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On A Statistical Problem Involving the Measurement of Strength and Duration-of-Load for Construction Materials

In: Contributions to Probability and Statistics

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  • Sam C. Saunders

    (Washington State University, Department of Pure and Applied Mathematics)

Abstract

This paper presents a new analysis, applicable to construction materials, for estimating the probabilistic behavior of the duration-of-load, say Tℓ when the load is of magnitude ℓ, based on the imposed stress ratio of load to characteristic material strength. The stochastic behavior of the logarithm of the duration-of-load, given the strength S exceeds ℓ, is of axiomatic importance. We assume the conditional distribution, presuming strength S were known, to be of the form $$\left[ {\ln {T_\ell }|S = s} \right] - H\left( {s/\ell } \right) \sim {\sigma _0}Z,$$ where the r.v. Z is a standard variate appropriately chosen for the material, and the regression H is a monotone increasing function of the form $$ H\left( x \right) = {{\alpha }_{0}} + {{\alpha }_{1}}x + {{\alpha }_{{ - 1}}}{{x}^{{ - 1}}} $$ for x

Suggested Citation

  • Sam C. Saunders, 1989. "On A Statistical Problem Involving the Measurement of Strength and Duration-of-Load for Construction Materials," Springer Books, in: Leon Jay Gleser & Michael D. Perlman & S. James Press & Allan R. Sampson (ed.), Contributions to Probability and Statistics, chapter 32, pages 486-495, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3678-8_35
    DOI: 10.1007/978-1-4612-3678-8_35
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