Highlights • Risk analysis addresses epistemic uncertainties in loading scenarios, quality of manufacturing or workmanship, human errors. • Risk analysis contributes a latent failure probability to structural design problem. • Optimal structural design largely dependent on latent failure probabilities. • System Reliability‐based Design Optimization and Risk Optimization formulations addressed.

Abstract In spite of extended recent interest in System Reliability-Based Design Optimization (System RBDO) and life-cycle cost or Risk Optimization (RO), there is a lack of published studies on optimal design of redundant hyperstatic systems with objective consideration of (a) progressive collapse and (b) the impact of epistemic uncertainties. This paper investigates the fundamental aspects of the problem, by addressing the optimal design of simple two-bar active and passive redundant systems. Progressive collapse is objectively addressed, differentiating consequences of direct collapse of statically determinate structures, and progressive collapse of redundant, statically indeterminate structures. A comprehensive study is performed, considering material post-failure behavior (fragile-ductile), strength correlation, dynamic amplification factors in load re-distribution, and material strength ratios. Physical uncertainty in material strengths and loads is considered. However, it is well known that reliability of a structural system also depends on nonstructural factors, or factors beyond structural design, such as unanticipated loading, manufacturing quality, quality of workmanship and human errors. These factors can be taken into account in an encompassing risk analysis, which accounts for physical and epistemic uncertainties, and which contributes a fixed latent failure probability to the structural optimization problem. Results presented herein show that the latent failure probability is the single most important parameter in determining optimal solutions, in System RBDO and in RO solutions. When the latent failure probability is smaller than target (System RBDO) or optimal (RO) failure probabilities, there is an equivalence between redundant and non-redundant (hyperstatic and isostatic) designs. However, when the latent reliability is smaller than target or optimal reliabilities, optimal designs become necessarily redundant (hyperstatic); as the only way to make system reliability larger than the latent reliability is by making structural systems redundant. This result is widely known in context of system reliability, but has been overlooked in past studies involving structural System RBDO and Risk Optimization.