Otimização de vigas trapezoidais de concreto armado submetidas a flexão simples

Abstract

This work had as main objective to presente a computational algorithm that returns the dimensions and steel area of the longitudinal bars of trapezoidal transversal sections of reinforced concrete beams subject to simple bending, in an optimized manner in terms of material and execution cost, respecting the established by ABNT standard NBR 6118:2014. It also aims to a comparison between the optimal solutions between the versions of the standard ABNT NBR 6118:2014 and ABNT NBR 6118:2003.For the computational implementation of the algorithm, MATLAB software and the fmincon routine present in its optimization library were used. For the individual costs of concrete, steel and formwork, the table SINAPI – National System of Research of Costs and Indices of Civil Construction, region of Curitiba and date of technical reference on August 15, 2020, was consulted. The results are significant despite in structural optimization context and allow to conclude that the design of trapezoidal cross sections beams presents a little higher cost when done according to the ABNT NBR 6118: 2014 version compared to the version dated in 2003, in addition to showing that the arrow check is more relevant in the desing of beams subjected to smaller efforts.