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 xvPreface to the Second Edition xviiPreface to the First Edition xviiiAcknowledgements xx1 Measures of Structural Reliability 11.1 Introduction 11.2 Deterministic Measures of Limit State Violation 21.3 A Partial Probabilistic Safety Measure of Limit State Violation—The Return Period 81.4 Probabilistic Measure of Limit State Violation 121.5 Generalized Reliability Problem 241.6 Conclusion 292 Structural Reliability Assessment 312.1 Introduction 312.2 Uncertainties in Reliability Assessment 332.3 Integrated Risk Assessment 452.4 Criteria for Risk Acceptability 512.5 Nominal Probability of Failure 562.6 Hierarchy of Structural Reliability Measures 602.7 Conclusion 613 Integration and Simulation Methods 633.1 Introduction 633.2 Direct and Numerical Integration 633.3 Monte Carlo Simulation 653.4 Importance Sampling 733.5 Directional Simulation∗ 823.6 Practical Aspects of Monte Carlo Simulation 903.7 Conclusion 934 Second-Moment and Transformation Methods 954.1 Introduction 954.2 Second-Moment Concepts 954.3 First-Order Second-Moment (FOSM) Theory 974.4 The First-Order Reliability (FOR) Method 1124.5 Second-Order Reliability (SOR) Methods 1264.6 Application of FOSM/FOR/SOR Methods 1284.7 Mean Value Methods 1294.8 Conclusion 1305 Reliability of Structural Systems 1315.1 Introduction 1315.2 Systems Reliability Fundamentals 1325.3 Monte Carlo Techniques for Systems 1475.4 System Reliability Bounds 1535.5 Implicit Limit States 1685.6 Functionally Dependent Limit States 1735.7 Conclusion 1776 Time-Dependent Reliability 1796.1 Introduction 1796.2 Time-Integrated Approach 1826.3 Discretized Approach 1856.4 Stochastic Process Theory 1916.5 Stochastic Processes and Outcrossings 1966.6 Time-Dependent Reliability 2156.7 Load Combinations 2266.8 Ensemble Crossing Rate and Barrier Failure Dominance 2346.9 Dynamic Analysis of Structures 2376.10 Fatigue Analysis 2416.11 Conclusion 2447 Load and Load Effect Modelling 2477.1 Introduction 2477.2 Wind Loading 2487.3 Wave Loading 2527.4 Floor Loading 2557.5 Conclusion 2718 Resistance Modelling 2738.1 Introduction 2738.2 Basic Properties of Hot-Rolled Steel Members 2738.3 Properties of Steel Reinforcing Bars 2808.4 Concrete Statistical Properties 2818.5 Statistical Properties of Structural Members 2848.6 Connections 2908.7 Incorporation of Member Strength in Design 2908.8 Conclusion 2929 Codes and Structural Reliability 2939.1 Introduction 2939.2 Structural Design Codes 2949.3 Safety-Checking Formats 2969.4 Relationship Between Level 1 and Level 2 Safety Measures 3019.5 Selection of Code Safety Levels 3049.6 Code Calibration Procedure 3059.7 Example of Code Calibration 3109.8 Observations 3159.9 Performance-Based Design 3179.10 Conclusion 31910 Probabilistic Evaluation of Existing Structures 32110.1 Introduction 32110.2 Assessment Procedures 32310.3 Updating Probabilistic Information 32710.4 Analytical Assessment 33310.5 Acceptance Criteria for Existing Structures 33810.6 Conclusion 34311 Structural Optimization and Reliability 34511.1 Introduction 34511.2 Types of Reliability-based Optimization Problems 34611.3 Reliability Based Design Optimization (RBDO) Using First Order Reliability (FOR) 35411.4 RBDO with System Reliability Constraints 36211.5 Simulation-based Design Optimization 36311.6 Life-cycle Cost and Risk Optimization 36711.7 Discussion and Conclusion 368A Summary of Probability Theory 371A.1 Probability 371A.2 Mathematics of Probability 371A.3 Description of Random Variables 373A.4 Moments of Random Variables 373A.5 Common Univariate Probability Distributions 375A.6 Jointly Distributed Random Variables 390A.7 Moments of Jointly Distributed Random Variables 392A.8 Bivariate Normal Distribution 393A.9 Transformation of Random Variables 397A.10 Functions of Random Variables 398A.11 Moments of Functions of Random Variables 400A.12 Approximate Moments for General Functions 402B Rosenblatt and Other Transformations 403B.1 Rosenblatt Transformation 403B.2 Nataf Transformation 405B.3 Orthogonal Transformation of Normal Random Variables 407B.4 Generation of Dependent Random Vectors 410C Bivariate and Multivariate Normal Integrals 415C.1 Bivariate Normal Integral 415C.2 Multivariate Normal Integral 419D Complementary Standard Normal Table 429D.1 Standard Normal Probability Density Function ;;(x) 432E Random Numbers 433F Selected Problems 435References 457Index 497