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Isaac Elishakoff - One of the best experts on this subject based on the ideXlab platform.

  • Stochasticity and safety factors: Part 1. Random Actual Stress and deterministic yield Stress
    Chaos Solitons & Fractals, 2005
    Co-Authors: Isaac Elishakoff
    Abstract:

    Abstract This paper makes a bridge between the classical concept of the safety factor and the structural reliability. It concentrates on a special case in which the material possesses deterministic yield Stress, and the element is subjected to the random Actual Stress. Various probability distribution functions are treated to describe the probabilistic behavior of the Stress; reliabilities are evaluated, and the connection with the safety factors is emphasized.

  • Safety Factors and Reliability: Friends or Foes?
    2004
    Co-Authors: Isaac Elishakoff
    Abstract:

    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 Frechet 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 Frechet 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 Bienayme-Markov and Chebychev Inequalities.- 8.1 Bienayme-Markov Inequality.- 8.2 Use of the Bienayme-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 Examples.- 8.7 Conclusion: Other Bounds of Probability of Failure.- 9 Japanese Contributions to the Interrelating Safety Factor and Reliability.- 9.1 Introduction.- 9.2 Ichikawa's Formula.- 9.3 Reiser's Correction.- 9.4 Another Set of Formulas by Ichikawa and Reiser.- 9.5 Application of the Camp-Meidell Inequality.- 9.6 Series Representation of the Probability Density Functions.- 9.7 Use of the Edgeworth Series by Murotsu et al.- 9.8 Hoshiya's Distinction of Seemingly Equivalent Designs.- 9.9 Contribution by Konishi et al: Proof Loads.- 9.10 Concluding Remarks.- 10 Epilogue.- Appendix A Accuracy of the Hasofer-Lind Method.- A.1 Introductory Comments.- A.2 Beam Subjected to a Concentrated Force.- A.3 Approximate Solutions.- A.4 Exact Solution.- A.5 Design of Structural Element.- Appendix B Biographical Notes.- I-J. Bienayme.- P.L. Chebychev.- Ch. A. de Coulomb.- A. M. Freudenthal.- A.M. Kakushadze.- G. Kazinczy.- M. Mayer.- G.M. Mukhadze.- L.M.H. Navier.- A.R. Rzhanitsyn.- N.S. Streletskii.- Author Index.

  • Safety Factors and Reliability: Deterministic Actual Stress & Random Yield Stress
    Safety Factors and Reliability: Friends or Foes?, 2004
    Co-Authors: Isaac Elishakoff
    Abstract:

    In the previous chapter we studied the case in which the Actual Stress was treated as a random variable, while the yield Stress was considered as a deterministic quantity. In this report we investigate the reverse case, namely, when the Actual Stress is deterministic, while the yield Stress is treated as a random variable. Various probability densities to model the Actual behavior of the structural element in question are considered.

  • safety factors and reliability deterministic Actual Stress random yield Stress
    2004
    Co-Authors: Isaac Elishakoff
    Abstract:

    In the previous chapter we studied the case in which the Actual Stress was treated as a random variable, while the yield Stress was considered as a deterministic quantity. In this report we investigate the reverse case, namely, when the Actual Stress is deterministic, while the yield Stress is treated as a random variable. Various probability densities to model the Actual behavior of the structural element in question are considered.

  • Safety Factors and Reliability: Random Actual Stress & Deterministic Yield Stress
    Safety Factors and Reliability: Friends or Foes?, 2004
    Co-Authors: Isaac Elishakoff
    Abstract:

    In this chapter we will deal with the simplest possible case, when the yield Stress constitutes a deterministic quantity but the Actual Stress is random, due to the randomness of the distribution or concentrated loads, or the randomness of distributed or the concentrated moments. It becomes possible to express the safety factor via the structural reliability.

Lu Sun - One of the best experts on this subject based on the ideXlab platform.

Yaoting Zhu - One of the best experts on this subject based on the ideXlab platform.

Yiqing Dai - One of the best experts on this subject based on the ideXlab platform.

  • research on the fatigue equation of asphalt mixtures based on Actual Stress ratio using semi circular bending test
    Construction and Building Materials, 2018
    Co-Authors: Jiwang Jiang, Qiao Dong, Yiqing Dai
    Abstract:

    Abstract The semi-circular bending (SCB) strength test and fatigue test were used in this paper to evaluate the strength property and fatigue performance of asphalt mixtures. The SCB strength test was carried out at 8 loading rates and 3 temperatures, followed by the SCB fatigue test at 5 load levels on one common stone matrix asphalt (SMA) mixture. The time–temperature characteristics of strength from SCB test were studied. The fatigue performance was evaluated based on displacement development and energy consumption during the cyclic loading process. And according to the established strength-loading rate model, the fatigue equation based on Actual Stress ratio was obtained as well. The results showed that asphalt mixture strength was affected by loading rate and temperature significantly, the relation between strength and loading rate could be approximately expressed as a power function; the relation between fatigue life and Stress level (or nominal Stress ratio) could also be expressed as a power function. The lower the Stress level, the longer the fatigue life was, and the fatigue life and the cumulative energy consumption showed a good linear relationship in the double logarithmic coordinates; the fatigue equation based on Actual Stress ratio revealed the connection between fatigue failure and strength failure.

Zeng Fan-f - One of the best experts on this subject based on the ideXlab platform.