Nonlinear Finite Element Analysis of Reinforced Concrete Beams with Large Opening under Flexure

Abstract

This paper describes a three- dimensional nonlinear finite element modelsuitable for the analysis of reinforced concrete Beams with Large Openingunder Flexure. The 20-node isoparametric brick elements have been used tomodel the concrete. The nonlinear equations of equilibrium have been solvedusing an incremental-iterative technique operating under load control. Thesolution algorithm used was the modified Newton-Raphson method. Thenumerical integration has been conducted using the 27-point Gaussian typerule. The reinforcing bars are idealized as axial members embedded withinthe concrete element and perfect bond between the concrete and thereinforcement has been assumed to occur. The behavior of concrete incompression is modeled using an elasto-plastic work hardening modelfollowed by a perfectly plastic response, which is terminated at the onset ofcrushing. In tension, a smeared crack model with fixed orthogonal cracks hasbeen used with the inclusion of models for the retained post-cracking tensilestress and the reduced shear modulus. Different types of reinforced concretebeams with large rectangular transverse openings have been analyzed and thefinite element solutions are compared with the experimental data. Generally,good agreement has been obtained between the numerical and experimentalload-deflection curves and ultimate load. Numerical studies including somematerial parameters such as concrete compressive strength, amount oflongitudinal tensile reinforcement and opening size on the load-deflectionresponse have been carried out to study their effect on the over all behavior ofreinforced concrete beams with Large opening under Flexure.The finiteelement solution revealed that the ultimate load and post-cracking stiffnessincrease with the increases of concrete compressive strength, increases withthe increase of the bottom steel reinforcement amount and decreases with theincrease of length or depth of opening.