Optimal risk-based design of reinforced concrete beams against progressive collapse

Risk analyses addressing consequences of progressive collapse have shown that, due to the small probabilities of element loss due to abnormal loads, structural strengthening for alternate load paths has negative cost-benefit for most buildings subjected to typical threats. This study addresses optimal risk-based design of reinforced concrete beams subjected to supporting column removal, with specific focus on reinforced concrete behavior. Nonlinear finite element analysis (NLFEA) is carried out, allowing both compressive arch and catenary actions to be predicted under large deflections. NLFEA results are compared to experimental data, showing good agreement and allowing quantification of model errors. Risk optimization results show that optimal beam designs change significantly with local damage probability, which is considered an independent parameter. More importantly, the study shows how different failure modes compete for limited construction and strengthening budgets. In case of intact structure, optimal design is governed by serviceability displacements, bending failure at midspan, and bending-shear failure at beam ends. Optimal design of the damaged structure is controlled by shear failure at beam ends and tensile rupture of steel rebar due to either catenary action or snap-through instability. Results highlight that, under significant column-loss probabilities, progressive collapse resistance is reached by larger beam depth, greater reinforcement area and reduced stirrup spacing. Such design measures against progressive collapse also provide greater safety margins against all failure modes of the intact structure.