Structural Reliability Theory and Its Applications

1. The Treatment of Uncertainties in Structural Engineering.- 1.1 Introduction.- 1.1.1 Current risk levels,.- 1.1.2 Structural codes,.- 1.2 Uncertainty.- 1.2.1 General,.- 1.2.2 Basic variables,.- 1.2.3 Types of uncertainty,.- 1.3 Structural Reliability Analysis and Safety Checking.- 1.3.1 Structural reliability,.- 1.3.2 Methods of safety checking,.- 2. Fundamentals of Probability Theory.- 2.1 Introduction.- 2.2 Sample Space.- 2.3 Axioms and Theorems of Probability Theory.- 2.4 Random Variables.- 2.5 Moments.- 2.6 Univariate Distributions.- 2.7 Random Vectors.- 2.8 Conditional Distributions.- 2.9 Functions of Random Variables.- 3. Probabilistic Models for Loads and Resistance Variables.- 3.1 Introduction.- 3.2 Statistical Theory Of Extremes.- 3.2.1 Derivation of the cumulative distribution of the ith smallest value of n identically distributed independent random variables Xi,.- 3.2.2 Normal extremes,.- 3.3 Asymptotic Extreme-Value Distributions.- 3.3.1 Type I extreme-value distributions (Gumbel distributions),.- 3.3.2 Type II extreme-value distributions,.- 3.3.3 Type III extreme-value distributions,.- 3.4 Modelling of Resistance Variables - Model Selection.- 3.4.1 General remarks,.- 3.4.2 Choice of distributions for resistance variables,.- 3.5 Modelling of Load Variables - Model Selection.- 3.5.1 General remarks,.- 3.5.2 Choice of distributions of loads and other actions,.- 3.6 Estimation of Distribution Parameters.- 3.6.1 Techniques for parameter estimation,.- 3.6.2 Model verification,.- 3.7 Inclusion of Statistical Uncertainty.- 4. Fundamentals of Structural Reliability Theory.- 4.1 Introduction.- 4.2 Elements of Classical Reliability Theory.- 4.3 Structural Reliability Analysis.- 4.3.1 General,.- 4.3.2 The fundamental case,.- 4.3.3 Problems reducing to the fundamental case,.- 4.3.4 Treatment of a single time-varying load,.- 4.3.5 The general case,.- 4.3.6 Monte-Carlo methods,.- 5. Level 2 Methods.- 5.1 Introduction.- 5.2 Basic Variables and Failure Surfaces.- 5.3 Reliability Index for Linear Failure Functions and Normal Basic Variables.- 5.4 Hasofer and Lind's Reliability Index.- 6. Extended Level 2 Methods.- 6.1 Introduction.- 6.2 Concept of Correlation.- 6.3 Correlated Basic Variables.- 6.4 Non-Normal Basic Variables.- 7. Reliability of Structural Systems.- 7.1 Introduction.- 7.2 Perfectly Brittle and Perfectly Ductile Elements.- 7.3 Fundamental Systems.- 7.4 Systems with Equally Correlated Elements.- 8. Reliability Bounds for Structural Systems.- 8.1 Introduction.- 8.2 Simple Bounds.- 8.3 Ditlevsen Bounds.- 8.4 Parallel Systems with Unequally Correlated Elements.- 8.5 Series Systems with Unequally Correlated Elements.- 9. Introduction to Stochastic Process Theory and its Uses.- 9.1 Introduction.- 9.2 Stochastic Processes.- 9.3 Gaussian Processes.- 9.4 Barrier Crossing Problem.- 9.5 Peak Distribution.- 10. Load Combinations.- 10.1 Introduction.- 10.2 The Load Combination Problem.- 10.3 The Ferry Borges-Castanheta Load Model.- 10.4 Combination Rules.- 11. Applications to Structural Codes.- 11.1 Introduction.- 11.2 Structural Safety and Level 1 Codes.- 11.3 Recommended Safety Formats for Level 1 Codes.- 11.3.1 Limit state functions and checking equations,.- 11.3.2 Characteristic values of basic variables,.- 11.3.3 Treatment of geometrical variables,.- 11.3.4 Treatment of material properties,.- 11.3.5 Treatment of loads and other actions,.- 11.4 Methods for the Evaluation of Partial Coefficients.- 11.4.1 Relationship of partial coefficients to level 2 design point,.- 11.4.2 Approximate direct method for the evaluation of partial coefficients,.- 11.4.3 General method for the evaluation of partial coefficients,.- 11.5 An Example of Probabilistic Code Calibration.- 11.5.1 Aims of calibration,.- 11.5.2 Results of calibration,.- 12. Applications to Fixed Offshore Structures.- 12.1 Introduction.- 12.2 Modelling the Response of Jacket Structures for ReliaBility Analysis.- 12.2.1 Sea-state model,.- 12.2.2 Wave model,.- 12.2.3 Loading model,.- 12.2.4 Natural frequency model,.- 12.2.5 Evaluation of structural response,.- 12.2.6 Evaluation of peak response,.- 12.2.7 Other models,.- 12.3 Probability Distributions for Important Loading Variables.- 12.3.1 Wind speed,.- 12.3.2 Morison's coefficients,.- 12.4 Methods of Reliability Analysis.- 12.4.1 General,.- 12.4.2 Level 2 method,.- 12.5 Some Results from the Study of a Jacket Structure.- 13. Reliability Theory and Quality Assurance.- 13.1 Introduction.- 13.2 Gross Errors.- 13.2.1 General,.- 13.2.2 Classification of gross errors,.- 13.3 Interaction of Reliability and Quality Assurance.- 13.3.1 General,.- 13.3.2 The effect of gross errors on the choice of partial coefficients,.- 13.4 Quality Assurance.- Appendix A. Random Number Generators.- 1. General.- 2. Uniform Random Number Generators.- 3. Multiplicative Congruence Method.- 5. Special Cases: Generation of Random Deviates Having Normal and Log-Normal Distributions.- Appendix B. Spectral Analysis of Wave Forces.- 1. Introduction.- 2. General Equations of Motion.- 3. Modal Analysis.- 4. Solution Strategy.- 5. Multiple Piles.- 6. Computational Procedure.