Optimal risk-based design of planar RC frames under progressive collapse: Influence of frame aspect ratio and column cross-section

The progressive collapse resistance of reinforced concrete (RC) frame buildings involves complex interactions between structural topology and resisting mechanisms, which strongly influence design for structural robustness. When a RC frame system is subjected to sudden column loss, different complementary resistance mechanisms can be activated in RC beams, depending on beam cross-section detailing and column stiffness. When a double-span beam fails, damage can propagate upwards, affecting upper beams, or laterally, affecting adjacent columns. Both the interaction between resistance mechanisms and optimal design of RC frame depend significantly on the frame aspect ratio and column cross-sections. Taller frames require stronger beams and columns to prevent both vertical and horizontal collapse propagation, whereas lower frames favor weaker beams due to the less critical consequences of upward beam collapse propagation. In this study, the influence of frame aspect ratio and column cross-section on the progressive collapse behavior of planar RC frames is investigated. Analysis results show that the optimal risk-based design of such structures is significantly influenced by the interactions between beam and column moments of inertia, as result of Vierendeel and catenary action intricacies. Specifically, it is shown how the aspect ratio of planar RC frames under multiple ground-floor column loss scenarios leads to different optimal risk-based designs. Nonlinear FE analysis in OpenSees is carried out, capturing Vierendeel, compressive arch and catenary actions in lower, intermediate, and taller RC frames. Weighted Average Simulation is used to compute failure probabilities, and Inverse Distance Weighting is adopted when integrating structural modeling, reliability analysis and risk-based optimization. In contrast to previous investigations, optimal design against progressive collapse is found to mainly depend on balance between beam and column flexural capacities. For the case-study frames, squared cross-section columns lead to greater beam depths, as columns are unable to resist the increased bending moments produced by beams in catenary action. In such cases, ultimate capacity is enhanced by means of compressive arch action. Yet, columns with rectangular cross-sections allow catenary action to be efficiently mobilized in all investigated frames. This later solution closely resembles the ‘weak beam – strong column’ design philosophy adopted against lateral actions produced by earthquake ground motion and wind.