Bridge design : concepts and analysis
Reis, Antonio J.
Bridge design : concepts and analysis - New Jersey John Wiley & Sons Ltd. 2019 - xvi,531p.
CONTENTS
About the Authors xiii
Preface xv
Acknowledgements xvii
1 Introduction 1
1.1 Generalities 1
1.2 Definitions and Terminology 1
1.3 Bridge Classification 4
1.4 Bridge Typology 6
1.5 Some Historical References 16
1.5.1 Masonry Bridges 16
1.5.2 Timber Bridges 18
1.5.3 Metal Bridges 18
1.5.4 Reinforced and Prestressed Concrete Bridges 24
1.5.5 Cable Supported Bridges 28
References 30
2 Bridge Design: Site Data and Basic Conditions 31
2.1 Design Phases and Methodology 31
2.2 Basic Site Data 32
2.2.1 Generalities 32
2.2.2 Topographic Data 32
2.2.3 Geological and Geotechnical Data 35
2.2.4 Hydraulic Data 36
2.2.5 Other Data 38
2.3 Bridge Location. Alignment, Bridge Length and Hydraulic Conditions 38
2.3.1 The Horizontal and Vertical Alignments 42
2.3.2 The Transverse Alignment 46
2.4 Elements Integrated in Bridge Decks 49
2.4.1 Road Bridges 49
2.4.1.1 Surfacing and Deck Waterproofing 50
2.4.1.2 Walkways, Parapets and Handrails 50
2.4.1.3 Fascia Beams 53
2.4.1.4 Drainage System 54
2.4.1.5 Lighting System 55
2.4.1.6 Expansion Joints 55
2.4.2 Railway Decks 58
2.4.2.1 Track System 59
2.4.2.2 Power Traction System (Catenary System) 61
2.4.2.3 Footways, Parapets/Handrails, Drainage and Lighting Systems 61
References 61
3 Actions and Structural Safety 63
3.1 Types of Actions and Limit State Design 63
3.2 Permanent Actions 65
3.3 Highway Traffic Loading – Vertical Forces 68
3.4 Braking, Acceleration and Centrifugal Forces in Highway Bridges 72
3.5 Actions on Footways or Cycle Tracks and Parapets, of Highway Bridges 74
3.6 Actions for Abutments and Walls Adjacent to Highway Bridges 75
3.7 Traffic Loads for Railway Bridges 76
3.7.1 General 76
3.7.2 Load Models 76
3.8 Braking, Acceleration and Centrifugal Forces in Railway Bridges: Nosing Forces 77
3.9 Actions on Maintenance Walkways and Earth Pressure Effects for Railway Bridges 78
3.10 Dynamic Load Effects 79
3.10.1 Basic Concepts 79
3.10.2 Dynamic Effects for Railway Bridges 82
3.11 Wind Actions and Aerodynamic Stability of Bridges 84
3.11.1 Design Wind Velocities and Peak Velocities Pressures 84
3.11.2 Wind as a Static Action on Bridge Decks and Piers 89
3.11.3 Aerodynamic Response: Basic Concepts 91
3.11.3.1 Vortex Shedding 94
3.11.3.2 Divergent Amplitudes: Aerodynamic Instability 95
3.12 Hydrodynamic Actions 98
3.13 Thermal Actions and Thermal Effects 99
3.13.1 Basic Concepts 99
3.13.2 Thermal Effects 102
3.13.3 Design Values 107
3.14 Shrinkage, Creep and Relaxation in Concrete Bridges 109
3.15 Actions Due to Imposed Deformations. Differential Settlements 117
3.16 Actions Due to Friction in Bridge Bearings 119
3.17 Seismic Actions 119
3.17.1 Basis of Design 119
3.17.2 Response Spectrums for Bridge Seismic Analysis 121
3.18 Accidental Actions 124
3.19 Actions During Construction 124
3.20 Basic Criteria for Bridge Design 125
References 125
4 Conceptual Design and Execution Methods 129
4.1 Concept Design: Introduction 129
4.2 Span Distribution and Deck Continuity 131
4.2.1 Span Layout 131
4.2.2 Deck Continuity and Expansion Joints 132
4.3 The Influence of the Execution Method 134
4.3.1 A Prestressed Concrete Box Girder Deck 134
4.3.2 A Steel‐Concrete Composite Steel Deck 136
4.3.3 Concept Design and Execution: Preliminary Conclusions 136
4.4 Superstructure: Concrete Bridges 138
4.4.1 Options for the Bridge Deck 138
4.4.2 The Concrete Material – Main Proprieties 139
4.4.2.1 Concrete 139
4.4.2.2 Reinforcing Steel 140
4.4.2.3 Prestressing Steel 140
4.4.3 Slab and Voided Slab Decks 142
4.4.4 Ribbed Slab and Slab‐Girder Decks 144
4.4.5 Precasted Slab‐Girder Decks 152
4.4.6 Box Girder Decks 155
4.5 Superstructure: Steel and Steel‐Concrete Composite Bridges 160
4.5.1 Options for Bridge Type: Plated Structures 160
4.5.2 Steels for Metal Bridges and Corrosion Protection 166
4.5.2.1 Materials and Weldability 166
4.5.2.2 Corrosion Protection 172
4.5.3 Slab Deck: Concrete Slabs and Orthotropic Plates 173
4.5.3.1 Concrete Slab Decks 174
4.5.3.2 Steel Orthotropic Plate Decks 176
4.5.4 Plate Girder Bridges 179
4.5.4.1 Superstructure Components 179
4.5.4.2 Preliminary Design of the Main Girders 182
4.5.4.3 Vertical Bracing System 188
4.5.4.4 Horizontal Bracing System 191
4.5.5 Box Girder Bridges 192
4.5.5.1 General 192
4.5.5.2 Superstructure Components 193
4.5.5.3 Pre‐Design of Composite Box Girder Sections 196
4.5.5.4 Pre‐Design of Diaphragms or Cross Frames 199
4.5.6 Typical Steel Quantities 201
4.6 Superstructure: Execution Methods 202
4.6.1 General Aspects 202
4.6.2 Execution Methods for Concrete Decks 203
4.6.2.1 General 203
4.6.2.2 Scaffoldings and Falseworks 203
4.6.2.3 Formwork Launching Girders 206
4.6.2.4 Incremental Launching 206
4.6.2.5 Cantilever Construction 212
4.6.2.6 Precasted Segmental Cantilever Construction 221
4.6.2.7 Other Methods 222
4.6.3 Erection Methods for Steel and Composite Bridges 223
4.6.3.1 Erection Methods, Transport and Erection Joints 223
4.6.3.2 Erection with Cranes Supported from the Ground 224
4.6.3.3 Incremental Launching 224
4.6.3.4 Erection by the Cantilever Method 227
4.6.3.5 Other Methods 227
4.7 Substructure: Conceptual Design and Execution Methods 229
4.7.1 Elements and Functions 229
4.7.2 Bridge Piers 229
4.7.2.1 Structural Materials and Pier Typology 229
4.7.2.2 Piers Pre‐Design 232
4.7.2.3 Execution Method of the Deck and Pier Concept Design 233
4.7.2.4 Construction Methods for Piers 240
4.7.3 Abutments 241
4.7.3.1 Functions of the Abutments 241
4.7.3.2 Abutment Concepts and Typology 241
4.7.4 Bridge Foundations 245
4.7.4.1 Foundation Typology 245
4.7.4.2 Direct Foundations 245
4.7.4.3 Pile Foundations 246
4.7.4.4 Special Bridge Foundations 247
4.7.4.5 Bridge Pier Foundations in Rivers 250
References 251
5 Aesthetics and Environmental Integration 255
5.1 Introduction 255
5.2 Integration and Formal Aspects 256
5.3 Bridge Environment 256
5.4 Shape and Function 258
5.5 Order and Continuity 260
5.6 Slenderness and Transparency 262
5.7 Symmetries, Asymmetries and Proximity with Other Bridges 266
5.8 Piers Aesthetics 267
5.9 Colours, Shadows, and Detailing 268
5.10 Urban Bridges 272
References 277
6 Superstructure: Analysis and Design 279
6.1 Introduction 279
6.2 Structural Models 280
6.3 Deck Slabs 283
6.3.1 General 283
6.3.2 Overall Bending: Shear Lag Effects 283
6.3.3 Local Bending Effects: Influence Surfaces 287
6.3.4 Elastic Restraint of Deck Slabs 295
6.3.5 Transverse Prestressing of Deck Slabs 297
6.3.6 Steel Orthotropic Plate Decks 300
6.4 Transverse Analysis of Bridge Decks 301
6.4.1 Use of Influence Lines for Transverse Load Distribution 301
6.4.2 Transverse Load Distribution Coefficients for Load Effects 302
6.4.3 Transverse Load Distribution Methods 303
6.4.3.1 Rigid Cross Beam Methods: Courbon Method 304
6.4.3.2 Transverse Load Distribution on Cross Beams 307
6.4.3.3 Extensions of the Courbon Method: Influence of Torsional Stiffness of Main Girders and Deformability of Cross Beams 307
6.4.3.4 The Orthotropic Plate Approach 308
6.4.3.5 Other Transverse Load Distribution Methods 313
6.5 Deck Analysis by Grid and FEM Models 313
6.5.1 Grid Models 313
6.5.1.1 Fundamentals 313
6.5.1.2 Deck Modelling 315
6.5.1.3 Properties of Beam Elements in Grid Models 317
6.5.1.4 Limitations and Extensions of Plane Grid Modelling 318
6.5.2 FEM Models 318
6.5.2.1 Fundamentals 318
6.5.2.2 FEM for Analysis of Bridge Decks 323
6.6 Longitudinal Analysis of the Superstructure 329
6.6.1 Generalities – Geometrical Non‐Linear Effects: Cables and Arches 329
6.6.2 Frame and Arch Effects 332
6.6.3 Effect of Longitudinal Variation of Cross Sections 334
6.6.4 Torsion Effects in Bridge Decks – Non‐Uniform Torsion 336
6.6.5 Torsion in Steel‐Concrete Composite Decks 343
6.6.5.1 Composite Box Girder Decks 343
6.6.5.2 Composite Plate Girder Decks 345
6.6.5.3 Transverse Load Distribution in Open Section Decks 348
6.6.6 Curved Bridges 350
6.6.6.1 Statics of Curved Bridges 350
6.6.6.2 Simply Supported Curved Bridge Deck 352
6.6.6.3 Approximate Method 353
6.6.6.4 Bearing System and Deck Elongations 353
6.7 Influence of Construction Methods on Superstructure Analysis 355
6.7.1 Span by Span Erection of Prestressed Concrete Decks 356
6.7.2 Cantilever Construction of Prestressed Concrete Decks 357
6.7.3 Prestressed Concrete Decks with Prefabricated Girders 360
6.7.4 Steel‐Concrete Composite Decks 361
6.8 Prestressed Concrete Decks: Design Aspects 364
6.8.1 Generalities 364
6.8.2 Design Concepts and Basic Criteria 364
6.8.3 Durability 364
6.8.4 Concept of Partial Prestressed Concrete (PPC) 364
6.8.5 Particular Aspects of Bridges Built by Cantilevering 365
6.8.6 Ductility and Precasted Segmental Construction 366
6.8.6.1 Internal and External Prestressing 367
6.8.7 Hyperstatic Prestressing Effects 367
6.8.8 Deflections, Vibration and Fatigue 368
6.9 Steel and Composite Decks 373
6.9.1 Generalities 373
6.9.2 Design Criteria for ULS 373
6.9.3 Design Criteria for SLS 375
6.9.3.1 Stress Limitations and Web Breathing 376
6.9.3.2 Deflection Limitations and Vibrations 377
6.9.4 Design Criteria for Fatigue Limit State 377
6.9.5 Web Design of Plate and Box Girder Sections 383
6.9.5.1 Web Under in Plane Bending and Shear Forces 383
6.9.5.2 Flange Induced Buckling 385
6.9.5.3 Webs Under Patch Loading 387
6.9.5.4 Webs under Interaction of Internal Forces 389
6.9.6 Transverse Web Stiffeners 390
6.9.7 Stiffened Panels in Webs and Flanges 391
6.9.8 Diaphragms 394
6.10 Reference to Special Bridges: Bowstring Arches and Cable‐Stayed Bridges 395
6.10.1 Generalities 395
6.10.2 Bowstring Arch Bridges 396
6.10.2.1 Geometry, Slenderness and Stability 396
6.10.2.2 Hanger System and Anchorages 402
6.10.2.3 Analysis of the Superstructure 403
6.10.3 Cable‐Stayed Bridges 404
6.10.3.1 Basic Concepts 404
6.10.3.2 Total and Partial Adjustment Staying Options 408
6.10.3.3 Deck Slenderness, Static and Aerodynamic Stability 411
6.10.3.4 Stays and Stay Cable Anchorages 414
6.10.3.5 Analysis of the Superstructure 416
References 418
7 Substructure: Analysis and Design 423
7.1 Introduction 423
7.2 Distribution of Forces Between Piers and Abutments 423
7.2.1 Distribution of a Longitudinal Force 423
7.2.2 Action Due to Imposed Deformations 424
7.2.3 Distribution of a Transverse Horizontal Force 425
7.2.4 Effect of Deformation of Bearings and Foundations 429
7.3 Design of Bridge Bearings 430
7.3.1 Bearing Types 430
7.3.2 Elastomeric Bearings 430
7.3.3 Neoprene‐Teflon Bridge Bearings 434
7.3.4 Elastomeric ‘Pot Bearings’ 435
7.3.5 Metal Bearings 437
7.3.6 Concrete Hinges 439
7.4 Reference to Seismic Devices 441
7.4.1 Concept 441
7.4.2 Seismic Dampers 441
7.5 Abutments: Analysis and Design 444
7.5.1 Actions and Design Criteria 444
7.5.2 Front and Wing Walls 446
7.5.3 Anchored Abutments 448
7.6 Bridge Piers: Analysis and Design 449
7.6.1 Basic Concepts 449
7.6.1.1 Pre‐design 449
7.6.1.2 Slenderness and Elastic Critical Load 449
7.6.1.3 The Effect of Geometrical Initial Imperfections 450
7.6.1.4 The Effect of Cracking in Concrete Bridge Piers 450
7.6.1.5 Bridge Piers as ‘Beam Columns’ 451
7.6.1.6 The Effect of Imposed Displacements 452
7.6.1.7 The Overall Stability of a Bridge Structure 453
7.6.1.8 Design Bucking Length of Bridge Piers 453
7.6.2 Elastic Analysis of Bridge Piers 454
7.6.3 Elastoplastic Analysis of Bridge Piers: Ultimate Resistance 459
7.6.4 Creep Effects on Concrete Bridge Piers 465
7.6.5 Analysis of Bridge Piers by Numerical Methods 465
7.6.6 Overall Stability of a Bridge Structure 471
References 473
8 Design Examples: Concrete and Composite Options 475
8.1 Introduction 475
8.2 Basic Data and Bridge Options 475
8.2.1 Bridge Function and Layout 475
8.2.2 Typical Deck Cross Sections 476
8.2.3 Piers, Abutments and Foundations 477
8.2.4 Materials Adopted 477
8.2.4.1 Prestressed Concrete Deck 478
8.2.4.2 Steel‐concrete Composite Deck 481
8.2.5 Deck Construction 481
8.3 Hazard Scenarios and Actions 481
8.3.1 Limit States and Structural Safety 482
8.3.2 Actions 482
8.3.2.1 Permanent Actions and Imposed Deformations 482
8.3.2.2 Variable Actions 484
8.4 Prestressed Concrete Solution 486
8.4.1 Preliminary Design of the Deck 486
8.4.2 Structural Analysis and Slab Checks 486
8.4.3 Structural Analysis of the Main Girders 492
8.4.3.1 Traffic Loads: Transverse and Longitudinal Locations 493
8.4.3.2 Internal Forces 497
8.4.3.3 Prestressing Layout and Hyperstatic Effects 497
8.4.3.4 Influence of the Construction Stages 498
8.4.4 Structural Safety Checks: Longitudinal Direction 498
8.4.4.1 Decompression Limit State – Prestressing Design 498
8.4.4.2 Ultimate Limit States – Bending and Shear Resistance 501
8.5 Steel–Concrete Composite Solution 502
8.5.1 Preliminary Design of the Deck 502
8.5.2 Structural Analysis and Slab Design Checks 503
8.5.3 Structural Analysis of the Main Girders 503
8.5.3.1 Traffic Loads Transverse and Longitudinal Positioning 504
8.5.3.2 Internal Forces 505
8.5.3.3 Shrinkage Effects 505
8.5.3.4 Imposed Deformation Effect 506
8.5.3.5 Influence of the Construction Stages 506
8.5.4 Safety Checks: Longitudinal Direction 507
8.5.4.1 Ultimate Limit States – Bending and Shear Resistance 507
8.5.4.2 Serviceability Limit States – Stresses and Crack Widths Control 509
References 510
Annex A: Buckling and Ultimate Strength of Flat Plates 511
A.1 Critical Stresses and Buckling Modes of Flat Plates 511
A.1.1 Plate Simply Supported along the four Edges and under a Uniform Compression (ψ = 1) 511
A.1.2 Bending of Long Rectangular Plates Supported at both Longitudinal Edges or with a Free Edge 513
A.1.3 Buckling of Rectangular Plates under Shear 513
A.2 Buckling of Stiffened Plates 514
A.2.1 Plates with One Longitudinal Stiffener at the Centreline under Uniform Compression 515
A.2.2 Plate with Two Stiffeners under Uniform Compression 516
A.2.3 Plates with Three or More Longitudinal Stiffeners 517
A.2.4 Stiffened Plates under Variable Compression. Approximate Formulas 518
A.3 Post‐Buckling Behaviour and Ultimate Strength of Flat Plates 518
A.3.1 Effective Width Concept 519
A.3.2 Effective Width Formulas 520
References 523
Index 525
9780470843635
624.2 / REI
Bridge design : concepts and analysis - New Jersey John Wiley & Sons Ltd. 2019 - xvi,531p.
CONTENTS
About the Authors xiii
Preface xv
Acknowledgements xvii
1 Introduction 1
1.1 Generalities 1
1.2 Definitions and Terminology 1
1.3 Bridge Classification 4
1.4 Bridge Typology 6
1.5 Some Historical References 16
1.5.1 Masonry Bridges 16
1.5.2 Timber Bridges 18
1.5.3 Metal Bridges 18
1.5.4 Reinforced and Prestressed Concrete Bridges 24
1.5.5 Cable Supported Bridges 28
References 30
2 Bridge Design: Site Data and Basic Conditions 31
2.1 Design Phases and Methodology 31
2.2 Basic Site Data 32
2.2.1 Generalities 32
2.2.2 Topographic Data 32
2.2.3 Geological and Geotechnical Data 35
2.2.4 Hydraulic Data 36
2.2.5 Other Data 38
2.3 Bridge Location. Alignment, Bridge Length and Hydraulic Conditions 38
2.3.1 The Horizontal and Vertical Alignments 42
2.3.2 The Transverse Alignment 46
2.4 Elements Integrated in Bridge Decks 49
2.4.1 Road Bridges 49
2.4.1.1 Surfacing and Deck Waterproofing 50
2.4.1.2 Walkways, Parapets and Handrails 50
2.4.1.3 Fascia Beams 53
2.4.1.4 Drainage System 54
2.4.1.5 Lighting System 55
2.4.1.6 Expansion Joints 55
2.4.2 Railway Decks 58
2.4.2.1 Track System 59
2.4.2.2 Power Traction System (Catenary System) 61
2.4.2.3 Footways, Parapets/Handrails, Drainage and Lighting Systems 61
References 61
3 Actions and Structural Safety 63
3.1 Types of Actions and Limit State Design 63
3.2 Permanent Actions 65
3.3 Highway Traffic Loading – Vertical Forces 68
3.4 Braking, Acceleration and Centrifugal Forces in Highway Bridges 72
3.5 Actions on Footways or Cycle Tracks and Parapets, of Highway Bridges 74
3.6 Actions for Abutments and Walls Adjacent to Highway Bridges 75
3.7 Traffic Loads for Railway Bridges 76
3.7.1 General 76
3.7.2 Load Models 76
3.8 Braking, Acceleration and Centrifugal Forces in Railway Bridges: Nosing Forces 77
3.9 Actions on Maintenance Walkways and Earth Pressure Effects for Railway Bridges 78
3.10 Dynamic Load Effects 79
3.10.1 Basic Concepts 79
3.10.2 Dynamic Effects for Railway Bridges 82
3.11 Wind Actions and Aerodynamic Stability of Bridges 84
3.11.1 Design Wind Velocities and Peak Velocities Pressures 84
3.11.2 Wind as a Static Action on Bridge Decks and Piers 89
3.11.3 Aerodynamic Response: Basic Concepts 91
3.11.3.1 Vortex Shedding 94
3.11.3.2 Divergent Amplitudes: Aerodynamic Instability 95
3.12 Hydrodynamic Actions 98
3.13 Thermal Actions and Thermal Effects 99
3.13.1 Basic Concepts 99
3.13.2 Thermal Effects 102
3.13.3 Design Values 107
3.14 Shrinkage, Creep and Relaxation in Concrete Bridges 109
3.15 Actions Due to Imposed Deformations. Differential Settlements 117
3.16 Actions Due to Friction in Bridge Bearings 119
3.17 Seismic Actions 119
3.17.1 Basis of Design 119
3.17.2 Response Spectrums for Bridge Seismic Analysis 121
3.18 Accidental Actions 124
3.19 Actions During Construction 124
3.20 Basic Criteria for Bridge Design 125
References 125
4 Conceptual Design and Execution Methods 129
4.1 Concept Design: Introduction 129
4.2 Span Distribution and Deck Continuity 131
4.2.1 Span Layout 131
4.2.2 Deck Continuity and Expansion Joints 132
4.3 The Influence of the Execution Method 134
4.3.1 A Prestressed Concrete Box Girder Deck 134
4.3.2 A Steel‐Concrete Composite Steel Deck 136
4.3.3 Concept Design and Execution: Preliminary Conclusions 136
4.4 Superstructure: Concrete Bridges 138
4.4.1 Options for the Bridge Deck 138
4.4.2 The Concrete Material – Main Proprieties 139
4.4.2.1 Concrete 139
4.4.2.2 Reinforcing Steel 140
4.4.2.3 Prestressing Steel 140
4.4.3 Slab and Voided Slab Decks 142
4.4.4 Ribbed Slab and Slab‐Girder Decks 144
4.4.5 Precasted Slab‐Girder Decks 152
4.4.6 Box Girder Decks 155
4.5 Superstructure: Steel and Steel‐Concrete Composite Bridges 160
4.5.1 Options for Bridge Type: Plated Structures 160
4.5.2 Steels for Metal Bridges and Corrosion Protection 166
4.5.2.1 Materials and Weldability 166
4.5.2.2 Corrosion Protection 172
4.5.3 Slab Deck: Concrete Slabs and Orthotropic Plates 173
4.5.3.1 Concrete Slab Decks 174
4.5.3.2 Steel Orthotropic Plate Decks 176
4.5.4 Plate Girder Bridges 179
4.5.4.1 Superstructure Components 179
4.5.4.2 Preliminary Design of the Main Girders 182
4.5.4.3 Vertical Bracing System 188
4.5.4.4 Horizontal Bracing System 191
4.5.5 Box Girder Bridges 192
4.5.5.1 General 192
4.5.5.2 Superstructure Components 193
4.5.5.3 Pre‐Design of Composite Box Girder Sections 196
4.5.5.4 Pre‐Design of Diaphragms or Cross Frames 199
4.5.6 Typical Steel Quantities 201
4.6 Superstructure: Execution Methods 202
4.6.1 General Aspects 202
4.6.2 Execution Methods for Concrete Decks 203
4.6.2.1 General 203
4.6.2.2 Scaffoldings and Falseworks 203
4.6.2.3 Formwork Launching Girders 206
4.6.2.4 Incremental Launching 206
4.6.2.5 Cantilever Construction 212
4.6.2.6 Precasted Segmental Cantilever Construction 221
4.6.2.7 Other Methods 222
4.6.3 Erection Methods for Steel and Composite Bridges 223
4.6.3.1 Erection Methods, Transport and Erection Joints 223
4.6.3.2 Erection with Cranes Supported from the Ground 224
4.6.3.3 Incremental Launching 224
4.6.3.4 Erection by the Cantilever Method 227
4.6.3.5 Other Methods 227
4.7 Substructure: Conceptual Design and Execution Methods 229
4.7.1 Elements and Functions 229
4.7.2 Bridge Piers 229
4.7.2.1 Structural Materials and Pier Typology 229
4.7.2.2 Piers Pre‐Design 232
4.7.2.3 Execution Method of the Deck and Pier Concept Design 233
4.7.2.4 Construction Methods for Piers 240
4.7.3 Abutments 241
4.7.3.1 Functions of the Abutments 241
4.7.3.2 Abutment Concepts and Typology 241
4.7.4 Bridge Foundations 245
4.7.4.1 Foundation Typology 245
4.7.4.2 Direct Foundations 245
4.7.4.3 Pile Foundations 246
4.7.4.4 Special Bridge Foundations 247
4.7.4.5 Bridge Pier Foundations in Rivers 250
References 251
5 Aesthetics and Environmental Integration 255
5.1 Introduction 255
5.2 Integration and Formal Aspects 256
5.3 Bridge Environment 256
5.4 Shape and Function 258
5.5 Order and Continuity 260
5.6 Slenderness and Transparency 262
5.7 Symmetries, Asymmetries and Proximity with Other Bridges 266
5.8 Piers Aesthetics 267
5.9 Colours, Shadows, and Detailing 268
5.10 Urban Bridges 272
References 277
6 Superstructure: Analysis and Design 279
6.1 Introduction 279
6.2 Structural Models 280
6.3 Deck Slabs 283
6.3.1 General 283
6.3.2 Overall Bending: Shear Lag Effects 283
6.3.3 Local Bending Effects: Influence Surfaces 287
6.3.4 Elastic Restraint of Deck Slabs 295
6.3.5 Transverse Prestressing of Deck Slabs 297
6.3.6 Steel Orthotropic Plate Decks 300
6.4 Transverse Analysis of Bridge Decks 301
6.4.1 Use of Influence Lines for Transverse Load Distribution 301
6.4.2 Transverse Load Distribution Coefficients for Load Effects 302
6.4.3 Transverse Load Distribution Methods 303
6.4.3.1 Rigid Cross Beam Methods: Courbon Method 304
6.4.3.2 Transverse Load Distribution on Cross Beams 307
6.4.3.3 Extensions of the Courbon Method: Influence of Torsional Stiffness of Main Girders and Deformability of Cross Beams 307
6.4.3.4 The Orthotropic Plate Approach 308
6.4.3.5 Other Transverse Load Distribution Methods 313
6.5 Deck Analysis by Grid and FEM Models 313
6.5.1 Grid Models 313
6.5.1.1 Fundamentals 313
6.5.1.2 Deck Modelling 315
6.5.1.3 Properties of Beam Elements in Grid Models 317
6.5.1.4 Limitations and Extensions of Plane Grid Modelling 318
6.5.2 FEM Models 318
6.5.2.1 Fundamentals 318
6.5.2.2 FEM for Analysis of Bridge Decks 323
6.6 Longitudinal Analysis of the Superstructure 329
6.6.1 Generalities – Geometrical Non‐Linear Effects: Cables and Arches 329
6.6.2 Frame and Arch Effects 332
6.6.3 Effect of Longitudinal Variation of Cross Sections 334
6.6.4 Torsion Effects in Bridge Decks – Non‐Uniform Torsion 336
6.6.5 Torsion in Steel‐Concrete Composite Decks 343
6.6.5.1 Composite Box Girder Decks 343
6.6.5.2 Composite Plate Girder Decks 345
6.6.5.3 Transverse Load Distribution in Open Section Decks 348
6.6.6 Curved Bridges 350
6.6.6.1 Statics of Curved Bridges 350
6.6.6.2 Simply Supported Curved Bridge Deck 352
6.6.6.3 Approximate Method 353
6.6.6.4 Bearing System and Deck Elongations 353
6.7 Influence of Construction Methods on Superstructure Analysis 355
6.7.1 Span by Span Erection of Prestressed Concrete Decks 356
6.7.2 Cantilever Construction of Prestressed Concrete Decks 357
6.7.3 Prestressed Concrete Decks with Prefabricated Girders 360
6.7.4 Steel‐Concrete Composite Decks 361
6.8 Prestressed Concrete Decks: Design Aspects 364
6.8.1 Generalities 364
6.8.2 Design Concepts and Basic Criteria 364
6.8.3 Durability 364
6.8.4 Concept of Partial Prestressed Concrete (PPC) 364
6.8.5 Particular Aspects of Bridges Built by Cantilevering 365
6.8.6 Ductility and Precasted Segmental Construction 366
6.8.6.1 Internal and External Prestressing 367
6.8.7 Hyperstatic Prestressing Effects 367
6.8.8 Deflections, Vibration and Fatigue 368
6.9 Steel and Composite Decks 373
6.9.1 Generalities 373
6.9.2 Design Criteria for ULS 373
6.9.3 Design Criteria for SLS 375
6.9.3.1 Stress Limitations and Web Breathing 376
6.9.3.2 Deflection Limitations and Vibrations 377
6.9.4 Design Criteria for Fatigue Limit State 377
6.9.5 Web Design of Plate and Box Girder Sections 383
6.9.5.1 Web Under in Plane Bending and Shear Forces 383
6.9.5.2 Flange Induced Buckling 385
6.9.5.3 Webs Under Patch Loading 387
6.9.5.4 Webs under Interaction of Internal Forces 389
6.9.6 Transverse Web Stiffeners 390
6.9.7 Stiffened Panels in Webs and Flanges 391
6.9.8 Diaphragms 394
6.10 Reference to Special Bridges: Bowstring Arches and Cable‐Stayed Bridges 395
6.10.1 Generalities 395
6.10.2 Bowstring Arch Bridges 396
6.10.2.1 Geometry, Slenderness and Stability 396
6.10.2.2 Hanger System and Anchorages 402
6.10.2.3 Analysis of the Superstructure 403
6.10.3 Cable‐Stayed Bridges 404
6.10.3.1 Basic Concepts 404
6.10.3.2 Total and Partial Adjustment Staying Options 408
6.10.3.3 Deck Slenderness, Static and Aerodynamic Stability 411
6.10.3.4 Stays and Stay Cable Anchorages 414
6.10.3.5 Analysis of the Superstructure 416
References 418
7 Substructure: Analysis and Design 423
7.1 Introduction 423
7.2 Distribution of Forces Between Piers and Abutments 423
7.2.1 Distribution of a Longitudinal Force 423
7.2.2 Action Due to Imposed Deformations 424
7.2.3 Distribution of a Transverse Horizontal Force 425
7.2.4 Effect of Deformation of Bearings and Foundations 429
7.3 Design of Bridge Bearings 430
7.3.1 Bearing Types 430
7.3.2 Elastomeric Bearings 430
7.3.3 Neoprene‐Teflon Bridge Bearings 434
7.3.4 Elastomeric ‘Pot Bearings’ 435
7.3.5 Metal Bearings 437
7.3.6 Concrete Hinges 439
7.4 Reference to Seismic Devices 441
7.4.1 Concept 441
7.4.2 Seismic Dampers 441
7.5 Abutments: Analysis and Design 444
7.5.1 Actions and Design Criteria 444
7.5.2 Front and Wing Walls 446
7.5.3 Anchored Abutments 448
7.6 Bridge Piers: Analysis and Design 449
7.6.1 Basic Concepts 449
7.6.1.1 Pre‐design 449
7.6.1.2 Slenderness and Elastic Critical Load 449
7.6.1.3 The Effect of Geometrical Initial Imperfections 450
7.6.1.4 The Effect of Cracking in Concrete Bridge Piers 450
7.6.1.5 Bridge Piers as ‘Beam Columns’ 451
7.6.1.6 The Effect of Imposed Displacements 452
7.6.1.7 The Overall Stability of a Bridge Structure 453
7.6.1.8 Design Bucking Length of Bridge Piers 453
7.6.2 Elastic Analysis of Bridge Piers 454
7.6.3 Elastoplastic Analysis of Bridge Piers: Ultimate Resistance 459
7.6.4 Creep Effects on Concrete Bridge Piers 465
7.6.5 Analysis of Bridge Piers by Numerical Methods 465
7.6.6 Overall Stability of a Bridge Structure 471
References 473
8 Design Examples: Concrete and Composite Options 475
8.1 Introduction 475
8.2 Basic Data and Bridge Options 475
8.2.1 Bridge Function and Layout 475
8.2.2 Typical Deck Cross Sections 476
8.2.3 Piers, Abutments and Foundations 477
8.2.4 Materials Adopted 477
8.2.4.1 Prestressed Concrete Deck 478
8.2.4.2 Steel‐concrete Composite Deck 481
8.2.5 Deck Construction 481
8.3 Hazard Scenarios and Actions 481
8.3.1 Limit States and Structural Safety 482
8.3.2 Actions 482
8.3.2.1 Permanent Actions and Imposed Deformations 482
8.3.2.2 Variable Actions 484
8.4 Prestressed Concrete Solution 486
8.4.1 Preliminary Design of the Deck 486
8.4.2 Structural Analysis and Slab Checks 486
8.4.3 Structural Analysis of the Main Girders 492
8.4.3.1 Traffic Loads: Transverse and Longitudinal Locations 493
8.4.3.2 Internal Forces 497
8.4.3.3 Prestressing Layout and Hyperstatic Effects 497
8.4.3.4 Influence of the Construction Stages 498
8.4.4 Structural Safety Checks: Longitudinal Direction 498
8.4.4.1 Decompression Limit State – Prestressing Design 498
8.4.4.2 Ultimate Limit States – Bending and Shear Resistance 501
8.5 Steel–Concrete Composite Solution 502
8.5.1 Preliminary Design of the Deck 502
8.5.2 Structural Analysis and Slab Design Checks 503
8.5.3 Structural Analysis of the Main Girders 503
8.5.3.1 Traffic Loads Transverse and Longitudinal Positioning 504
8.5.3.2 Internal Forces 505
8.5.3.3 Shrinkage Effects 505
8.5.3.4 Imposed Deformation Effect 506
8.5.3.5 Influence of the Construction Stages 506
8.5.4 Safety Checks: Longitudinal Direction 507
8.5.4.1 Ultimate Limit States – Bending and Shear Resistance 507
8.5.4.2 Serviceability Limit States – Stresses and Crack Widths Control 509
References 510
Annex A: Buckling and Ultimate Strength of Flat Plates 511
A.1 Critical Stresses and Buckling Modes of Flat Plates 511
A.1.1 Plate Simply Supported along the four Edges and under a Uniform Compression (ψ = 1) 511
A.1.2 Bending of Long Rectangular Plates Supported at both Longitudinal Edges or with a Free Edge 513
A.1.3 Buckling of Rectangular Plates under Shear 513
A.2 Buckling of Stiffened Plates 514
A.2.1 Plates with One Longitudinal Stiffener at the Centreline under Uniform Compression 515
A.2.2 Plate with Two Stiffeners under Uniform Compression 516
A.2.3 Plates with Three or More Longitudinal Stiffeners 517
A.2.4 Stiffened Plates under Variable Compression. Approximate Formulas 518
A.3 Post‐Buckling Behaviour and Ultimate Strength of Flat Plates 518
A.3.1 Effective Width Concept 519
A.3.2 Effective Width Formulas 520
References 523
Index 525
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