Load – Deflection Behavior of Rectangular R.C. Slabs with Three Edges Fixed and The Fourth Free Under Uniformly Load


A method is proposed for the prediction of load – deflection relationship of rectangular R.C slabs with three edges fixed and the fourth free under uniformly distributed loading. The analysis is carried out in three stages. The first stage represents the initial pre-cracking elastic stage. In this stage, use is made of the classical plate theory to predict the load and deflection up to the cracking load. The second stage represents the elasto-plastic stage and starts from the cracking load to Johansen’s yield line theory load. In this stage, the cracking of concrete and yielding of steel reinforcement are accounted for by suitability modifying the flexural rigidity. Changes that occur in the support conditions along the fixed edges due to the formation of the yield line lines at Johansen’s load are also considered. In the third stage of analysis, a method based on the flow theory of rigid plastic bodies, is developed for assessing the ultimate strength as well as determining the post yield behavior of such slabs. The method takes into account the significant effect of membrane forces which are usually induced in the plane of the slab along sagging and hogging yield lines as the slab deflects. Considering equilibrium and compatibility of the deformed slab elements, load-deflection relation is derived starting from the initial compressive membrane action up to the full-depth cracking at large deflections. The rigid- perfectly plastic behavior is adopted with modification to obtain the actual maximum ultimate load including membrane action and the deflection at this ultimate load. The predicted load- deflection relationship is fairly comparable with typical load- deflection curves of restrained slabs.