Bounding Approximations to Some Quadratic Limit States

Abstract

In second‐order reliability problems the limit state surface is (locally) replaced by a quadratic surface. This leads to a study of quadratic forms in the basic uncertainty variables. The present paper exploits a simple, closed‐form expression for the distribution function of a special class of quadratic forms in zero‐mean Gaussian variables to obtain bounds on the distribution function of general quadratic forms in such variables. It is shown that these bounds can be used to obtain useful estimates of the failure probability for such models.