Reliability-based design optimization of post-tensioned self-centering rocking steel frame structures

This paper reports the Reliability-Based Design Optimization (RBDO) of post-tensioned self-centering rocking steel frame structures with buckling-restrained bracing systems. The objective was to investigate the reliability index, optimization of self-centering structures to reach minimum weight using metaheuristic algorithms, and their application in linear and nonlinear reliability problems. For this purpose, three steel structures (10-, 15-, and 20-storey structures) were each evaluated with three steel framing systems (buckling-restrained bracing, post-tensioned self-centering multiple rocking steel frame with buckling-restrained bracing, and post-tensioned self-centering single rocking steel frame with buckling-restrained bracing), making a total of nine models. Subsequently, specific 2D frames of the structural models were numerically simulated using nonlinear dynamic analysis (NDA) in OpenSees software. Optimization was carried out in two stages: with and without considering the uncertainties. Finally, for calculating the failure probability and structural reliability index, Monte-Carlo Simulation (MCS) was employed. Results indicate that, although considering the reliability index leads to heavier structures, structural safety was increased and failure probability was reduced to even lower specified levels. Furthermore, among the incorporated algorithms, the Colliding Bodies Optimization (CBO) and Charged System Search (CSS) algorithms proved to have superior performances in terms of accuracy and converging time. On average, using these two algorithms for cases without uncertainty resulted in maximum weight reductions of 36%, 30%, and 32% for 10-, 15-, and 20-storey structures. In addition, for cases with uncertainty, these two algorithms with reliability index (β) of 2 respectively reduced the weight of 10-, 15-, and 20-storey structures by 21%. Also, it was shown that not considering the uncertainties can increase the failure probability by up to 23%.