ULTIMATE STRENGTH OF CLAMPED R.C SQUARE SLABS WITH CENTRAL SQUARE OPENING UNDER COMBIEND BENDING AND MEMBRANE ACTION

Abstract

Based on the flow theory of rigid-plastic bodies, a method is developed for assessing the ultimate strength as well as determining the post yield behavior of uniformly loaded R.C square slabs with central square opening which have all edges restrained against rotation and lateral movement . The method takes into account the significant effects 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 element, load-deflections relations are derived starting from the initial compressive membrane action up to tensile membrane and full-depth cracking at large deflection. The solution shows that axially restrained slabs can sustain loads far beyond those predicated by Johansen's yield line theory and the enhancement in load is greatest for thinner slabs having lighter reinforcement and smaller opening. On the basis of an estimated deflection, theoretical ultimate loads are found comparable with those of existing experimental tests. A theoretical study of the maximum yield load reveals a promising saving in reinforcement for using stronger concrete. For an interior square panel with central square opening, such saving in reinforcement could be as high as 48% if the panel is lightly loaded, and 25% for a panel under moderate loads.