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

This paper presents a new analysis, applicable to construction materials, for estimating the probabilistic behavior of the duration-of-load, say T_ℓ 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 < 0.