V

Contents

/

Preface Acknowledgements Disclaimer Authors

1 Introduction 1

1.1 Introduction 1 1.2 Factors affecting structural form J 1.3 Cross sections 2

1.3.1 Solid rectangular 2 -1.3.2 Voided rectangular 3 ' 1.3.3 T-section 4 1.3.4 Box sections 5 1.3.5 Older concepts 6

1.4 Bridge elevations 7 \ 1.4.1 Simply supported beam/slab 8 1.4.2 Series of simply supported beams/slabs 8 1.4.3 Continuous beam/slab with full propping during construction 8 1.4.4 Partially continuous beam/slab 9 1.4.5 Continuous beam/slab: Span-by-span construction 12 1.4.6 Continuous beam/slab: Balanced cantilever construction 13 1.4.7 Continuous beam/slab: Push-launch construction 16 1.4.8 Arch bridges 16 1.4.9 Frame or box culvert (integral bridge) 19 1.4.10 Beams/slabs with drop-in span 21 1.4.11 Cable-stayed bridges 22 1.4.12 Suspension bridges 24

^ 1.5 Articulation 24 1.6 Bearings 27

1.6.1 Sliding hearings 27 ' 1.6.2 Pot bearings 28 ^ \ 1.6.3 Elastomeric hearings 28

1.7 Joints 29 1.7.1 Buried joint 30

X V

xvii xix

viii Contents

1.7.2 Asphaltic plug joint 3 0 1.7.3 Nosing joint 30 1.7.4 Reinforced elastomeric joint 31 1.7.5 Elastomeric in metal runners joint 31 1.7.6 Cantilever comb or tooth joint 32

1.8 Bridge aesthetics 32 1.8.1 Single-span beam/slab/frame bridges of constant depth 33 1.8.2 Multiple spans 34

2 Bridge loading

2.1 Introduction 39 2.2 Dead loading 40 ^ 2.3 Imposed traffic loading 41 \ ...

2.3.1 Pedestrian traffic 41 2.3.2 Nature of road traffic loading 41 2.3.3 Code models for road traffic 44 2.3.4 Imposed loading due to rail traffic 45

2.4 Shrinkage and creep 46 2.4.1 Shrinkage 47 2.4.2 Creep 47

2.5 Thermal loading 47 2.5.1 Uniform changes in temperature 48 2.5.2 Differential changes in temperature 50

2.6 Impact loading 56 2.7 Dynamic effects 57 ^ 2.8 Prestress loading 61

2.8.1 Equivalent loads and linear transformation 61 2.8.2 Prestress losses 67 2.8.3 Non-prismatic bridges 69

3 Introduction to bridge analysis

3.1 Introduction 73 3.2 Positioning the traffic load model on the bridge 73 3.3 Differential settlement of supports 77 3.4 Thermal expansion and contraction 78

3.4.1 Equivalent loads method 81 , 3.5 Differential temperature effects 83

3.5.1 Temperature effects in three dimensions 93 '. 3.6 Prestress 96

3.7 Analysis for the effects of creep 102

39

73

Integral bridges

4.1

109

4.2

4.3 4.4

4.5 4.6

Introduction 109 4.1.1 Integral construction

4.1.2 . 4.1.3 , Contract 4.2.1 4.2.2 Convem Modellij 4.4.1 4.4.2 4.4.3 Run-on Time-dt

5 Slab bridge d

5.1 5.2

5.3

5.4

5.5

Introdu Thin-pi 5.2.1 5.2.2 5.2.3 5.2.4 5.2.5 Grillagt 5.3.1 5.3.2 5.3.3 5.3.4 5.3.5 5.3.6 5.3.7 Planar, 5.4.1 5.4.2 5.4.3 5.4.4 5.4.5 5.4.6 Woodc 5.5.1 5.5.2

109

Application

6.1 Introdv 6.2 Simple 6.3 Edge a 6.4 Voided

Contents ix

4.1.2 Lateral earth pressures on abutments 111 4.1.3 Stiffness of soil 114

4.2 Contraction of bridge deck 116 4.2.1 Contraction of bridge fully fixed at the supports 116 4.2.2 Contraction of bridge on flexible supports 116

4.3 Conventional spring model for deck expansion 120 4.4 Modelling expansion with an equivalent spring at deck level 123

4.4.1 Development of general expression 123 4.4.2 Expansion of frames with deep abutments 126 4.4.3 Expansion of bank-seat abutments 128

4.5 Run-on slab 131 4.6 Time-dependent effects in composite integral bridges 133

5 Slab bridge decks: Behaviour and modelling 137

5.1 Introduction 137 5.2 Thin-plate theory 137

5.2.1 Orthotropic and isotropic plates 137 5.2.2 Bending of materially orthotropic thin plates 138 5.2.3 Stress in materially orthotropic thin plates 144 5.2.4 Moments in materially orthotropic thin plates 146 5.2.5 Shear in thin plates 153

5.3 Grillage analysis of slab decks 155 5.3.1 Similitude between grillage and bridge slab 156 5.3.2 Grillage member properties: Isotropic slabs 158 5.3.3 Grillage member properties: Geometrically orthotropic slabs 162 5.3.4 Computer implementation of grillages 164 5.3.5 Sources of inaccuracy in grillage models 164 5.3.6 Shear force near point supports 166 5.3.7 Recommendations for grillage modelling 166

5.4 Planar finite element analysis of slab decks 168 " ^•^ 5.4.1 PE theory: Beam elements 168

5.4.2 FE theory: Plate elements 171 5.4.3 Similitude between plate FE model and bridge slab 175 5.4.4 Properties of plate finite elements 176 5.4.5 Shear forces in plate FE models 178 5.4.6 Recommendations for FE analysis 179

5.5 Wood and Armer equations 182 5.5.1 Resistance to twisting moment 186

\ New bridge design 187

109 6 Application of planar grillage and finite element methods 189

6.1 Introduction 189 ^ 6.2 Simple isotropic slabs 189 ^ 6.3 Edge cantilevers and edge stiffening 192 6.4 Voided slab bridge decks 200 \

X Contents

6.5 Beam-and-slab bridges 206 6.5.1 Grillage modelling 207 6.5.2 Finite element modelling 213 6.5.3 Transverse local behaviour of beam-and-slab bridges 215

6.6 Cellular bridges 215 6.6.1 Grillage modelling 216 j. _

6.7 Skew and curved bridge decks 222 . y 6.7.1 Grillage modelling 223 6.7.2 FE modelling 224

7 Three-dimensional modelling of bridge decks 225

7.1 Introduction 225 , " , 7.2 Shear lag and effective flange width 225 ^

7.2.1 Effective flange width 226 7.3 Three-dimensional analysis using brick elements 228

7.3.1 Interpretation of results of brick models 228 7.4 Upstand grillage modelling 239 7.5 Upstand finite element modelling 240

7.5.1 Upstand finite element modelling of voided slab bridge decks 244 7.5.2 Upstand FE modelling of other bridge types 247 7.5.3 Prestress loads in upstand FE models 248

8 Probabilistic assessment of bridge safety 251

8.1 Introduction 251 8.2 Code treatment of probability of failure 252

8.2.1 Eurocode 1990 253 ^ - . . • 8.2.2 ISO/CD 13822:2010 254 . / 8.2.3 Nordic Committee on Building Regulations 255 8.2.4 International Federation for Structural Concrete Bulletin 65 255 8.2.5 AASHTO 256

8.3 Calculation of the probability of failure, Pf 256 8.3.1 Basic statistical concepts 258

8.4 Resistance modelling 262 8.4.1 Reinforced concrete 263 8.4.2 Prestressed concrete 265 8.4.3 Structural steel 265 8.4.4 Soils 266 ' 8.4.5 Material model uncertainty 266

, 8.5 Deterioration modelling 268 it 8.6 Load modelling 273

8.6.1 Permanent and quasi-permanent loads 273 8.6.2 Variable imposed loads 274

8.7 Probabilistic assessment of LS violation 274 8.8 Component vs. system reliability analysis 275

Contents xi

9 Case studies 277

9.1 Introduction 277 9.2 Reinforced concrete beam-and-slab deck 277

9.2.1 Bridge model 277 9.2.2 Probabilistic classification and modelling 280 9.2.3 Results of probabilistic assessment 285

9.3 Post-tensioned concrete slab deck 287 9.3.1 Bridge model 288 9.3.2 Probabilistic classification and modelling 289 9.3.3 Results of probabilistic assessment 291

9.4 Steel truss bridge 293 . 9.4.1 Bridge model 294 ' 9.4.2 Probabilistic classification and modelling 296 9.4.3 Results of probabilistic assessment 299

9.5 Conclusion 301

References 303 Appendix A: Stiffness of structural members and associated bending

moment diagrams 309 Appendix B: Location of centroid of a section 311 Appendix C: Derivation of shear area for grillage member representing

cell with flange and web distortion 313 Index 315