Contenido Wind Effects on Cable-Supported Bridges

As an in-depth guide to understanding wind effects on cable-supported bridges, this book uses analytical, numerical and experimental methods to give readers a fundamental and practical understanding of the subject matter. It is structured to systemically move from introductory areas through to advanced topics currently being developed from research work. The author concludes with the application of the theory covered to real-world examples, enabling readers to apply their knowledge.

The author provides background material, covering areas such as wind climate, cable-supported bridges, wind-induced damage, and the history of bridge wind engineering. Wind characteristics in atmospheric boundary layer, mean wind load and aerostatic instability, wind-induced vibration and aerodynamic instability, and wind tunnel testing are then described as the fundamentals of the subject. State-of-the-art contributions include rain-wind-induced cable vibration, wind-vehicle-bridge interaction, wind-induced vibration control, wind and structural health monitoring, fatigue analysis, reliability analysis, typhoon wind simulation, non-stationary and nonlinear buffeting response. Lastly, the theory is applied to the actual long-span cable-supported bridges.

Structured in an easy-to-follow way, covering the topic from the fundamentals right through to the state-of-the-art
Describes advanced topics such as wind and structural health monitoring and non-stationary and nonlinear buffeting response
Gives a comprehensive description of various methods including CFD simulations of bridge and vehicle loading
Uses two projects with which the author has worked extensively, Stonecutters cable-stayed bridge and Tsing Ma suspension bridge, as worked examples, giving readers a practical understanding

Table Contents

Foreword
by Ahsan Kareem
Foreword
by Hai-Fan Xiang
Preface
Acknowledgements

1 Wind Storms and Cable-Supported Bridges

1.1 Preview

1.2 Basic Notions of Meteorology

1.2.1 Global Wind Circulations
1.2.2 Pressure Gradient Force
1.2.3 Coriolis Force
1.2.4 Geostrophic Wind
1.2.5 Gradient Wind 4
1.2.6 Frictional Effects

1.3 Basic Types of Wind Storms

1.3.1 Gales from Large Depressions
1.3.2 Monsoons
1.3.3 Tropical Cyclones (Hurricanes or Typhoons)
1.3.4 Thunderstorms
1.3.5 Downbursts
1.3.6 Tornadoes
1.3.7 Downslope Winds

1.4 Basic Types of Cable-Supported Bridges

1.4.1 Main Features of Cable-Supported Bridges
1.4.2 Suspension Bridges
1.4.3 Cable-Stayed Bridges
1.4.4 Hybrid Cable-Supported Bridges

1.5 Wind Damage to Cable-Supported Bridges

1.5.1 Suspension Bridges
1.5.2 Cable-Stayed Bridges
1.5.3 Stay Cables
1.5.4 Road Vehicles Running on Bridge

1.6 History of Bridge Aerodynamics
1.7 Organization of this Book
1.8 Notations

References

2 Wind Characteristics in Atmospheric Boundary Layer

2.1 Preview
2.2 TurbulentWinds in Atmospheric Boundary Layer

2.3 Mean Wind Speed Profiles

2.3.1 The “Logarithmic Law”
2.3.2 The “Power Law”
2.3.3 Mean Wind Speed Profile Over Ocean
2.3.4 Mean Wind Speed Profile in Tropical Cyclone

2.4 Wind Turbulence

2.4.1 Standard Deviations
2.4.2 Turbulence Intensities
2.4.3 Time Scales and Integral Length Scales
2.4.4 Probability Density Functions
2.4.5 Power Spectral Density Functions
2.4.6 Covariance and Correlation
2.4.7 Cross-Spectrum and Coherence
2.4.8 Gust Wind Speed and Gust Factor

2.5 Terrain and Topographic Effects

2.5.1 Change of Surface Roughness
2.5.2 Amplification of Wind by Hills
2.5.3 Amplification Factor and Speed-up Ratio
2.5.4 Funneling Effect

2.6 Design Wind Speeds

2.6.1 Exceedance Probability and Return Period
2.6.2 Probability Distribution Function
2.6.3 Generalized Extreme Value Distribution
2.6.4 Extreme Wind Estimation by the Gumbel Distribution
2.6.5 Extreme Wind Estimation by the Method of Moments
2.6.6 Design Lifespan and Risk
2.6.7 Parent Wind Distribution

2.7 Directional Preference of High Winds
2.8 Case Study: Tsing Ma Bridge Site

2.8.1 Anemometers in WASHMS
2.8.2 Typhoon Wind Characteristics
2.8.3 Monsoon Wind and Joint Probability Density Function

2.9 Notations

References

3 Mean Wind Load and Aerostatic Instability

3.1 Preview

3.2 Mean Wind Load and Force Coefficients

3.2.1 Bernoulli’s Equation and Wind Pressure
3.2.2 Mean Wind Load
3.2.3 Wind Force Coefficients

3.3 Torsional Divergence
3.4 3-D Aerostatic Instability Analysis

3.5 Finite Element Modeling of Long-Span Cable-Supported Bridges

3.5.1 Theoretical Background
3.5.2 Spine Beam Model
3.5.3 Multi-Scale Model
3.5.4 Modeling of Cables

3.6 Mean Wind Response Analysis

3.6.1 Determination of Reference Position
3.6.2 Mean Wind Response Analysis

3.7 Case Study: Stonecutters Bridge

3.7.1 Main Features of Stonecutters Bridge
3.7.2 Finite Element Modeling of Stonecutters Bridge
3.7.3 Aerodynamic Coefficients of Bridge Components
3.7.4 Mean Wind Response Analysis

3.8 Notations
References

4 Wind-Induced Vibration and Aerodynamic Instability

4.1 Preview

4.2 Vortex-Induced Vibration

4.2.1 Reynolds Number and Vortex Shedding
4.2.2 Strouhal Number and Lock-In
4.2.3 Vortex-Induced Vibration

4.3 Galloping Instability

4.3.1 Galloping Mechanism
4.3.2 Criterion for Galloping Instability
4.3.3 Wake Galloping

4.4 Flutter Analysis

4.4.1 Introduction
4.4.2 Self-Excited Forces and Aerodynamic Derivatives
4.4.3 Theodorsen Circulatory Function
4.4.4 1-D Flutter Analysis
4.4.5 2-D Flutter Analysis
4.4.6 3-D Flutter Analysis in the Frequency Domain
4.4.7 Flutter Analysis in the Time Domain

4.5 Buffeting Analysis in the Frequency Domain

4.5.1 Background
4.5.2 Buffeting Forces and Aerodynamic Admittances
4.5.3 3-D Buffeting Analysis in the Frequency Domain

4.6 Simulation of Stationary Wind Field
4.7 Buffeting Analysis in the Time Domain

4.8 Effective Static Loading Distributions

4.8.1 Gust Response Factor and Peak Factor
4.8.2 Effective Static Loading Distributions

4.9 Case Study: Stonecutters Bridge

4.9.1 Dynamic and Aerodynamic Characteristics of Stonecutters Bridge
4.9.2 Flutter Analysis of Stonecutters Bridge
4.9.3 Buffeting Analysis of Stonecutters Bridge

4.10 Notations

References

5 Wind-Induced Vibration of Stay Cables

5.1 Preview

5.2 Fundamentals of Cable Dynamics

5.2.1 Vibration of a Taut String
5.2.2 Vibration of an Inclined Cable with Sag

5.3 Wind-Induced Cable Vibrations

5.3.1 Buffeting by Wind Turbulence
5.3.2 Vortex-Induced Vibration
5.3.3 Galloping of Dry Inclined Cables
5.3.4 Wake Galloping for Groups of Cables

5.4 Mechanism of Rain-Wind-Induced Cable Vibration

5.4.1 Background
5.4.2 Analytical Model of SDOF
5.4.3 Horizontal Cylinder with Fixed Rivulet
5.4.4 Inclined Cylinder with Moving Rivulet
5.4.5 Analytical Model of 2DOF

5.5 Prediction of Rain-Wind-Induced Cable Vibration

5.5.1 Analytical Model for Full-Scale Stay Cables
5.5.2 Prediction of Rain-Wind-Induced Vibration of Full-Scale Stay Cable
5.5.3 Parameter Studies

5.6 Occurrence Probability of Rain-Wind-Induced Cable Vibration

5.6.1 Joint Probability Density Function (JPDF) of Wind Speed and Direction
5.6.2 Probability Density Function of Rainfall Intensity
5.6.3 Occurrence Range of Rain-Wind-Induced Cable Vibration
5.6.4 Occurrence Probability of Rain-Wind-Induced Cable Vibration

5.7 Case Study: Stonecutters Bridge

5.7.1 Statistical Analysis of Wind Data
5.7.2 Joint Probability Density Function of Wind Speed and Wind Direction
5.7.3 Statistical Analysis of Rainfall Data
5.7.4 Probability Density Function of Rainfall Intensity
5.7.5 Occurrence Range of Rain-Wind-Induced Cable Vibration
5.7.6 Hourly Occurrence Probability and Annual Risk

5.8 Notations

References

6 Wind.-Vehicle-Bridge Interaction

6.1 Preview

6.2.Wind-Road Vehicle Accidents

6.2.1.Wind.Induced Vehicle Accidents
6.2.3 Modeling of Road Surface Roughness
6.2.4 Aerodynamic Forces and Moments on Road Vehicle
6.2.5 Governing Equations of Motion of Road Vehicle
6.2.6 Case Study
6.2.7 Effects of Road Surface Roughness
6.2.8 Effects of Vehicle Suspension System
6.2.9 Accident Vehicle Speed

6.3 Formulation of Wind-Road Vehicle-Bridge Interaction

6.3.1 Equations of Motion of Coupled Road Vehicle-Bridge System
6.3.2 Equations of Motion of Coupled Wind-Road Vehicle-Bridge System

6.4 Safety Analysis of Road Vehicles on Ting Kau Bridge under Crosswind

6.4.1 Ting Kau Bridge
6.4.2 Wind Forces on Bridge
6.4.3 Scenario for Extreme Case Study
6.4.4 Dynamic Response of High-Sided Road Vehicle
6.4.5 Accident Vehicle Speed
6.4.6 Comparison of Safety of Road Vehicle Running on Bridge and Ground

6.5 Formulation of Wind-Railway Vehicle Interaction

6.5.1 Modeling of Vehicle Subsystem
6.5.2 Modeling of Track Subsystem
6.5.3 Wheel and Rail Interaction
6.5.4 Rail Irregularity
6.5.5 Wind Forces on Ground Railway Vehicles
6.5.6 Numerical Solution

6.6 Safety and Ride Comfort of Ground Railway Vehicle under Crosswind

6.6.1 Vehicle and Track Models
6.6.2 Wind Forces on Railway Vehicle
6.6.3 Rail Irregularity
6.6.4 Response of Coupled Vehicle-Track System in Crosswind
6.6.5 Safety and Ride Comfort Performance

6.7 Wind-Railway Vehicle-Bridge Interaction

6.7.1 Formulation of Wind-Railway Vehicle-Bridge Interaction
6.7.2 Engineering Approach for Determining Wind Forces on Moving Vehicle
6.7.3 Case Study

6.8 Notations

References

7 Wind Tunnel Studies

7.1 Preview

7.2 Boundary Layer Wind Tunnels

7.2.1 Open-Circuit Wind Tunnel
7.2.2 Closed-Circuit Wind Tunnel
7.2.3 Actively Controlled Wind Tunnel

7.3 Model Scaling Requirements

7.3.1 General Model Scaling Requirements
7.3.2 Notes on Model Scaling Requirements
7.3.3 Blockage Consideration

7.4 Boundary Wind Simulation

7.4.1 Natural Growth Method
7.4.2 Augmented Method
7.4.3 Actively Controlled Grids and Spires
7.4.4 Actively Controlled Multiple Fans
7.4.5 Topographic Models
7.4.6 Instrumentation for Wind Measurement in Wind Tunnel

7.5 Section Model Tests

7.5.1 Models and Scaling
7.5.2 Section Model Tests for Force Coefficients
7.5.3 Section Model Tests for Flutter Derivatives and Vortex-Induced Vibration
7.5.4 Section Model Tests with Pressure Measurements
7.5.5 Section Model Tests for Aerodynamic Admittance

7.6 Taut Strip Model Tests
7.7 Full Aeroelastic Model Tests

7.8 Identification of Flutter Derivatives

7.8.1 Free Vibration Test of Section Model
7.8.2 Forced Vibration Test of Section Model
7.8.3 Free Vibration Test of Taut Strip Model and Full Aeroelastic Model

7.9 Identification of Aerodynamic Admittance
7.10 Cable Model Tests

7.10.1 Inclined Dry Cable Tests
7.10.2 Rain-Wind Simulation of Inclined Stay Cable

7.11 Vehicle-Bridge Model Tests

7.11.1 Vehicles on Ground
7.11.2 Stationary Vehicle on Bridge Deck
7.11.3 Moving Vehicle on Bridge Deck

7.12 Notations

References

8 Computational Wind Engineering

8.1 Preview
8.2 Governing Equations of Fluid Flow

8.2.1 Mass Conservation
8.2.2 Momentum Conservation
8.2.3 Energy Conservation and Newtonian Flow
8.2.4 Navier-Stokes Equations
8.2.5 Governing Equations of Wind Flow
8.2.6 Vorticity Description of Navier-Stokes Equations

8.3 Turbulence and its Modeling

8.3.1 Direct Numerical Simulation
8.3.2 Reynolds Averaged Method
8.3.3 Large Eddy Simulation
8.3.4 Detached Eddy Simulation
8.3.5 Discrete Vortex Method

8.4 Numerical Considerations

8.4.1 Finite Difference Method
8.4.2 Finite Element Method 307
8.4.3 Finite Volume Method 309
8.4.4 Solution Algorithms for Pressure-Velocity Coupling in Steady Flows
8.4.5 Solution for Unsteady Flows
8.4.6 Boundary Conditions
8.4.7 Grid Generation
8.4.8 Computing Techniques
8.4.9 Verification and Validation

8.4.10 Applications in Bridge Wind Engineering

8.5 CFD for Force Coefficients of Bridge Deck

8.5.1 Computational Domain
8.5.2 Meshing
8.5.3 Boundary Conditions and Numerical Method
8.5.4 Aerodynamic Force Coefficients and Flow Field

8.6 CFD for Vehicle Aerodynamics

8.6.1 Computational Domain
8.6.2 Meshing
8.6.3 Boundary Conditions and Numerical Method
8.6.4 Simulation Results
8.6.5 Vehicle Moving on Ground

8.7 CFD for Aerodynamics of Coupled Vehicle-Bridge Deck System

8.7.1 Computational Domain
8.7.2 Meshing
8.7.3 Boundary Conditions and Numerical Method
8.7.4 Simulation Results
8.7.5 Moving Vehicle on Bridge Deck

8.8 CFD for Flutter Derivatives of Bridge Deck

8.8.1 Modeling and Meshing
8.8.2 Numerical Method
8.8.3 Simulation Results

8.9 CFD for Non-Linear Aerodynamic Forces on Bridge Deck

8.9.1 Modeling and Meshing
8.9.2 Numerical Method
8.9.3 Simulation Results

8.10 Notations

References

9 Wind and Structural Health Monitoring

9.1 Preview
9.2 Design of Wind and Structural Health Monitoring Systems

9.3 Sensors and Sensing Technology

9.3.1 Anemometers and Other Wind Measurement Sensors
9.3.2 Accelerometers
9.3.3 Displacement Transducers and Level Sensors
9.3.4 Global Positioning Systems
9.3.5 Strain Gauges
9.3.6 Fiber Optic Sensors
9.3.7 Laser Doppler Vibrometers
9.3.8 Weather Stations
9.3.9 Wireless Sensors

9.4 Data Acquisition and Transmission System (DATS)

9.4.1 Configuration of DATS
9.4.2 Hardware of Data Acquisition Units
9.4.3 Network and Communication
9.4.4 Operation of Data Acquisition and Transmission

9.5 Data Processing and Control System

9.5.1 Data Acquisition Control
9.5.2 Signal Pre-Processing and Post-Processing

9.6 Data Management System
9.6.1 Components and Functions of Data Management System
9.6.2 Maintenance of Data Management System

9.7 Structural Health Monitoring System of Tsing Ma Bridge

9.7.1 Overview of WASHMS
9.7.2 Anemometers in WASHMS
9.7.3 Temperature Sensors in WASHMS
9.7.4 Displacement Transducers in WASHMS
9.7.5 Level Sensing Stations in WASHMS
9.7.6 GPS in WASHMS
9.7.7 Strain Gauges in WASHMS
9.7.8 Accelerometers in WASHMS

9.8 Monitoring Results of Tsing Ma Bridge during Typhoon Victor

9.8.1 Typhoon Victor
9.8.2 Local Topography
9.8.3 Calculations of Mean Wind Speed and Fluctuating Wind Components
9.8.4 Mean Wind Speed and Direction
9.8.5 Turbulence Intensity and Integral Scale
9.8.6 Wind Spectra
9.8.7 Acceleration Response of Bridge Deck
9.8.8 Acceleration Response of Bridge Cable
9.8.9 Remarks

9.9 System Identification of Tsing Ma Bridge during Typhoon Victor

9.9.1 Background
9.9.2 EMDþHT Method
9.9.3 Natural Frequencies and Modal Damping Ratios
9.10 Notations

References

10 Buffeting Response to Skew Winds

10.1 Preview

10.2 Formulation in the Frequency Domain

10.2.1 Basic Assumptions
10.2.2 Coordinate Systems and Transformation Matrices
10.2.3 Wind Components and Directions
10.2.4 Buffeting Forces and Spectra under Skew Winds
10.2.5 Aeroelastic Forces under Skew Winds
10.2.6 Governing Equation and Solution in the Frequency Domain

10.3 Formulation in the Time Domain

10.3.1 Buffeting Forces due to Skew Winds in the Time Domain
10.3.2 Self-Excited Forces due to Skew Winds in the Time Domain
10.3.3 Governing Equation and Solution in the Time Domain

10.4 Aerodynamic Coefficients of Bridge Deck under Skew Winds
10.5 Flutter Derivatives of Bridge Deck under Skew Winds
10.6 Aerodynamic Coefficients of Bridge Tower under Skew Winds

10.7 Comparison with Field Measurement Results of Tsing Ma Bridge

10.7.1 Typhoon Sam and Measured Wind Data
10.7.2 Measured Bridge Acceleration Responses
10.7.3 Input Data to Computer Simulation
10.7.4 Comparison of Buffeting Response in the Frequency Domain
10.7.5 Comparison of Buffeting Response in the Time Domain

10.8 Notations

References

11 Multiple Loading-Induced Fatigue Analysis

11.1 Preview

11.2 SHM-oriented Finite Element Modeling 60605

11.2.1 Background
11.2.2 Main Features of Tsing Ma Bridge
11.2.3 Finite Element Modeling of Tsing Ma Bridge

11.3 Framework for Buffeting-Induced Stress Analysis

11.3.1 Equation of Motion
11.3.2 Buffeting Forces
11.3.4 Determination of Bridge Responses

11.4 Comparison with Field Measurement Results of Tsing Ma Bridge

11.4.1 Wind Characteristics
11.4.2 Measured Acceleration Responses of Bridge Deck
11.4.3 Measured Stresses of Bridge Deck
11.4.4 Wind Field Simulation
11.4.5 Buffeting Forces and Self-Excited Forces
11.4.6 Comparison of Bridge Acceleration Responses
11.4.7 Comparison of Bridge Stress Responses

11.5 Buffeting-Induced Fatigue Damage Assessment

11.5.1 Background
11.5.2 Joint Probability Density Function of Wind Speed and Direction
11.5.3 Critical Stresses and Hot Spot Stresses
11.5.4 Hot Spot Stress Characteristics
11.5.5 Damage Evolution Model
11.5.6 Buffeting-Induced Fatigue Damage Assessment

11.6 Framework for Multiple Loading-Induced Stress Analysis

11.6.1 Equation of Motion
11.6.2 Pseudo Forces in Trains and Road Vehicles
11.6.3 Contact Forces between Train and Bridge
11.6.4 Contact Forces between Road Vehicles and Bridge
11.6.5 Wind Forces on Bridge
11.6.6 Wind Forces on Vehicles
11.6.7 Numerical Solution

11.7 Verification by Case Study: Tsing Ma Bridge

11.7.1 Finite Element Models of Bridge, Train and Road Vehicles
11.7.2 Rail Irregularities and Road Roughness
11.7.3 Wind Force Simulation
11.7.4 Selected Results

11.8 Fatigue Analysis of Long-Span Suspension Bridges under Multiple Loading

11.8.1 Establishment of Framework
11.8.2 Simplifications used in Engineering Approach
11.8.3 Dynamic Stress Analysis using Engineering Approach
11.8.4 Verification of Engineering Approach
11.8.5 Determination of Fatigue-Critical Locations
11.8.6 Databases of Dynamic Stress Responses to Different Loadings
11.8.7 Multiple Load-Induced Dynamic Stress Time Histories in Design Life
11.8.8 Fatigue Analysis at Fatigue-Critical Locations

11.9 Notations

References

12 Wind-Induced Vibration Control

12.1 Preview

12.2 Control Methods for Wind-Induced Vibration

12.3 Aerodynamic Measures for Flutter Control

12.3.1 Passive Aerodynamic Measures
12.3.2 Active Aerodynamic Control

12.4 Aerodynamic Measures for Vortex-Induced Vibration Control

12.5 Aerodynamic Measures for Rain-Wind-Induced Cable Vibration Control

12.5.1 Wind Tunnel Investigation and Cable Drag Coefficients
12.5.2 Rain-Wind Tunnel Investigation of Stay Cables of Different Surfaces
12.6 Mechanical Measures for Vortex-Induced Vibration Control
12.7 Mechanical Measures for Flutter Control
12.7.1 Passive Control Systems for Flutter Control
12.7.2 Active Control Systems for Flutter Control
12.7.3 Semi-Active Control Systems for Flutter Control
12.8 Mechanical Measures for Buffeting Control
12.8.1 Multiple Pressurized Tuned Liquid Column Dampers
12.8.2 Semi-Active Tuned Liquid Column Dampers
12.9 Mechanical Measures for Rain-Wind-Induced Cable Vibration Control
12.10 Case Study: Damping Stay Cables in a Cable-Stayed Bridge
12.11 Notations

References

13 Typhoon Wind Field Simulation

13.1 Preview

13.2 Refined Typhoon Wind Field Model
13.2.1 Background
13.2.2 Refined Typhoon Wind Field Model
13.2.3 Typhoon Wind Decay Model
13.2.4 Remarks

13.3 Model Solutions

13.3.1 Decomposition Method
13.3.2 Friction-Free Wind Velocity
13.3.3 Friction-Induced Wind Velocity
13.3.4 Procedure of Typhoon Wind Field Simulation

13.4 Model Validation

13.4.1 Typhoon York
13.4.2 Main Parameters of Typhoon York
13.4.3 Wind Field Simulation at Waglan Island
13.4.4 Spatial Distribution of Typhoon Wind Field
13.4.5 Wind Speed Profiles in Vertical Direction

13.5 Monte Carlo Simulation

13.5.1 Background
13.5.2 Typhoon Wind Data
13.5.3 Probability Distributions of Key Parameters
13.5.4 K-S Test
13.5.5 Typhoon Wind Decay Model Parameters
13.5.6 Procedure for Estimating Extreme Wind Speeds and Averaged Wind Profiles

13.6 Extreme Wind Analysis

13.6.1 Basic Theory
13.6.2 Extreme Wind Speed Analysis using the Refined Typhoon Wind Field Model
13.6.3 Extreme Wind Speed Analysis based on Wind Measurement Data
13.6.4 Comparison of Results and Discussion
13.6.5 Mean Wind Speed Profile Analysis

13.7 Simulation of Typhoon Wind Field over Complex Terrain

13.7.1 Background
13.7.2 Directional Upstream Typhoon Wind Speeds and Profiles
13.7.3 Representative Directional Typhoon Wind Speeds and Profiles at Site
13.7.4 Training ANN Model for Predicting Directional Typhoon Wind Speeds and Profiles
13.7.5 Directional Design Typhoon Wind Speeds and Profiles at Site

13.8 Case Study: Stonecutters Bridge Site

13.8.1 Topographical Conditions
13.8.2 Directional Upstream Typhoon Wind Speeds and Profiles
13.8.3 Representative Typhoon Wind Speeds and Profiles
13.8.4 Establishment of ANN Model
13.8.5 Directional Design Wind Speeds and Wind Profiles

13.9 Notations

References

14 Reliability Analysis of Wind-Excited Bridges

14.1 Preview

14.2 Fundamentals of Reliability Analysis

14.2.1 Limit-States
14.2.2 First-Order Second Moment (FOSM) Method
14.2.3 Hasofer and Lind (HL) Method
14.2.4 Monte Carlo Simulation (MCS) and Response Surface Method (RSM)
14.2.5 Threshold Crossing
14.2.6 Peak Distribution

14.3 Reliability Analysis of Aerostatic Instability
14.4 Flutter Reliability Analysis

14.5 Buffeting Reliability Analysis

14.5.1 Failure Model by First Passage
14.5.2 Reliability Analysis based on Threshold Crossings
14.5.3 Reliability Analysis based on Peak Distribution
14.5.4 Notes on Buffeting Reliability Analysis

14.6 Reliability Analysis of Vortex-Induced Vibration

14.7 Fatigue Reliability Analysis based on Miner’s Rule for Tsing Ma Bridge

14.7.1 Framework for Fatigue Reliability Analysis
14.7.2 Probabilistic Model of Railway Loading
14.7.3 Probabilistic Model of Highway Loading
14.7.4 Probabilistic Model of Wind Loading
14.7.5 Multiple Load-Induced Daily Stochastic Stress Response
14.7.6 Probability Distribution of the Daily Sum of m-power Stress Ranges
14.7.7 Probability Distribution of the Sum of m-power Stress Ranges within the Period
14.7.8 Reliability Analysis Results

14.8 Fatigue Reliability Analysis based on Continuum Damage Mechanics

14.8.1 Basic Theory of Continuum Damage Mechanics
14.8.2 Non-Linear Properties of Fatigue Damage Accumulation
14.8.3 Continuum Damage Model used in This Study
14.8.4 Verification of Continuum Damage Model
14.8.5 Framework of Fatigue Reliability Analysis
14.8.6 Reliability Analysis Results 657

14.9 Notations

References

15 Non-Stationary and Non-Linear Buffeting Response

15.1 Preview

15.2 Non-Stationary Wind Model I

15.2.1 Non-Stationary Wind Model I
15.2.2 Empirical Mode Decomposition
15.2.3 Non-Stationary Wind Characteristics
15.2.4 Case Study: Typhoon Victor

15.3 Non-Stationary Wind Model II

15.3.1 Time-Varying Mean Wind Speed and Mean Wind Profile
15.3.2 Evolutionary Spectra
15.3.3 Coherence Function
15.3.4 Case Study: Typhoon Dujuan

15.4 Buffeting Response to Non-Stationary Wind

15.4.1 Time-Varying Mean Wind Forces
15.4.2 Non-Stationary Self-Excited Forces
15.4.3 Non-Stationary Buffeting Forces
15.4.4 Governing Equations of Motion
15.4.5 Time-Varying Mean Wind Response
15.4.6 Modal Equations for Non-Stationary Buffeting Response
15.4.7 Pseudo Excitation Method for Solving Modal Equations
15.4.8 Case Study: Stonecutters Bridge

15.5 Extreme Value of Non-Stationary Response

15.5.1 Background
15.5.2 Approximate Estimation of Extreme Value
15.5.3 Possion Approximation
15.5.4 Vanmarcke Approximation
15.5.5 Statistical Moment of Extreme Value
15.5.6 Case Study: Stonecutters Bridge

15.6 Unconditional Simulation of Non-Stationary Wind

15.6.1 Background
15.6.2 Unconditional Simulation

15.7 Conditional Simulation of Non-Stationary Wind

15.7.1 Background
15.7.2 Problem Statement
15.7.3 Conditional Simulation Method
15.7.4 Computational Difficulties in Conditional Simulation
15.7.5 Alternative Formulas for Decomposition
15.7.6 Fast Algorithm for Conditional Simulation
15.7.7 Implementation Procedure
15.7.8 Validation and Application

15.8 Non-Linear Buffeting Response

15.8.1 Introduction
15.8.2 Linearization Model for Non-Linear Aerodynamic Forces
15.8.3 Hysteretic Behavior of Non-Linear Aerodynamic Forces
15.8.4 Hysteretic Models for Non-Linear Aerodynamic Forces
15.8.5 ANN-Based Hysteretic Model of Non-Linear Buffeting Response

15.9 Notations

References

16 Epilogue: Challenges and Prospects

16.1 Challenges
16.1.1 Typhoon Wind Characteristics and Topography Effects
16.1.2 Effects of Non-Stationary and Non-Gaussian Winds
16.1.3 Effects of Aerodynamic Non-Linearity
16.1.4 Wind Effects on Coupled Vehicle-Bridge Systems
16.1.5 Rain-Wind-Induced Vibration of Stay Cables
16.1.6 Uncertainty and Reliability Analysis
16.1.7 Advancing Computational Wind Engineering and Wind Tunnel Test Techniques

16.1.8 Application of Wind and Structural Health Monitoring Technique
16.2 Prospects

Index