Collapse and allowable displacements in the context of reliability analysis of nonlinear structures

Abstract

In this work, we study the relation between collapse and allowable displacements in the context of reliability analysis of nonlinear structures. We show that the probability of failure according to some finite allowable displacement is an upper bound for the probability of collapse. Consequently, it is possible to obtain safe estimates for the reliability according to collapse considering only allowable displacements limit state functions. This idea can be particularly useful in cases where it is computationally efficient to work with allowable displacements. The results are also important from the conceptual point of view. Three numerical examples are presented to illustrate the developed concepts.