Otimização de vigas de concreto armado de seção retangular utilizando o Método GRG e o Excel Solver

Abstract

the present study aims to optimize simply supported reinforced concrete beams with rectangular sections subjected to simple bending and shear, minimizing material and labor costs. The Generalized Reduced Gradient (GRG) technique implemented in Excel Solver is used to enhance the final cost of the beams, considering the dimensions of the cross-section as variables. The optimization was conducted in two stages: the first evaluated the influence of varying beam length and distributed loading (5 to 25 kN/m); the second analyzed the variation in beam length and fck (20 to 45 MPa). The design variables included the base and height dimensions of the cross-section, the tension and compression reinforcement, and the stirrups. The constraints followed the norms of NBR 6118/2023. The results showed that the height of the cross-section is the most sensitive variable, while the base remained relatively constant. With the increase in length and loading, there was an increase in the total cost of the beam, requiring a larger area of steel and the application of camber to meet deflection limits. The increase fck resulted in a reduction of the cross-sectional dimensions up to a stabilization point at 40 MPa, where the total cost reached its minimum value. It was observed that formwork cost represented the largest portion of the total cost, followed by steel and concrete. The applied methodology proved to be feasible and practical in the structural optimization of reinforced concrete beams. However, it is recommended to include the reuse of formwork and explore different optimization methods in future studies.