Cost optimization considering the probability of failure in reinforced concrete beams in bending

Abstract

This paper aims to demonstrate the feasibility and relevance of applying structural optimization methods together with the probability of failure constraints, integrating the search for the optimum solution and the guarantee of structural safety. The methodology involved optimization methods such as sequential quadratic (SQP), interior-point, and active-set, along with the FORM probability of failure calculation method. Computational tools such as MATLAB enabled a comparative analysis of the performance of these methods. The study stands out for integrating structural optimization and reliability, applying it to reinforced concrete beams, a relevant topic for structural engineering. The results of the analysis of simply supported beams showed satisfactory convergence between the methods, with minimal variability and superior performance of the SQP and interior-point optimizers. The introduction of standardized safety coefficients increased the reinforcement rate, reducing the probability of failure and costs. The study highlighted the synergy between optimization and structural safety, contributing theoretically by showing the effectiveness of combining optimization with probability of failure restrictions, and methodologically by comparatively evaluating different optimization methods.