Optimal redundancy allocation and quality control in structural systems

Abstract

Reliability-Based and Risk-Based design optimization are popular research topics nowadays. Yet, not many studies have addressed the progressive collapse, the optimal robustness nor the optimal redundancy of structural systems. By way of fundamental examples, it is shown herein that redundancy is of little benefit, unless the structural system is exposed to external ‘shocks’. These ‘shocks’ are abnormal loading events; unanticipated failure modes; gross errors in design, construction or operation; operational abuse; and other factors that have historically contributed to observed structural collapses. Shocks may lead to structural damage or complete loss of structural members. The effect of such shocks on system reliability is generically represented by a member damage probability. This is a hazard-imposed damage probability, which is shown to be the key factor justifying the additional spending on structural redundancy. In structural reliability theory, it is understood that quality control should handle gross errors and their impacts; yet, it is shown herein that optimal redundancy is related to the frequency of inspections. The study reveals an intricate interaction between optimal redundancy and optimal quality control by way of inspections, challenging the separation between structural reliability theory and quality control in safety management.