Structural Reliability Analysis and Prediction

ROBERT E. MELCHERS, PhD, is a Professor in the Department of Civil Engineering at The University of Newcastle, Australia. His main areas of research expertise are in structural engineering risk and reliability analyses, probabilistic modelling of engineering systems, corrosion and deterioration modeling, and investigation of structural failures. ANDRÉ T. BECK, PhD, is an Associate Professor in the Department of Structural Engineering at the University of São Paulo, Brazil. His research interests include structural mechanics and structural safety.

Preface xv

Preface to the Second Edition xvii

Preface to the First Edition xviii

Acknowledgements xx

1 Measures of Structural Reliability 1

1.1 Introduction 1

1.2 Deterministic Measures of Limit State Violation 2

1.3 A Partial Probabilistic Safety Measure of Limit State Violation—The Return Period 8

1.4 Probabilistic Measure of Limit State Violation 12

1.5 Generalized Reliability Problem 24

1.6 Conclusion 29

2 Structural Reliability Assessment 31

2.1 Introduction 31

2.2 Uncertainties in Reliability Assessment 33

2.3 Integrated Risk Assessment 45

2.4 Criteria for Risk Acceptability 51

2.5 Nominal Probability of Failure 56

2.6 Hierarchy of Structural Reliability Measures 60

2.7 Conclusion 61

3 Integration and Simulation Methods 63

3.1 Introduction 63

3.2 Direct and Numerical Integration 63

3.3 Monte Carlo Simulation 65

3.4 Importance Sampling 73

3.5 Directional Simulation∗ 82

3.6 Practical Aspects of Monte Carlo Simulation 90

3.7 Conclusion 93

4 Second-Moment and Transformation Methods 95

4.1 Introduction 95

4.2 Second-Moment Concepts 95

4.3 First-Order Second-Moment (FOSM) Theory 97

4.4 The First-Order Reliability (FOR) Method 112

4.5 Second-Order Reliability (SOR) Methods 126

4.6 Application of FOSM/FOR/SOR Methods 128

4.7 Mean Value Methods 129

4.8 Conclusion 130

5 Reliability of Structural Systems 131

5.1 Introduction 131

5.2 Systems Reliability Fundamentals 132

5.3 Monte Carlo Techniques for Systems 147

5.4 System Reliability Bounds 153

5.5 Implicit Limit States 168

5.6 Functionally Dependent Limit States 173

5.7 Conclusion 177

6 Time-Dependent Reliability 179

6.1 Introduction 179

6.2 Time-Integrated Approach 182

6.3 Discretized Approach 185

6.4 Stochastic Process Theory 191

6.5 Stochastic Processes and Outcrossings 196

6.6 Time-Dependent Reliability 215

6.7 Load Combinations 226

6.8 Ensemble Crossing Rate and Barrier Failure Dominance 234

6.9 Dynamic Analysis of Structures 237

6.10 Fatigue Analysis 241

6.11 Conclusion 244

7 Load and Load Effect Modelling 247

7.1 Introduction 247

7.2 Wind Loading 248

7.3 Wave Loading 252

7.4 Floor Loading 255

7.5 Conclusion 271

8 Resistance Modelling 273

8.1 Introduction 273

8.2 Basic Properties of Hot-Rolled Steel Members 273

8.3 Properties of Steel Reinforcing Bars 280

8.4 Concrete Statistical Properties 281

8.5 Statistical Properties of Structural Members 284

8.6 Connections 290

8.7 Incorporation of Member Strength in Design 290

8.8 Conclusion 292

9 Codes and Structural Reliability 293

9.1 Introduction 293

9.2 Structural Design Codes 294

9.3 Safety-Checking Formats 296

9.4 Relationship Between Level 1 and Level 2 Safety Measures 301

9.5 Selection of Code Safety Levels 304

9.6 Code Calibration Procedure 305

9.7 Example of Code Calibration 310

9.8 Observations 315

9.9 Performance-Based Design 317

9.10 Conclusion 319

10 Probabilistic Evaluation of Existing Structures 321

10.1 Introduction 321

10.2 Assessment Procedures 323

10.3 Updating Probabilistic Information 327

10.4 Analytical Assessment 333

10.5 Acceptance Criteria for Existing Structures 338

10.6 Conclusion 343

11 Structural Optimization and Reliability 345

11.1 Introduction 345

11.2 Types of Reliability-based Optimization Problems 346

11.3 Reliability Based Design Optimization (RBDO) Using First Order Reliability (FOR) 354

11.4 RBDO with System Reliability Constraints 362

11.5 Simulation-based Design Optimization 363

11.6 Life-cycle Cost and Risk Optimization 367

11.7 Discussion and Conclusion 368

A Summary of Probability Theory 371

A.1 Probability 371

A.2 Mathematics of Probability 371

A.3 Description of Random Variables 373

A.4 Moments of Random Variables 373

A.5 Common Univariate Probability Distributions 375

A.6 Jointly Distributed Random Variables 390

A.7 Moments of Jointly Distributed Random Variables 392

A.8 Bivariate Normal Distribution 393

A.9 Transformation of Random Variables 397

A.10 Functions of Random Variables 398

A.11 Moments of Functions of Random Variables 400

A.12 Approximate Moments for General Functions 402

B Rosenblatt and Other Transformations 403

B.1 Rosenblatt Transformation 403

B.2 Nataf Transformation 405

B.3 Orthogonal Transformation of Normal Random Variables 407

B.4 Generation of Dependent Random Vectors 410

C Bivariate and Multivariate Normal Integrals 415

C.1 Bivariate Normal Integral 415

C.2 Multivariate Normal Integral 419

D Complementary Standard Normal Table 429

D.1 Standard Normal Probability Density Function ;;(x) 432

E Random Numbers 433

F Selected Problems 435

References 457

Index 497