Análise não linear de vigas de concreto armado com método secante

Abstract

This work aims to develop and implement computational routines of a simple and efficient finite element model for nonlinear analysis of reinforced concrete beams, considering the material nonlinearity using the moment-curvature relation of cross sections, that are obtained before structural analysis. Computational routines were developed to obtain the moment-curvature relations of general reinforced concrete cross sections, using an alternative development of the traditional fibers approach. The routines are simple, general and flexible, allowing practical employment, and can also be used with different constitutive laws of steel and concrete. Then, a finite element model was developed for nonlinear analysis of reinforced concrete beams based on the moment-curvature relation, employing the Euler-Bernoulli beam element. In order to solve the nonlinear equilibrium equations and obtain the internal displacements and stresses, the Secant iterative method is employed. In this method, the secant stiffness matrix of the structure is updated at each iteration, using the values of the node curvatures and the moment-curvature relations to obtain the stiffness matrices of the elements. The finite element model developed was implemented in computational routines and validated by comparisons with numerical and experimental results from the literature. Based on the results obtained it can be concluded that the computational routines for nonlinear analysis of reinforced concrete beams developed in this work are accurate and efficient.