Robustness-oriented optimal design for reinforced concrete frames considering the large uncertainty of progressive collapse threats

Abstract

Design optimization of building structures under progressive collapse threats is a challenging problem. This is not only because the progressive collapse is a system failure phenomenon involving complicated material and geometrical nonlinearities, but also because the extremely low probability and the much larger uncertainty associated with the initiating events that trigger such a failure could render most risk reduction strategies economically unjustified, should the conventional risk-neutral decision making approach be followed. Facing these challenges, this paper presents an innovative two-stage optimization method for progressive collapse design of reinforced concrete frame structures. The first, tactical stage involves a bi-objective optimization that maximizes the structural robustness while minimizing the total additional reinforcement beyond the conventional design. This stage of optimization results in a Pareto efficiency frontier between the increase in longitudinal reinforcement and structural robustness, which is measured by a new risk-based robustness index. At each efficiency point, the optimal allocation of reinforcement across the beams affected by a column removal scenario is determined. The second, strategic stage includes a descriptive decision making module based on the cumulative prospect theory (CPT) in order to characterize the bounded rationality of a decision maker when facing large uncertainty. Based on an empirically calibrated CPT model, the study finds that the threshold for the probability of initiating event below which no additional investment is justified for progressive collapse design is pushed to the lower end of the empirical incidence rate. This is completely in contrast to previous research results based on the risk-neutral argument. Using a multi-storey plane frame for illustration, the study also clearly shows that the Alternate Path Method following the linear static procedure is not efficient from a purely engineering perspective. When the decision maker’s risk attitude is considered, the APM design is found to be unduly conservative.