Optimal risk-based design of a RC frame under column loss scenario

Abstract

Structural systems may be subject to abnormal loads with small probability of occurrence but great intensity, which may lead to local damage, and even loss of loadbearing elements. In this context, it is important to design structural systems to avoid disproportionate progressive collapse. In this paper, we address the optimal risk-based design of a simple RC frame subjected to sudden loss of an internal column. The optimization targets compressive arch, Vierendeel and catenary actions under column loss condition, also considering both serviceability and ultimate failure modes under normal loading conditions. Since initial damage is associated with large uncertainties, the column loss probability is treated as an independent parameter in the optimization. The numerical model employed in the analysis combines physical and geometrical non-linearities. Steel rebar behavior is represented by an elastoplastic model with isotropic hardening, whereas confined concrete is simulated via a combination of Mazars μ model with the modified Park-Kent model. Failure probabilities are evaluated by weighted average simulation, and the risk optimization is performed using the Firefly algorithm. Kriging metamodels of limit states and reliability indexes are employed to cope with the high computational burden. Results show two quite different optimal configurations for beams and columns of the frame: a more conventional design is obtained under small column loss probability, whereas the optimal solutions clearly benefit from catenary action under large column loss probability since enough ductility is provided in terms of ultimate steel strain. These results confirm, in a more practical setting, a previous outcome by the authors that the column loss probability is the main parameter controlling optimal design of the frames. The transition between optimal solutions mentioned above can be associated with a threshold column loss probability, above which designing or strengthening the structure to withstand column loss becomes cost-effective.