System reliability-based design optimization and risk-based optimization: a benchmark example considering progressive collapse

System Reliability-Based Design Optimization (RBDO) considers a single system failure probability constraint. The formulation allows different failure modes to compete with each other. Very few methods and benchmark examples involving optimal design considering system behaviour with progressive failure can be found in the literature. In this article, the conventional System RBDO formulation is compared with a risk-based formulation. A benchmark example involving progressive failure of hyper-static truss is addressed. It is demonstrated that typical System RBDO formulations always lead to isostatic structures, since the formulation does not offer any incentive for the permanence of hyper-static members. In the risk-based formulation, failure costs are differentiated with respect to primary member failure, in hyper-static structures (existence of warning before eventual collapse), and failure of isostatic members (no warning). In this formulation, optimal designs also include hyper-static structures. Results presented herein are relevant in the modern context of robust design considering progressive collapse.