Preface
 
1 Measures of Structural Safety 1
 
1.1 Introduction 1
 
1.2 Uncertainties in Structural Design 1
 
1.2.1 Uncertainties in the Properties of Structures and Their Environment 1
 
1.2.2 Sources and Types of Uncertainty 3
 
1.2.3 Treatment of Uncertainties 4
 
1.2.4 Design and Decision Making Under Uncertainties 7
 
1.3 Deterministic Measures of Safety 8
 
1.4 Probabilistic Measure of Safety 8
 
1.5 Summary 9
 
2 Fundamentals of Structural Reliability Theory 10
 
2.1 The Fundamental Case 10
 
2.2 Performance Function and Failure Probability 14
 
2.2.1 Performance Function 14
 
2.2.2 Probability of Failure 14
 
2.2.3 Reliability Index 16
 
2.3 Monte Carlo Simulation 20
 
2.3.1 Introduction 20
 
2.3.2 Generation of Random Numbers 21
 
2.3.3 Direct Sampling 24
 
2.4 A Brief Review on Structural Reliability Theory 28
 
2.5 Summary 30
 
3 Moment Evaluation for Performance Functions 31
 
3.1 Introduction 31
 
3.2 Moment Computation for Some Simple Functions 33
 
3.2.1 Moment Computation for Linear Sum of Random Variables 33
 
3.2.2 Moment Computation for Multiply of Random Variables 35
 
3.2.3 Moment Computation for Power of a Lognormally Distributed Random Variable 37
 
3.2.4 Moment Computation for Power of an Arbitrarily Distributed Random Variable 41
 
3.2.5 Moment Computation for Reciprocal of an Arbitrary Distributed Random Variable 43
 
3.3 Point Estimate for a Function of One Random Variable 44
 
3.3.1 Rosenblueth's Two-Point Estimate 44
 
3.3.2 Gorman's Three-Point Estimate 45
 
3.4 Point Estimates in Standardized Normal Space 50
 
3.4.1 Basic ideas 50
 
3.4.2 Two- and Three-point Estimates in the Standard Normal Space 52
 
3.4.3 Five-Point Estimate in Standard Normal Space 53
 
3.4.4 Seven-Point Estimate in Standard Normal Space 54
 
3.4.5 General Expression of Estimating Points and Their Corresponding Weights 57
 
3.4.6 Accuracy of the Point Estimate 59
 
3.5 Point Estimates for a Function of Multiple Variables 61
 
3.5.1 General Expression of Point Estimate for a Function of n Variables 61
 
3.5.2 Approximate Point Estimate for a Function of n Variables 63
 
3.5.3 Dimension Reduction Integration 67
 
3.6 Point Estimates for a Function of Correlative Random Variables 71
 
3.7 Hybrid Dimension-Reduction Based Point Estimate Method 75
 
3.8 Summary 78
 
4 Direct Methods of Moment 79
 
4.1 Basic Concept of Methods of Moment 79
 
4.1.1 Introduction 79
 
4.1.2 The Second-Moment Method 79
 
4.1.3 General Expressions for Methods of Moment 82
 
4.2 Third-Moment Reliability Method 83
 
4.2.1 Introduction 83
 
4.2.2 Third-Moment Reliability Indices 85
 
4.2.3 Empirical Applicable Range of Third-Moment Reliability Method 88
 
4.2.4 Simplification of Third-Moment Reliability Method 91
 
4.2.5 Applicable Range of the Second-Moment method 94
 
4.3 Fourth-Moment Reliability Method 99
 
4.3.1 Introduction 99
 
4.3.2 Fourth-Moment Reliability Index on the Basis of the Pearson System 101
 
4.3.3 Fourth-Moment Reliability Index Based on Third-Order Polynomial Transformation 104
 
4.3.4 Applicable range of Fourth-Moment method 106
 
4.3.5 Simplification of Fourth-Moment reliability index 110
 
4.4 Summary 112
 
5 Methods of Moment Based on First/Second Order Transformation 113
 
5.1 Introduction 113