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

Resumo

The sudden loss of a single supporting element in a reinforced concrete (RC) frame can result in disproportionate structural collapse if its design fails to confine the initial damage through resistance mechanisms. Given the significant impact of uncertainties related to material properties and geometric parameters on the behavior of these resisting mechanisms, and considering the high stakes involved in such failure events, risk optimization provides a practical approach to striking the right balance between cost-efficiency and safety. This is demonstrated herein through the optimization of a two-story, four-bay RC frame under two scenarios of column
removal at the first floor: middle column and corner column. Design variables include cross-sectional depth, steel rebar areas, and concrete strength of beams and columns. Failure consequences are assessed for both the intact structure (considering beam serviceability, beam bending, shear failure of beams, and flexo-compression failure for the columns) and for both column removal scenarios (involving steel rupture of the top rebar layer at the interface between the beam and adjacent column, shear failure of beams, and flexo-compression failure of the columns). A physical and geometrical nonlinear static analysis is conducted, with sample points subjected to bay pushdown analysis. Material behavior is characterized by an elastoplastic model with isotropic hardening for the steel rebars and the Mazars μ model for the concrete (using the modified Park-Kent model for calibration reference). Failure probabilities are assessed using the Weighted Average Simulation Method, and risk optimization is performed using the Firefly Algorithm. To mitigate the computational cost arising from the nonlinearities and the high number of required sample points, Kriging is employed to generate an accurate metamodel for the limit states and reliability indexes. The optimal conventional design prioritizes resistance against bending failure at the beam ends rather than serviceability failure. Beyond a certain threshold value of local
damage probability, an increase in the overall frame robustness is observed for both column loss scenarios, with the most significant improvement occurring for corner column removal. This is attributed to this scenario leading to lower resistance against steel rupture and to keep bending moments at the adjacent column close to zero.