backfill. A more detailed investigation is
required when the specified conditions relating to native material, ground slope, or groundwater
position are not satisfied. This investigation might be used when well-accepted standard specifications
have been used in the past and these were based on different native material, different ground slope,
or different groundwater position to those specified in Clause 6.9.2.3. The investigation would enable
other backfill situations known to be acceptable to be converted to equivalent fluid pressures.
Equivalent fluid pressure gives a linear distribution of pressure increasing with wall height and
having a resultant at 0.33 of the wall height above the underside of the footing supporting the wall.
Some codes suggest that a value of 0.40 should be used instead of 0.33 (AASHTO 1994). The value of
0.40 does not apply in the Code.
C6.9.3 Compaction surcharge
Compaction surcharge pressures are a function of the mass and type of compaction equipment.
Broms (1971) and Ingold (1979) have developed procedures whereby the magnitude of the
compaction pressure can be calculated.
Many jurisdictions in their specifications limit the size of compactor that can be used adjacent to a
retaining structure. The compaction surcharge pressure shown on Figure 6.6 applies to cases where
the mass of the hand operated vibratory compaction equipment is about 120 kg and construction
controls apply. For other cases, the compaction surcharge should be calculated and specified by the
Geotechnical Engineer.
The compaction pressures quoted in Clause 6.9.3 are an approximation of the probable compaction
pressures. In order to simplify the calculation, a constant pressure has been specified and this pressure
extends to a specified depth.
C6.9.4 Effects of loads
The design of an earth-retaining structure is controlled in part by overall stability of the wall,
overturning, and bearing or horizontal resistance. All of these depend on load inclination and the soil
or rock characteristics.
Footing size is a function of both inclination and magnitude of the factored load. A small resultant
load with high inclination may require a larger footing than a high resultant load with a small
inclination. Both cases should be considered. The resultant force and inclination to be chosen for
design will depend on that ratio of the horizontal force, with a load factor equal to either 1.00 or 1.25,
to the vertical force, load factor equal to either 1.00 or 1.25, which gives the maximum footing size.
In the design of an unrestrained cantilever structure, active earth pressure conditions are assumed to
apply when considering the overall external stability of a wall. Such conditions may develop due to
horizontal displacement or rotation of the wall and its supporting foundation (Table C6.6). Any
pressure due to compaction is lost when such movements occur. The effects of external surcharge
loads should be added. The factored bearing resistance, Rqr , will be a function of the geometry of the
foundation and the wall, the depth of embedment of the footing, the ratio of the heel to toe
dimensions, and the inclination of the resultant of the various forces that are applied to the footing.
For restrained structures, earth pressures are larger than those acting on unrestrained structures, and
consist of at-rest pressure along with compaction surcharge. For box culverts and portal frame bridges,
these pressures may lead to larger forces than those which have been used in design in the past.
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C6.9.5 Surcharge
The lateral earth pressure coefficient, K, for active pressure, and those for dead or live load surcharge
corresponding to an active state, are equal. The same rule applies to at-rest and backfill pressures.
The surcharge loading specified in Clause C6.9.5 provides for the load effect from live load and dead
load and should be used in the design of all retaining structures where the loading meets the criteria
illustrated in Figure C6.21 for two typical walls. The load factor to be applied should correspond to the
type of load represented by the surcharge. Such load factors are given in Section 3.
A live load surcharge need not be used when an approach slab is present and limits the transfer of the
effects of wheel load, in terms of increased soil pressure, directly to the backfill. When an approach slab
will not be present during Construction, and construction or other vehicles are permitted at the approach
slab location, surcharge should be considered in design.
The lateral earth pressure coefficient for surcharge corresponds to the type of pressure, either active or
at-rest, acting on the retaining wall. The load factor to be applied to the effects of earth pressure should
correspond to the type of load represented by the surcharge. Earlier codes use a blanket value of 1.25 as a
surcharge load factor. This blanket value does not apply to the truck load specified in the Code.
Alternatively, where applicable, live load surcharge due to a special vehicle with known
axle-configuration and axle loads may be considered. A load factor of 1.25 is appropriate for such vehicles
with known loads.
Surcharge due to
truck loads within
this zone
Surcharge due to
truck loads within
this zone
1
1
1
Abutment or earth-retaining wall
1
Wing wall
Figure C6.21
Surcharge loading conditions
(See Clause C6.9.5.)
C6.10 Ground anchors
C6.10.1 Application
Ground anchors are systems used to transfer tensile loads to soil or rock, normally beyond the critical
wedge behind the anchored structure. Ground anchors systems comprise prestressing steel tendons, steel
anchorages, corrosion protection, sheathing, spacers, centralizers, and grout. Clause 6.10.1 does not
apply to soil nailing systems, which normally transfer tensile loads throughout the critical wedge as well as
beyond it. Figures C6.22 to C6.24 illustrate the configuration of a typical ground anchor system.
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Ground surface
Soldier pile
Critical
wedge
Free stressing zone
Jack
Reaction
Excavation level
Bond zone
45
Figure C6.22
Ground anchor retaining wall schematic
(See Clause C6.10.1.)
Trumpet
corrosion inhibitor or grout-filled
Seal
Anchorage
Anchor grout
Cover required
if exposed
Centralizer
Internal spacer/centralizer
Corrosion inhibitor-filled
or grout-filled sheath
Prestressing steel
Encapsulation
grout-filled
Figure C6.23
Class I protection — Encapsulated anchor (PTI 1996)
(See Clause C6.10.1.)
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Trumpet
corrosion inhibitor or grout-filled
Seal
Anchorage
Anchor grout
Cover required for
exposed, permanent
anchors
Centralizer
Corrosion inhibitor-filled sheath
or heat shrink sleeve
Prestressing steel
Figure C6.24
Class II protection — Grout-protected anchor (PTI 1996)
(See Clause C6.10.1.)
C6.10.2 Design
C6.10.2.1 General
The ground anchor system needs to resist imposed tensile loads and limit displacements of the structure to
within SLS during the service life of the installation.
Guidelines for design, installation, stressing, inspection, and testing of ground anchors are available in a
number of publications, including PTI (1996).
Site conditions, construction methods, and material properties should be considered in the design of
ground anchor systems.
C6.10.2.2 Factored geotechnical resistance at the ULS and geotechnical
reaction at the SLS
Both immediate and time-dependent failure mechanisms for ground anchor components (including
tendons, anchorages, grout), soil/rock foundation materials and anchor/foundation bond should be
considered. Ground anchor serviceability performance, including allowable movements both away from
and into the foundation material, should be considered. Provided that the strength and durability of
ground anchor components is adequate, design can be based on the bond stress at the interface between
the anchor grout and the soil or rock. Bond zone diameter, bond zone length, overburden pressures, and
construction procedures including bond length grout pressures are variables affecting anchor
performance. Where the bond zone is in frictional materials, pullout capacity may depend on overburden
pressure.
Ground anchor pullout resistance should be verified by in-situ testing.
C6.10.2.3 Spacing, bond length, and free-stressing length
The publication identified in Clause C6.10.2.1 provides details for design of spacing, bond length, and
free-stressing length.
Spacing requirements should prevent or otherwise address interference between bond zones that could
reduce the pullout resistance of affected ground anchors.
Bond length requirements should be sufficient for the ground anchor to provide acceptable stress-strain
performance over its service life. Ground anchor load and prestress should be considered, as well as the
performance of the anchored structure. A minimum bond length of about 3 m is typically required to
account for installation uncertainties.
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Free-stressing length should be sufficient to transfer load resistance beyond the assumed failure
wedge of the foundation material. The approximate angle of the failure wedge can be calculated by
well-established methods, with consideration to the geometry of the anchored structure and the
internal strength of the foundation material. A minimum free-stressing length is usually required to
permit prestressing and subsequent anchorage installation.
C6.10.3 Materials and installation
PTI (1996) provides details for
(a) prestressing steel and attachments;
(b) grout or concrete for bond zone;
(c) backfill for free-stressing length; and
(d) corrosion protection.
The design should ensure the performance and durability of the ground anchor materials over their
service life.
C6.10.4 Anchor testing
PTI (1996) provides details of generally accepted standards for ground anchor tests. Specific
jurisdictions may impose specific criteria.
C6.10.4.1 General
Test installations should model as closely as possible the production installations.
(a) Pre-production tests are to provide design information prior to project construction. They are
conducted at the construction site or at site locations that are representative. The number of
pre-production tests should be determined by the scope, complexity, and risk of the installations,
but typically range from 0 to 3 or more. Preproduction tests consist of a rigorous test procedure
characterized by a number of cyclic loadings and maintenance of the maximum test load for
12 to 24 hours.
(b) Performance tests for design verification should be carried out at the initial stages of project
construction. The rationale for determining their location and number is similar to that for
preproduction tests. Performance test procedures are less rigorous than those for preproduction
tests and the test loads are maintained for a shorter duration.
(c) Proof tests are for anchor performance verification. They should be carried out on all ground
anchors as part of prestressing and anchorage operations. Proof tests are of relatively short
duration.
(d) Liftoff tests are also for anchor performance verification. They should be carried out on a
representative number of ground anchors, usually less than 10%, for as long a period as practical
after completion of proof testing, in order to monitor any loss of anchor resistance over that
period. Liftoff tests are of relatively short duration typically involving measurement of the load
required to lift the anchorage.
C6.10.4.2 Acceptance criteria
Acceptance criteria for ground anchor tests specify minimum performance for pullout resistance,
creep, and structure displacement. Time-dependent aspects, such as creep, are modelled by
projecting measured movement through log time cycles representing the service life of the
installation.
C6.11 Sheet pile structures
C6.11.1 Application
Sheet pile walls may be constructed of steel, concrete, or wood; however, steel is most commonly
used. Anchors for sheet pile walls normally consist of concrete deadmen, either blocks or continuous
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walls, piles, or sheet piling. Anchors are usually connected to the sheet pile walls by steel tie rods. Sheet
pile walls may also be supported by soil or rock anchors, in which case the provisions of Clause 6.10 apply.
Clause 6.11 also applies to cellular sheet pile structures in which interconnected cells, usually formed of
straight web steel sheet piling and filled with soil or rock, are employed as permanent walls or cofferdams.
C6.11.2 Design
Two methods have been most commonly used to design sheet pile structures using working stress design,
i.e., the free earth support method (Rowe 1955) and the fixed earth support method (Tschebotarioff
1951).
The former applies to most cases, since the depth of penetration of the piles required for stability usually
means that there is no point of contraflexure in the deflected shape of the piling below the ground level in
front of the piling. The fixed earth support method applies where the piles are driven into very hard or
dense soil or intact rock, or where they are driven unusually deep into other soils. In such cases, a point of
contraflexure occurs and there is passive resistance behind the wall at the toe of the piles.
The ULS conditions that must be considered in the design of sheet pile walls are
(a) instability due to inadequate penetration of the sheet piles below the ground surface in front of the
wall; and
(b) inadequate passive resistance of the soil at the anchors.
Structural design needs to consider shears and moments in the piling, and stresses in the tie rods,
walers, and connections.
The height of a sheet pile wall driven into cohesive soil, whether cantilever or anchored, is limited by the
undrained shear strength of the soil. Failure will occur when the free height of the wall is such that the
passive resistance in front of the wall is insufficient. The calculation of limiting height should be the first
step in the design of sheet pile walls driven into cohesive soil.
Interlock resistance is not normally a consideration in the design of cantilever or anchored sheet pile
walls, as the piling is usually driven in straight lines or with very small curvature. The possibility of interlock
damage exists, however, during pile installation under hard driving conditions, such as in bouldery soil.
Sheet pile walls with free-draining granular backfill, and water in front of the piling, are sometimes
considered to be sufficiently permeable that unbalanced hydrostatic heads will not occur. This assumption
may not always be realistic. If the wall abuts a large body of water, storm waves can overtop the wall and
quickly saturate the backfill. Similarly, coastal installations in tidal waters with a high tide range may be
subjected to unbalanced heads during a falling tide. If the wall is part of a cofferdam structure, seepage
pressures and the risk of piping in granular soils needs to be considered.
Cantilever and anchored sheet pile structures are relatively flexible and may not be suitable in those
circumstances where existing utilities or vulnerable structures are nearby and need to be protected against
lateral deformation.
In choosing the type of pile for a site, the driving conditions should be considered, since the depth of
penetration necessary to develop the required passive resistance needs to be achieved. Where bedrock
exists at shallow depths below the ground level in front of the piles, the required passive resistance may be
developed by penetration into the rock, by penetration into bedrock loosened by blasting, by toe pins, or
by strong points. Examples of the latter two are steel box piles or pipe piles incorporated into the wall at a
selected spacing and socketed into bedrock.
C6.11.3 Ties and anchors
Tie rods are usually installed horizontally. If they are inclined, a vertical component of load is induced in
the sheet piles. Consequently, the bearing resistance of the sheet piles should be checked.
C6.11.3.1 Deadman anchors
Ideally, deadman anchors, blocks, or continuous walls should be sufficiently far behind the wall that the
theoretical active failure wedge behind the sheeting does not encroach on the passive failure wedge in
front of the deadmen. If the wedges do intersect because of a site space limitation, there will be a
reduction in passive resistance.
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C6.11.3.3 Tie load
The Clause 6.11.3.3 requirement for the factored resistance to be larger than the factored load is to
account for possible redistribution of loads among tie rods, repetition of heavy surcharge loads, and
unforeseen sheet pile deflections.
C6.11.3.4 Sagging of tie rods
The problem of induced stresses can be solved by encasing tie rods in conduits that can settle without
transferring loads to the tie rods, or by supporting them at the third points by piles.
C6.11.4 Cellular sheet pile structures
For cellular sheet pile structures, the following ULS conditions should be considered:
(a) horizontal sliding for structures founded on bedrock at shallow depth below ground;
(b) for cofferdams on rock, upward movement of rear piles allowing loss of soil;
(c) vertical shearing along the centreline of the cells;
(d) horizontal shearing of fill within the cells allowing failure by tilting;
(e) bearing failure of inboard sheet piles due to vertical friction forces from cell fill;
(f) bursting due to tension failure of interlocks of sheet piling;
(g) piping due to unbalanced water pressure; and
(h) rotation of the structure as a unit.
For the ULS conditions involving vertical shearing through the structure, interlock friction resistance
should be considered in the analysis.
Free-draining granular material is the preferred fill for the cells. It provides the high shearing
resistance and high skin friction, which aids stability, and results in a more favourable gradient of the
saturation line within the cell. This type of fill also provides protection against frost pressures.
Steel sheet pile cellular structures should employ flat web sheet piles for deflection angles up to 10°.
For smaller diameter cells with larger deflection angles, piles with dog leg webs are usually used.
Interconnecting junction points, where cells interconnect, are constructed with prefabricated sections
in the shape of 90° Ts or 30° or 120° Ys.
C6.12 MSE structures
C6.12.1 Application
MSE structures are systems that incorporate all design, material, and construction elements necessary
to meet established performance criteria. MSE structures consist of facing elements, soil-reinforcing
elements, reinforced soil mass, and connections from soil reinforcing to facing. Applications for MSE
systems include resisting horizontal loads for steepened slopes, retaining walls, and abutments.
C6.12.2 Design
C6.12.2.1 General
Design, material, and construction criteria are available in the technical literature, e.g., FHWA (1996)
and AASHTO (1997).
C6.12.2.2 Calibration
MSE structures are increasingly proprietary systems. Consequently, MSE designs may originate in other
jurisdictions and may be based on working stress methods or on experience and may not meet the
requirements of the Code. In cases where proprietary designs are not in accordance with the Code,
variations may be considered where adequately justified and documented.
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C6.12.2.3 Factors for consideration
The essential objective of MSE design is to provide sufficient pullout resistance between the reinforcement
and the soil. The reinforcing elements provide the retaining function while, contrary to conventional
gravity or cantilever retaining structures, the facing elements provide only surficial stability. Soil-reinforcing
elements for MSE structures generally consist of metallic strips, metallic grid, or geosynthetic grid.
The following aspects are typically addressed in design of an MSE system:
(a) stability of slopes during Construction;
(b) sliding of the base;
(c) overturning;
(d) bearing resistance;
(e) surcharge loading;
(f) global stability;
(g) internal stability of the MSE system;
(h) material durability and compatibility; and
(i) performance and movements.
C6.12.3 Backfill
Backfill should be specified that will develop the interaction with MSE soil-reinforcing elements and
provide the pullout resistance required for the design. The properties of the backfill should be compatible
with any durability requirements of the MSE soil-reinforcing elements, and with drainage and settlement
requirements.
C6.13 Pole foundations
C6.13.1 Application
The essential function of high mast pole foundations is to resist lateral wind loads, including repeated
loading cycles. Vertical loads are usually small. Pole foundations are usually caissons and installation
techniques have an impact on performance. Verification of design assumptions by inspection during
Construction permits standard designs to be less conservative since designs can be altered during
Construction to address site-specific problems.
C6.13.2 Design
C6.13.2.1 General
Pole foundation criteria can be given as an SLS deformation or rotation limitation. The rotational criterion
may be more valid for installations, such as high mast lighting, in which suspended pulley systems are
required to service suspended luminaires and need to operate without interference from the pole. Pole
foundations may be founded in cohesive or noncohesive soils, in fill, in rock, and on level ground or on or
near cut or embankment slopes. The specific foundation condition and site location should be considered
in the design.
By the nature of their function, numerous widely spaced pole foundations may be required for a project.
It is often uneconomical to acquire site-specific subsurface information for pole design at every pole
location. Consequently, representative subsurface conditions are often used for design and are then
verified during Construction. This procedure can be justified by the relatively low risk/low consequence of
a pole foundation failure.
Information concerning pole foundations is available in MTO (1994).
C6.13.2.2 Assumptions
There are a number of procedures for calculating resistance to lateral forces on caissons intended to
achieve more economical designs, including the following:
(a) Shaft Force system is a complex 3-D approach dominated by lateral resistance that is usually
condensed to a 2-D model.
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(b) Undrained capacity analysis expresses lateral resistance in terms of lateral bearing factor using soil
strength parameters.
(c) The Reese method analyzes a 3-D wedge failure.
(d) The Hanson method uses horizontal translation for shallow conditions, Rankine passive wedge for
moderate depth, and horizontal plastic failure analysis for deep conditions.
(e) Stevens and Audibert uses assessed values.
(f) Randolph and Houlsby uses shallow wedge and deep plastic flow analysis.
(g) Broms uses assumed lateral resistance distribution based on available theories.
(h) Davidson uses moment influence theory.
(i) The subgrade reaction or beam response approach uses spring constants to model lateral
resistance.
Fixity conditions and pile rigidity are important considerations for all models.
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CSA (Canadian Standards Association)
CAN/CSA-S6-88 (withdrawn)
Design of highway bridges
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Section C7 — Buried structures
C7.1
C7.3
C7.3.2
C7.4
C7.5
C7.5.1
C7.5.2
C7.5.3
C7.5.4
C7.5.4.1
C7.5.4.2
C7.5.4.3
C7.5.4.4
C7.5.4.5
C7.5.5
C7.5.5.1
C7.5.5.2
C7.5.5.3
C7.5.5.4
C7.5.6
C7.6
C7.6.1
C7.6.2
C7.6.2.1
C7.6.2.2
C7.6.2.3
C7.6.3
C7.6.3.1
C7.6.3.2
C7.6.3.3
C7.6.3.4
C7.6.3.5
C7.6.3.6
C7.6.4
C7.6.4.1
C7.6.4.2
C7.6.4.3
C7.6.5
C7.6.5.1
C7.6.5.2
C7.6.5.3
C7.6.5.4
C7.6.5.5
C7.6.5.6
C7.6.6
C7.6.7
C7.7
C7.7.1
C7.7.3
C7.7.3.1
C7.7.3.2
Scope 267
Abbreviations and symbols 267
Symbols 267
Hydraulic design 267
Structural design 268
Limit states 268
Load factors 268
Material resistance factors 268
Geotechnical considerations 268
Geotechnical investigation 269
Soil properties 269
Camber 269
Footings 269
Control of soil migration 270
Seismic requirements 270
General 270
Seismic design of soil-metal structures 270
Seismic design of metal box structures 270
Seismic design of concrete structures 271
Minimum clear spacing between conduits 271
Soil-metal structures 271
General 271
Structural materials 271
Structural metal plate 271
Corrugated steel pipe 271
Soil materials 272
Design criteria 274
Thrust 274
Wall strength in compression 275
Wall strength in bending and compression 277
Connection strength 277
Maximum difference in plate thickness 278
Radius of curvature 278
Additional design requirements 278
Minimum depth of cover 278
Foundation treatment for pipe-arches 279
Durability 279
Construction 280
General 280
Deformation during construction 280
Foundations 281
Bedding 281
Assembly and erection 281
Structural backfill 281
Special features 282
Site supervision and construction control 282
Metal box structures 282
General 282
Design criteria 283
Design criteria for crown and haunches 283
Design criteria for connection 284
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C7.7.4
Additional design considerations 285
C7.7.4.1 Depth of cover 285
C7.7.5
Construction 285
C7.7.5.1 Structural backfill 285
C7.7.5.2 Deformation during construction 285
C7.7.6
Special features 285
C7.8
Reinforced concrete buried structures 285
C7.8.1
Standards for structural components 285
C7.8.2
Standards for joint gaskets for precast concrete units 286
C7.8.3
Installation criteria 286
C7.8.3.1 Backfill soils 286
C7.8.3.2 Minimum depth of cover for structures with curved tops 286
C7.8.3.3 Compaction 286
C7.8.3.4 Frost penetration 286
C7.8.3.5 Standard installations for circular precast concrete pipes 286
C7.8.3.6 Standard installations for precast and cast-in-place concrete boxes 287
C7.8.3.7 Non-standard installations 287
C7.8.4
Loads and load combinations 287
C7.8.4.1 Load combinations 287
C7.8.4.2 Earth load 287
C7.8.5
Earth pressure distribution from loads 288
C7.8.5.1 General 288
C7.8.5.2 Circular pipe in standard installations 288
C7.8.5.3 Box sections in standard installations 289
C7.8.6
Analysis 289
C7.8.7
Ultimate limit state 289
C7.8.7.1 Additional factors 289
C7.8.8
Strength design 290
C7.8.8.1 Flexure 290
C7.8.8.2 Design for shear 291
C7.8.9
Serviceability limit state 293
C7.8.9.1 Control of cracking 293
C7.8.10 Fatigue limit state 293
C7.8.11 Minimum reinforcement 294
C7.8.11.1 Parallel to span 294
C7.8.11.2 Perpendicular to span 294
C7.8.12 Distribution reinforcement 294
C7.8.13 Details of the reinforcement 294
C7.8.14 Joint shear for top slab of precast concrete box sections with depth of cover less than 0.6 m 294
C7.8.15 Construction 294
C7.8.15.3 Bedding for precast concrete structures 294
C7.8.15.5 Structural backfill 295
C7.8.15.8 Trenches 295
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Section C7
Buried structures
C7.1 Scope
Unlike other sections of the Code, Section 7 specifies minimum standards of both design and
construction. This is because the performance of a buried metal or concrete structure is governed by
the soil-structure interaction and depends as much on methods of construction as it does on design.
Good construction practices for these structures are now established and it is the intent of this
Commentary to emphasize the geotechnical requirements and recommended construction practice.
Section 7 applies only to buried structural systems greater than 3 m in span. Design provisions are also
given for soil-metal structures with deep corrugations. Concrete structures covered by Section 7
include round pipes, box culverts, three-sided box culverts, and arches with footings.
C7.3 Abbreviations and symbols
C7.3.2 Symbols
AL represents the live truck load and AC the construction load to be considered above the conduit.
Either AL or AC is equal to the load of a single axle, if the spacing between axles is more than one-third
the span of the conduit. For tandem axles spaced at less than one-third the span of the conduit, either
AL or AC is the sum of the loads carried by both axles.
C7.4 Hydraulic design
Although the design of buried structures is based primarily on the structural and geotechnical
considerations specified in Section 7, failures of those structures, which convey water, are often caused
by washouts and/or hydraulic uplift. Experience indicates that most hydraulic failures could be
prevented by provision of one or more of the following:
(a) an adequate waterway to carry the design flood;
(b) adequate inlet and outlet treatments to prevent scour, erosion, undermining, percolation and
piping, and/or hydraulic uplift;
(c) invert protection against corrosion, erosion, or bedload abrasion; and
(d) end treatments.
Hydraulic uplift and erosive forces are known to affect the stability of inlets and outlets of buried
structures conveying water. Such hydraulic forces are especially significant for steep gradients and high
flow velocities. Where potential headponding may occur, the possibility exists of percolation flow
through the backfill along the conduit wall. Therefore, appropriate end treatments should be provided
to reduce the most likely hydraulic gradient to a value at least 10% less than that of the critical
hydraulic gradient, ic , given by
ic = (Gs – 1) / (1 + e)
where Gs and e are, respectively, the specific gravity and void ratio of the soil surrounding the conduit
walls.
The end treatments may consist of
(a) headwalls;
(b) cut-off walls of metal, masonry, or concrete to prevent percolation, scouring, and/or uplift;
(c) embankment shaping to improve flow characteristics;
(d) slope treatment to reduce scour and erosion; or
(e) clay seals to prevent infiltration, percolation, erosion, and scour.
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C7.5 Structural design
C7.5.1 Limit states
Clause 7.5.1 covers four types of buried structures with different specified ultimate, service, and fatigue
limit states as listed in Table 7.2. The following may also be noted with reference to the ULS:
(a) Recent design practice (OHBDC 1991, AASHTO 1993) accounts for the ultimate limit state of
soil-metal structures with shallow corrugations on the basis of the buckling load and seam strength of
their metallic shells. This concept is not changed in Section 7, where the limit states considered are
the failure of conduit walls in compression and the failure of seams. Snap-through buckling is a
special form of buckling of the conduit wall in the upper segments. Therefore, the buckling formulas
in Clause 7.6.3.2 have been developed to include considerations for snap-through buckling, in
combination with plastic hinge formation, particularly of the top portions of the conduit wall.
(b) The plastic hinge formation in soil-metal structures with shallow corrugations is also an ultimate limit
state of concern, but only during construction.
(c) In soil-metal structures with deep corrugations, the formation of the plastic hinge of the completed
structure is also considered for the ULS.
(d) Metal box structures are subjected mainly to bending moment and thus their ULS includes failure by
forming a plastic hinge in the top arch, as well as the connection failure.
(e) Reinforced concrete structures follow the requirements of Section 8. In addition, radial tension failure
is to be accounted for in curved concrete walls.
C7.5.2 Load factors
A reference to Clause 3.5.1 in Clause 7.5.2 might suggest that the load factor used for earth pressures
should be the same as the load factor for loads due to earth pressures. It is clarified that when the live load
earth pressure on buried structures is used to calculate the responses in the conduit wall, the load factor
should be the same as that for live loads.
C7.5.3 Material resistance factors
Statistical data on the strength of the various components of soil-metal and metal box structures is, at
present, insufficient for realistic estimation of the values of the resistance factors. Subjective estimates of
the resistance factors have been made in such a way that the margins of safety of structures designed in
accordance with the provisions of Section 7 are consistent with those assumed in the design of existing
successful structures. For concrete buried structures, the resistance factors follow Section 8, with the
exception of φ c for precast pipes and box sections.
The resistance factor for concrete, φ c , is specified for use with strength in
(a) shear without stirrups or ties, or with stirrups and ties;
(b) radial tension with or without stirrups and ties; and
(c) flexural compression.
The resistance factor for concrete is also applied to the strength of shear and radial tension
reinforcement, because the strength of this reinforcement may be governed by either the reinforcement
yield strength or its anchorage capacity.
C7.5.4 Geotechnical considerations
The design of buried structures requires consideration of several geotechnical engineering aspects, such as
the ability of the foundation to support the embankment fills, the long-term settlement of the foundation
beneath the structure, the interaction between the backfill and the conduit wall, and soil arching due to
deformations and settlement. Thus, geotechnical considerations constitute an integral, and often vital,
component of the buried structure design process.
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C7.5.4.1 Geotechnical investigation
Geotechnical investigation of the foundation should be carried out at those sites where no previous
reliable knowledge exists as to the nature and extent of subsoil, groundwater, and bedrock conditions.
The extent of such investigations depends on the nature and economic worth of the project, the
availability of reliable ground data from geological or other sources, and the nature of the ground and
foundation materials.
Subsoil conditions should be known to an adequate depth to ensure that any soft or deleterious soil
layers are identified and that their potential influence on the future performance of the structure is
assessed at the design stage. Should bedrock or other relatively incompressible material be
encountered at a shallow depth, the foundation investigation need only confirm the continuity and
reliability of such incompressible strata. The foundation investigation report should include logs of all
borings and test pits made at the site, the results of laboratory tests on soil and rock samples, and a
written description of the site conditions. In addition, a professional assessment should be made as to
the nature, extent, and potential behaviour of the foundation materials under the proposed buried
structure during and after Construction. Such an assessment should comment on the stability of fills,
the total and differential long-term settlements beneath and adjacent to the structure, and the time
rate of such settlements. Recommendations should be made with respect to excavation of unwanted
materials, dewatering, backfilling, and any in-place treatment of the foundation soils to improve their
bearing and compressibility characteristics.
C7.5.4.2 Soil properties
Some soil property values can be assumed with confidence, such as the relative density (specific
gravity) of solid soil constituents being taken as 2.7, without introducing large errors in the design.
However, some values, such as unit weights of overburden materials, greatly influence the structural
design; hence, considerable judgment is required in using assumed soil values in design. Some soil
properties, such as grain size distribution and plastic and liquid limits, are needed to classify the soil
properly and to facilitate material selection and use. Other soil properties are needed to model the soil
in order to utilize the design methods given in Section 7. Advance knowledge of the soil properties for
the design procedure that is to be adopted can help considerably in conducting an effective
geotechnical program.
The values of Es given in Table 7.5 are nominal values based on a review of existing literature and
results from a limited number of instrumented structures. Some of these values have been recently
corroborated by new research (e.g., Moore, 2001). The value of Es given in the Code for a given soil
type and degree of compaction, or for a CLSM of a given mix, can be superseded by a value obtained
from well-conducted specialized laboratory tests.
C7.5.4.3 Camber
Due to its trapezoidal cross-section, a road embankment subjects the foundation beneath its centre to
greater stresses than beneath the adjacent toes of the side slopes. These differential stresses in the
foundation cause differential consolidation and/or “elastic” compressions and, consequently,
non-uniform settlement along the length of the conduit. This non-uniform settlement can be
corrected by cambering the bedding profile in the longitudinal direction to ensure the achievement
and maintenance of the designed invert gradient in the long term. In general practice, the upstream
half of the conduit length is placed on an almost horizontal bedding grade, whereas the other half is
placed on a sloping grade. On completion of settlement, the invert should assume a continuous (i.e.,
unbroken) profile along the conduit length.
C7.5.4.4 Footings
In the design of footings, the passive resistance of any soil located adjacent to the footing within the
zone of frost penetration should be neglected unless the soil is granular and well drained. To
accommodate wall thrust adequately, the footing may either be widened at the base or deepened so
as to increase the passive resistance component. Pile footings may be necessary for some buried arch
structures.
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C7.5.4.5 Control of soil migration
When soils with different gradations are placed against one another, the fines from one soil can easily
migrate into the voids of the other soil, under even small hydraulic gradients. When this happens, the
permeability of the soil increases, causing greater water flow and greater soil migration. If unchecked, such
soil migration can remove the soil support required to maintain the stability of the soil-metal or metal box
structure or the haunch and side support of reinforced concrete structures. It is therefore important to
analyze the natural and imported soils to ensure that this does not happen. Generally, soil migration can
be minimized with the use of graded soil filters or by providing a suitable woven or nonwoven geotextile
separator that can be placed between the different soil types to achieve the same effect.
C7.5.5 Seismic requirements
C7.5.5.1 General
Seismic loads on buried structures arise from inertia forces due to earthquake shaking and/or from large
permanent ground movements generally associated with strength and stiffness loss of loose or sensitive
saturated foundation soils.
The performance of buried structures during past earthquakes is well documented by Youd and
Beckman (1996). Corrugated metal pipe culverts, reinforced concrete pipe culverts, and concrete box
culverts suffered only minor damage when subjected to earthquake accelerations in excess of 0.4 g,
provided that significant permanent ground displacement due to liquefaction or lateral spreading did not
occur. Severe damage and failure occurred in a number of structures where permanent ground
displacement was significant. The possibility of liquefaction and significant ground displacement can be
assessed in accordance with Clause 4.6.
The increased forces and moments from shaking arise from both horizontal and vertical components of
accelerations and can be computed from dynamic analyses (Byrne et al., 1996). Such analyses show that
the increase in thrust is largely controlled by the vertical component of the earthquake, while the increase
in moment is largely controlled by the horizontal component of the earthquake.
The vertical component of the earthquake acceleration, expressed as the vertical acceleration ratio, AV ,
will effectively increase the unit weight of the soil from y to y (1 + AV). AV can be taken as two-thirds of the
horizontal acceleration ratio, AH , which is equal to the zonal acceleration ratio, A, for the region in
question, as given in Clause 4.4.3 (e.g., for Zone 3, AH = A = 0.2 and AV = 0.133).
Horizontal accelerations given in Clause 4.4.4 are for rock or firm ground, but may be amplified in an
overlying layer of less competent soil. Amplification can be computed directly using dynamic analysis
procedures or estimated from experience based on Idriss (1990).
C7.5.5.2 Seismic design of soil-metal structures
For soil-metal structures, the additional thrust due to earthquake loading, TE , would be TD AV .
Analyses show that horizontal accelerations have little effect on thrust. Since thrust alone is the basis for
design of soil-metal structures with shallow corrugations, only TE need be considered in these structures. It
is unlikely that the peak ground acceleration and the peak live load should be considered at the same time.
Thus, for earthquake loading the factored load, Tf , is (α D TD + TE ).
In soil-metal structures with deep corrugations, the effect of earthquake loads on increasing dead load
moments should be investigated by referring to the method given in Clause 7.5.5.3.
C7.5.5.3 Seismic design of metal box structures
For metal box and concrete arch structures, dynamic analyses indicate that significant additional moments
are induced by the horizontal component of the earthquake. The vertical component is less important
than the horizontal component. However, there is no simple way to incorporate the horizontal component
into the design formulas. Clause 7.5.5.3 provides a simplified approach in dealing with this matter.
Axial load or thrust due to earthquake events or seismic loading is not considered in the design of box
structures.
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C7.5.5.4 Seismic design of concrete structures
The additional vertical loads due to earthquake are MvWAV and WpAV, where W is the weight of the fill
material above the conduit and Wp is the self-weight of the structure. The soil reaction pressures for
these loads are distributed in the same manner as for gravity loading.
For concrete arch structures, the additional moment due to earthquake loading is calculated as for
metal box structures in Clause C7.5.5.3.
C7.5.6 Minimum clear spacing between conduits
The spacing between adjacent conduits affects the behaviour and strength of walls of multi-span
conduits, as described in Clause C7.6.3.2.
The minimum clear spacing between two or more structures should also be sufficient for practicality
of construction and especially for the placement and compaction of soil. Cast-in-place concrete or
mortar may also be used in lieu of CLSM. If CLSM or other cementitious material is used, the design
should ensure against uplift of the metal components of the structure until the material has set.
C7.6 Soil-metal structures
C7.6.1 General
Soil-metal structures are closed or open conduits with spans equal to or greater than 3 m to qualify the
structure as a bridge. Such structures derive their strength from beneficial interaction between the
metal and soil components, where the soil provides the resistance against deformation of the metallic
shell or walls of the structure.
C7.6.2 Structural materials
The structural components of a soil-metal structure comprise the corrugated steel pipe or metal plates
and connections, which are usually made with high-strength threaded bolts and nuts. The corrugated
sheets of metal are generally galvanized when the metal is steel. Other structural components may
include longitudinal thrust beams placed above the springline and/or transverse stiffeners consisting of
I-beam or inverted corrugated plates placed across the crown. At the inlet and outlet, structural
components could also include interlocking steel, other metal or timber sheeting to reduce seepage
pressures and to minimize conduit underflow, and similar end-treatment accessories made with
reinforced concrete or metallic components.
C7.6.2.1 Structural metal plate
The industry has developed standards for structural steel and aluminum plates used in soil-metal
structures. The designer should consult the latest specifications pertaining to available structural
metallic components for design calculations.
CSA G401 includes both shallow and deep corrugations. ASTM B 746 (1993) includes a 380 × 140
mm steel profile and a 230 × 64 mm aluminum profile, both of which are available in the Canadian
market.
C7.6.2.2 Corrugated steel pipe
The industry has developed standards for corrugated steel pipe used in soil-metal structures. The
designer should consult the latest specifications pertaining to available structural metallic components
for design calculations.
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C7.6.2.3 Soil materials
Table 7.4 has been devised to help classify soils into two basic groups:
(a) Group I soils are noncohesive and coarse-grained and exhibit time-independent behaviour. They are
usually angular or subangular due to crushing or inclusion of crushed aggregate products and exhibit
fairly high effective stress internal friction values, with the angle of internal friction being > 32°. Their
moduli depend on the void ratio after compaction and the prevailing effective stresses. The strengths
and stiffness of Group I soils remain more or less unchanged during the design life of the structure.
(b) Group II soils are finer grained than Group I soils. They are essentially noncohesive, containing less
than 12% clay and silt-sized particles. They will exhibit lower effective stress angles of internal friction
and moduli for similar effective stress conditions in comparison with Group I soils.
The secant modulus of soil stiffness, Es , affects
(a) the dead load thrust in the conduit wall through the axial stiffness parameter, Cs (Clause 7.6.3.1.2);
(b) the wall strength in compression (Clause 7.6.3.2);
(c) the bending moments in the conduit wall during Construction (Clause 7.6.3.3.1); and
(d) the bending moments of the completed soil-metal structures with deep corrugations
(Clause 7.6.3.3.2).
Soil is anisotropic and its response to load is nonlinear and inelastic. For analysis, soil is commonly
modelled as an isotropic material with either incremental elastic or equivalent elastic properties, using
tangent or secant moduli that depend on the soil type and density or compaction level, as well as the
stress state. For such an elastic and isotropic model, two elastic parameters describe the response: a
Young’s modulus and Poisson’s ratio, or a shear modulus and a bulk modulus. Young’s modulus is most
commonly used for soil (Duncan et al., 1980; Byrne et al., 1987).
The stress-strain response of a soil element under a confining stress, σ c , and loaded axially under a stress
difference, σ d , can be approximated by the solid line in Figure C7.1, which is made up of a curved line
(shown in dotted line) up to failure and a constant linear portion after failure.
sd
(sd)ult
El
sc
(sd)f
1
sd
e1
Es
I
sc
sc
e1
Figure C7.1
Soil stress-strain relationships
(See Clause C7.6.2.3.)
Assuming the curved portion can be approximated by a hyperbola, the secant stiffness, Es , can be
expressed as
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Es = Ei [1 – RF (σ d / (σ d) f )]
where
= kE PA (σ c / PA)
= a Young’s modulus number that depends on soil type and compaction
= a Young’s modulus exponent, 0 < m < 1
= atmospheric pressure in the chosen units
σd
= the current level of major principal stress difference
(σ d ) f = the major principal stress difference at failure
(σ d ) ult = the ultimate stress difference from the best fit hyperbola to the data
RF
= the failure ratio
= (σ d)f / (σ d)ult , 0.5 < RF < 0.9
Based on laboratory and field experience (Duncan et al., 1980; Byrne et al., 1987), approximate
ranges of kE values for soil Types I and II are listed in column 3 of Table C7.1, and suggested values in
column 4.
The exponent, m, ranges between 0.2 and 0.8 for most soils, and m = 0.5 is recommended for use
here. To evaluate Es , the confining stress, σ c , and the stress ratio, (σ d)f /(σ c)f , are required. The
confining stress, σ c , depends on the average fill height as shown in Figure C7.2.
m
Ei
kE
m
PA
Table C7.1
Calculated and recommended kE and Es values
(See Clause C7.6.2.3.)
1
Soil
group
2
Standard Proctor
density (%)
3
4
kE
5
Calculated
Es , MPa
6
Recommended
Es , MPa
kE range
I
85–90
90–95
> 95
200–400
400–1000
1000–2000
300
600
1200
7.5
15
30
6
12
24
II
85–90
90–95
> 95
100–200
200–500
500–1000
150
300
600
3.75
7.5
15
3
6
12
sv
2.5 m
sc
Figure C7.2
Buried structure and soil section
(See Clause C7.6.2.3.)
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Assuming an average soil depth = 2.5 m and a unit weight of soil = 20 kN/m3
σv
= 2.5 (20)
= 50 kPa
σc
= ko σ v
= 25 kPa for ko = 0.5
0.5
= kE 100 (25/100)
= 50 kE kPa
(σd) / (σd)f ≈ 2/3, and
RF
≈ 0.75
Hence,
Es
= 50 kE (1 – 0.66 × 0.75)
= 25 kE kPa
= 0.025 kE MPa
The Es values based on Es = 0.025 kE MPa are listed in column 5 of Table C7.1. The recommended values
(Table 7.5) are listed in column 6. These recommended values for secant modulus are similar to those
recommended in OHBDC (1991) when dealing with wall strength in compression (buckling). They are
about one-half the values proposed in the OHBDC when dealing with dead load and the axial stiffness
parameter. The proposed values are two to three times those recommended by Duncan when dealing
with bending stresses and plastic hinge formations.
The secant Young’s modulus values proposed by Duncan et al. (1980) are conservatively low compared
with measured values and field performance. The soil modulus values proposed in column 6 of Table C7.1
are realistic for Soil Groups I and II based on both laboratory tests and field experience. They are in close
agreement with the values of soil modulus recommended for evaluating wall strength in compression for
the OHBDC and are considered reasonably conservative values for use in other aspects of buried structure
design.
Ei
C7.6.3 Design criteria
C7.6.3.1 Thrust
C7.6.3.1.1 General
The factored thrust in the conduit wall is assumed to be an algebraic sum of the thrust due to factored
dead load and the thrust due to factored live load. In spite of the nonlinear behaviour of soil-metal
structures, it is considered sufficiently accurate for the purpose of design to superimpose the separate load
effects due to live and dead loads in this manner. The dynamic load allowance (DLA) used in the
calculation of thrust Tf is obtained from Clause 3.8.4.5.2 and the ULS Combination 1 of Table 3.1. The live
load factor αL is 1.75, which compares with a value of 1.40 in the 1991 edition of the OHBDC. The
increase was in response to a corresponding decrease in axle loads of the CL-W Truck.
C7.6.3.1.2 Dead loads
The method of calculating TD by the equation specified in Clause 7.6.3.1.2 is derived from the work of
Haggag (1989) in which, after an extensive analytical study, the author concludes that the segments of soil
identified as W1 and W2 in Figure C7.3 can be accounted for in the calculation of TD through factors Af 1
and Af 2 , respectively. These factors are provided by Haggag (1989) for a wide range of values of the
following parameters:
(a) axial stiffness parameter, Cs , as defined in Clause 7.6.3.1.2;
(b) flexural stiffness parameter, Bs , relating the flexural rigidity of the conduit wall to the stiffness of the
soil support;
(c) ratio Dh /Dv ;
(d) ratio H /Dh ;
(e) quality of the backfill;
(f) extent of the engineered backfill around the conduit; and
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(g) the stiffness of the foundation stratum below the structure.
From the results provided by Haggag (1989), it is concluded that within the range of Bs
encountered in practice, TD is little affected by Bs . The results also confirm the observation of Mufti
et al. (1989) that the “soft” foundation tends to increase TD in horizontally elliptical pipes; the reverse
trend occurs in vertically elliptical pipes. A finite element approach is applied to Haggag’s method of
analysis to derive the side thrust TD . The values of the variable that affect TD , such as Bs and the
foundation stiffness, are such that an upper limit of TD is obtained. Provided that the extent of the
engineered fill is not less than Dh /2, the upper limit of TD , as expressed by Haggag’s method, is given
by
TD = 0.5 (1.0 – 0.095 Cs) Af 1 W1 + 0.5 (1.0 – 0.11 Cs) Af 2 W2
Furthermore, both of the multipliers of Cs can be changed to 0.10 without significant loss of
accuracy, so that the above equation can be rewritten as the one given in Clause 7.6.3.1.2 in which
the weight of the column of earth and pavement above the conduit, W = W1 + W2.
W2
H
0.1 Dh
W1
Dv
Dh
Figure C7.3
Identification of W1 and W2
(See Clause C7.6.3.1.2.)
C7.6.3.1.3 Live loads
The rationale for the version of Clause 7.6.3.1.3 in the previous edition of the Code is given by Bakht
(1981), who provides details of several tests on actual soil-steel structures. The distribution of live load
through the fill is influenced by the flexibility of the structure, and is therefore different than for a rigid
concrete structure. It is based on a dispersion of 1 horizontal to 1 vertical through the soil and the
Code formula is based on a 1.2 m spacing between the axles. In the previous edition of the Code, the
term lt was defined to be 1.45+2H. Plates with deep corrugations soil-metal structures can have much
greater spans than was possible with plates with shallow corrugations. While live load thrusts in shorter
spans were governed by the two-axle tandem of the CL-W Truck, in longer spans these thrusts might
be governed by more than two axles. Accordingly, the definition of lt has been revised to include as
many axles as could be accommodated on the span.
C7.6.3.2 Wall strength in compression
The live load and dead loads acting on a soil-metal structure with shallow corrugations are carried
mainly by the metal conduit wall acting in compression, although the wall is also subject to some
degree of bending. For the purposes of design, the provisions of the Code for soil-metal structures
with shallow corrugations are based on the assumption that the wall is subjected to compressive forces
only, i.e., to be in a state of ring compression. The justification for this assumption lies in the manner in
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which the interface pressure between the metal conduit wall and the surrounding soil mass changes with
movement of the wall. If a bending moment occurs locally that is high enough to cause partial yielding of
the conduit wall with shallow corrugations, the resultant movement of the conduit wall causes an increase
in the interface pressure developed in the adjacent soil mass and this increase in pressure tends to inhibit
further movement. The failure of a conduit wall with shallow corrugations under thrust alone may be due
to wall crushing, when the compressive stress s = T/A reaches the yield point; or by elastic buckling; or by
a combination of the two (Abdel-Sayed, 1978). For the purpose of calculating the elastic buckling load,
the conduit wall is divided into the following two zones:
(a) the lower zone, in which the radial displacements of the wall are toward the soil; and
(b) the upper zone, in which the radial displacements of the wall are toward the inside of the conduit.
The first equation for fb given in Clause 7.6.3.2 applies when R ≤ Re ; it relates to inelastic behaviour of
the conduit wall. The second equation for fb , which applies when R > Re , relates to elastic behaviour.
An additional aspect of the first two equations for fb in Clause 7.6.3.2, which has no counterpart in the
AASHTO Specifications (1993), is that they have been made applicable to the upper portion of the wall
also; this has been achieved by increasing the value of λ , and hence of K, to allow for the effect of the
tangential movement of the points of zero radial displacement. In the case of the lower portion of the
conduit wall, where radial movements are toward the surrounding soil mass, tangential movements at the
points of zero radial displacement have relatively little effect on buckling behaviour. By contrast, such
movements can have a significant effect on the buckling behaviour of the upper portion of the conduit,
where radial movements are away from the surrounding soil mass. It is because of this difference in the
behaviour of the two portions of the conduit wall that two expressions for λ are needed in the equations.
The inelastic buckling is considered to start when fb is equal to half the yield stress. A parabolic equation is
assumed for the transition zone between full yielding (KR/r = 0) and the elastic zone at Fy /2.
The design provisions account for the effect of shallow cover through an approximate approach, in two
steps:
(a) The modulus of soil stiffness, Es , is modified to account for the shallow depth of soil, i.e., Es is replaced
by Em. The formula for Em has been developed by using an equivalent soil cylinder with thickness
equal to the average cover height (Luscher, 1966; Meyerhof and Baikie, 1963). This formula remains
unchanged from the 1991 edition of the OHBDC.
(b) A second reduction factor, ρ , is applied to account for
(i) the variation of soil stiffness over the length of the upper arch; and
(ii) the local effects (bending) due to the live load on the embankment.
In most cases, it will be found that for spans in excess of 9 m, it may not be possible to satisfy the
requirements of Clause 7.6.3.2 using the 152 × 51 mm corrugation profile plate alone. For spans longer
than 9 m, the addition of special features, as mentioned in Clause C7.6.6, may be necessary. Long-span
soil-metal structures with plate having shallow corrugations and without any special feature are rare.
Thrust is not the only load effect considered in soil-metal structures with deep corrugations.
Clause 7.6.3.3 requires that the conduits of these structures also be designed for bending moments.
The equations for fb in the previous edition of the Code, when applied to a condition when the fill is just
at the crown level, i.e., when H = 0.0, led to fb = 0.0. The commentary to the OHBDC (1991) confirms that
the formula for Em was derived by using an equivalent soil cylinder around the conduit wall having
thickness equal to the average cover height. In an unpublished report, Bakht et al. (2003) determined that
when the backfill around the pipe has just reached the crown, the average cover height is not zero, but
half the vertical distance between the crown and the spring line; this distance is denoted as H’. In
Clause 7.6.3.2, the equations for ρ and Em have been revised to replace (H) in the previous equations with
(H+H’), thus correcting an obvious error in the previous equations.
There are two principal reasons for requiring a minimum clear distance between adjacent conduits. The
first is the need to accommodate compacting equipment between the conduits for adequate compaction.
The second is the need to avoid a situation in which a soil mass contained between the inside shoulders of
the two adjacent conduits could fail by upheaval as a consequence of two surface loads being applied
simultaneously that are eccentric to, and are on either side of, the two conduits. To explain the influence
of conduit spacing in a multiconduit structure on the buckling resistance of the conduit wall, a structure
with two closely spaced conduits is considered. The segments of the conduit wall in the vicinity of the
adjacent conduit are referred to in Section 7 as “internal segments”, and the others as “external”. It can
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readily be appreciated that the stiffness of the lateral support to internal segments of the conduit wall,
being influenced by the deformation characteristics of the adjacent pipe, is likely to be different from
that experienced by external segments. Analyses reported by Girgis (1993) have shown that a conduit
spacing, S, of 0.1Dh leads to a reduction of about 12% in the buckling resistance of the conduits, and
that no reduction is needed if S is greater than 0.5Dh. To reflect this reduction, the multiplier Fm is
introduced in Clause 7.6.3.2.
C7.6.3.3 Wall strength in bending and compression
C7.6.3.3.1 Wall strength during construction
The requirements of Clause 7.6.3.3.1 replace the check for the flexibility factor that was required in
OHBDC (1991). The intent of Clause 7.6.3.3.1 is to prevent permanent deformation during
backfilling, or overloading under construction live loads. Critical stages of Construction include the
point at which the backfill is at the crown and at subsequent stages of backfilling. The structure should
also be checked for construction live loads at the minimum depth of cover specified during
Construction.
C7.6.3.3.2 Wall strength of completed structure
Clause 7.6.3.3.2 was introduced for the conduit walls of soil-metal structures with deep corrugations
because their large flexural rigidities attract substantial bending moments that cannot be ignored in
the design. The equations are mainly derived from those in Clause 7.6.3.3.1, which are based on the
work of Duncan et al. (1980). Choi et al. (2004) have shown that the equations developed for conduit
walls with shallow corrugations are slightly conservative for conduit walls with deep corrugations.
C7.6.3.4 Connection strength
The ultimate strengths of seams for various bolting arrangements shown in Figure C7.4 are based on
seam strength tests conducted on straight short corrugated plates with shallow corrugations by the
Utah Department of Highways in 1964 and by Pittsburgh Testing Laboratories in 1965. Similar values
are also used in the AASHTO Specifications (1993) and in the Handbook of Steel Drainage and Highway
Construction Products (AISI 1984). Since the Code allows the use of steel plates with deep corrugations
and also the use of aluminum plate, Clause 7.6.3.4 provides that the value of Ss may be evaluated
experimentally or obtained from Approved tests or published standards. It is important to note that
the connection strength is affected significantly by the bolting arrangement.
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3000
Bolting
arrangement
no.
2800
76
mm
Unfactored seam strength, Ss , kN/m
2600
76
mm
76
mm
Ridge
(typ.)
For bolting
arrangement
no. 1
Visible
edge
2 (typ.)
For bolting
arrangement
no. 2
2400
1
2200
2000
1800
1600
1400
Valley (typ.)
1200
1000
800
600
400
200
0
0
1
2
3
4
5
6
7
8
Plate thickness, mm
Figure C7.4
Longitudinal seam strengths of bolted steel plates with
152 × 51 mm corrugation profiles and 20 mm diameter bolts
(See Clauses C7.6.3.4 and C7.7.3.2.)
C7.6.3.5 Maximum difference in plate thickness
The specification for the maximum difference in plate thicknesses at seams ensures the ease of assembly
and smooth stress transition between the mating plates.
C7.6.3.6 Radius of curvature
For design purposes, the interactive soil pressure at any location on the conduit wall is determined from
the radius of curvature of the wall at a point under consideration and the thrust in the wall at that point.
The ring compression theory (White and Layer 1960) indicates that the wall thrust remains substantially
constant over the entire cross-section and, hence, the soil pressure increases as the radius of curvature of
the wall decreases. The limitation on the minimum radius of curvature in wall segments is intended to limit
the maximum interface soil pressure to an amount that engineered soils can safely sustain at the specified
compaction limit.
C7.6.4 Additional design requirements
C7.6.4.1 Minimum depth of cover
The minimum depth of cover requirements for conduit walls with shallow corrugations take account of
(a) the need to keep bending moments in the conduit wall, due to live loads, at a level which may be
safely neglected in the design;
(b) the possibility of upheaval of a soil wedge above one side of the conduit due to an eccentric on the
other side of the conduit; and
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(c) the provision for shallower depth of cover with the use of special features or reinforced earth
above the conduit, if Approved.
The work of Abdel-Sayed and Salib (2002) provides the basis for the depth of cover requirements for
soil-metal structures with deep corrugations.
C7.6.4.2 Foundation treatment for pipe-arches
Investigations by Bakht and Agarwal (1988) have shown that distress in the haunches of pipe-arches
can be caused not only by insufficient compaction of the fill under them, but also by soft underlying
foundation. This is so because the bulb of high radial soil pressure acting over the haunches has its
influence over the foundation as well. To ensure that pipe-arches do not suffer distress due to a soft
foundation, the Code requires that trench reinforcement, according to the scheme of Figure 7.4, be
provided under the haunches when the foundation comprises soft to firm cohesive soils or loose to
compact cohesionless soils.
C7.6.4.3 Durability
The design life for soil-metal structures varies from 50 to 100 years. In order to achieve this expected
life, the chemistry and electrical conductivity of the soil and water in contact with the structure and
the bedload that may flow through the structure must be considered.
Various protective coatings may be added to the base metal to achieve the required service life.
These include metallic coatings such as zinc, aluminum-zinc, and aluminum. Nonmetallic coatings
include bituminous coating, bituminous coating and paving, polymers, fiber-bond, epoxy, and
concrete lining.
Another method of protecting the metallic shell against corrosion is through sacrificial cathodic
protection. In this protective system, the steel plate is connected through an electrical conductor to a
sacrificial zinc or aluminum plate that acts as an anode and corrodes, thereby preventing the steel
plate from corroding.
Only two effective measures have been used to increase the durability of the zinc-coated steel plate
used in the construction of soil-metal structures and metal box structures. One of these is to ensure
that the engineered backfill is a granular soil that is free of salts and organic matter; the other is to
increase the thickness of the plate for a design life cycle based on an acceptable loss rate for the
structure. There are various methods for determining loss rate.
The California Method uses the pH and minimum resistivity of either the soil side or the water side
to determine service in years to perforation.
The American Iron and Steel Institute (AISI 1984) has developed a chart similar to the California
Method that is based on the assumption that culverts can continue to provide service until most of the
invert is lost. This point corresponds to a total metal loss approximately twice that corresponding to
first perforation.
The Modified California Method developed by the U.S. Department of Transportation (FHWA 1991)
uses the interaction of alkalinity, hardness, and free CO2 to develop a scaling tendency factor. The
scaling factor is then plotted against conductivity to establish the time to first perforation.
Loss models for zinc-coated steel structures have also been proposed in a study at the University of
British Columbia (1995) and by AASHTO (1993). Zinc coating loss rates are based on loss rates
obtained from sites with a minimum resistivity greater than 1000 ohm-cm.
For nonsaturated areas not affected by stream water, the maximum mass presumed lost per side
due to corrosion, at the end of the designated design life, may be calculated assuming a uniform loss
model with the rates given in Tables C7.2 and C7.3.
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Table C7.2
Non-saturated loss rates
(See Clause C7.6.4.3.)
Loss rate/year/side
Material
Period
UBC
AASHTO
Zinc coating
First two years
subsequently
6 µm
3 µm
15 µm
4 µm
Carbon steel
After zinc depletion
15 µm
12 µm
Note: UBC, from University of British Columbia (1995).
Table C7.3
Saturated loss rate
(saturated soil area and water side inverts)
(See Clause C7.6.4.3.)
Loss rate/year/side
Material
Period
UBC
AASHTO
Zinc coating
Until zinc depletion
15 µm
—
Carbon steel
After zinc depletion
20 µm
—
C7.6.5 Construction
C7.6.5.1 General
Construction and installation procedures have a profound influence on the integrity of soil-metal structure
design. For this reason, their specification by the Engineer is made a requirement. Mirza and Porter (1981)
and Chapter 6 of Abdel-Sayed et al. (1994) provide overviews of construction practices for soil-steel
structures.
C7.6.5.2 Deformation during construction
During the initial stages of backfilling, when the conduit is not fully contained by the soil, the conduit wall
undergoes high deformations. These, if allowed to exceed certain limits, will induce permanent
deformations in the conduit wall. Clause 7.6.5.2 is aimed at restricting such excessive deformations.
For all shapes, the limit on vertical deflection to 2% of the rise, upward or downward, is based mostly
on empirical considerations rather than on analysis.
The crown deflection limits specified in Clause 7.6.5.2 are meant for Construction rather than design
control. With the present state of the art, it is difficult to “design” a conduit wall with shallow corrugations
to comply with Clause 7.6.5.2 without external help. If the deformations of the conduit wall begin to
exceed the specified limits, measures should be taken to contain them.
The conduit walls of some soil-metal structures tend to deflect excessively during assembly due to their
own dead weight. For such structures, struts are sometimes placed inside the conduit to maintain its shape
during Construction. The struts, however, should not restrict crown movement. During earlier stages of
backfilling when the crown begins to move upward, the struts should allow free upward movement of the
crown. In no case should the struts be allowed to restrict the downward movement of the crown during
the later stages of the backfilling operation. Prevention of downward crown movement inhibits the
development of passive soil pressure at the sides of the conduit.
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C7.6.5.3 Foundations
Foundations with reasonably uniform settlement properties are necessary to avoid situations where the
invert may be founded partially on compressible materials and partially on incompressible materials.
Lack of uniformity along the invert bedding could induce undesirable stress concentrations in the
conduit wall above the transition areas between the compressible and incompressible soils.
A condition in which the foundation under the conduit is less compressible than that of the adjacent
areas should be avoided. In such conditions, columns of soil adjacent to the conduit settle more than
the column of soil above the conduit, thus inducing negative arching which, in turn, increases the
thrust.
Foundations with fairly uniform settlement properties can be provided by adjusting the bedding
thickness, replacing compressible materials, breaking up bedrock, and other similar treatments.
C7.6.5.4 Bedding
The bedding serves to receive loads from the conduit wall and transfer them to the foundation both
during and after Construction. The use of either flat or shaped bedding is permitted. A shaped
bedding is preferable for larger structures, as a flat bedding under such structures renders compaction
under the haunches difficult. Preshaped bedding interferes with the assembly of field-bolted
structures; therefore, proper field bolting of the invert plates becomes the criterion for shaping the
bedding. If shaped bedding is selected, a uniform blanket of uncompacted bedding material of nearly
200 mm thickness should be provided to allow for proper embedment of the invert corrugations. It is
important that the bedding material be in full contact with the entire bottom portion of the conduit.
C7.6.5.5 Assembly and erection
Assembly instructions and drawings, provided by the manufacturer, should be made part of the Plans.
The metallic shell may be either preassembled and moved onto a prepared bedding, or it may be
assembled in place using a bottom-side-top plate bolting sequence.
The torque requirement for bolting of longitudinal and circumferential seams does not refer to
retightening of the bolts. General practice is to tighten the bolts to specification torques during
assembly and erection. It is recognized that some relaxation and easing of the torque will occur after
installation. The requirement of the Code is to ensure that the initial torquing has been reliably carried
out. If plate ends in the seams are kept reasonably parallel during assembly and bolt torquing, the
closure of the conduit walls is seldom a problem. If unusually high force is required to effect the
closure, the designer and the manufacturers should be consulted.
The following sequence of construction is recommended:
(a) The walls should be assembled using a minimum number of bolts until all the plates are in place.
Normally, it should be possible to erect a segment of the conduit with as few as three to six bolts
along each seam, untightened, and placed near the centre of each plate.
(b) After overall “loose assembly”, the remaining bolts should be inserted, working away from the
centre of a seam toward the corners of the plates. Corner bolts should be inserted last, and only
after all other bolts are in place and nominally tightened.
(c) Final torquing should be done on one circumferential seam after another, starting at one end of
the structure.
(d) For long conduits, the sequence of final torquing may be provided by the fabricator to avoid the
possibility of a cumulative rotation of the cross-section.
C7.6.5.6 Structural backfill
The requirement for non-frost-susceptible soils adjacent to the structure is not intended to prevent
frost action on the structure, but to avoid any strength reduction in the structural backfill under
repeated freeze-thaw action.
Current practice is to limit backfill lifts to 300 mm of uncompacted thickness. The Code specifies
maximum lifts of 200 mm compacted thickness. Current practice requires that the backfill be raised
evenly on both sides of the conduit. The Code permits an imbalance of up to 200 mm compacted
thickness, typically one lift, on either side of a conduit as long as the deformation criteria of
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Clause 7.6.5.2 are met. This does not preclude the placement of consecutive lifts on one side of a
structure, provided that the imbalance does not exceed the 200 mm compacted thickness at any time.
The intent of Clause 7.6.5.6 is to encourage proper compaction and to prevent lateral deformations of
the conduit wall due to imbalanced backfilling.
The use of heavy vibratory equipment is not allowed close to the conduit in order to limit the
development of incremental earth pressures that may cause excessive deformation of the conduit walls
during backfilling. Under compactive effort, earth pressures often exceed the at-rest values. During
placement and compaction of backfill material, all equipment needs to be specified to operate parallel to
the longitudinal axis of the conduit, unless special circumstances or constraints of space dictate otherwise.
Compaction parallel to the longitudinal axis produces less incremental earth pressure loading than
compaction perpendicular to the longitudinal axis. If the structure is to be assembled and backfilled before
work on the adjoining approach is commenced, the backfill should extend along both sides at least one
span distance and should be raised to provide a cover of at least 0.6 m or one-sixth of the span, whichever
is greater. This provision is meant to ensure the retention of the conduit in its original position and shape
when the adjoining embankments are built.
C7.6.6 Special features
Some of the special features for improving the structural performance include
(a) longitudinal beams connected to the conduit wall at the soil-metal interface in shoulder areas;
(b) a reinforced or prestressed concrete relieving slab above the crown;
(c) transverse stiffeners connected to the conduit wall;
(d) compressible material incorporated in footings of an arch; and
(e) longitudinal seams with slotted holes that permit predetermined shortening of the circumference of
the conduit wall under deep soil cover.
Notwithstanding the use of any special features to improve the soil-metal interaction, all requirements
of Clause 7.6.6 should still be met unless otherwise Approved.
Due to the difficulty of connecting curved stiffeners and plates and ensuring adequate horizontal shear
resistance in the bolted connections, the design of structures with transverse stiffeners should assume that
the structural plate and the stiffener act independently in a cumulative matter, unless special measures,
confirmed by laboratory testing, are taken to ensure the composite action between the stiffeners and the
parent plate.
C7.6.7 Site supervision and construction control
The aim of Clause 7.6.7 is to ensure a minimum standard of quality assurance during Construction. The
construction inspection stages identified in the Code for various sizes of structures are minimum
requirements for quality assurance. It is expected that the Contractor will independently provide quality
control at each stage of Construction, including checking the quality of all imported soils and control of lift
thicknesses, differences in backfill thicknesses on either side of a conduit, and soil compaction.
C7.7 Metal box structures
C7.7.1 General
The first corrugated metal box structures were built in 1975 using ribbed aluminum structural plates. The
design of these structures was completely empirical, relying on field load tests to establish acceptable
structural plate thicknesses and rib spacing. Within three years, a considerable number of metal box
structures had been constructed, and the demand for larger sizes increased to a point where completely
empirical design procedures were no longer appropriate.
In 1978, a study was undertaken at the University of California (Duncan et al., 1984) to develop rational
design procedures for aluminum box structures. The first phase of these studies was the development of a
finite element program to determine the bending moments and axial forces in box structures under loads
imposed by backfill and live loads. Experimental studies were also conducted to evaluate the stiffness and
bending moment capacity of aluminum structural plates with stiffener ribs bolted to one or both sides. In
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1980, additional finite element analyses were performed to assess the behaviour of aluminum box
structures with spans up to 8 m. In 1981, full-scale loading tests were performed on an instrumented
box structure to provide a basis for detailed comparison of design calculations and observed
behaviour.
In 1984, additional finite element analyses were conducted to develop bending moment
coefficients for box structures with concrete relieving slabs over the top. The results of these studies,
summarized by Duncan et al. (1984), have been used to design a family of aluminum box structures
ranging from 2.7 to 7.7 m in span, and from 0.8 to 3.2 m in height. The design formulas and
coefficients are also applicable to steel box structures.
Design procedures and geometric requirements have been published in the AASHTO Standard
Specifications for Highway Bridges (1993) for steel and aluminum box structures and in the ASTM
Standard Specifications for Corrugated Steel Box Culverts (1996). In each case, the span and rise limits
from the original research were used. For the purpose of these provisions, the upper limit of the span
was rounded to 8 m. The dimensional limitations, proposed by Duncan, are shown in Figure 7.6. The
span is the only geometric component appearing in the formulas developed for the calculations of
internal force components.
With the introduction of deep corrugations, it became practical to increase the span of metal box
structures beyond 8 m. Since soil metal interaction data are not available, the larger and stiffer steel
box structures may be analyzed using elastic frame analysis, ignoring any beneficial effects of
soil-structure interaction.
C7.7.3 Design criteria
C7.7.3.1 Design criteria for crown and haunches
C7.7.3.1.1 General
Duncan et al. (1984) analyzed 100 structures by the finite element method to study bending moments
and axial forces in metal box structures with various ranges of span, rise, depth of cover, relieving slab
stiffness, relieving slab length, vehicle load, wheel configuration, load position, backfill type, and
degree of compaction. Based on these analyses, a number of important conclusions were reached that
guided the development of the design method.
For depths of cover smaller than 1.5 m, the effects of axial forces in metal box structures are usually
small in comparison with the effects of bending moments, and only bending moments need be
considered in design.
Rise has only a small effect on moments due to live load. Bending moments in low-rise metal box
structures are slightly larger than those in high-rise metal box structures.
The critical position for axle loads is always at or near the midspan. Backfill quality and density affect
bending moments only slightly, with better backfill quality and higher degrees of compaction resulting
in small reduction in moments.
The dynamic load allowance (DLA) to be used in the calculation for crown and haunch moments is
obtained from Clause 3.8.4.5.2.
C7.7.3.1.2 Dead loads
Bending moments induced by backfill up to the crown level of box structures vary quite significantly
with the rise/span ratio of the structure. High-rise structures bend inward more at the sides and
upward more at the crown during early stages of backfilling than low-rise structures. As cover is placed
over the crown, and as live loads are applied to the backfill over the structure, the crowns of both
high-rise and low-rise structures bend downward. The critical design condition is always one of
downward bending at the crown due to cover and live load. It has been found to be conservative to
neglect the early upward bending in high-rise box structures, and to base designs of both high-rise
and low-rise structures on the results of analyses of low-rise structures. Such an approximation appears
justified in view of the simplicity it affords by eliminating rise as a factor, and by the fact that the
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bending moments due to backfilling just up to the crown level are a small fraction (typically less than
10%) of the total design moment. The design method in Clause 7.7.3.1.2, developed for low-rise
structures, will be slightly conservative for high-rise structures.
The factors k1 and k2 have been determined from the results of Duncan’s finite element analyses
(Duncan et al. 1984).
AASHTO (1993) has published a range of proportioning values for the crown moment based on the
upper and lower boundaries of test values as a function of span. However, the Code relies on the mean
test values and does not use proportioning.
C7.7.3.1.3 Live loads
As a vehicle moves across a corrugated metal box structure, the bending moments around the structure
vary in both magnitude and sign. Therefore, to determine bending moments for design, it is necessary to
study a range of live load positions from the centre of the span to the edge of the structure. For most
metal box structure shapes, the critical load positions for both crown and haunch moments are at or near
midspan. The live load bending moments used in the Code are the largest values calculated for the crown
and the haunch, even though these may not correspond to exactly the same position of the load. The
maximum moments at the crown are always positive, causing tension on the inside face. The bending
moments at the haunch are negative
Live load moment equations were developed by Duncan et al. (1984) for metal box structures up to
8 m in span. The factor kR represents an allowance for load spreading longitudinally along the structure
with increasing distance from the load; its value was determined from the results of tests on full-scale
models by Duncan et al. (1984). Bending moments due to live loads vary quite significantly with cover
depth; the deeper the cover, the smaller are the moments induced by a given vehicle load. This effect
results from greater spreading of the load at greater cover depth. The spreading that occurs parallel to the
span of a structure can be modelled by finite element analyses, but the spreading that occurs parallel to
the structure axis cannot be modelled easily. To account for load spreading along the structure axis,
equivalent line loads were used in plain strain finite element analyses. These equivalent line loads are
selected so that they produce the same peak vertical stress at the level of the crown of the structure as the
actual discrete wheel loads that they model, based on Boussinesq elastic theory. Values of equivalent line
load can be expressed in terms of the design axle load divided by a load coefficient k4 , which is given in
Table 7.6. Because the vertical stress due to a line load is the same at every section along the line, the use
of equivalent line loads is inherently conservative. The structure is treated as if it were loaded uniformly all
along its length with the same intensity of load.
C7.7.3.1.4 Flexural capacity at the ultimate limit state
In the current edition of the Code, the resistance factor for plastic hinge formation in metal box structures
has been revised from 0.7 to 0.9 because the resistance factor in the previous edition of the Code has been
judged too conservative.
C7.7.3.1.5 Fatigue resistance
Bolted connections in metal box structures are subjected to stress reversals due to moving live loads. While
fatigue damage has not been observed in metal box structures, a potential fatigue damage does exist in
structures with large spans.
C7.7.3.2 Design criteria for connection
Longitudinal seam strength values have been published by the American Iron and Steel Institute
(AISI 1984), the American Association of State Highway and Transportation Officials (AASHTO 1993), and
the American Society for Testing and Materials (ASTM 1990). Since the published values are based on
Imperial units for plate thickness, bolts and nuts, metric equivalents of seam strengths should be obtained
by interpolation. Alternatively, test results may be used for design purposes. Typical longitudinal seam
strengths for 51 × 152 mm bolted steel plates are shown in Figure C7.4. Data for other corrugation
profiles and materials may be evaluated experimentally or obtained from Approved published standards.
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C7.7.4 Additional design considerations
C7.7.4.1 Depth of cover
The minimum depth of cover of 0.6 m for soil-metal structures takes into account the bending
moments caused by live load, the dynamic load allowance, and soil wedge failure.
Metal box structures differ greatly from soil-metal structures. The minimum depth of cover for metal
box structures has been reduced to 0.3 m, provided that the design accounts for the change in live
load moment, dynamic load allowance, and soil wedge failure.
When the road above a metal box structure is sprayed with de-icing salts, a small depth of cover
may lead to corrosion on the soil side of the metal plate; in such situations, protective measures in the
form of bituminous coatings or plastic membranes should be employed.
C7.7.5 Construction
C7.7.5.1 Structural backfill
Since the design of a metal box structure is not based on the same degree of soil-structure interaction
as the design of a soil-metal structure, the requirements for the extent of structural backfill for the
former are less stringent than those for the latter.
C7.7.5.2 Deformation during construction
Box structures deflect downward during Construction. Pressure on the straight sidewall is usually
insufficient to induce significant upward movement of the crown during Construction. Duncan et al.
(1984) have estimated that the downward deflection of the crown under a depth of cover ranging
from about 0.4 to 1.5 m is between 0.5 and 1% of the span.
Duncan et al. (1984) have also found that the downward crown deflection due to live loads is about
0.5% of the span. This corresponds to the AASHTO specification limiting live load deflection to 1/200
of the span.
C7.7.6 Special features
(a) Continuous longitudinal stiffeners may be connected to the corrugated plates at each side of the
top arc. Stiffeners may be metal or reinforced concrete, either singly or in combination.
(b) Reinforcing ribs formed from structural shapes may be used to stiffen metal box structures. Where
used, they should be curved to conform to the curvature of the plates, fastened to the structure
as required to ensure cumulative action with the corrugated metal box shell. The stiffeners should
be spaced at such intervals as necessary to increase the flexural resistance of the section to that
required for design.
(c) Continuous corrugated reinforcing plates should be curved to conform to the curvature of the
plates and fastened to the structure as required to ensure cumulative action with the corrugated
metal box shell.
(d) Although concrete relieving slabs are not commonly used in metal box structure design, they can
reduce the bending moments in box structures significantly and thus permit shallower cover.
Relieving slabs may be used across the crown with no soil cover, across the crown with soil cover
over the slab, or above the structure with soil cover between the bottom of the slab and the top
of the structure. Procedures are available, based on work by Duncan et al. (1984), for the design
of relieving slabs over box structures.
C7.8 Reinforced concrete buried structures
C7.8.1 Standards for structural components
The manufacturing standards cited for precast concrete structures are already in use by the precast
concrete pipe industry. These standards contain the criteria that should be used for manufacturing
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each type of structure. Since Clause 7.8 specifies design procedures for reinforced concrete structures,
different design procedures given in the cited reference standards for manufacturing are superseded by
the provisions of Clause 7.8.
The standard diameters, spans, and wall thicknesses given in the cited standards are those in frequent
use by the industry. They facilitate the standardization of manufacturing equipment and formwork.
However, the use of the standard dimensions is not mandatory if other dimensions are more appropriate
for a particular application. An example is the use of thicker walls for structures under very high fills.
Materials and fabrication requirements for cast-in-place structures are the same as those given in
Section 8 for cast-in-place reinforced concrete structures.
Concrete placement methods for precast concrete pipe and box sections are sometimes unique to the
machinery used in this industry. Any special requirements for concrete are found in the standards
referenced in Clause 7.8.1.
The steel reinforcement used predominantly in precast concrete pipe and box sections is the smooth or
deformed cold drawn wire that is assembled on a cage-making machine, or welded wire fabric.
The Code does not have explicit design provisions for buried concrete arches; however, the following
references will be found useful in the design and construction of these structures: Segrestin and Brockbank
(1995), Brockbank et al. (2001), Procter and Seow (2000), and Weinreb and Wu (1991).
C7.8.2 Standards for joint gaskets for precast concrete units
These gaskets are sometimes used for sealing joints in precast concrete conduits. Clause 7.8.2 is not
intended to imply that gaskets are required for all precast concrete conduits. For many such structures,
concrete joints may not require sealing, or joints may be adequately sealed by internally applied cement
mortar, or by other means.
C7.8.3 Installation criteria
C7.8.3.1 Backfill soils
Because the design of a buried concrete structure takes into account the soil-structure interaction, a zone
of influence around the buried structure is specified and the soil materials in this zone are required to
comply with the soil properties and dimensions for the type of installation specified in the Plans.
Standard soil classifications and compaction procedures are specified in order to promote more uniform
use of terminology in project specifications.
C7.8.3.2 Minimum depth of cover for structures with curved tops
A minimum depth of cover and rigid or flexible pavement with a minimum thickness are specified above
the top of buried pipes to distribute the concentrated wheel loads over the pipe.
C7.8.3.3 Compaction
The design procedures for circular pipe and box sections in standard installations are based on the use of
soils defined in Clause 7.8.3.1 and soil compaction based on Standard Proctor density levels —
ASTM D 698 (or equivalent Modified Proctor density levels — ASTM D 1557).
C7.8.3.4 Frost penetration
Freezing and thawing may loosen compacted fine-grained soils that are susceptible to structural changes
with freezing and thawing. Use of frost-susceptible soils should be avoided in the zone of influence, but if
such soils are used, compaction is considered to be ineffective for the purposes of design.
C7.8.3.5 Standard installations for circular precast concrete pipes
Standard installations for circular precast concrete pipes are promoted in American Society of Civil
Engineers (ASCE) Standard 15-93 (ACPA, 1994; Heger, 1988; Heger, 1993).
The standard installation types specified in Clause 7.8.3.5 permit a designer to select appropriate soil
materials based on local availability, cost, and magnitude of fill heights. It is important that the soil types
and associated minimum compaction levels be provided for soils in each zone of the specified standard
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installation type, if the pipe design is based on the earth loads and pressure distributions specified in
Clause 7.8.5.2.
The soil-structure interaction analyses and parametric studies providing the basis for the design
criteria given in Clause 7.8.3.5 are limited to circular pipe and the four standard installations. While
similar data are not available for conduits with noncircular shapes, the conceptual criteria will be found
useful in their designs.
C7.8.3.6 Standard installations for precast and cast-in-place concrete
boxes
Concrete boxes are designed by using simplifying assumptions for the magnitude and distribution of
earth pressure. The two specified standard installations in Table 7.11 reflect the differences in total
earth load and lateral earth pressure applied to the box due to well-compacted and loose soil at its
sides.
Figures 7.10 and 7.11 require that the middle bedding under cast-in-place concrete boxes be
loosely placed uncompacted bedding. This bedding is required to be kept uncompacted to avoid a
“hard point” effect between the walls of the box.
C7.8.3.7 Non-standard installations
Installations other than the standard installations specified for circular pipe in Clause 7.8.3.5, or for box
sections in Clause 7.8.3.6, may be used if the designer can determine the proper soil loads and
pressure distributions by taking account of the soil type, compaction level, and other installation
characteristics of the installation. The procedures described in Clause C7.8.4.2.2 will be found useful in
determining the distribution of soil pressures.
C7.8.4 Loads and load combinations
C7.8.4.1 Load combinations
The load combinations given in Clause 7.8.4.1 are typical of those expected on buried concrete
structures. If a buried structure is to be subjected to a load not covered in Clause 7.8.4.1, the designer
is responsible for identifying the load and taking it into account.
C7.8.4.2 Earth load
C7.8.4.2.2 Earth load on circular pipe in standard installations
The traditional soil-structure interaction analysis for buried rigid pipes was developed by Marston and
Spangler in the 1920s and 1930s, based on relative deformation of soil prisms over and adjacent to
the buried conduits and the frictional resistance that could be developed between these soil prisms.
The Marston-Spangler theories and their applications to buried rigid pipes are presented by the
American Concrete Pipe Association (ACPA, 1988, 1994), which also references the basic technical
papers by Marston, Spangler, and others.
Modern soil-structure interaction analyses are usually performed using finite element methods with
nonlinear properties for both soil and reinforced concrete. Two computer programs incorporating the
finite element methods for soil-structure interaction are SPIDA and CANDE. SPIDA is described by the
American Concrete Pipe Association (ACPA, 1994) and by Heger et al. (1985). CANDE is described by
the U.S. Federal Highway Administration (FHWA, 1989). The soil model used in SPIDA is described by
Selig (1988); it is also one of the models that can be used in CANDE.
Nondimensional coefficients for determining earth loads and pressure distributions have been
developed for circular pipes in the four standard installation types specified in Clause 7.8.3.5. The total
vertical load acting over the outside diameter of the pipe and the total vertical reaction acting on the
bottom are determined by multiplying the weight of the prism of earth directly over the outside
diameter (prism load, W) by the vertical soil-structure interaction factor (arching factor), λ v. The total
equal and opposite lateral force acting on each side of the pipe is determined by multiplying the prism
load by the horizontal soil-structure interaction factor, λ h.
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C7.8.4.2.3 Earth load on box sections in standard installations
Similar to the procedure for circular pipe, nondimensional soil-structure interaction factors λ v and λ h are
provided in Clause 7.8.4.2.3 for determining the total vertical earth load acting on the top of the box and
the equal and opposite lateral soil pressures acting on the sides of the box, respectively. The soil-structure
interaction factors for box sections are based on previous practice and limited soil-structure interaction
analyses by the finite element method. Thus, for soil pressures, separate analyses are performed using the
design vertical earth load combined with a high limit and a low limit value for λ h to cover the range of
probable values. The governing condition from these two analyses is used for obtaining the critical force
effects.
C7.8.5 Earth pressure distribution from loads
C7.8.5.1 General
Refer to Clause C7.8.4.2.2 for a discussion of soil-structure interaction.
C7.8.5.2 Circular pipe in standard installations
C7.8.5.2.1 Pipe weight
Normally, a pipe is first placed on flat bedding. Accordingly, a narrow bedding is assumed in the standard
installation. In the initial stage of Construction, the pipe is assumed to press into the loosely compacted
soil in the middle region of the bedding and be supported over an arc of 30° subtended centrally over the
invert.
C7.8.5.2.2 Earth load
The vertical earth load is determined from the prism load, W, and the vertical arching factor, λ v . The same
load produces the vertical support reaction. The horizontal earth load is determined from the prism load,
W, and the horizontal arching factor, λ h . The vertical and horizontal components of earth pressure acting
on the exterior of the pipe are determined using the vertical and horizontal earth loads, and the pressure
distributions shown in Figure 7.12 together with nondimensional coefficients given in Tables 7.14 to 7.16.
The four standard installations, with their associated nondimensional earth load and pressure
distribution coefficients, are based on soil-structure interaction analyses using SPIDA (ACPA, 1994; Heger
et al., 1985; Heger, 1993; Heger, 1988).
C7.8.5.2.3 Water loads
The water weight is assumed to be supported using the same earth pressure distribution as specified for
support of vertical earth load.
C7.8.5.2.4 Live load
The vertical distributed live load due to wheel loads on the pavement is determined by spreading the load
from an individual wheel or from multiple adjacent wheels over the tire imprint areas and through the
earth as specified in Clause 6.9.6. Based on prior practice, the longitudinal stiffness and strength of the
pipe can be assumed to provide an additional longitudinal spread distance for the supporting length equal
to three-quarters of the height of the pipe as shown in Figure C7.5. This procedure allows the live load to
be distributed over an additional length 0.375Do . The live load effect on buried structures is assumed to be
distributed uniformly over the specified distance at the top of the buried structure.
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L
H
0.75 Do
Do
Ls = L + 1.75 (0.75 Do)
Figure C7.5
Effective supporting length of pipe
(See Clause C7.8.5.2.4.)
C7.8.5.3 Box sections in standard installations
C7.8.5.3.1 Box weight
The pressure on the bottom of the box section is assumed to be uniformly distributed across the
outside width of the box section.
C7.8.5.3.2 Earth load
The earth pressures on the top and bottom of the box are assumed to be uniformly distributed across
the outside width of the box section. This assumption is generally conservative for the top of the box
and, if the bottom bearing is flat or slightly concave, is also conservative for the bottom of the box. It
is important to maintain a flat or concave bottom bearing surface to avoid excessive concentration of
pressure toward the bottom midspan region.
C7.8.5.3.3 Live load
The vertical distributed live load acting at the top of the buried box section is determined by the
methods described in Clause C7.8.5.2.4. The supporting vertical reactions for live load are assumed to
be uniformly distributed across the outside width of the box section.
C7.8.6 Analysis
Analysis of buried concrete structures has been dealt with extensively in the technical literature. The
following references will be found useful in dealing this analysis: Heger (1963), FHWA (1992, 1994),
McGrath et al. (1988), ACPA (1987, 1994), and Smith (1978).
C7.8.7 Ultimate limit state
C7.8.7.1 Additional factors
For structures with a curved bottom, the usual load factor is multiplied by 1.1 to allow for the
increased difficulty of compacting soils below the haunches of such structures.
The load factor applied to compressive thrust is specified to be no greater than 1.0 for flexural,
shear, and radial tension strength determinations where compressive thrust reduces the required
reinforcement. This is to recognize that moment and shear can be increased when the soil installation
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falls short of the specified requirements, resulting in a more severe distribution of soil pressure without a
commensurate increase in compressive thrust.
C7.8.8 Strength design
C7.8.8.1 Flexure
C7.8.8.1.1 General
The flexural reinforcement is based on the ultimate limit state conforming to the criteria for flexure and
axial loads given in Clause 8.8.3.
The cross-sectional area of flexural reinforcement required by Clause 8.8.3 for concrete pipes subject to
combined bending and compressive thrust can be calculated from either of the following two equations
for As.
At the location of maximum moment,
2
As = ( gj s d − Nu − g ⎡ g (j s d ) − Nu (2j s d − h ) − 2Mu ⎤ )
⎣
⎦
g = α1 ϕc f’c
α1 = 0.85 for precast concrete structures. For cast-in-place structures, α shall be reduced when f’c exceeds
30 MPa in accordance with Clause 8.8.3.
The above equation for As gives the minimum reinforcement to limit the factored maximum tensile
stress to the yield strength. An alternative and more familiar form of this equation is
(h − a )
2
fy (d − a / 2)
Mu − Nu
As =
a=
fy As + Nu
g
The compression limit equation for maximum As gives the flexural tensile reinforcement area that
develops its yield strength when the flexural compression force in the concrete is 0.75 times the ultimate
compressive strength, based on a rectangular stress block. This limit is typically used in reinforced concrete
design practice to ensure ductile behaviour of flexural components (ACI, 1995) and may be expressed as
follows:
⎡ 380 g ′j d ⎤ 0.75N
c
u
⎥−
As ≤ ⎢
fy
⎢ 600 + fy fy ⎥
⎣
⎦
(
)
g’ = bf’c [0.85 – 0.008(f’c – 30)]
0.65 b f’c ≤ g’ ≤ 0.85 b f’c
C7.8.8.1.2 Maximum flexural reinforcement without stirrups or ties
The maximum amount of tensile reinforcement that can be developed for resisting flexural tension in pipe
without stirrups or ties is limited by the radial tension strength of the concrete surrounding the curved
inner cage reinforcement and by the compression strength at sections of maximum compression due to
combined flexure and compressive thrust. These limits to the flexural reinforcement area, obtained from
Clause 7.8.8.1.2, are explained below.
The equation for Asi for radial tension gives the maximum flexural tensile reinforcement area of
cross-section, whose yield strength can be developed by the radial tension strength of the concrete
surrounding the inner cage (convexly curved) reinforcement at sections of maximum factored inside
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flexural tension. The limiting radial tension strength, trc, as determined by tests on curved slabs and
evaluations of three-edge bearing test strengths and longstanding design practice for pipe, is given by
Heger and McGrath (1983) as follows:
trc = 0.111Frt jc fc′
Frt is a size factor that reduces the radial tension strength to account for effects associated with
concentration of greater force in each reinforcing wire or bar as pipe size increases above a reference
diameter of 1800 mm. For pipe diameters less than 1800 mm, Frt increases the radial tension strength.
Although pipe in this diameter range have spans that are lower than the 3 m span limit for application
of the Code, the following equation for Frt for pipe with internal diameters between 300 mm and
1800 mm is given for completeness:
Frt = 1+
(1800 − Di )
3000
for 300 mm < Di < 1800 mm
The empirical equations for Frt were determined from many three-edge bearing tests on pipes with
diameters ranging from 300 to 2400 mm.
The radial tension stress, tr , caused by the tensile force that develops the yield strength, Asi fy , in a
convexly curved reinforcement wire or bar with a radius, rs , is
tr =
j s Asi fy
b rs
When tr = trc , the reinforcement area, Asi , is the maximum area that can be stressed to fy without
producing radial tension stresses that exceed the ultimate radial tension strength, trc .
When a circular conduit is subjected to internal pressure, the resulting circumferential axial tensile
force does not produce radial tension, because the radial component of the circumferential force
counteracts the internal pressure. Therefore, only circumferential tension in reinforcement near the
inside surface that is associated with flexure produces radial tension. The amount of reinforcement
provided to resist internal pressure is not limited by radial tension strength.
C7.8.8.2 Design for shear
C7.8.8.2.1 Circular, elliptical, and arch pipe without stirrups or ties
The equation for Vb gives the basic shear (diagonal tension) strength of the conduit wall without
stirrups for flexurally cracked regions of the structure. A large number of tests on box sections, slabs,
beams (without stirrups), and frames show that under uniformly distributed loads, failure by diagonal
tension does not necessarily occur at the section of maximum shear, but typically at a section of high
shear where flexural cracks already exist. Evaluation of test data on slab and frame type components
with load distributions that simulate the distributions on buried conduits led to the finding that the
section where M/Vu d = 3.0 approximates the location of the critical section for failure by diagonal
tension. Evaluations of shear strengths achieved in these tests and in many three-edge bearing tests
(whose M/Vu d ratio approximates 3.0), provide the basis for the equation for Vb (Heger and McGrath,
1982). The tests show that increasing the reinforcement ratio, p, significantly increases the shear
strength. This is in agreement with the more general procedure for shear strength of slabs given in
Clause 8.9.4.1.
The equation for Fd gives a size factor based on tests showing that greater relative shear strength is
developed as wall thickness decreases, reflecting less stress concentration from flexural cracking, and a
greater proportion of concrete cover to wall thickness. This size factor is derived from three-edge
bearing test results and previous design practice for three-edge bearing strength (Heger and
McGrath, 1982). The following limits to increases in Fd apply to very small diameter pipes:
(a) Fd ≤ 1.3 for pipe with two cages or a single elliptical cage; and
(b) Fd ≤ 1.4 for pipe through 900 mm diameter with a single circular cage.
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The equation for Fc gives a curvature factor indicating a small reduction in the shear strength of
members with convexly curved tensile reinforcement that results because of the combined effects of shear
and radial tension in curved members (Heger and McGrath, 1982).
The equations for Fn give thrust factors that reflect the increase in shear strength produced by
compressive thrust and the decrease that results from tensile thrust. These equations are the same as the
thrust factor equation used in prior practice for reinforced concrete flexural members (ACI, 1995).
The critical section for shear, M/Vu d, is also influenced by thrust, since compressive thrust reduces
flexural cracking and tensile thrust increases flexural cracking.
Thus, an effective moment, Mnu , that accounts for the decreased or increased flexural tension produced
by thrust is used when determining the critical section for shear, Mnu /Vu d = 3.0. The equation for Mnu is
taken from ACI-318 (ACI, 1995).
C7.8.8.2.2 Box sections and segmental structures without stirrups or
ties
Recognizing that the top slabs of concrete boxes develop an arching action similar to concrete deck slabs
of girder bridges (e.g., Sheikh and Biddah, 1998), the design provisions in Clause 7.8.8.2.2 have been
revised to be parallel in spirit with the empirical design method of Section 8 for deck slabs.
When the empirical design method is not used, the general procedure for shear strength of slabs given
in Section 8 may be used for these buried structures. Usually, the sections within 2d of the support govern
the design so that Clause 8.10 may be used and the calculated shear strength will be significantly higher
than that calculated using Clause 8.9.
Generally, the shear design requirements given in Clause 7.8.8.2.2.2(b) are much easier to interpret and
apply using the alternative equation for vc . This procedure also reflects current industry practice for
determining the shear strength of single-cell box sections.
C7.8.8.2.3 Stirrup reinforcement for shear and radial tension
When flexural strength requirements exceed radial or diagonal tension limits, stirrups may be provided for
increased resistance to radial tension produced by flexural tension in the curved inner cage reinforcement
and resistance to diagonal tension caused by shears. In curved structures, stirrups required for diagonal
tension need to be designed for the full radial tension forces in addition to the shear effects as provided by
the equation for Avs . The maximum shear strength of the concrete that can be used to supplement the
stirrup reinforcement strength is the concrete shear strength given by the equation for Vc , but not more
than the shear strength used in prior practice.
Note that the ϕ associated with fv might theoretically be considered to be ϕ s instead of ϕ c . However,
the more conservative ϕ c should be used because fv should be governed by anchorage considerations
instead of yield strength.
The maximum transverse (i.e., circumferential) spacing of stirrups is limited to 0.75 times the effective
depth, taken as ϕ c d, so that each stirrup will cross a 45° diagonal tension crack which is also the assumed
inclination of the compressive strut in the truss analogy. The maximum longitudinal spacing of stirrups in
members with curvature that are subject to radial tension is the spacing between adjacent wires or bars.
This is because when concrete radial tension strength is exceeded, each curved tension element requires a
tie for the full radial component of tensile force in the wire of bar. For members with straight reinforcing
where stirrups are required for diagonal tension, there is no requirement that every wire or bar be
anchored by a stirrup. Thus, the maximum longitudinal spacing is set at a practical limit of 1.5 times the
effective depth to the reinforcement, d.
The stirrups should extend over all regions where concrete radial tension and/or shear stresses exceed
the design limits and at least to a point where Vu is not greater than Vc , plus the thickness of the conduit
wall, h. For circular pipe, the stirrups should extend over an additional arc length, Iθ , that accounts for a
disorientation of the pipe by as much as the orientation angle, θ . The angle θ should not be taken less
than a practical minimum of 10°. A positive means for locating the invert and crown in the field should be
provided when circular pipe contain stirrups, noncircular reinforcement, or cut-off reinforcement
(i.e., mats).
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When stirrups are used in the relatively thin slabs or walls of the structural types covered in
Section 7, special arrangements may be employed to achieve sufficient anchorage to develop the
design strength of the stirrup while also facilitating efficient fabrication procedures in a precast
concrete manufacturing plant.
Tests have demonstrated that stirrups can develop their design strength if they are anchored around
tension reinforcing at one end with their other (loop) end extending well into the compression zone.
A key to the fabrication efficiency achieved with these stirrup types is that because they do not have to
be anchored around reinforcement on the compression side, they can be inserted in one operation,
working from only one side of the precast unit prior to placing the form on that side.
Because the details used with these stirrup types are not covered by the anchorage provisions in
Clause 8.15.1.5, their developable anchorage strength needs to be determined from proper full-scale
tests, preferably on components similar to the component being designed to use them.
When stirrups are required for shear and radial tension strength, the maximum value of concrete
shear strength, Vc , that can be used to reduce the required area of stirrup reinforcement is limited to
0.166 ϕ c bd fc′ instead of the limiting value for shear strength without stirrups of 0.25 ϕ c bd fc′,
because after diagonal cracks have occurred and stirrup reinforcement has become effective, the
contribution of the concrete to shear resistance differs from that prior to the onset of diagonal
cracking.
Thus, no increase in this contribution is justified beyond that determined empirically to be effective
by reinforced concrete research that is the basis of prior reinforced concrete design practice.
C7.8.9 Serviceability limit state
C7.8.9.1 Control of cracking
The crack width control criteria in Clauses 8.12.2 and 8.12.3 may not be conservative for structures
with closely spaced reinforcement having a small diameter, such as the welded wire fabric and
plant-fabricated smooth wire or small-diameter rod cages used in precast concrete pipe and box
sections and in some cast-in-place conduits. Therefore, they are not applicable to these types of
structures.
For closely spaced welded wire fabric, or small diameter bars, which are mostly used in precast
concrete pipe and box sections, the crack width control factor, Fcr , is defined as four times the
estimated average maximum crack width in millimetres, caused by the design service load at 25 mm
toward the tension surface from the principal (circumferential) tensile reinforcing.
The equation for Fcr was developed semi-empirically from a theoretical and practical evaluation of
the variables that affect the average reinforcement strain between flexural cracks in fully cracked slabs
and walls of the types of structures covered by Clause 7.8.9.1, and from statistical evaluations of 0.25
mm crack test data from several hundred three-edge bearing tests on pipe and box sections with
inside diameters ranging from 1200 to 2400 mm, with 25 mm of nominal concrete cover thickness
over the tension reinforcement. Typical reinforcement was welded wire fabric with main wires spaced
at 50 mm and cross-wires spaced at 150 mm or more. Some test specimens used smooth cold drawn
wire reinforcement with cross-wires spaced up to 600 mm (Heger and McGrath, 1984). When the
calculated crack control factor, Fcr , equals 1.0, the average maximum crack width is predicted to be
0.25 mm at 25 mm from the outside of the tension reinforcement.
C7.8.10 Fatigue limit state
Welded wire fabric manufactured with resistance-welded cross-wires has long been in use for the top
slabs of precast concrete boxes, as well as for many other types of highway bridge and road
components, based on designs that use approximately the same fatigue limits as those used for bar
reinforcing.
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C7.8.11 Minimum reinforcement
C7.8.11.1 Parallel to span
Many tests on precast concrete pipe and boxes, as well as experience in the pipe industry, have confirmed
that to avoid brittle type failure it is not necessary to have sufficient reinforcement to develop the cracking
strength of the concrete. Also, commonly used design requirements for slab structures in many other
codes are similar to the requirements in Clause 7.8.11.1 (e.g., ACI, 1995).
C7.8.11.2 Perpendicular to span
The minimum amounts of reinforcement required by Clause 7.8.11.2 are based on the requirements of
Clause 8.12.6 for portions of cast-in-place structures with minimum earth cover of less than 600 mm.
Requirements for reinforcement are reduced for precast concrete structures of limited length with a
depth of cover of 600 mm or less, and for cast-in-place structures with more than 600 mm cover. The
required amount of reinforcement is reduced further for precast concrete structures of limited length with
more than 600 mm of cover so that only one layer of longitudinal reinforcement is required. These
reductions are justified by the fact that typical precast concrete pipe and box sections have demonstrated
successful performance using design standards that require only enough reinforcement perpendicular to
the span to hold the cages together for manufacture. The amount needed for this purpose varies with the
method of manufacture and should be determined by the product manufacturer. The absence of specific
requirements for shrinkage and temperature reinforcement in other standards for precast concrete pipe
and box sections are justified by the limited length of the precast components and the fact that they are
usually buried, thereby protecting them from severe drying and extremes of temperature variation.
C7.8.12 Distribution reinforcement
Top slabs of boxes with less than 600 mm of earth cover are considered to be similar to bridge deck slabs.
Thus, they are to meet the same minimum bottom reinforcement requirements for distributing
concentrated wheel loads longitudinally over the lane widths as required for bridge deck slabs. In addition,
for precast boxes with discontinuous joints between sections that do not transfer bending moments, a top
layer of distribution reinforcement is required to resist bending caused by wheel loads near the joints.
C7.8.13 Details of the reinforcement
Special requirements for detailing reinforcement for precast concrete pipe and box sections reflect
industry practice and anchorage requirements for the types of reinforcement and fabrication procedures
used in the concrete pipe industry. The stress limits given in Section A6.5.2 (Welds Splices and
Development of Circumferential Reinforcement) of ASCE 15-93 sometimes may control when determining
the yield strength to be used in design.
C7.8.14 Joint shear for top slab of precast concrete box sections with
depth of cover less than 0.6 m
Standard joints between adjacent units of precast concrete box sections usually incorporate a shiplap
configuration. Unless positive connection for joint shear transfer is provided at these joints, the differential
deflection caused by a wheel on one side of the joint could cause cracking in an asphaltic concrete, or thin
concrete pavement overlay. The minimum spacing of 800 mm is to allow two shear connectors to share
the load transfer between adjacent units.
C7.8.15 Construction
C7.8.15.3 Bedding for precast concrete structures
The standard installations for buried pipes are based on the concept that a loosely placed, uncompacted
bedding layer under the middle third of the pipe reduces the reaction forces near the invert of the pipe.
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Compacted bedding and embedment soil directly under the haunches promotes transfer of the
reaction force below the pipe away from the invert toward a more favourable location below the pipe
haunches. This transfer reduces the magnitude of the maximum moment at the pipe invert. It also
tends to reduce the severity of shear effects. Conversely, compacted bedding directly under the invert,
without very good compaction below the haunch region, increases the moment at the invert and
increases the severity of shear effects.
The bedding layer under the middle third of the pipe should be only firm enough to support the
pipe at the correct grade until the haunch material is compacted. When the backfill load is applied to
the pipe, the pipe should settle slightly into the bedding and compacted haunch material, increasing
support at the haunches rather than at the invert. The intent is to let the compacted haunch material
support the pipe as much as possible and maintain grade and alignment.
C7.8.15.5 Structural backfill
In order to reduce the load on the pipe, the soil immediately over the top of the pipe should not be
compacted for a depth of about one-third the outside pipe diameter above the top of the pipe, unless
the project specifications require compaction in this area.
C7.8.15.8 Trenches
Maintaining trench walls in a stable condition to permit safe construction operations and compliance
with safety standards typically requires the use of properly sloped trench walls, braced sheeting, or
trench boxes.
C7.8.15.8.2 Width control
Trench width should be sufficient to permit access for compaction in the bedding and haunch zones in
full compliance with the specified requirements. Design of structures for reduced earth load in narrow
trenches should take into account realistic field conditions related to the control of width and access
for compaction below the haunches.
C7.8.15.8.3 Sheathing removal
If sheathing is removed, it is important to place and compact the backfill in the voids that are created
by the sheathing removal.
C7.8.15.8.4 Trench shields and boxes
It may be necessary to restrain the installed structure by use of deadman anchors or other means.
Voids in the sidefill that are created by movement of a shield or box should be filled and compacted.
References
CSA (Canadian Standards Association)
G401-01
Corrugated steel pipe products
Other publications
AASHTO. 1993. Standard Specification for Highway Bridges. American Association of State Highway and
Transportation Officials, Washington, DC.
Abdel-Sayed, G. 1978. “Stability of Flexible Conduits Embedded In Soil.” Canadian Journal of Civil
Engineering, 5(3): 324–333.
Abdel-Sayed, G., Bakht, B., and Jaeger, L.G. 1994. Soil-Steel Bridges. McGraw-Hill, New York.
Abdel-Sayed, G., and Salib, S.R. 2002. “Minimum Depth of Soil Cover above Soil-Steel Bridges.”
Journal of Geotechnical and Geoenvironmental Engineering, pp. 672–681.
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© Canadian Standards Association
© Canadian Standards Association
ACI. 1995. Building Code Requirements for Reinforced Concrete, ACI 318, and Commentary. ACI 318R.
American Concrete Institute, Detroit.
ACPA. 1987. Concrete Pipe Design Manual, Seventh Printing. American Concrete Pipe Association, Vienna,
Virginia.
ACPA. 1988. Concrete Pipe Handbook, Third Printing. American Concrete Pipe Association, Vienna, Virginia.
ACPA. 1994. Concrete Pipe Technology Handbook, Second Printing. American Concrete Pipe Association,
Vienna, Virginia.
AISI. 1984. Handbook of Steel Drainage and Highway Construction Products, Canadian Edition. American
Iron and Steel Institute, Washington, DC.
ASTM. 1990. Standard Practice for Structural Design of Corrugated Steel Pipe, Pipe-Arches and Arches for
Storm and Sanitary Sewers and other Buried Applications. ASTM A 796-90, American Society for Testing and
Materials, Philadelphia.
ASTM. 1993. Standard Specifications for Corrugated Aluminum Alloy Structural Plate for Field-Bolted Pipe,
Pipe-Arches and Arches. ASTM B 746/B 746M-93, American Society for Testing and Materials, Philadelphia.
ASTM. 1996. Standard Specification for Corrugated Steel Box Culverts. ASTM A 964-96, American Society for
Testing and Materials, Philadelphia.
Bakht, B. 1981. “Soil-Steel Structure Response to Live Loads.” ASCE Journal of Geotechnical Engineering
Division, 107(GT6): 779–818.
Bakht, B., and Agarwal, A.C. 1988. “On Distress in Pipe-Arches.” Canadian Journal of Civil Engineering,
15(4): 589–595.
Bakht, B., Jaeger, L.G., and Mufti, A.A. 2003. “Buckling of Upper Portions of Conduit Wall under Shallow
Covers.” Report submitted to Atlantic Industries Ltd.
Brockbank, B., Chan, S., and Handley, D. 2001, “Holdich Creek Culvert Replacement with Precast Arch
Encased in High MSE Walls.” CSCE Annual Conference, held in Victoria, BC.
Byrne, P.M., Anderson, D.L., and Jitno, H. 1996. Seismic Analysis of Large Buried Culvert Structures.
Transportation Research Record, (1541): 133–139. Transportation Research Board, Washington, DC.
Byrne, P.M., Cheung, H., and Yan, L. 1987. “Soil Parameters for Deformation Analysis of Sand Masses.”
Canadian Geotechnical Journal, 24(3).
Choi, D.H., Kim, G.-N., and Byrne, P.M. 2004. “Evaluation of Moment Equation in the 2000 Canadian
Highway Bridge Design Code for Soil-Metal Arch Structures.” Canadian Journal of Civil Engineering, 31(2),
pp. 281–291.
Duncan, J.M., Byrne, P.M., Wong, K.S., and Mabry, P. 1980. Strength, Stress-Strain and Bulk Modulus
Parameters for Finite Element Analyses of Stresses and Movements in Soil Masses. Report No. UCB/GT/80-01.
Office of Research Services, College of Engineering, University of California, Berkeley.
Duncan, J.M., Seed, R.B., and Drawsky, R.H. 1984. Design of Corrugated Metal Box Culverts. Report
No. UCB/GT/84-10. Department of Civil Engineering, University of California, Berkeley.
FHWA. 1989. CANDE-89 Culvert Analysis and Design Computer program User Manual. Federal Highway
Administration. Publication No. FHWA-RD-89-169. U.S. Department of Transportation, Washington, DC.
(Available from McTrans Center, 512 Weil Hall, Gainesville, Florida).
FHWA. 1991. Durability of Special Coatings for Corrugated Steel Pipe. Federal Highway Administration.
Publication No. FHWA-FLP-91-006. U.S. Department of Transportation, Washington, DC.
FHWA. 1992. BOXCAR Version 1.0 — Micro Computer Program and User and Programmer Manual. Federal
Highway Administration. Publication No. FHWA-IP-89-018. U.S. Department of Transportation,
Washington, DC. (Available from McTrans Center 512 Weil Hall, Gainesville, Florida).
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FHWA. 1994. PIPECAR Version 2.1 — Micro Computer Program and User and Programmer Manual.
Federal Highway Administration. Publication No. FHWA-IP-89-019. U.S. Department of Transportation,
Washington, DC. (Available from McTrans Center, 512 Weil Hall, Gainesville, Florida).
Girgis, Y. 1993. Three-dimensional Analysis of Soil-Steel Structures. PhD dissertation, Dept. of Civil
Engineering, University of Windsor, Windsor, Ontario.
Haggag, A.A. 1989. Structural Backfill Design for Corrugated Metal Buried Structures. PhD dissertation,
Dept. of Civil Engineering, University of Massachusetts.
Heger, F.J. 1963. “Structural Behaviours of Circular Reinforced Concrete Pipe — Development of
Theory.” Journal of the American Concrete Institute, November 1963.
Heger, F.J. 1988. “New Installation Designs for Buried Concrete Pipe. Pipeline infrastructure.”
Proceedings of the International Conference, American Society of Civil Engineers, New York,
pp. 117–135.
Heger, F.J. 1993. “New Standard Installations for Concrete Pipe — Key to Improved Design Practice.
Structural Performance of Pipe.” Proceedings of an International Conference on Structural
Performance of Pipes, Columbus, Ohio.
Heger, F.J., and Liepins, A.A. 1985. “Stiffness of Flexurally Cracked Reinforced Concrete Pipe.” Journal
of the American Concrete Institute, 82(3): 331–342.
Heger, F.J., Liepins, A.A., and Selig, E.T. 1985. “SPIDA: An Analysis and Design System for Buried
Concrete Pipe. Advances in Underground Pipeline Engineering.” Proceedings of the International
Conference, American Society of Civil Engineers, pp. 143–154.
Heger, F.J., and McGrath, T.J. 1982. “Shear Strength of Pipe, Box-Sections and Other One-Way Flexural
Members.” Journal of the American Concrete Institute, 79(6).
Heger, F.J., and McGrath, T.J. 1983. “Radial Tension Strength of Pipe and Other Curved Flexural
Members.” Journal of the American Concrete Institute, 80(1).
Heger, F.J., and McGrath, T.J. 1984. “Crack Width Control in Design of Reinforced Concrete Pipe and
Box Sections.” Journal of the American Concrete Institute, 81(2): 149–157.
Idriss, I.M. 1990. “Response of Soft Soil Sites during Earthquakes.” H. Bolton Seed Memorial
Proceedings, Vol. 2. BiTech Publishers, Vancouver.
Luscher, U. 1966. “Buckling of Soil-Surrounded Tubes.” ASCE Journal of the Soil Mechanics and
Foundation Division, 92(SM6): 211–228. (Discussed in 93(SM2): 163; 93(SM3): 179–183; 93(SM5):
337–340; Author’s closure in 94(SM4): 1037–1038).
McGrath, T.J., Tigue, D.B., and Heger, F.J. 1988. PIPECAR and BOXCAR — Microcomputer Programs for
the Design of Reinforced Concrete Pipe and Box Sections. Transportation Research Record (1191):
99–105. Transportation Research Board, Washington, DC.
Meyerhof, G.G., and Baikie, L.D. 1963. Strength of Steel Culvert Sheets Bearing against Compacted Sand
Backfill. Highway Research Record, 30: 1–19. Highway Research Board, Washington, DC.
Mirza, C., and Porter, W.A. 1981. “Construction Considerations and Controls for Soil-Steel Bridge
Structures.” Canadian Journal of Civil Engineering, 8(4): 519–534.
Moore, I.D. 2001. “Culverts and Buried Pipelines,” in R.K. Rowe, ed., Geotechnical and
Geoenvironmental Handbook, Kluwer Academic Publishers, pp. 541–568.
Mufti, A.A., Bakht, B., and Jaeger, L.G. 1989. “Mechanics of Behaviour of Soil-Steel Structures.”
Proceedings of the CSCE Annual Conference, St. John’s, Newfoundland, Vol. 1A, pp. 130–150.
OHBDC. 1991. Ontario Highway Bridge Design Code. Ministry of Transportation of Ontario,
Downsview, Ontario.
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© Canadian Standards Association
Proctor, P., and Seow, K. 2000. “Bridge Replacement Using Low Profile Three Hinged Precast Arch in
Newfoundland.” CSCE Annual Conference, held in London, Ontario, proceedings on CD.
Selig, E.T. 1988. “Soil Parameters For Design of Buried Pipelines. Pipeline Infrastructure.“ Proceedings of
the International Conference, American Society of Civil Engineers, New York, pp. 99–116.
Segrestin, P., and Brockbank, W.J. 1995. “Precast Arches as Innovative Alternative to Short-Span Bridges.”
Proceedings, 4th International Bridge Engineering Conference, San Francisco, pp. 219–226.
Sheikh, S.A., and Biddah, A. 1998. “Behaviour of Concrete Box Culverts and Their Strengthening by Fibre
Reinforced Plastic.” Department of Civil Engineering, University of Toronto, report prepared for the
Ministry of Transportation of Ontario.
Smith, W.W. 1978. “Stresses in Rigid Pipe.” ASCE Transportation Engineering Journal, 104(TE3).
University of British Columbia. 1995. Durability of Buried Galvanized Steel Structures in British Columbia.
Vancouver.
Weinreb, D., and Wu, P.L. 1991. Design and Construction of Precast Concrete Arch Structures (TechSpan).
1991. CSCE Annual Conference, held in Vancouver, pp. 365–374.
White, H.L., and Layer, J.P. 1960. The Corrugated Metal Conduit as a Compression Ring. Highway Research
Board, Proceedings of the Annual Meeting, 39: 389–397.
Youd, T.L., and Beckman, C.J. 1996. Highway Culvert Performance during Past Earthquakes. National Centre
for Earthquake Engineering Research, Buffalo.
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Section C8 — Concrete structures
C8.1
C8.3
C8.4
C8.4.1
C8.4.1.1
C8.4.1.2
C8.4.1.3
C8.4.1.4
C8.4.1.5
C8.4.1.6
C8.4.1.7
C8.4.1.8
C8.4.2
C8.4.2.1
C8.4.2.2
C8.4.3
C8.4.3.1
C8.4.3.2
C8.4.4
C8.4.4.5
C8.4.5
C8.4.5.1
C8.4.5.2
C8.4.6
C8.5
C8.5.1
C8.5.2
C8.5.2.1
C8.5.2.2
C8.5.2.3
C8.5.3
C8.5.3.1
C8.5.3.2
C8.5.4
C8.6
C8.6.1
C8.6.2
C8.6.2.1
C8.6.2.2
C8.6.2.3
C8.6.2.4
C8.6.2.5
C8.6.2.6
C8.6.2.7
C8.6.3
C8.7
C8.7.1
C8.7.2
C8.7.3
C8.7.4
C8.7.4.1
Scope 304
Symbols 304
Materials 305
Concrete 305
Compliance with CAN/CSA-A23.1/CAN/CSA-A23.2 305
Concrete strength 306
Thermal coefficient 306
Poisson’s ratio 306
Shrinkage 307
Creep 307
Modulus of elasticity 308
Cracking strength 308
Reinforcing bars and deformed wire 309
Reinforcing bars 309
Steel wires and welded wire fabric 309
Tendons 309
General 309
Stress-strain relationship 309
Anchorages, mechanical connections, and ducts 309
Ducts 310
Grout 310
Post-tensioning 310
Other applications 310
Material resistance factors 310
Limit states 311
General 311
Serviceability limit states 311
General 311
Cracking 311
Deformation 311
Fatigue limit state 311
Reinforcing bars 311
Tendons 312
Ultimate limit states 312
Design considerations 312
General 312
Design 312
General 312
Member stiffness 313
Imposed deformations 313
Stress concentrations 313
Secondary effects due to prestress 313
Redistribution of force effects 313
Directional change of tendons 313
Buckling 316
Prestressing 317
Stress limitations for tendons 317
Concrete strength at transfer 317
Grouting 317
Loss of prestress 317
General 317
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C8.7.4.2 Losses at transfer 319
C8.7.4.3 Losses after transfer 320
C8.8
Flexure and axial loads 322
C8.8.2
Assumptions for the serviceability and fatigue limit states 322
C8.8.3
Assumptions for the ultimate limit states 323
C8.8.4
Flexural components 323
C8.8.4.1 Factored flexural resistance 323
C8.8.4.2 Tendon stress at the ultimate limit states 324
C8.8.4.3 Minimum reinforcement 324
C8.8.4.4 Cracking moment 324
C8.8.4.5 Maximum reinforcement 325
C8.8.4.6 Prestressed concrete stress limitations 325
C8.8.5
Compression components 325
C8.8.5.1 General 325
C8.8.5.4 Maximum factored axial resistance 327
C8.8.5.5 Biaxial loading 327
C8.8.5.6 Reinforcement limitations 327
C8.8.5.8 Hollow rectangular components 327
C8.8.6
Tension components 328
C8.8.7
Bearing 328
C8.9
Shear and torsion 328
C8.9.1
General 328
C8.9.1.1 Consideration of torsion 328
C8.9.1.2 Regions requiring transverse reinforcement 328
C8.9.1.3 Minimum amount of transverse reinforcement 328
C8.9.1.4 Design yield strength of transverse reinforcement 328
C8.9.1.5 Effective shear depth 329
C8.9.1.6 Effective web width 329
C8.9.1.7 Variable-depth components 329
C8.9.1.8 Reduced prestress within transfer length 329
C8.9.2
Design procedures 329
C8.9.2.1 Flexural regions 329
C8.9.2.2 Regions near discontinuities 329
C8.9.2.3 Interface regions 329
C8.9.2.4 Slabs, walls, and footings 330
C8.9.2.5 Detailed analysis 330
C8.9.3
Sectional design model 330
C8.9.3.1 Sections near supports 330
C8.9.3.3 Factored shear resistance 330
C8.9.3.4 Determination of Vc 330
C8.9.3.5 Determination of Vs 330
C8.9.3.6 Determination of β and θ for non-prestressed components (simplified method) 330
C8.9.3.7 Determination of β and θ (general method) 331
C8.9.3.8 Determination of εx 332
C8.9.3.9 Proportioning of transverse reinforcement 333
C8.9.3.10 Extension of longitudinal reinforcement 334
C8.9.3.11 Longitudinal reinforcement on the flexural tension side 334
C8.9.3.12 Longitudinal reinforcement on the flexural compression side 335
C8.9.3.13 Compression fan regions 335
C8.9.3.14 Anchorage of longitudinal reinforcement at exterior supports 336
C8.9.3.15 Transverse reinforcement for combined shear and torsion 336
C8.9.3.17 Factored torsional resistance 337
C8.9.3.18 Cross-sectional dimensions to avoid crushing for combined shear and torsion 337
C8.9.3.19 Determination of ε x for combined shear and torsion 337
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C8.9.4
Slabs, walls, and footings 337
C8.9.4.1 Critical sections for shear 337
C8.9.4.3 Two-way action 337
C8.9.5
Interface shear transfer 337
C8.9.5.1 General 337
C8.9.5.2 Values of c and µ 338
C8.9.5.4 Anchorage of shear-friction reinforcement 339
C8.10
Strut-and-tie model 339
C8.10.1 General 339
C8.10.2 Structural idealization 340
C8.10.3 Proportioning of a compressive strut 340
C8.10.3.2 Effective cross-sectional area of strut 340
C8.10.3.3 Limiting compressive stress in strut 340
C8.10.3.4 Reinforced strut 342
C8.10.4 Proportioning of a tension tie 342
C8.10.4.2 Anchorage of tie 342
C8.10.5 Proportioning of node regions 342
C8.10.5.1 Stress limits in node regions 342
C8.10.5.2 Satisfying stress limits in node regions 342
C8.10.6 Crack control reinforcement 343
C8.11
Durability 343
C8.11.1 Deterioration mechanisms 343
C8.11.2 Protective measures 344
C8.11.2.1 Concrete quality 344
C8.11.2.2 Concrete covers and tolerances 346
C8.11.2.3 Corrosion protection for reinforcement, ducts, and metallic components 347
C8.11.2.4 Sulphate-resistant cements 347
C8.11.2.6 Drip grooves 347
C8.11.3 Detailing for durability 348
C8.11.3.1 Reinforcement detailing 348
C8.11.3.2 Confining reinforcement cage 348
C8.11.3.3 Debonding of pretensioned strands 348
C8.12
Control of cracking 349
C8.12.1 General 349
C8.12.2 Distribution of reinforcement 349
C8.12.3 Reinforcement 349
C8.12.3.1 Maximum crack width 349
C8.12.3.2 Calculation of crack width 349
C8.12.4 Crack control in the side faces of beams 349
C8.12.5 Flanges of T-beams 350
C8.13
Deformation 350
C8.13.1 General 350
C8.13.2 Dimensional changes 350
C8.13.3 Deflections and rotations 350
C8.13.3.2 Refined method 350
C8.13.3.3 Simplified method 350
C8.13.3.4 Total deflection and rotation 350
C8.14
Details of reinforcement and special detailing requirements 351
C8.14.1 Hooks and bends 351
C8.14.2 Spacing of reinforcement 351
C8.14.2.1 Reinforcing bars 351
C8.14.2.2 Tendons 351
C8.14.3 Transverse reinforcement for flexural components 352
C8.14.4 Transverse reinforcement for compression components 352
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C8.14.4.2 Spirals 352
C8.14.5 Reinforcement for shear and torsion 352
C8.15
Development and splices 352
C8.15.1 Development 352
C8.15.2 Development of reinforcing bars and deformed wire in tension 352
C8.15.3 Development of reinforcing bars in compression 352
C8.15.4 Development of pretensioning strand 352
C8.15.5 Development of standard hooks in tension 353
C8.15.5.1 General 353
C8.15.5.3 Factors modifying hook development length 353
C8.15.7 Development of welded wire fabric in tension 353
C8.15.9 Splicing of reinforcement 353
C8.15.9.4 Splices of deformed bars in compression 354
C8.16
Anchorage zone reinforcement 354
C8.16.1 General 354
C8.16.2 Post-tensioning anchorage zones 354
C8.16.2.1 General 354
C8.16.2.2 General zone 356
C8.16.2.3 Local zone 366
C8.16.3 Pretensioning anchorage zones 368
C8.16.5 Intermediate anchorages 368
C8.16.6 Anchorage blisters 368
C8.16.7 Anchorage of attachments 369
C8.16.7.1 General 369
C8.16.7.2 Transfer of tensile load from anchor to concrete 369
C8.16.7.3 Transfer of shear load from anchor to concrete 370
C8.16.7.4 Reinforcement 371
C8.16.7.5 Compressive resistance of concrete 372
C8.16.7.6 Design requirements for anchors 372
C8.17
Seismic design and detailing 373
C8.18
Special provisions for deck slabs 373
C8.18.1 Design methods 373
C8.18.2 Minimum slab thickness 373
C8.18.3 Allowance for wear 374
C8.18.4 Empirical design method 374
C8.18.4.1 General 374
C8.18.4.2 Cast-in-place deck slabs 374
C8.18.4.3 Cast-in-place deck slabs on precast panels 374
C8.18.4.4 Full-depth precast panels 374
C8.18.5 Diaphragms 375
C8.18.6 Edge stiffening 375
C8.18.7 Distribution reinforcement 375
C8.19
Composite construction 375
C8.19.2 Flexure 375
C8.19.3 Shear 375
C8.19.4 Semi-continuous structures 376
C8.19.4.1 General 376
C8.19.4.2 Positive moments 376
C8.19.4.3 Negative moments 378
C8.20
Concrete girders 378
C8.20.1 General 378
C8.20.3 Flange thickness for T- and box girders 378
C8.20.4 Isolated girders 378
C8.20.5 Top and bottom flange reinforcement for cast-in-place T- and box girders 379
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C8.21
Multi-beam decks 379
C8.22
Segmental construction 379
C8.22.1 General 379
C8.22.2 Additional ducts and anchorages 379
C8.22.2.2 During construction 379
C8.22.2.3 Future strengthening 380
C8.22.4 Deviators for external tendons 380
C8.22.6 Special provisions for various bridge types 380
C8.22.6.1 Precast segmental 380
C8.22.6.3 Balanced cantilever construction 380
C8.22.6.4 Span-by-span construction 380
C8.22.6.5 Incrementally launched construction 381
C8.22.7 Precast segmental beam bridges 382
C8.22.7.2 Joints 382
C8.23
Concrete piles 383
C8.23.2 Specified concrete strength 383
C8.23.4 Splices 383
C8.23.5 Pile dimensions 383
C8.23.7 Prestressed concrete piles 383
C8.23.7.1 Effective prestress 383
C8.23.7.2 Concrete stress limitations 383
C8.23.7.3 Factored resistance 383
C8.23.7.4 Sections within development length 383
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Section C8
Concrete structures
C8.1 Scope
The concrete structural components may be reinforced with non-prestressed or prestressed reinforcement
or both, thus permitting partial prestressing. Although prestressing forces can be introduced in various
ways, Section 8 is based on the use of high-strength steel prestressing tendons. The post-tensioning
tendons may be internal or external but they must be protected by grouting. The use of low-density or
semi-low-density concretes should be based on the availability of suitable low-density or semi-low-density
aggregates.
A majority of the requirements in Section 8 have been based on Section 8 of the Ontario Highway Bridge
Design Code (OHBDC 1991) and the American Association of State Highways and Transportation Officials
LRFD Bridge Design Specifications (AASHTO LRFD 1994) with appropriate modifications.
The Section does not provide requirements for concrete poles. The requirements for concrete poles are
given in CSA A14.
C8.3 Symbols
CSA A23.3 symbols have been used wherever possible. The following additional symbols have been used
in this Commentary:
the longitudinal reinforcement in the flange, mm2
Al
At
the transverse reinforcement in the flange, mm
C
the force in the concrete strut, N
Cc1
the factored compressive force in the overhanging portion of the flange, as shown in Figure C8.8,
N
Cc2
the factored compressive force in the web, as shown in Figure C8.8, N
Cc
the factored compressive force in the equivalent rectangular stress block, N
CRt
the prestress loss due to creep up to t days after transfer, MPa
C’s
the factored force in the compression reinforcement, N
dk
the depth of corrugated shear keys, mm
ds
the distance from extreme compression fibre to the centroid of the non-prestressed tension
reinforcement, mm
d
the distance from the extreme compression fibre to the centroid of the non-prestressed
compression reinforcement, mm
the modulus of elasticity of the bearing plate, MPa
Eb
Fst
the total prestressing force at transfer, N
fb
the stress in anchor plate at a section taken at the edge of the wedge hole or holes, MPa
fca
the compressive stress in the strut, MPa
f min
the algebraic minimum stress, with tension positive and compression negative, MPa
fp
the stress at the extreme fibre in tension due to moment acting on the precast portion of a
composite section, MPa; or the stress in prestressing steel, MPa
fpe
the compressive stress in concrete due to effective prestress at the extreme fibre of a section at
which tensile stresses can be caused by live load, MPa
fsr
the stress range in reinforcing bars, MPa
f2
the principal compressive stress in concrete, MPa
hf
the depth of compression flange, mm
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L
lb
lt
MD
Msec
Mct
M∞
Mp
Mst
P
rh
SF
SHt
sθ
T
Tp
Ts
t’
tf min
V
w
yt
βf
βs
γ
εc
εp
ε s2
ε2
ρp
τ
ψ s2
Commentary on CAN/CSA-S6-06,
Canadian Highway Bridge Design Code
the length of base plate, mm
the flexural bond length, mm
the transfer length, mm
the moment due to dead load at transfer, N•mm
the moment caused by restraint of deformation due to the primary prestressing force, N•mm
the moment computed by applying the loads and/or prestressing force to the completed
structure, N•mm
the final moment at any section along a structure constructed in stages, N•mm
the moment acting on the precast portion of a composite section, N•mm
the moment obtained by superimposing moment due to load and/or prestressing force
applied in stages, N•mm
the applied point load, N
the ratio of base radius to height of rolled-on transverse deformations
the shape factor function in Clause C8.7.4.3
the shrinkage loss up to t days after transfer, MPa
the spacing of diagonal cracks inclined at θ to the longitudinal reinforcement, mm
tension in longitudinal reinforcement, N; or
tension in interface reinforcement, N
the factored tensile force in prestressing tendons, N
the factored tensile force in reinforcing bars, N
the width of the strut at depth a from the loaded face, mm
the minimum flange thickness, mm
shear at interface, N
the average crack opening at crack interface, mm; or
the dimension of the strut in the direction of the thickness of the component, mm
the distance from the centroidal axis of the gross section resisting live load to the extreme
fibre in tension, mm
a function corresponding to the development of delayed plasticity with time, depending on
notional thickness
a function corresponding to the change of shrinkage with time, depending on notional
thickness
a nondimensional factor in Clause C8.7.4.2.5
the compressive strain in concrete
the strain in prestressing steel at stress fp
a function of notional thickness for shrinkage
the principal compressive strain, taken as a positive quantity, in cracked concrete due to
factored loads
the ratio of the area of prestressing steel to that of the gross concrete area, Aps /Ag
a function of the age at transfer in Clause C8.7.4.3
a function of notional thickness for creep
C8.4 Materials
C8.4.1 Concrete
C8.4.1.1 Compliance with CAN/CSA-A23.1/CAN/CSA-A23.2
The specifications governing the use of air entrainment agents, supplementary cementing materials
and chemical admixtures are indirectly referenced in CAN/CSA-A23.1. The applicable Standards
governing the use of these materials are as follows:
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(a) air entrainment: CSA CAN3-A266.1-M78;
(b) supplementary cementing materials: CAN/CSA-A23.5-M86; and
(c) chemical admixtures: CSA CAN3-A266.2-M78.
C8.4.1.2 Concrete strength
A minimum concrete strength of 30 MPa has been specified to enhance durability. Lower strength
concretes do not possess the durability characteristics necessary for bridge construction and may be used
only if Approved.
The minimum specified strength has been set at 35 MPa for prestressed concrete as it is generally not
economical or desirable to use lower strength for prestressed concrete work.
The availability of concrete with strengths in excess of 50 MPa should be confirmed before specifying it.
Higher strengths may require prequalification of concrete suppliers and contractors and special
construction techniques. The use of higher strength concrete can result in slender components and
attention should be given to constructability and instability aspects during the design stage. PCI Special
Issue (1993) provides a number of articles dealing with high-strength prestressed concrete.
The structural response of concrete with compressive strengths less than 85 MPa is adequately
predicted using the mathematical models contained in the Code. When concrete strengths exceed
85 MPa, special consideration of the structural response of this material may be warranted
(ACI Committee 363, 1984).
C8.4.1.3 Thermal coefficient
The thermal coefficient of linear expansion for concrete varies due to the composite nature of normal
Portland cement concrete, and will depend largely on the type and proportions of aggregate and cement
used, the moisture content of the hardened concrete, and the method of curing employed.
Table C8.1 gives typical values of thermal coefficients for normal-density concrete (Bonnel and Harper
1951). In order to simplify calculations, it is customary to use the same value of thermal coefficient for
both reinforcement and concrete. Low- and semi-low-density concretes typically exhibit a coefficient of
–6
thermal expansion of about 7 to 11 × 10 /°C. In cases where increased accuracy in determining the
thermal expansion is required, thermal coefficient values characteristic of the low- and semi-low-density
concrete being used should be established.
Table C8.1
Typical thermal coefficients for concrete
(See Clauses C3.9.4.5 and C8.4.1.2.)
Coefficient of linear thermal expansion × 106/°C
Type of aggregate
Air-cured
concrete
Water-cured
concrete
Air-cured and
wetted concrete
Gravel
Granite
Quartzite
Dolerite
Sandstone
Limestone
Portland Stone
13.1
9.5
12.8
9.5
11.7
7.4
7.4
12.2
8.6
12.2
8.5
10.1
6.1
6.1
11.7
7.7
11.7
7.9
8.6
5.9
6.5
C8.4.1.4 Poisson’s ratio
Poisson’s ratio for low- and semi-low-density concrete has been found to vary between 0.15 and 0.25. As
a result, no alternative value for Poisson’s ratio for low- and semi-low-density concrete has been specified.
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C8.4.1.5 Shrinkage
C8.4.1.5.1 General
The requirement that design values of shrinkage strains in low-density and semi-low-density concrete
be determined on the basis of test data on the same mix of concrete to be used on construction has
been maintained from the previous edition of the Code. Some low- and semi-low-density concretes
have lower shrinkage than normal-density concrete, especially at early ages. One-year shrinkage values
for low- and semi-low-density concrete can vary from 450 to 750 micro-strains for 25 MPa concrete
and from 600 to 950 micro-strains for 50 MPa concrete.
For normal-density concrete, the requirement that design values of shrinkage strains for concrete in
segmental bridges be determined on the basis of test data has been removed. The choice of whether
to use test data or the provisions of Clause 8.4.1.5.2 is most appropriately made in consideration of
the consequences of possible inaccuracies in shrinkage strains calculated from Clause 8.4.1.5.2
compared to test data. This reflects current practice in the design and construction of segmental
bridges, which has in recent years produced no significant problems in performance that can be
attributed to problems with analytical models for calculating shrinkage strains.
C8.4.1.5.2 Calculation of shrinkage strain
The provisions of Clause 8.4.1.5.2 have been adapted from the CEB-FIP Model Code 1990.
Several parameters in the CEB-FIP provisions have been assigned fixed values in the Code to reflect
current Canadian practice. These include the following:
(a) βsc , a coefficient that depends on the type of cement, which has been set to 5 for normal or
rapid-hardening cements;
(b) t1, which has been set to 1 day;
(c) h0, which has been set to 100 mm; and
(d) fcm0, which has been set to 10 MPa.
The quantity a in Clause 8.4.1.5.2 is used to convert specified compressive strength at 28 days to
mean compressive strength at 28 days. Mean compressive strength is used in the corresponding
Model Code provisions.
The surface areas used to determine rv should include only the area that is exposed to atmospheric
drying. For poorly vented enclosed cells, only 50% of the interior perimeter should be used in
calculating the surface area.
C8.4.1.6 Creep
C8.4.1.6.1 General
Clause 8.4.1.6.2 has been adapted from the CEB-FIP Model Code 1990. The relation between creep
strain and stress can be considered linear for stresses below the limit prescribed in Clause 8.4.1.6.2.
The requirement that design values of time-varying strains due to stress in low-density and
semi-low-density concrete be determined on the basis of test data on the same mix of concrete to be
used on construction has been maintained from the previous edition of the Code.
For normal-density concrete in segmental bridges, the requirement that design values of
time-varying strains due to stress be determined on the basis of test data has been removed. The
choice of whether to use test data or the provisions of Clause 8.4.1.6.2 is most appropriately made in
consideration of the consequences of possible inaccuracies in creep strains calculated from
Clause 8.4.1.6.2 compared to test data. This reflects current practice in the design and construction of
segmental bridges, which has in recent years produced no significant problems in performance that
can be attributed to problems with analytical models for calculating creep strains.
C8.4.1.6.2 Calculation of time-varying strain due to stress
Total time-varying strain due to a constant stress is the sum of an instantaneous strain and a creep
strain.
An integral expression for the principle of superposition is given in the CEB-FIP Model Code 1990.
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C8.4.1.6.3 Creep coefficient
Several parameters in the CEB-FIP provisions have been assigned fixed values in the Code to reflect current
Canadian practice. These include the following:
(a) t1, which has been set to 1 day;
(b) h0, which has been set to 100 mm; and
(c) fcm0 , which has been set to 10 MPa.
The quantity a in Clause 8.4.1.6.3 is used to convert specified compressive strength at 28 days to mean
compressive strength at 28 days. Mean compressive strength is used in the corresponding Model Code
provisions.
The surface areas used to determine rv should include only the area that is exposed to atmospheric
drying. For poorly vented enclosed cells, only 50% of the interior perimeter should be used in calculating
the surface area.
C8.4.1.7 Modulus of elasticity
The secant modulus of elasticity, Ec , is defined as the slope of the line that passes through the 0.4 f’c point
as shown in Figure C8.1. The value of Ec is approximate and is strongly influenced by the aggregate
fraction in the mix and the modulus of elasticity of the aggregate.
fc
f’c
0.4f’c
Ec
1
ec
Figure C8.1
Modulus of elasticity, Ec
(See Clause C8.4.1.7.)
The expression for calculating the modulus of elasticity is based on CSA A23.3-94.
C8.4.1.8 Cracking strength
This term has been adopted instead of the usual term “modulus of rupture” to define the stress level at
which concrete cracks. The tensile strength is influenced by factors that are difficult to include in
calculations, e.g., the restraint of shrinkage and thermal strains. The selected value of 0.4 fc′ is considered
to be a conservative estimate of the cracking strength of large concrete sections used typically in bridge
construction (FIP 1984). Research suggests that larger concrete sections exhibit more shrinkage cracking
than smaller sections, and as a result, their value of fcr is slightly lower than the value given in earlier design
codes. For high-strength low- and semi-low-density concrete, the use of more detailed information
regarding the concrete cracking strength may be warranted. The cracking strength of low- and
semi-low-density concrete, as a percentage of compressive strength, has been found to decrease for
higher strength concretes.
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C8.4.2 Reinforcing bars and deformed wire
C8.4.2.1 Reinforcing bars
Grade W reinforcing bars conforming to CAN/CSA-G30.18 are weldable and have a more closely
controlled chemical composition which results in a more predictable and more ductile stress-strain
response. Grade R reinforcing bars conforming to CAN/CSA-G30.18 with an elongation as low as 6%
as compared to the 10% for Grade W bars can result in unsatisfactory behaviour under extreme loads.
Therefore, the minimum elongation at rupture requirement for Grade R bars has been increased to
that for Grade 500W bars. About 80% of the Grade R bars produced by most Canadian mills normally
meet the increased elongation and tighter bend test requirements. Grade 300R bars are normally only
available as 10M and 15M.
C8.4.2.2 Steel wires and welded wire fabric
Welded wire fabric conforming to CSA G30.5 should have welded intersections not farther apart than
200 mm in the direction of the principal reinforcement, and with cross-wires having a cross-sectional
area of not less than 35% of that of the principal reinforcement.
Welded deformed wire fabric conforming to CSA G30.15 should have welded intersections not
farther apart than 400 mm in the direction of the principal reinforcement, and with cross-wires having
a cross-sectional area of not less than 35% of that of the principal reinforcement.
C8.4.3 Tendons
C8.4.3.1 General
Wires and stress-relieved strands are not included in Section 8, as they are no longer cost-effective and
are not used for new construction. Section 14 provides data required for these steels for bridge
evaluation purposes.
C8.4.3.2 Stress-strain relationship
The following mathematical stress-strain relationships for low-relaxation 7-wire prestressing strand
may be used:
For εp ≤ 0.008
fp = εp Ep
For εp > 0.008
Grade 1760 Strand:
fp = 1749 −
0.433
≤ 0.98fpu
e p − 0.00614
Grade 1860 Strand:
fp = 1848 −
0.517
≤ 0.98fpu
e p − 0.0065
High-strength bars may be assumed to exhibit a bilinear stress-strain relationship with a slope Ep
equal to 205 000 MPa prior to yield point and a slope of zero beyond the yield point.
The modulus of elasticity of high-strength bars with couplers can be as low as 195 000 MPa and
should be established by tests.
C8.4.4 Anchorages, mechanical connections, and ducts
The dimensions of anchorages are dependent on the jacking force and the concrete strength at
transfer and are established by the manufacturers of post-tensioning systems. The provisions in the
Code place no restriction on bearing stresses immediately behind post-tensioning anchorages, as a
number of structures with anchorage bearing stresses considerably higher than those recommended
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by ACI-ASCE Committee 343 (1988) have been successfully built in Canada over the years. The anchorage
zones should, however, be adequately reinforced in accordance with Clause 8.16.
Anchorages and mechanical connections should meet the requirements given in FIP (1972).
The dynamic tests specified in AASHTO (1991) may be used for anchorages and couplers of unbonded
external tendons.
C8.4.4.5 Ducts
C8.4.4.5.2 Size
Clause 8.4.4.5.2 is based on OHBDC (1991) and AASHTO (1983).
For long tendons, where the tendons may be placed by the pull-through method, consideration should
be given to using sheaths with a cross-sectional area of 2.5 times the cross-sectional area of the tendon.
C8.4.4.5.3 Steel sheaths
Post-tensioning ducts for internal tendons are usually grouted under a pressure of 700 kPa after the
concrete has achieved a required strength. The sheaths must be watertight when tested under an internal
water pressure of 350 kPa.
The wall thicknesses and bend radii for steel sheaths are based on current practice.
For segmental construction, it is usually necessary to bend sheaths to radii as small as 3 m. In such cases,
short lengths of ducts are pre-bent to standard radii using special procedures. Rigid sheaths less than
40 mm in diameter may not be readily available and manufacturers should be consulted prior to
specifying them.
C8.4.4.5.4 Plastic sheaths
The requirements in Clause 8.4.4.5.4 are based on AASHTO (1989) and PTI (1994).
PVC sheaths in bridges exposed to fire can generate hydrochloric acid and are therefore not permitted.
High-density polyethylene sheaths, with a thermal coefficient of expansion larger than that for concrete
or steel, can soften when hot and should be treated with care during installation.
The unsupported length of external post-tensioning tendons should be limited to 7.5 m unless a
dynamic analysis indicates that a longer unsupported length can be used without adverse effects.
C8.4.4.5.5 Vents and drains
Ducts should be provided with vents at all high points and at the anchorages, so as to facilitate grouting.
Drains should be provided at low points for construction in cold weather, to avoid the possibility of
trapped moisture freezing in the ducts. The location of the vents should be shown on the Plans.
C8.4.5 Grout
C8.4.5.1 Post-tensioning
Grouts with strengths less than 35 MPa are considered to be permeable and do not provide efficient
bonding of the tendons.
C8.4.5.2 Other applications
Grout for applications such as bedding for bearing or anchors should be nonshrink, nonstaining, resistant
to chloride scaling, and should have a strength of at least 35 MPa (MTO 1987).
C8.4.6 Material resistance factors
The Code has adopted the concept of material resistance factors as used in OHBDC (1991) and
CSA A23.3. The material resistance factors are applied to the material strength rather than to the nominal
resistance. Material resistance factors are intended to account for variations in material properties and in
section dimensions to allow for variations in bar placing and inaccuracies in the design equations.
Material resistance factors for concrete and reinforcement are based on MTO (1990).
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C8.5 Limit states
C8.5.1 General
Three limit states govern the design of bridge components, namely SLS, FLS, and ULS. The FLS is
generally not applicable to retaining walls.
C8.5.2 Serviceability limit states
C8.5.2.1 General
Cracking, deformation, stress, and vibration are SLS considerations.
C8.5.2.2 Cracking
In general, non-prestressed and partially prestressed concrete components are designed to crack
under service loads. The Code does not specify any minimum level of prestress for partially prestressed
components. However, for bridges, it is considered to be a good practice to provide sufficient prestress
so that, under permanent loads, the cracks previously caused due to application of live load remain
closed in order to enhance durability.
C8.5.2.3 Deformation
Deformation can affect the function of a structure by
(a) reducing clearances below those specified;
(b) causing water to pond on the deck;
(c) degrading ride quality as a result of
(i) angular change at expansion joints due to deflection of adjoining spans; or
(ii) an excessive gap at expansion joints due to elastic shortening, shrinkage, creep, and thermal
effects.
Rotation at bearings should be investigated to ensure adequate clearance between the
superstructure and the substructure.
C8.5.3 Fatigue limit state
Tack welding of reinforcing bars is not permitted, since it can reduce fatigue resistance by creating a
stress-raising notch effect.
In non-prestressed and fully prestressed concrete members, the change of stress in reinforcement
under the effects of repetitive live loads is generally not critical since non-prestressed concrete
members are assumed to be permanently cracked, while fully prestressed members are assumed to be
permanently uncracked. However, in partially prestressed members, the section may be uncracked
due to permanent load effects, but application of live load will cause cracking to develop or previously
formed cracks to reopen. As cracking takes place, the location of the neutral axis shifts, causing a
higher rate of increase in both the extreme fibre concrete stress and in the steel stress. In time, the
repetitive changes in stresses due to live load cause fatigue damage to the reinforcement, in addition
to the increase in deflections, crack widths, and reduction in bond between steel and concrete.
In partially prestressed concrete members, fatigue is considered to be a critical limit state. A
comprehensive reliability analysis by Naaman and Siriaksorn (1982) of partially prestressed concrete
beams revealed that fatigue failure of either prestressing or reinforcing steels is most critical. A general
review of information on fatigue data for partially prestressed beams is given by Naaman (1982).
C8.5.3.1 Reinforcing bars
The arching action in concrete bridge decks reduces the stress in reinforcing bars, thus resulting in a
lower stress range. As a result, fatigue is not considered to be a problem in deck slabs designed by the
empirical method. However, when the slab reinforcement is also part of a longitudinal or transverse
beam, fatigue must be considered. The response of a composite girder could subject such
reinforcement to a significant cyclic stress range.
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The stress ranges specified apply to all grades of reinforcing bars.
Fatigue design provisions for deformed reinforcing bars as reported by Helgason et al. (1976)
recommend that the following relationship be used to determine the permissible range of stress in straight
reinforcing bars:
fsr = 145 – 0.33 f min + 55 rh
where rh can be taken as 0.3 when the actual value is not known.
The stress range specified in Clause 8.5.3.1 was adopted in the interests of simplicity, since the ratio rh
would probably not be readily known and an accurate value of f min would often be difficult to determine
and would affect the stress range only slightly. The specified value provides a lower bound stress range.
The concrete tensile strength should be neglected in the calculation of the stress range.
Bends and welded joints reduce the fatigue strength significantly. The stress range specified for straight
bars is in reasonable agreement with the values observed in limited experimental data. If possible, bends in
primary reinforcement should be avoided in regions of high stress range.
C8.5.3.2 Tendons
Investigations reported by Oertle et al. (1987), Oertle (1988), Oertle and Thurliman (1987), and Wollman
et al. (1988) indicate that fretting fatigue failure can occur if the small relative movements between the
strand and the steel duct after cracking combine with the high bearing stresses between the strand and
the duct corrugations due to tendon curvature. The reduced allowable stress range for strands bent
around radii of curvature of less than 10 m reflect the increased likelihood of fretting fatigue as reported by
Rigon and Thurliman (1984). According to Ganz (1992), the use of corrugated polyethylene ducts with
flat surfaces greatly reduces or eliminates this problem.
Anchorages and mechanical connections should meet the requirements of Clause 8.4.4 and, where
possible, they should not be located in zones where externally applied loads cause significant changes of
stress.
C8.5.4 Ultimate limit states
Many aspects of the design of concrete structures are controlled by the need to provide adequate strength
and to ensure stability.
C8.6 Design considerations
C8.6.1 General
The strut-and-tie model should be considered for the design of deep footings, pile caps, and in other
situations where the distance between the centres of applied load and the supporting reactions is less than
about twice the component depth.
C8.6.2 Design
C8.6.2.1 General
Members should be investigated at all load stages that may be significant. The main stages usually are as
follows:
(a) transfer of prestress;
(b) during handling, transportation, erection, and Construction;
(c) SLS;
(d) FLS; and
(e) ULS.
For structures constructed in stages, the effects of loads prior to and after redistribution of load effects
due to creep and shrinkage in the completed structure should be investigated.
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C8.6.2.2 Member stiffness
For statically indeterminate structures, the cross-sectional properties to be used in computing the
relative stiffness of various members may be determined from either the uncracked concrete
cross-section neglecting the reinforcement, or from the transformed cracked cross-section, provided
that the same method is used throughout the analysis.
C8.6.2.3 Imposed deformations
Clause 8.6.2.3 is based on AASHTO LRFD (1994).
The force effects due to creep shortening of the superstructure on substructure elements, that are
monolithically or pin connected to the superstructure, can be considered to be offset by concrete
creep in the substructure element. For rigid frames, where the deck is prestressed, any increase in
moments due to creep shortening of the deck is usually offset by the concurrent relaxation of
moments due to creep of concrete in the frame legs and may be neglected.
Creep of concrete will significantly reduce stresses caused by restraint of shrinkage deformation
according to CEB-FIP (1978) and ACI Committee 209 (1971).
C8.6.2.4 Stress concentrations
Stress concentrations resulting from prestressing or other concentrated loads can be significant. The
stresses and reinforcement requirements may be computed from Clauses 8.8.7 and 8.16.
The maximum stresses in the vicinity of applied loads or reactions may be averaged over an area
equal to the bearing area of the load or the reaction.
C8.6.2.5 Secondary effects due to prestress
The secondary effects resulting from restraint of deformations due to prestressing can be significant.
These effects should be treated in the same manner as effects due to loading.
C8.6.2.6 Redistribution of force effects
In statically indeterminate structures constructed in stages from precast or cast-in-place elements that
are subjected to permanent forces prior to being made continuous, the distribution of force effects
within the completed structure changes during the subsequent life of the structure (Muller 1967 and
PCI/PTI 1978). The distribution approaches that which would have occurred if the forces applied to
the individual elements in stages before establishing continuity had been applied to the structure after
establishing continuity. This applies regardless of whether the permanent forces are prestress forces or
forces due to dead load. The final moment at any section along such a structure may be computed
from the following relationship:
M∞ = Mst + (Mct – Mst)(1 – e–ψ )
The ratio of creep strain to elastic strain, ψ , is affected by relative ambient humidity,
volume-to-exposed-surface ratio, age at loading, method of curing, type of cement, and
water-cement ratio, and may be computed from data in Clause 8.4.1.6 or PCI/PTI (1978).
There is no significant redistribution of force effects due to creep in statically indeterminate
structures erected or constructed in their final configuration.
Redistribution of force effects resulting from concrete cracking and material non-linearity may be
estimated using a non-linear method of analysis.
C8.6.2.7 Directional change of tendons
C8.6.2.7.1 Thrusts in plane of tendons
Changes in direction of prestressing steel, either in plan or in elevation, will induce thrusts and stresses
in the surrounding concrete. The concrete should be capable of resisting the resultant tensile and
compressive stresses. Otherwise, non-prestressed reinforcement is required to counteract the thrust.
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An example of thrust due to directional change of prestressing steel occurs when tendons in the web
are flared to accommodate anchorages in end blocks or blisters as shown in Figure C8.2.
Prestressing
tendons
Thrust
1
Non-prestressed
reinforcement around
prestressing ducts
1
Anchorages
1-1
Non-prestressed
reinforcement
required in this zone
(a) End blocks
Deviation forces push off
concrete cover on inside
of curvature
Unbalanced compression force
components push off concrete
cover on outside of curvature
Reinforcement for
in plane forces
(b) Blisters
Figure C8.2
Thrusts due to directional change of the prestressing steel
(See Clause C8.6.2.7.1.)
The method of calculating the resistance of the concrete in the plane of the tendon curvature is based on
the recommendations given by Van Landuyt (1991), assuming an effective length of shear plane as
illustrated in Figure C8.3.
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Fs
Fs
Fr
R
Vcd/
Vcd/
2
2
cd
1
sd
2
sd
Fr
Fr
sd
dd
Inside
face
Vcd/
2
Vcd/
bw
sd >
– dd
1 deff = 2 (bw – dd/2)
Inside
face
2
sd < dd
deff = 2 (cd – dd/4)
2 deff = 2 (cd + dd/4 + Ssd/2)
Figure C8.3
Resistance of concrete
(See Clause C8.6.2.7.1.)
C8.6.2.7.2 Multi-strand tendons
The lateral forces in multistrand post-tensioning tendons are caused by the spreading of the strands
within the duct as shown in Figure C8.4. The provisions of Clause 8.6.2.7.2 are similar to those given
in AASHTO LRFD (1994). The expression for the lateral force, Fl , is based on the assumption that the
strands occupy one-half of the duct. A more detailed procedure to account for the lateral forces is
given by Stone and Breen (1984).
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Stirrup
Fl
Fl
At Stressing
Radial forces due to
flattening out of tendon
bundle at sharp curves
Failure
Side rupture at point
of sharpest curvature
Figure C8.4
Lateral forces due to strand bunching
(See Clause C8.6.2.7.2.)
The confinement reinforcement should be proportioned to resist the lateral forces due to the bunching
of strands.
C8.6.2.7.3 Webs and flanges of box girders
The post-tensioning tendons in the bottom flange of variable depth segmental girders, whose bottom
flange consists of chords that are nontangential at the joints between the segments, exert thrusts at the
joints due to their direction change. The reinforcement is intended to resist the thrusts.
C8.6.2.7.5 Centre of gravity of tendons in ducts
The provisions of Clause 8.6.2.7.5 are similar to those given in AASHTO (1989).
C8.6.3 Buckling
Clause 8.6.3 refers to local and overall instability of components. An investigation of the stability of a
component, or part thereof, requires the use of a second order analysis.
Components may also become unstable during handling and erection. Consideration should be given
to geometry, location of lifting points, method of lifting, and construction tolerances. Slender beams tend
to tip and deflect laterally when being lifted by slings attached to lifting points. The initial tilting, which is
due to imperfections in geometry and improper location of lifting points, causes lateral bending moments
that may lead to cracking and lateral instability of the beam. Methods of estimating the lateral buckling
capacity of a component during lifting have been given by Mast (1989 and 1993), Swann and Godden
(1966), and Monnier (1972).
If the duct for an internal tendon is only slightly larger than the tendon, it is not possible to buckle the
component under the prestressing force being introduced. However, if the duct is significantly larger than
the unbonded tendon, lateral deformation will be induced during prestressing. These deformations, the
calculation of which has been discussed by Wilby (1963), should be considered. Precautions should be
taken to prevent buckling of post-tensioned members in the regions between the contact points where
the tendon makes contact with the member intermittently.
Thin webs under high shear or compression and flanges in compression are susceptible to buckling
between supports (Bennett and Balasooriya 1971).
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C8.7 Prestressing
C8.7.1 Stress limitations for tendons
Tendons with an effective prestress of less than 0.45 fpu should be considered non-prestressed
reinforcement. Use of prestressing tendons in such a manner is not cost-effective and results in strains
that may lead to excessive component deformation.
The stress limit of 0.78 fpu at jacking for pretensioning strand has been specified to reduce the
probability of strand breakage and to enhance safety. For post-tensioning, the stress limit of 0.80 fpu
provides some reserve capacity in case of unanticipated strand breakages or higher friction losses
encountered during Construction when a jacking stress up to 0.85 fpu may be used to achieve the
required prestress.
For deformed high-strength bar, the stress limit of 0.75 fpu at jacking has been adopted so as not to
exceed 0.94 fpy (PCI Committee on Prestress Losses 1975). The stress limits for smooth high-strength
bar are based on AASHTO LRFD (1994). The stress limit of 0.70 fpu at transfer, for strand at
post-tensioning anchorages and couplers, has been specified to reduce the probability of breakage of
strand wires at the grips. All other stress limits at transfer are such that they do not exceed 0.82 fpy .
C8.7.2 Concrete strength at transfer
For pretensioned concrete, the minimum concrete strength at transfer has been specified to ensure
adequate bond between the strands and the concrete. Concrete transfer strengths in excess of 30 MPa
may be difficult to achieve when the components are produced on a 24-hour cycle. For
post-tensioned concrete, it is sometimes desirable to provide some prestress at an early age to control
shrinkage cracks. In such cases, particular attention should be given to the size and details of the
anchorages.
For segmental construction, where it is desirable to introduce some prestress in the closure pour as
soon as possible, it is suggested that the minimum strength should be 10 MPa.
C8.7.3 Grouting
The restriction on the application or removal of loads after grouting and prior to the grout reaching a
strength of 20 MPa has been imposed to avoid cracking of the grout, thereby reducing its protection
of the tendons.
C8.7.4 Loss of prestress
C8.7.4.1 General
In order to check the limit states of cracking and deformation, it is necessary to calculate the loss in
prestress force in components from the time of transfer to the time of application of loading.
Prestress losses depend on material properties, the environment and stress levels at the application
of various loads, and on special circumstances, such as restraints, temporary prestressing, and the
amount of non-prestressed reinforcement.
Prestress losses are divided into two groups. “Losses at Transfer” take place up to the time
immediately after the prestressing force is transferred to the concrete element. The “Losses after
Transfer” commence at transfer and continue throughout the life of the structure.
Figure C8.5 is a schematic diagram of stress levels during the lifetime of both pretensioned and
post-tensioned components. A method for computing prestress losses in components of
normal-density concrete and with a ratio of As /Aps less than 1.0, constructed and prestressed in a
single stage, is given in the Code. A more detailed method is outlined by PCI Committee on Prestress
Losses (1975). Detailed methods for calculating losses in all types of components are presented by
Comité Euro-International Du Beton (CEB 1984), CPCI (1996), Batchelor et al. (1988), Ghali (1988),
and Collins and Mitchell (1987), and one method is discussed in Clause C8.7.4.3.
For components constructed and prestressed in multiple stages, the stress level at the
commencement and termination of each stage should be considered.
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The lump-sum losses given in Table C8.2 are for normal-density concrete components constructed and
prestressed in a single stage, and may be used for preliminary design of components with a ratio of As /Aps
equal to or less than 1.0. These losses are based on the highest allowable transfer stresses in Clause 8.7.1
and Grade 1860 low-relaxation strand. The lump sum losses do not include anchorage and friction loss in
post-tensioned tendons.
Lump-sum losses for beams of high-strength concrete with partial prestressing are given by Naaman
and Hamza (1993).
fsj
ANC + FR + ES
fsi
Dfs
Dfs1
ES
fst
Transfer
Pretensioned
members
Transfer
Stress in steel
REL1
Dfs2 =
CR +SH + REL2
fse
Post-tensioned
members
fse
jacking
1 day
1 month
1 year
10 25 50
Time t, after jacking
Figure C8.5
Schematic diagram of stress levels during lifetime of a component
(See Clause C8.7.4.1.)
Table C8.2
Estimate of lump sum losses, MPa
(See Clause C8.7.4.1.)
Pretensioning
Post-tensioning
REL1
ES
Δ f s 1 = REL1 + ES
10
110
120
—
20
20
After transfer
CR
SH
REL2
Δ f s 2 = CR + SH + REL2
80
40
20
140
55
35
30
120
Total Δfs
Δf s1 + Δ f s2
260
140
At transfer
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C8.7.4.2 Losses at transfer
C8.7.4.2.1 General
Losses at transfer are due to anchorage slip, friction, pure relaxation of the prestressing steel, and the
elastic shortening of the concrete at transfer of prestress.
C8.7.4.2.2 Anchorage slip
Where slip at the anchorage is used to control the stress in prestressing steel at transfer, the magnitude
of the slip should not be less than the value recommended by the manufacturer of the particular
anchorage. A value of slip smaller than that recommended by the manufacturer is difficult to achieve.
The recommended minimum values of slip are shown in Table C8.3.
Table C8.3
Anchorage slip
(See Clause C8.7.4.2.2.)
Tendon
Anchorage slip, mm
Up to 7 strands
8 to 12 strands
More than 12 strands
High-strength bars
8
10
12
1.5
C8.7.4.2.3 Friction loss
Friction loss calculations should consider both horizontal and vertical tendon alignment.
The values of K and µ for strand tendons in rigid bright steel sheath are based on experience in
Ontario. The values for strands in semirigid bright sheaths over 75 mm O.D. are similar to the values
given in CAN/CSA-S6-88. The values for strands in semirigid bright sheaths up to 75 mm O.D. and for
smooth and deformed bars are based on the manufacturers’ recommendations. Values of µ for
galvanized sheath may be smaller than for bright sheath, depending on method of galvanizing. The
values of K and µ specified for external ducts with rigid steel pipe deviators are similar to the values
given in AASHTO (1989). Values for plastic ducts are taken from Ganz (1992).
C8.7.4.2.4 Relaxation of tendons
See Clause C8.7.4.2.5.
C8.7.4.2.5 Elastic shortening
The expression for pure relaxation of prestressing strand was well established by Magura et al. (1964).
Pure relaxation loss takes place prior to transfer and pertains only to pretensioned components.
It is usual to assume a value of t = 0.75 days for pretensioned components produced on a 24-hour
cycle.
The compressive stress, fcir , in the expression for ES may be expressed as follows:
fcir =
Fst Fst e 2 Msec e MD e
+
+
−
Ag
Ig
Ig
Ig
where fcir is consistent with the force effects as shown in Figure C8.6.
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Md
e
Msec
Fst
Figure C8.6
Force effects at a section
(See Clause C8.7.4.2.5.)
In post-tensioned components, the elastic shortening is different in each tendon and varies according to
its sequence in the tensioning process. Hence, the factor (N – 1)/ 2N is incorporated in the expression for
ES (Grouni 1973).
Since fst is limited to 0.74 fpu , the jacking stress for pretensioned components may be computed by
starting at fst and working upwards to fsj. The stress, fsi , may be computed directly from the following
expression:
⎡
⎤
M
fsi = fst ⎢(1+ g ) − D g − nrp ⎥
Fst e
⎣
⎦
(
)
where
n
= Ep/Eci
γ
= nρp[1 + (e/r)2]
The jacking stress, fsj , may be computed from the following expression:
fsj
= fsi [1+ 0.029log(24t)] – 0.017fpulog(24t)
C8.7.4.3 Losses after transfer
Losses after transfer are due to creep and shrinkage of the concrete and relaxation of the prestressing steel.
These three phenomena are interdependent. Traditionally, expressions used to calculate these effects have
been developed for components in which the effect of non-prestressed reinforcement on losses has been
ignored. However, it has been shown by CPCI (1996), Batchelor et al. (1988), Ghali (1988), and Naaman
and Hamaza (1993) that the presence of non-prestressed reinforcement can influence prestress losses
significantly, and should not be neglected in loss calculations. Thus, the calculation of prestress losses is
discussed under two headings:
(a) the Simplified Method, which applies to components in which the ratio As /Aps is equal to or less than
1.0; and
(b) the Detailed Method, which applies to any type of prestressed concrete component.
Simplified method
The expressions used in this method for calculating losses due to creep, shrinkage, and relaxation of
prestressing steel are presented in Clauses 8.7.4.3.2 to 8.7.4.3.4. It has been shown by Batchelor et al.
(1988) and Ghali (1988) that this simplified method, while giving reasonable results for components in
which the ratio As /Aps is equal to or less than 1.0, overestimates losses in components in which this ratio
exceeds 1.0, and should not be used for the latter type. However, when As /Aps is greater than 1.0, the
approximate loss reduction due to the presence of non-prestressed reinforcement may be established by
using the reduction factors taken from Figure C8.7.
The basic expression for creep loss given in Clause 8.7.4.3.2 is obtained from Zia et al. (1979) but is
modified to include the effect of the mean annual relative humidity. The expression within the first set of
2
brackets, namely [1.37 – 0.77 (0.01 H) ], yields approximately unity for H = 70%. This expression is
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derived from the data given by PCI Committee on Prestress Losses (1975). Creep is also affected by the
shape factor, SF, of the component, and for moist-cured components, by a function of its age at
transfer, τ, computed as follows:
SF
= 1.14 – 0.036 rv > 0.68, and
τ
= 1.20 – 0.05 (t)0.67
The effects of these factors are included in the expression for CR given in the Code by using nominal
values of SF = 0.8 and τ = 1.0 at t = 7 days.
The amount of prestress loss due to creep that occurs up to t days after transfer, CRt , as a function of
total creep loss, CR, may be computed from
)
(
CRt = 1− e −0.08 t CR
The expression given in Clause 8.7.4.3.3 for prestress loss due to shrinkage is based on AASHTO
(1983) and includes the effects of mean annual relative humidity. At jacking in post-tensioned
components, approximately 20% of the strain due to shrinkage has already taken place; hence, the
shrinkage loss for such components is reduced from that in a comparable pretensioned component.
The amount of prestress loss due to shrinkage that occurs up to t days after placing of concrete may
be computed from
)
(
SHt = 1− e −0.10 t SH
After transfer, the stress in the prestressing steel changes with time as a result of creep and shrinkage
strains in the concrete and relaxation in the steel. The expression in Clause 8.7.4.3.4 includes the
effect of inelastic strains in the concrete (Grouni 1973 and 1978).
The expression in Clause 8.7.4.3.4 can be rearranged into a format found in AASHTO (1983) and
CAN/CSA-S6-88, as follows:
REL2 = C[ A – B (CR + SH)]
where A, B, and C are variables depending on the type, specified strength, and transfer stress of the
prestressing reinforcement. For Grade 1860 low-relaxation strand, A and B may be taken as 42 and
0.053 respectively.
Table C8.4 gives values of C for various combinations of the independent variables.
Relaxation losses in high-strength bars are generally lower than those for strand. At present, there
are insufficient data to formulate general expressions for computing the relaxation losses in
high-strength bars. The relaxation losses should, therefore, normally be based on test data supplied by
the manufacturers, otherwise a value of 20 MPa may be used for REL2.
Table C8.4
Values of C
(See Clause C8.7.4.3.)
fst /fpu
0.75
0.74
0.73
0.72
0.71
0.70
0.69
0.68
0.67
0.66
0.65
C
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
Detailed method
A number of general methods by Collins and Mitchell (1990) and Gilbert (1988) exist for predicting
losses in prestressed concrete components. One useful general method is the age-adjusted effective
modulus method (Batchelor et al. 1988, Bazant 1972, and Neville et al. 1983), which takes into
account the many factors affecting the time-dependent stress loss in steel, including the effect of
non-prestressed reinforcement.
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The age-adjusted effective modulus (AAEM) method requires the creep and shrinkage of concrete, and
relaxation of prestressing steel to be determined initially. The calculations by this method are tedious and
are best carried out by means of a computer program, such as those presented by Collins and Mitchell
(1987) and Srinivasan (1987).
Detailed manual calculations are presented in CPCI (1996) and Srinivasan (1987).
In order to facilitate calculations using the Simplified Method, the curves shown in Figure C8.7 have
been developed using the AAEM method. The loss reduction factor obtained from these curves may be
applied to the losses obtained from the simplified method to account for the influence of non-prestressed
reinforcement in concrete components.
Generally, the simplified method tends to predict higher total losses than those of the AAEM method,
although both methods yield comparable results where the ratio As /Aps is equal to or less than 1. The
difference is mainly due to the effect of non-prestressed reinforcement in reducing prestress losses. The
AAEM method also allows the calculation of stress in prestressed and non-prestressed reinforcement at any
stage of Construction, and is recommended for general use in calculating prestress losses.
1.0
Loss reduction factor
I-sections
0.9
T-sections
0.8
0.7
0.2
Rectangular
sections
fy = 400 MPa
fpu = 1860 MPa
0.4
0.6
[1 + (As /Aps)(fy / fpu
0.8
1.0
)] – 1
Figure C8.7
Prestress loss reduction in partially prestressed components
(See Clause C8.7.4.3.)
C8.8 Flexure and axial loads
C8.8.2 Assumptions for the serviceability and fatigue limit states
Except as noted, the assumptions made in Clause 8.8.2 are those normally made in flexural theory.
The tensile strength of the concrete can be relied upon in components, prior to cracking of the
concrete, except in tension components that are covered in Clause 8.8.6.
In a deep beam, the distribution of flexural stress departs radically from that in shallow components
(MacGregor 1988). Typical stress distributions for deep components are given by Chow et al. (1953).
Loss of concrete area due to openings for ducts, coupler sheaths, or transition trumpets in
post-tensioned components becomes significant when such loss exceeds 5% of the gross area.
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C8.8.3 Assumptions for the ultimate limit states
Except for deep beams, where the flow of forces can be investigated by means of a strut-and-tie
approach, as given in Clause 8.10 and by MacGregor (1988), the assumptions made in Clause 8.8.3
are those normally made in the application of flexural theory to reinforced concrete components.
The variation of strain across the depth of the section is assumed to be linear, with the maximum
strain in the concrete at the extreme compression fibre equal to 0.0035. The strain distribution and an
acceptable stress distribution in the concrete at the ultimate condition based on CSA A23.3 are shown
in Figure C8.8.
The stress in the reinforcement, as determined by a strain compatibility analysis or other suitable
approach, should be reduced by multiplying it by the appropriate material resistance factor from
Clause 8.4.6.
If the concrete in the compression zone is confined, for example by hoop reinforcement, its
deformability is increased and higher strains may be sustained at ULS as reported by
Scott et al. (1982). When a strain greater than 0.0035 is assumed, a strain compatibility analysis,
employing a representative stress-strain relationship for the concrete should be used to compute the
flexural resistance.
d¢
A¢s
ec
b
hf
Equivalent
rectangular
stress block
hf /2
C¢s = fs fy A¢s
Cc1 = a1 fc f¢c hf (b – bw)
Cc2 = a1 fc f¢c abw
a = b1c
c
dp
a/2
ds
Aps
a1 fc f¢c
ep
es
Tp = fp fps Aps
Ts = fs fy As
As
bw
Cross-section
Strain
Stress block
Figure C8.8
Strain and stress distribution and forces at ULS
(See Clauses C8.3 and C8.8.3.)
C8.8.4 Flexural components
C8.8.4.1 Factored flexural resistance
The assumptions in Clause 8.8.3 lead to the following equation for the flexural resistance of a T- or
I-section when the neutral axis is located in the web as shown in Figure C8.8:
a⎞
a⎞
a⎞
⎛
⎛
⎛
⎛h a ⎞
Mr = fs Asfy ⎜ ds − ⎟ + f p Apsfps ⎜ d p − ⎟ − fs As′fy ⎜ d ′ − ⎟ − a1fc fc′hf (b − bw ) ⎜ f − ⎟
2
2
2
⎝
⎠
⎝
⎠
⎝
⎠
⎝ 2 2⎠
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where
a=
fs Asfy + f p Apsfps − fs As′fy − a1fc fc′hf (b − bw )
a1fc fc′bw
When the neutral axis is located in the compression flange (a < hf), or for a rectangular section, bw
should be taken as b.
Generally, the non-prestressed steel stresses can be taken as equal to the yield stress, fy . However, care
should be taken, particularly with compression reinforcement, to verify that the steel will yield at the
ultimate condition.
C8.8.4.2 Tendon stress at the ultimate limit states
The equation for the steel stress in a bonded tendon at ultimate is taken from Loov (1988) and Naaman
(1989).
The values for kp have been determined from the following equation (Loov 1988), assuming values of
fp y /f pu of 0.9 for prestressing strand, 0.85 for smooth high-strength bar, and 0.8 for deformed
high-strength bar and then rounded off:
kp = 2(1.04 – fpy/fpu )
The value of c/ dp for prestressed components may be determined from the following expression:
c / dp =
f p Apsfpu + fs Asfy − fs As′fy − a1fc fc′hf (b − bw )
a1fc b1fc′bw d p + f p kp Apsfpu
For slender bridge components with long unbonded tendons, which may be unbonded internal
tendons during the construction stage, or external tendons, the increase in the stress of a tendon at
ultimate beyond the effective prestress level will be relatively small, even for large deformation of the
component (Aeberhard et al. 1988). Consequently, this increase has been specified as zero unless an
analysis accounting for actual deformation (Ghali 1988) demonstrates that an increase is possible. The
presence of bonded non-prestressed reinforcement reduces the stress level in the tendon at ultimate
(Chouinard 1989).
Components with external grouted tendons can be proportioned conservatively by assuming that the
tendons are unbonded (Aeberhard et al. 1988, Sowlat and Rabbat 1987), since bond between a tendon
and the concrete in a component will exist only at the deviation points.
C8.8.4.3 Minimum reinforcement
It is desirable that components contain sufficient flexural reinforcement at critical sections to ensure that a
reserve of strength exists after initial cracking. If the components do not contain enough reinforcement,
they may fail abruptly with rupture of the steel occurring immediately after cracking. The factor 1.20 is
chosen to make allowance for likely variations in the strength of the materials and in the prestressing force.
C8.8.4.4 Cracking moment
A section cracks when the stress at the extreme tensile face, computed for the transformed section,
reaches the tensile strength of the concrete, fcr . Computation of the cracking moment should account for
any effective prestress. The cracking moment may be computed from the following:
(a) For monolithic sections
Mcr =
lg
yt
(fpe + fcr )
(b) For composite sections
Mcr = Mp +
324
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yt
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C8.8.4.5 Maximum reinforcement
Sections with c/ d less than 0.5 tend to be under-reinforced and will exhibit ductile behaviour prior to
failure. For some components, values of c/ d greater than 0.5 may be necessary. While such sections
will be brittle, the requirements of Clause 8.8.3 will still apply and the strain compatibility approach
should be used to determine the moment of resistance.
The flexural resistance of a component in which c /d > 0.5 may be estimated as follows:
h ⎞
⎛
Mr = 0.3a1fc fc′bw d 2 + a1fc fc′ (b − bw ) hf ⎜ d − f ⎟ + fsfy As′ (d − d ′)
2⎠
⎝
This expression is based on the assumption that the depth of the equivalent stress block is 0.36 d.
In flanged sections where hf > 0.36d, or for rectangular sections, bw should be taken as b.
C8.8.4.6 Prestressed concrete stress limitations
At transfer and during Construction
The permissible concrete stresses in prestressed components at this stage are the same as those
specified in OHBDC (1991). These stresses are of short duration. They may occur before the concrete
has reached the specified strength. The reinforcing bars provided to resist the temporary tensile stress
should be distributed evenly near the tensile face of the component.
The limits on the stress levels at transfer are used to control the level of prestress, which in turn
controls the camber in a prestressed component.
At SLS
To cover the range of possible designs from non-prestressed to fully prestressed, absolute limits have
not been set on the stresses at service loads. As a result, components may be cracked under SLS loads.
When the cracking moment is likely to be exceeded, control of cracking should be investigated
according to Clause 8.12. It is preferable that tensile stresses should not develop in prestressed
concrete components under permanent loads.
No limitation is specified for compressive stress that is consistent with the approach used in the
design of non-prestressed sections. Serviceability is ensured by crack control and deformation
limitations.
Tension is not allowed in segmental construction without bonded non-prestressed reinforcement
passing through the joints. This is to avoid the separation of the segments at the joints and the
eventual formation of potential weak spots where corrosion of prestressing tendons may take place.
Slabs with longitudinal circular voids
The limit on the average compressive stress due to prestress alone, in post-tensioned decks with round
voids, is based on the report by Csagoly and Holowka (1974). There is a critical average stress level in
longitudinal compression in voided components, above which the transverse tension due to stress
concentrations over the voids can exceed the flexural tensile strength of the concrete. Post-tensioned
bridge decks with round voids and without transverse prestressing have in the past developed
longitudinal cracks over the voids. These decks should therefore be prestressed transversely as
recommended in the reports by Csagoly and Holowka (1974), Campbell (1974), Meades and Green
(1974), and McNiece (1974). The length of the solid slab at the ends of the deck should be at least
equal to the distance from the outermost anchorage to the edge of the deck, so as to disperse the
prestressing forces, but should not be less than 0.07 of the span length. Abrupt changes in the
cross-section should also be avoided.
C8.8.5 Compression components
C8.8.5.1 General
The provisions for the design of concrete compression components are based on the magnified
moment approach for non-prestressed components as given in CSA A23.3 and ACI (1989). Further
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refinements of this approach for prestressed compression components are given by PCI Committee on
Prestressed Concrete Columns (1988).
Moments induced by deflection must be taken into account in the analysis of slender columns. A
rigorous analysis of this type is generally regarded as too complicated for routine design; consequently,
simplified, and largely empirical, approaches such as those given in Clause 8.8.5.3 are adopted.
The basis for the approximate evaluation of slenderness effects is outlined in ACI (1989). The effective
length of a column with different end conditions is indicated in Table C8.5, which is taken from BS5400
(1984). The basis of Table C8.5 has been outlined by Jackson (1988), which points out the importance of
the rotational and translational characteristics of the bearing at the end of a column.
Table C8.5
Effective length factor of compression components
(See Clause C8.8.5.1.)
Case
Idealized column and buckling
mode
1
Restraint
location
Top
Restraint against
Translation Rotation
Full2
Full
0.70
lu
2
Bottom
Full
Full2
Top
Full
None
0.85
lu
3
Bottom
Full
Full2
Top
Full
None
1.0
lu
4
lu
Bottom
Full
None
Top
None
1
None
Elastomeric
bearing
5
lu
Effective length
factor, k
1
1.3
Bottom
Full
Full2
Top
None
None
Sliding below
rotational bearing
1.4
Bottom
Full
Full2
(Continued)
326
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S6.1-06
Table C8.5 (Concluded)
Case
Idealized column and buckling
mode
6
Restraint against
Restraint
location
Translation Rotation
Top
None
Full2
1.5
lu
7
lu
Effective length
factor, k
Bottom
Full
None2
Top
None
None
lu
or
2.3
Bottom
Full
Full3
Notes:
(1) Lateral and rotational rigidities of elastomeric bearings are zero.
(2) Rotational restraint is at least 4 EI /l u .
(3) Rotational restraint is at least 8 EI /l u .
C8.8.5.4 Maximum factored axial resistance
The axial resistance is limited to account for accidental eccentricities that are not considered in design
and the possibility that the concrete strength may be reduced under sustained high axial loads. The
factored axial resistance of a section in pure compression, Po , may be computed from
(
)
Po = a1fc fc′ Ag − Ast − Aps + fsfy Ast − f pfps Aps
where fps is the stress in prestressing steel when concrete reaches a limiting concrete strain.
C8.8.5.5 Biaxial loading
The provisions for biaxial loading are the same as those given in AASHTO (1983). They are based on
the approximate interaction surface diagrams such as those given by Bresler (1960) and PCA (1995).
C8.8.5.6 Reinforcement limitations
The maximum and minimum amounts of longitudinal reinforcement are the same as those specified in
AASHTO LRFD (1994). A minimum amount of reinforcement is necessary to provide resistance to
bending, which may occur whether or not indicated by computations, and to reduce the effects of
creep and shrinkage. In practice, it is desirable to limit the maximum ratio to 0.04. When lapped
splices are used, the ratio should be based on the total area of longitudinal reinforcement in the
cross-section. For components in which the cross-sectional area is larger than that required by analysis,
the minimum area, based on the actual cross-section, can result in unnecessarily large amounts of
reinforcement. In such a case, the area of the cross-section required by analysis should be used.
C8.8.5.8 Hollow rectangular components
Hollow rectangular components with a wall slenderness ratio of 15 or greater may exhibit reduced
strengths due to local compression flange buckling. The design recommendations in Cla