  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. 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.
