Structural Reliability Theory and Its Applications

Structural reliability theory is concerned with the rational treatment of uncertainties in struc­ tural engineering and with the methods for assessing the safety and serviceability of civil en­ gineering and other structures. It is a subject which has grown rapidly during the last decade and has evolved from being a topic for academic research to a set of well-developed or develop­ ing methodologies with a wide range of practical applications. Uncertainties exist in most areas of civil and structural engineeri'1.g and rational design decisions cannot be made without modelling them and taking them into account. Many structural en­ gineers are shielded from having to think about such problems, at least when designing simple structures, because of the prescriptive and essentially deterministic nature of most codes of practice. This is an undesirable situation. Most loads and other structural design parameters are rarely known with certainty and should be regarded as random variables or stochastic processes, even if in design calculations they are eventually treated as deterministic. Some problems such as the analysis of load combinations cannot even be formulated without recourse to probabilistic reasoning.

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.