Nonlinear analysis of reinforced concrete skew slabs

Abstract

This study deals with the non-linear finite element analysis of reinforced concrete skew slabs based on layered Mindlin plate element formulations. An eight-node isoparametric plate element is used. The Mindlin thick plate theory is applied to account for transverse shear deformations. Only material nonlinearity has been considered here. The layered technique is adopted in order to allow for the development of cracks through the thickness at different sampling points. Each layer is assumed to be in a state of plane stress. The non-linear effects due to the cracking and crushing of concrete and the yielding of steel reinforcement are included. The material model behaviour is based on the experimental observation reported by various authors. The reinforcing steel is treated as an equivalent layered material having uniaxial stiffness. The model describes nonlinear stress-strain relationship proposed by Richard and Abbott (1975) similar to Ramberg and Osgood (1943). An incremental finite element technique is used which simulates the non-linear load-deflection behaviour of reinforced concrete structural slab systems. This work is an attempt to correlate the experimental behaviour of some skew slabs with the numerical predictions using simple and popularly accepted material models. A total of ten skew slabs are experimentally tested in the Laboratory to verify the numerical formulation. Three types of reinforcement are used. The steel arrangements are either parallel or perpendicular to the supporting edges or the free edges. Three angles of skew selected are 30, 40, and 50 degrees. Two types of loading, namely (a) centrally located single point load and (b) two points loading, are considered. The supports for all the slabs are simple supports on two opposite edges. The ultimate load carrying capacities determined numerically are compared with the available experimental data and the loads obtained by using yield line theory. Some numerical examples are considered to study the effectiveness of the proposed model. From a comparison of the numerical and the experimental results, it is concluded that the layering technique employed is suitable for analysing reinforced concrete slabs. The good agreement obtained between the numerical and the experimental results establish the validity and the accuracy of the present proposed computational models. This model is perfectly general and can be used for any arbitrarily shaped plates. It is also useful in predicting cracking patterns and ultimate load carrying capacity. Finally, some formulations have been proposed for estimating deflections and moments relating angle of skew and aspect ratio.