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Actual Stress
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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, 2005CoAuthors: Isaac ElishakoffAbstract: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?
, 2004CoAuthors: Isaac ElishakoffAbstract: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 StressStrength 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 LogNormal 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 LogNormal 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 NonProbabilistic Factor of Safety. 6.1 Introductory Comments. 6.2 Sensitivity of Failure Probability. 6.3 Remarks on Convex Modeling of Uncertainty. 6.4 “WorstCase” Probabilistic Safety Factor. 6.5 Which Concept Is More Feasible: NonProbabilistic Reliability or NonProbabilistic 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 BienaymeMarkov and Chebychev Inequalities. 8.1 BienaymeMarkov Inequality. 8.2 Use of the BienaymeMarkov 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 DaoThien 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 CampMeidell 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 HasoferLind 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. IJ. 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?, 2004CoAuthors: Isaac ElishakoffAbstract: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.
Lu Sun – One of the best experts on this subject based on the ideXlab platform.

a serial two stage viscoelastic viscoplastic constitutive model with thermodynamical consistency for characterizing time dependent deformation behavior of asphalt concrete mixtures
Construction and Building Materials, 2013CoAuthors: Lu Sun, Yaoting ZhuAbstract:Abstract A serial twostage viscoelastic–viscoplastic constitutive model is developed using internal variables theory and orthogonality principle of thermodynamics for modeling timedependent behavior of asphalt concrete mixtures. In one stage when the Actual Stress is lower than the yield Stress, the constitutive model only exhibit viscoelastic component, while in another stage when the Actual Stress exceeds the yield Stress, the constitutive model exhibit both viscoelastic and viscoplastic components. Model parameters of viscoelastic component are estimated using data obtained from dynamic modulus test, whereas model parameters of viscoplastic component are consecutively estimated from creep test, assuming a known viscoelastic component.

A serial twostage viscoelastic–viscoplastic constitutive model with thermodynamical consistency for characterizing timedependent deformation behavior of asphalt concrete mixtures
Construction and Building Materials, 2013CoAuthors: Lu Sun, Yaoting ZhuAbstract:Abstract A serial twostage viscoelastic–viscoplastic constitutive model is developed using internal variables theory and orthogonality principle of thermodynamics for modeling timedependent behavior of asphalt concrete mixtures. In one stage when the Actual Stress is lower than the yield Stress, the constitutive model only exhibit viscoelastic component, while in another stage when the Actual Stress exceeds the yield Stress, the constitutive model exhibit both viscoelastic and viscoplastic components. Model parameters of viscoelastic component are estimated using data obtained from dynamic modulus test, whereas model parameters of viscoplastic component are consecutively estimated from creep test, assuming a known viscoelastic component.
Yaoting Zhu – One of the best experts on this subject based on the ideXlab platform.

a serial two stage viscoelastic viscoplastic constitutive model with thermodynamical consistency for characterizing time dependent deformation behavior of asphalt concrete mixtures
Construction and Building Materials, 2013CoAuthors: Lu Sun, Yaoting ZhuAbstract:Abstract A serial twostage viscoelastic–viscoplastic constitutive model is developed using internal variables theory and orthogonality principle of thermodynamics for modeling timedependent behavior of asphalt concrete mixtures. In one stage when the Actual Stress is lower than the yield Stress, the constitutive model only exhibit viscoelastic component, while in another stage when the Actual Stress exceeds the yield Stress, the constitutive model exhibit both viscoelastic and viscoplastic components. Model parameters of viscoelastic component are estimated using data obtained from dynamic modulus test, whereas model parameters of viscoplastic component are consecutively estimated from creep test, assuming a known viscoelastic component.

A serial twostage viscoelastic–viscoplastic constitutive model with thermodynamical consistency for characterizing timedependent deformation behavior of asphalt concrete mixtures
Construction and Building Materials, 2013CoAuthors: Lu Sun, Yaoting ZhuAbstract:Abstract A serial twostage viscoelastic–viscoplastic constitutive model is developed using internal variables theory and orthogonality principle of thermodynamics for modeling timedependent behavior of asphalt concrete mixtures. In one stage when the Actual Stress is lower than the yield Stress, the constitutive model only exhibit viscoelastic component, while in another stage when the Actual Stress exceeds the yield Stress, the constitutive model exhibit both viscoelastic and viscoplastic components. Model parameters of viscoelastic component are estimated using data obtained from dynamic modulus test, whereas model parameters of viscoplastic component are consecutively estimated from creep test, assuming a known viscoelastic component.
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, 2018CoAuthors: Jiwang Jiang, Qiao Dong, Yiqing DaiAbstract:Abstract The semicircular 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 strengthloading raterate 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 Fanf – One of the best experts on this subject based on the ideXlab platform.

Calculation model and optimization design research of the steel fiber reinforced concrete
, 2007CoAuthors: Zeng FanfAbstract:It represents the differentiation of the pavement constitution between the steel fibefiber reinreinforced concrete and the general concrete easily,and brings forward the calculation model and optimization design scheme meeting the Actual Stress condition of the steel fibefiber reinreinforced concrete pavement according to the recent researches and tests,which will have important meaning to the steel fibefiber reinreinforced concrete pavement development.