A reliability based measure of structural robustness for coherent systems

Abstract

Progressive collapse (the spread of a relatively minor local damage through a chain of failures to the collapse of a significant portion of a structure) constitutes an important mode of system failure. A robust structure is able to locally confine the effects of a relatively minor initial damage. As a technical term, robustness has different connotations in different fields; a variety of robustness measures, phenomenological in nature, are also available in the structural engineering literature. The measure of structural robustness against progressive collapse must ideally be a monotonic function of a suitable damage measure, must help identify and prioritize critically important initial damages, and must be able to rank different structures in terms of their susceptibility to progressive collapse under similar loading and initial damages. It must also take all uncertainties into account. Starting with relative entropy between the joint distributions of safety margins and the generalized Birnbaum/Barlow-Proschan-Iyer component importance measure, we propose a new robustness index for binary, coherent structural systems that is bounded by zero and one; zero signifying certain collapse given the initial damage and one signifying the structure’s complete indifference to the given initial damage. The methodology is demonstrated on an indeterminate planar truss structure. The initial damage considered is the failure of any one given member. Element strengths and the load are taken to be random. Progressive collapse being a sequence driven event, an enumerative scheme is adopted for reliability analyses of the intact and damaged structures. The relations between robustness index, importance measure, element reliability and correlation between intact and damage safety margins are investigated; comparison of the proposed index with existing robustness measures is undertaken.