Wind Effects on Cable-Supported Bridges

Title Page
......Page 4
Contents......Page 8
Foreword by Ahsan Kareem......Page 22
Foreword by Hai-Fan Xiang......Page 24
Preface......Page 26
Acknowledgements......Page 28
1.2.1 Global Wind Circulations......Page 30
1.2.4 Geostrophic Wind......Page 32
1.2.5 Gradient Wind......Page 33
1.2.6 Frictional Effects......Page 34
1.3.2 Monsoons......Page 35
1.3.3 Tropical Cyclones (Hurricanes or Typhoons)......Page 36
1.3.4 Thunderstorms......Page 37
1.3.5 Downbursts......Page 38
1.3.6 Tornadoes......Page 39
1.4.1 Main Features of Cable-Supported Bridges......Page 40
1.4.2 Suspension Bridges......Page 41
1.4.3 Cable-Stayed Bridges......Page 42
1.4.4 Hybrid Cable-Supported Bridges......Page 44
1.5.1 Suspension Bridges......Page 45
1.5.2 Cable-Stayed Bridges......Page 46
1.5.3 Stay Cables......Page 47
1.6 History of Bridge Aerodynamics......Page 48
1.7 Organization of this Book......Page 50
References......Page 51
2.2 TurbulentWinds in Atmospheric Boundary Layer......Page 54
2.3 Mean Wind Speed Profiles......Page 56
2.3.1 The “Logarithmic Law”......Page 57
2.3.3 Mean Wind Speed Profile Over Ocean......Page 59
2.4.1 Standard Deviations......Page 60
2.4.2 Turbulence Intensities......Page 61
2.4.3 Time Scales and Integral Length Scales......Page 62
2.4.4 Probability Density Functions......Page 63
2.4.5 Power Spectral Density Functions......Page 64
2.4.6 Covariance and Correlation......Page 65
2.4.7 Cross-Spectrum and Coherence......Page 66
2.4.8 Gust Wind Speed and Gust Factor......Page 67
2.5.2 Amplification of Wind by Hills......Page 69
2.5.4 Funneling Effect......Page 71
2.6.1 Exceedance Probability and Return Period......Page 72
2.6.2 Probability Distribution Function......Page 73
2.6.4 Extreme Wind Estimation by the Gumbel Distribution......Page 74
2.6.5 Extreme Wind Estimation by the Method of Moments......Page 75
2.6.6 Design Lifespan and Risk......Page 76
2.7 Directional Preference of High Winds......Page 77
2.8 Case Study: Tsing Ma Bridge Site......Page 78
2.8.1 Anemometers in WASHMS......Page 79
2.8.2 Typhoon Wind Characteristics......Page 80
2.8.3 Monsoon Wind and Joint Probability Density Function......Page 83
2.9 Notations......Page 86
References......Page 87
3.2.1 Bernoulli’s Equation and Wind Pressure......Page 90
3.2.2 Mean Wind Load......Page 91
3.3 Torsional Divergence......Page 92
3.4 3-D Aerostatic Instability Analysis......Page 95
3.5 Finite Element Modeling of Long-Span Cable-Supported Bridges......Page 96
3.5.2 Spine Beam Model......Page 97
3.5.3 Multi-Scale Model......Page 98
3.5.4 Modeling of Cables......Page 100
3.6.2 Mean Wind Response Analysis......Page 102
3.7.1 Main Features of Stonecutters Bridge......Page 103
3.7.2 Finite Element Modeling of Stonecutters Bridge......Page 104
3.7.4 Mean Wind Response Analysis......Page 107
References......Page 109
4.1 Preview......Page 112
4.2.1 Reynolds Number and Vortex Shedding......Page 113
4.2.2 Strouhal Number and Lock-In......Page 114
4.2.3 Vortex-Induced Vibration......Page 115
4.3.1 Galloping Mechanism......Page 117
4.3.3 Wake Galloping......Page 119
4.4.1 Introduction......Page 120
4.4.2 Self-Excited Forces and Aerodynamic Derivatives......Page 121
4.4.3 Theodorsen Circulatory Function......Page 122
4.4.4 1-D Flutter Analysis......Page 123
4.4.5 2-D Flutter Analysis......Page 124
4.4.6 3-D Flutter Analysis in the Frequency Domain......Page 125
4.5.2 Buffeting Forces and Aerodynamic Admittances......Page 130
4.5.3 3-D Buffeting Analysis in the Frequency Domain......Page 132
4.6 Simulation of Stationary Wind Field......Page 136
4.7 Buffeting Analysis in the Time Domain......Page 138
4.8.1 Gust Response Factor and Peak Factor......Page 141
4.8.2 Effective Static Loading Distributions......Page 142
4.9.2 Flutter Analysis of Stonecutters Bridge......Page 144
4.9.3 Buffeting Analysis of Stonecutters Bridge......Page 149
4.10 Notations......Page 155
References......Page 158
5.2 Fundamentals of Cable Dynamics......Page 160
5.2.1 Vibration of a Taut String......Page 161
5.2.2 Vibration of an Inclined Cable with Sag......Page 162
5.3.2 Vortex-Induced Vibration......Page 165
5.3.3 Galloping of Dry Inclined Cables......Page 166
5.4.1 Background......Page 167
5.4.2 Analytical Model of SDOF......Page 168
5.4.3 Horizontal Cylinder with Fixed Rivulet......Page 173
5.4.4 Inclined Cylinder with Moving Rivulet......Page 176
5.4.5 Analytical Model of 2DOF......Page 179
5.5 Prediction of Rain-Wind-Induced Cable Vibration......Page 180
5.5.1 Analytical Model for Full-Scale Stay Cables......Page 181
5.5.2 Prediction of Rain-Wind-Induced Vibration of Full-Scale Stay Cable......Page 183
5.5.3 Parameter Studies......Page 185
5.6 Occurrence Probability of Rain-Wind-Induced Cable Vibration......Page 187
5.6.1 Joint Probability Density Function (JPDF) of Wind Speed and Direction......Page 188
5.6.3 Occurrence Range of Rain-Wind-Induced Cable Vibration......Page 190
5.6.4 Occurrence Probability of Rain-Wind-Induced Cable Vibration......Page 191
5.7.1 Statistical Analysis of Wind Data......Page 192
5.7.2 Joint Probability Density Function of Wind Speed and Wind Direction......Page 194
5.7.3 Statistical Analysis of Rainfall Data......Page 196
5.7.5 Occurrence Range of Rain-Wind-Induced Cable Vibration......Page 199
5.8 Notations......Page 202
References......Page 204
6.1 Preview......Page 206
6.2.2 Modeling of Road Vehicle......Page 207
6.2.3 Modeling of Road Surface Roughness......Page 208
6.2.4 Aerodynamic Forces and Moments on Road Vehicle......Page 209
6.2.5 Governing Equations of Motion of Road Vehicle......Page 211
6.2.6 Case Study......Page 215
6.2.7 Effects of Road Surface Roughness......Page 217
6.2.8 Effects of Vehicle Suspension System......Page 221
6.2.9 Accident Vehicle Speed......Page 222
6.3.1 Equations of Motion of Coupled Road Vehicle-Bridge System......Page 225
6.3.2 Equations of Motion of Coupled Wind-Road Vehicle-Bridge System......Page 227
6.4.1 Ting Kau Bridge......Page 229
6.4.2 Wind Forces on Bridge......Page 230
6.4.3 Scenario for Extreme Case Study......Page 231
6.4.4 Dynamic Response of High-Sided Road Vehicle......Page 232
6.4.5 Accident Vehicle Speed......Page 233
6.4.6 Comparison of Safety of Road Vehicle Running on Bridge and Ground......Page 234
6.5 Formulation of Wind-Railway Vehicle Interaction......Page 235
6.5.1 Modeling of Vehicle Subsystem......Page 236
6.5.3 Wheel and Rail Interaction......Page 238
6.5.4 Rail Irregularity......Page 240
6.5.5 Wind Forces on Ground Railway Vehicles......Page 241
6.5.6 Numerical Solution......Page 244
6.6.1 Vehicle and Track Models......Page 246
6.6.2 Wind Forces on Railway Vehicle......Page 247
6.6.3 Rail Irregularity......Page 249
6.6.5 Safety and Ride Comfort Performance......Page 250
6.7.1 Formulation of Wind-Railway Vehicle-Bridge Interaction......Page 257
6.7.2 Engineering Approach for Determining Wind Forces on Moving Vehicle......Page 258
6.7.3 Case Study......Page 259
6.8 Notations......Page 263
References......Page 267
7.2 Boundary Layer Wind Tunnels......Page 270
7.2.1 Open-Circuit Wind Tunnel......Page 271
7.2.2 Closed-Circuit Wind Tunnel......Page 272
7.3.1 General Model Scaling Requirements......Page 273
7.3.2 Notes on Model Scaling Requirements......Page 274
7.3.3 Blockage Consideration......Page 275
7.4.2 Augmented Method......Page 276
7.4.3 Actively Controlled Grids and Spires......Page 278
7.4.4 Actively Controlled Multiple Fans......Page 280
7.4.5 Topographic Models......Page 281
7.4.6 Instrumentation for Wind Measurement in Wind Tunnel......Page 282
7.5.1 Models and Scaling......Page 283
7.5.2 Section Model Tests for Force Coefficients......Page 284
7.5.3 Section Model Tests for Flutter Derivatives and Vortex-Induced Vibration......Page 285
7.5.4 Section Model Tests with Pressure Measurements......Page 286
7.6 Taut Strip Model Tests......Page 287
7.7 Full Aeroelastic Model Tests......Page 288
7.8.1 Free Vibration Test of Section Model......Page 289
7.8.2 Forced Vibration Test of Section Model......Page 292
7.8.3 Free Vibration Test of Taut Strip Model and Full Aeroelastic Model......Page 294
7.9 Identification of Aerodynamic Admittance......Page 295
7.10.1 Inclined Dry Cable Tests......Page 297
7.10.2 Rain-Wind Simulation of Inclined Stay Cable......Page 301
7.11 Vehicle-Bridge Model Tests......Page 303
7.11.1 Vehicles on Ground......Page 304
7.11.2 Stationary Vehicle on Bridge Deck......Page 308
7.11.3 Moving Vehicle on Bridge Deck......Page 311
7.12 Notations......Page 312
References......Page 314
8.2.1 Mass Conservation......Page 318
8.2.2 Momentum Conservation......Page 319
8.2.3 Energy Conservation and Newtonian Flow......Page 320
8.2.5 Governing Equations of Wind Flow......Page 321
8.3.1 Direct Numerical Simulation......Page 322
8.3.2 Reynolds Averaged Method......Page 323
8.3.3 Large Eddy Simulation......Page 329
8.3.4 Detached Eddy Simulation......Page 332
8.4 Numerical Considerations......Page 333
8.4.1 Finite Difference Method......Page 334
8.4.2 Finite Element Method......Page 336
8.4.3 Finite Volume Method......Page 338
8.4.4 Solution Algorithms for Pressure-Velocity Coupling in Steady Flows......Page 340
8.4.5 Solution for Unsteady Flows......Page 343
8.4.7 Grid Generation......Page 344
8.4.8 Computing Techniques......Page 346
8.5.1 Computational Domain......Page 348
8.5.2 Meshing......Page 349
8.5.4 Aerodynamic Force Coefficients and Flow Field......Page 350
8.6.1 Computational Domain......Page 352
8.6.2 Meshing......Page 353
8.6.4 Simulation Results......Page 354
8.6.5 Vehicle Moving on Ground......Page 357
8.7 CFD for Aerodynamics of Coupled Vehicle-Bridge Deck System......Page 359
8.7.2 Meshing......Page 360
8.7.4 Simulation Results......Page 361
8.7.5 Moving Vehicle on Bridge Deck......Page 363
8.8.1 Modeling and Meshing......Page 365
8.8.2 Numerical Method......Page 366
8.8.3 Simulation Results......Page 367
8.9.1 Modeling and Meshing......Page 368
8.9.3 Simulation Results......Page 369
8.10 Notations......Page 370
References......Page 372
9.1 Preview......Page 374
9.2 Design of Wind and Structural Health Monitoring Systems......Page 375
9.3.1 Anemometers and Other Wind Measurement Sensors......Page 376
9.3.3 Displacement Transducers and Level Sensors......Page 377
9.3.5 Strain Gauges......Page 378
9.3.8 Weather Stations......Page 379
9.4.2 Hardware of Data Acquisition Units......Page 380
9.4.4 Operation of Data Acquisition and Transmission......Page 382
9.5.2 Signal Pre-Processing and Post-Processing......Page 383
9.6.2 Maintenance of Data Management System......Page 384
9.7.1 Overview of WASHMS......Page 385
9.7.2 Anemometers in WASHMS......Page 387
9.7.3 Temperature Sensors in WASHMS......Page 388
9.7.4 Displacement Transducers in WASHMS......Page 389
9.7.6 GPS in WASHMS......Page 390
9.7.7 Strain Gauges in WASHMS......Page 391
9.8.1 Typhoon Victor......Page 392
9.8.3 Calculations of Mean Wind Speed and Fluctuating Wind Components......Page 393
9.8.4 Mean Wind Speed and Direction......Page 396
9.8.5 Turbulence Intensity and Integral Scale......Page 399
9.8.6 Wind Spectra......Page 400
9.8.7 Acceleration Response of Bridge Deck......Page 402
9.8.8 Acceleration Response of Bridge Cable......Page 403
9.8.9 Remarks......Page 404
9.9.2 EMD+HT Method......Page 405
9.9.3 Natural Frequencies and Modal Damping Ratios......Page 408
9.10 Notations......Page 410
References......Page 411
10.1 Preview......Page 414
10.2.2 Coordinate Systems and Transformation Matrices......Page 415
10.2.4 Buffeting Forces and Spectra under Skew Winds......Page 419
10.2.5 Aeroelastic Forces under Skew Winds......Page 426
10.2.6 Governing Equation and Solution in the Frequency Domain......Page 427
10.3.1 Buffeting Forces due to Skew Winds in the Time Domain......Page 430
10.3.2 Self-Excited Forces due to Skew Winds in the Time Domain......Page 434
10.3.3 Governing Equation and Solution in the Time Domain......Page 437
10.4 Aerodynamic Coefficients of Bridge Deck under Skew Winds......Page 438
10.5 Flutter Derivatives of Bridge Deck under Skew Winds......Page 442
10.6 Aerodynamic Coefficients of Bridge Tower under Skew Winds......Page 447
10.7.1 Typhoon Sam and Measured Wind Data......Page 453
10.7.2 Measured Bridge Acceleration Responses......Page 454
10.7.3 Input Data to Computer Simulation......Page 455
10.7.4 Comparison of Buffeting Response in the Frequency Domain......Page 457
10.7.5 Comparison of Buffeting Response in the Time Domain......Page 458
10.8 Notations......Page 462
References......Page 466
11.1 Preview......Page 468
11.2.1 Background......Page 469
11.2.2 Main Features of Tsing Ma Bridge......Page 470
11.2.3 Finite Element Modeling of Tsing Ma Bridge......Page 471
11.3.1 Equation of Motion......Page 474
11.3.2 Buffeting Forces......Page 475
11.3.3 Self-Excited Forces......Page 478
11.3.4 Determination of Bridge Responses......Page 480
11.4 Comparison with Field Measurement Results of Tsing Ma Bridge......Page 481
11.4.1 Wind Characteristics......Page 482
11.4.2 Measured Acceleration Responses of Bridge Deck......Page 483
11.4.3 Measured Stresses of Bridge Deck......Page 484
11.4.4 Wind Field Simulation......Page 485
11.4.5 Buffeting Forces and Self-Excited Forces......Page 488
11.4.6 Comparison of Bridge Acceleration Responses......Page 490
11.4.7 Comparison of Bridge Stress Responses......Page 491
11.5.1 Background......Page 493
11.5.2 Joint Probability Density Function of Wind Speed and Direction......Page 494
11.5.3 Critical Stresses and Hot Spot Stresses......Page 498
11.5.4 Hot Spot Stress Characteristics......Page 500
11.5.5 Damage Evolution Model......Page 501
11.5.6 Buffeting-Induced Fatigue Damage Assessment......Page 503
11.6.1 Equation of Motion......Page 505
11.6.2 Pseudo Forces in Trains and Road Vehicles......Page 507
11.6.3 Contact Forces between Train and Bridge......Page 508
11.6.4 Contact Forces between Road Vehicles and Bridge......Page 509
11.6.6 Wind Forces on Vehicles......Page 510
11.6.7 Numerical Solution......Page 511
11.7 Verification by Case Study: Tsing Ma Bridge......Page 512
11.7.1 Finite Element Models of Bridge, Train and Road Vehicles......Page 513
11.7.3 Wind Force Simulation......Page 514
11.7.4 Selected Results......Page 515
11.8.1 Establishment of Framework......Page 517
11.8.3 Dynamic Stress Analysis using Engineering Approach......Page 519
11.8.4 Verification of Engineering Approach......Page 521
11.8.5 Determination of Fatigue-Critical Locations......Page 522
11.8.6 Databases of Dynamic Stress Responses to Different Loadings......Page 527
11.8.7 Multiple Load-Induced Dynamic Stress Time Histories in Design Life......Page 528
11.8.8 Fatigue Analysis at Fatigue-Critical Locations......Page 529
11.9 Notations......Page 532
References......Page 536
12.2 Control Methods for Wind-Induced Vibration......Page 538
12.3.1 Passive Aerodynamic Measures......Page 542
12.3.2 Active Aerodynamic Control......Page 544
12.4 Aerodynamic Measures for Vortex-Induced Vibration Control......Page 547
12.5.1 Wind Tunnel Investigation and Cable Drag Coefficients......Page 549
12.5.2 Rain-Wind Tunnel Investigation of Stay Cables of Different Surfaces......Page 551
12.6 Mechanical Measures for Vortex-Induced Vibration Control......Page 552
12.7.1 Passive Control Systems for Flutter Control......Page 554
12.7.2 Active Control Systems for Flutter Control......Page 558
12.8.1 Multiple Pressurized Tuned Liquid Column Dampers......Page 559
12.8.2 Semi-Active Tuned Liquid Column Dampers......Page 563
12.9 Mechanical Measures for Rain-Wind-Induced Cable Vibration Control......Page 570
12.10 Case Study: Damping Stay Cables in a Cable-Stayed Bridge......Page 581
12.11 Notations......Page 593
References......Page 595
13.1 Preview......Page 598
13.2.1 Background......Page 599
13.2.2 Refined Typhoon Wind Field Model......Page 600
13.2.3 Typhoon Wind Decay Model......Page 602
13.3.1 Decomposition Method......Page 603
13.3.3 Friction-Induced Wind Velocity......Page 604
13.4.1 Typhoon York......Page 605
13.4.3 Wind Field Simulation at Waglan Island......Page 607
13.4.4 Spatial Distribution of Typhoon Wind Field......Page 608
13.4.5 Wind Speed Profiles in Vertical Direction......Page 610
13.5.1 Background......Page 614
13.5.3 Probability Distributions of Key Parameters......Page 615
13.5.4 K-S Test......Page 617
13.5.5 Typhoon Wind Decay Model Parameters......Page 618
13.5.6 Procedure for Estimating Extreme Wind Speeds and Averaged Wind Profiles......Page 619
13.6.1 Basic Theory......Page 622
13.6.3 Extreme Wind Speed Analysis based on Wind Measurement Data......Page 623
13.6.5 Mean Wind Speed Profile Analysis......Page 624
13.7.1 Background......Page 626
13.7.4 Training ANN Model for Predicting Directional Typhoon Wind Speeds and Profiles......Page 627
13.8.1 Topographical Conditions......Page 629
13.8.2 Directional Upstream Typhoon Wind Speeds and Profiles......Page 631
13.8.3 Representative Typhoon Wind Speeds and Profiles......Page 632
13.8.4 Establishment of ANN Model......Page 635
13.8.5 Directional Design Wind Speeds and Wind Profiles......Page 637
13.9 Notations......Page 640
References......Page 641
14.2.1 Limit-States......Page 644
14.2.2 First-Order Second Moment (FOSM) Method......Page 646
14.2.3 Hasofer and Lind (HL) Method......Page 647
14.2.4 Monte Carlo Simulation (MCS) and Response Surface Method (RSM)......Page 650
14.2.5 Threshold Crossing......Page 651
14.2.6 Peak Distribution......Page 653
14.4 Flutter Reliability Analysis......Page 655
14.5.1 Failure Model by First Passage......Page 657
14.5.2 Reliability Analysis based on Threshold Crossings......Page 658
14.5.3 Reliability Analysis based on Peak Distribution......Page 659
14.5.4 Notes on Buffeting Reliability Analysis......Page 660
14.7 Fatigue Reliability Analysis based on Miner’s Rule for Tsing Ma Bridge......Page 661
14.7.1 Framework for Fatigue Reliability Analysis......Page 663
14.7.2 Probabilistic Model of Railway Loading......Page 664
14.7.3 Probabilistic Model of Highway Loading......Page 666
14.7.5 Multiple Load-Induced Daily Stochastic Stress Response......Page 668
14.7.6 Probability Distribution of the Daily Sum of m-power Stress Ranges......Page 672
14.7.7 Probability Distribution of the Sum of m-power Stress Ranges within the Period......Page 674
14.7.8 Reliability Analysis Results......Page 677
14.8 Fatigue Reliability Analysis based on Continuum Damage Mechanics......Page 679
14.8.1 Basic Theory of Continuum Damage Mechanics......Page 680
14.8.3 Continuum Damage Model used in This Study......Page 682
14.8.4 Verification of Continuum Damage Model......Page 683
14.8.5 Framework of Fatigue Reliability Analysis......Page 685
14.8.6 Reliability Analysis Results......Page 686
14.9 Notations......Page 687
References......Page 688
15.1 Preview......Page 690
15.2.2 Empirical Mode Decomposition......Page 691
15.2.4 Case Study: Typhoon Victor......Page 693
15.3 Non-Stationary Wind Model II......Page 702
15.3.2 Evolutionary Spectra......Page 703
15.3.4 Case Study: Typhoon Dujuan......Page 705
15.4.2 Non-Stationary Self-Excited Forces......Page 709
15.4.4 Governing Equations of Motion......Page 710
15.4.6 Modal Equations for Non-Stationary Buffeting Response......Page 712
15.4.8 Case Study: Stonecutters Bridge......Page 713
15.5.2 Approximate Estimation of Extreme Value......Page 717
15.5.3 Possion Approximation......Page 719
15.5.4 Vanmarcke Approximation......Page 720
15.5.6 Case Study: Stonecutters Bridge......Page 721
15.6.2 Unconditional Simulation......Page 726
15.7.1 Background......Page 727
15.7.3 Conditional Simulation Method......Page 728
15.7.4 Computational Difficulties in Conditional Simulation......Page 730
15.7.5 Alternative Formulas for Decomposition......Page 731
15.7.6 Fast Algorithm for Conditional Simulation......Page 733
15.7.8 Validation and Application......Page 735
15.8.1 Introduction......Page 740
15.8.2 Linearization Model for Non-Linear Aerodynamic Forces......Page 741
15.8.3 Hysteretic Behavior of Non-Linear Aerodynamic Forces......Page 743
15.8.4 Hysteretic Models for Non-Linear Aerodynamic Forces......Page 746
15.8.5 ANN-Based Hysteretic Model of Non-Linear Buffeting Response......Page 748
15.9 Notations......Page 750
References......Page 756
16.1.1 Typhoon Wind Characteristics and Topography Effects......Page 758
16.1.3 Effects of Aerodynamic Non-Linearity......Page 759
16.1.5 Rain-Wind-Induced Vibration of Stay Cables......Page 760
16.1.7 Advancing Computational Wind Engineering and Wind Tunnel Test Techniques......Page 761
16.2 Prospects......Page 762
Index......Page 764