Otimização de seções transversais circulares para pilares em concreto armado submetidos a flexão composta oblíqua

Abstract

This study is situated within the context of sustainability and structural efficiency, contributing to the development of safer and more economical buildings. The present work addresses the optimization of reinforced concrete columns with circular cross-sections, which are fundamental structural elements responsible for transferring vertical loads to the foundations. A computational program was developed in MATLAB to minimize the total cost of the column, ensuring safety and economy in compliance with ABNT NBR 6118:2026. Initially, the study reviews fundamental concepts of reinforced concrete columns, highlighting ultimate limit states (ULS), serviceability limit states (SLS), stresses and strains, and normative limits for reinforcement and slenderness. It also explores the properties of concrete and steel, which are essential for structural performance. The methodology employs the MATLAB `fmincon` function. Input data include the normal force, bending moments, and concrete strength, which can range from 20 MPa to 90 MPa.As output, the program provides optimal reinforcement diameters and ratios, as well as an estimated total cost per linear meter. To validate the tool, the results were compared against manual design via interaction charts and Eberick® commercial software. The comparisons demonstrated that the algorithm produces results consistent with manual methods, while also validating its capacity to find lower-cost solutions compared to non-optimized designs.