# OBTENÇÃO DA CURVA TENSÃO-DEFORMAÇÃO DO CONCRETO REFORÇADO COM FIBRAS DE AÇO POR MEIO DE ANÁLISE INVERSA

## Palavras-chave:

Steel fiber reinforced concrete, Inverse analysis, Genetic algorithm## Resumo

One way to measure the increase of ductility, from the addition of steel fibers in concrete, is

from the uniaxial tension tests. However, this test is difficult to carry out and the equipment is highly

rigid and is not present in most concrete laboratories. Thus, the solution could be obtaining the stress-

strain diagram for uniaxial tension of steel fiber reinforced concrete (SFRC) from inverse analysis of a

bending tests. The inverse analysis proposed in this paper consists of an automatic search of the

softening behavior of the SFRC. To achieve this, the objective function is defined to minimize the

difference between load-deflection curve obtained by the finite element software DIANA®

10.1 and

experimental curves obtained by test a simply supported beam under third-point loading, as proposed

by ASTM C1609/C1609M-12. The optimization process is performed in two steps, that is, first it is

determined the flexural modulus of the SFRC, which defines the initial linear elastic part of the load-

deflection curve. Then, points of the softening diagram of SFRC are determined. Since the design

variables are not explicit in optimization process of the objective function, it was necessary to use a

heuristic method, among which a genetic algorithm (GA) available on MATLAB (2007) was chosen.

The GA algorithmic has been showed efficient to obtain the softening diagram of SRFC with two

volume of steel fibers, 0.5% and 1.5%, with index of agreement over 90%.