Empirical Failure Criteria with Correlated Resistance Variables

When a member is subjected to combined loading, such as combined bending and compression, the failure criterion contains more than one resistance variable. This paper addresses the practical effects of correlation among those resistance variables, both during the experimental inference of the failure criterion itself and during subsequent reliability analyses that employ it. There are two main findings. The first, of interest to experimental researchers, is that the mean failing load of a population is always less than the load that would be obtained from the exact (but as yet unknown) failure criterion applied to an individual member, provided that the failure criterion is concave downward, as all realistic engineering failure criteria are likely to be. The second finding, of interest to reliability analysts, is that the reliability of a member under combined loading is at a minimum when the resistance variables are maximally correlated. It is therefore conservative to assume perfect correlation. In that case, the problem is effectively univariate, that is, the effects of less‐than‐perfect correlation may be safely and conveniently ignored.