Non linear finite element analysis of reinforced concrete beams with rectangular opening

Abstract

This study deals with the non linear finite element analysis of reinforced concrete beams with opening basea on rate independent material non' linearity. Rate-independent plasticity is characterized by the irreversible straining that occurs in a material once a certain level of stress is reached. The plastic strains are assumed to develop instantaneously, that is, independent of time. An eight-nodded iso-parametric threedimensional solid element is used to model the inelastic response of brittle materials based on a constitutive model for the tri-axial behaviour of concrete after Willam KJ. and Wamke E.D. (1975). The intemal reinforcements were modelled using three dimensional spar elements with plasticity. The non linear effects due to the cracking and crushing of concrete and the yielding of steel reinforcement are included. An incremental finite element technique is used which simulates the non linear load-deflection behaviour of reinforced concrete stmcture. This work is an attempt to correlate the numerical observation regarding the behaviour of some reinforced concrete beam having rectangular web opening with those from the previously experimented results. The entire numerical analysis has been perfonned using general-purpose finite element code ANSYS. Results of the numerical study are compared to that of the available experimental values. Several parameters such as opening length and depth, horizontal and vertical location of the opening have been varied. The effect of opening on the behaviour of beams under one point loading has been presented in this study. Deflection due to opening at high moment end, stress distribution over the entire section of the beam, strain distribution in the vicinity of the opening, crack propagation pattern and failure mechanisms have been observed. From a comparison of the numerical and the experimental results, it is concluded that the developed finite element model used in the present study is suitable for analysing and capturing the behaviour of reinforce concrete beam with opening. The good agreement between the numerical and the experimental results establishes the validity and rationality of the computational models. This model is general and may be used for any arbitrary shaped structure. It is also useful in predicting cracking pattern, yield and ultimate load carrying capacity. In addition it should be particularly attractive to designers when it is required to predict deflection of a reinforced concrete system, for a given load, in addition to its ultimate strength. From the finite element analysis of reinforced concrete beams with web opening, it is observed that stiffness as well as yield capacity of the beams decreases with the increase in opening length, depth and moment-shear ratio but stiffness increases with the increase of opening eccentricity. In all cases of beam, change in stress pattern occurred both in top and bottom chord. Long-term deflection has been calculated using ACI Code (2002) formula from service load deflection. It was found that immediate deflection due to service load is within the ACI Code (2002) limit.