Synopsis
1 Prologue.- 2 Reliability of Structures.- 2.1 Introductory Comments.- 2.2 Basic Concepts.- 2.3 How Accurate Is Minimum Distance Reliability Index?.- 2.4 Safety Factors as Discussed in Literature.- 2.5 About the Acceptable Probability of Failure.- 2.6 A Priority Question.- 2.7 Concluding Comments on the Stress-Strength Interference Method.- 3 Safety Factors and Reliability: Random Actual Stress & Deterministic Yield Stress.- 3.1 Introductory Comments.- 3.2 Four Different Probabilistic Definitions of a Safety Factor.- 3.3 Case 1: Stress Has an Uniform Probability Density, Strength Is Deterministic.- 3.4 Case 2: Stress Has an Exponential Probability Density, Yield Stress Is Deterministic.- 3.5 Case 3: Stress Has a Rayleigh Probability Density, Yield Stress is Deterministic.- 3.6 Case 4: Stress Has a Normal Probability Density, Yield Stress Is Deterministic.- 3.7 Case 5: Actual Stress Has a Log-Normal Probability Density, Yield Stress is Deterministic.- 3.8 Case 8: Actual Stress Has a Weibull Probability Density, Strength is Deterministic.- 3.9 Actual Stress Has a Fréchet Probability Distribution, Yield Stress Is Deterministic.- 3.10 Actual Stress Has Two Parameter Weibull Probability density, Yield Stress Is Deterministic.- 3.11 Actual Stress Has a Three Parameter Weibull Probability Density, Yield Stress Is Deterministic.- 3.12 Discussion: Augmenting Classical Safety Factors, via Reliability.- 4 Safety Factors and Reliability: Deterministic Actual Stress & Random Yield Stress.- 4.1 Yields Stress Has an Uniform Probability Density, Actual Stress is Deterministic.- 4.2 Yield Stress Has an Exponential Probability Density, Actual Stress Is Deterministic.- 4.3 Strength Has a Rayleigh Probability Density, Stress Is Deterministic.- 4.4 Various Factors of Safety in Buckling.- 4.5 Yield Stress Has a Weibull Probability Density, Actual Stress Is Deterministic.- 4.6 Yield Stress Has a Fréchet Distribution, and Actual Stress Is Deterministic.- 4.7 Yield Stress has a Three Parameter Weibull Distribution, and Actual Stress Is Deterministic.- 4.8 Yield Stress Has a Two Parameter Weibull Distribution, and Actual Stress is Deterministic.- 4.9 Concluding Comments on Proper Distribution Functions.- 5 Safety Factor and Reliability: Both Actual Stress and Yield Stress Are Random.- 5.1 Introductory Comments.- 5.2 Both Actual Stress and Yield Stress Have Normal Probability Density.- 5.3 Actual Stress Has an Exponential Density, Yield Stress Has a Normal Probability Density.- 5.4 Actual Stress Has a Normal Probability Density, Strength Has an Exponential Probability Density.- 5.5 Both Actual Stress and Yield Stress Have Log-Normal Probability Densities.- 5.6 The Characteristic Safety Factor and the Design Safety Factor.- 5.7 Asymptotic Analysis.- 5.8 Actual Stress and Yield Stress Are Correlated.- 5.9 Both Actual Stress and Yield Stress Follow the Pearson Probability Densities.- 5.10 Conclusion: Reliability and Safety Factor Can Peacefully Coexist.- 6 Non-Probabilistic Factor of Safety.- 6.1 Introductory Comments.- 6.2 Sensitivity of Failure Probability.- 6.3 Remarks on Convex Modeling of Uncertainty.- 6.4 "Worst-Case" Probabilistic Safety Factor.- 6.5 Which Concept Is More Feasible: Non-Probabilistic Reliability or Non-Probabilistic Safety Factor?.- 6.6 Concluding Comments on How to Treat Uncertainty in a Given Situation.- 7 Stochastic Safety Factor by Birger and Maymon.- 7.1 Introductory Comments.- 7.2 Definition of Stochastic Safety Factor.- 7.3 Implication of the Stochastic Safety Factor.- 7.4 Cantilever Beam with Restricted Maximum Displacement.- 7.5 Concluding Comments.- 8 Safety Factor in Light of the Bienaymé-Markov and Chebychev Inequalities.- 8.1 Bienaymé-Markov Inequality.- 8.2 Use of the Bienaymé-Markov Inequality for Reliability Estimation.- 8.3 Derivation of the Chebychev's Inequality.- 8.4 Application of the Chebychev's Inequality: Mischke's Bound.- 8.5 Application of the Chebychev's Inequality by My Dao-Thien and Massoud.- 8.6
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