PREDICTION OF POST CRACKING BEHAVIOUR OF RCC PLATE STRUCTURES

Abstract

Prediction of the first cracking load, cracking pattern, ultimate load, mode of failure and determination of the behaviour of a RCC structure through these stages is of direct importance in limit state design concept, especially with the increasing trend towards the use of richer concrete mixes and high strength steel, greater emphasis on limit state method of analysis and design in the national codes of practices of various countries and use of prefabricated components which usually result in thinner and slenderer members cracking at or near working load. It also becomes equally important from consideration of serviceability of the structure itself and of the safety and design of supported structures, fixtures, partition walls, flooring, doors, windows etc., that a reasonably accurate estimate of deflect ions and crack patterns at different load stages is made. The prediction of deformations becomes difficult as "behaviour after cracking is complex due to continuous changing topology, deteriorating rigidities with the initiation and propagation of cracks, material anisotropy caused by cracks and different stress levels in orthogonal directions at various stages of loading and nonhomogeneity resulting from the presence of steel. Classical methods of plastic analysis are incapable of treating such complex problems. For some structures like conventional slabs, the yield line theory v^es yield some information but the method is too simple to -iicope with all the complexities of the problem. Only a computer oriented and a powerful method like the finite element method can successfully consider all aspects of such a complicated nonlinear problem. Such amethod must necessarily be economic so that it can replace the expensive and the time consuming full scale model tests. Methods that are simple enough and workable on medium size computers will be an added attraction for most of the design offices. The present investigation has been undertaken to develop afinite element method of analysis to analyse rectangular slabs, folded plates, cylindrical shells and box girders of reinforced cement concrete under monotonically increasing loads till failure. The method developed can be used to trace the load deformation response and crack propogation through the elastic, inelastic and ultimate load ranges. The internal stresses in concrete and steel can also be determined throughout the structure at any stage of loading. The proposed nonlinear analysis includes the effects of cracking and nonlinear stress strain relationship of concrete and of steel reinforcement. In tension, concrete is assumed to be elastic until it cracks on tensile strain reaching limiting cracking strain. In compression, the stress strain relationship is taken to be nonlinear and concrete is assumed to be crushed when the principal compress ive strain is more than adefined value of crushing strain. -iii- Steel is assumed to be ideally bilinear. Explicit expressions useful in the finite element analysis have been developed for bending, in-plane and bending in-plane coupling effects at various material condi tions for three dimensional plate structures and bending of slabs. Numerical integration scheme has been used allowing the elements to be partially cracked/crushed/yielded so that definition of element mesh can remain unchanged through all stages of loading including those after development of cracks. This also permits use of large sized elements for discretization. For slabs, conforming rectangular plate element using complete 16 terms bicubic expression for transverse displace ment »w- in terms of Hermite interpolation polynomial as proposed by Bogner, Fox and Schmit has been used. For three dimensional plate structures, a rectangular flat shell element obtained by combining nonconforming 12 d.o.f. rectangular Plate element with 12 d.o.f. rectangular membrane element allowing linear variation of '«• and cubic variation of »v' to maintain conformity of deformations at fold lines has been used. Amixed type of incremental iterative procedure capable of taking advantage of both the tangent and constant stiffness approach is used. Computer programs have been developed to implement the analysis. •».. -iv- A variety of typical reinforced concrete plate structures consisting of square two-way slabs with simply supported edges, clamped edges and corner supported conditions under uniform or concentrated loads, simple folded plate and butterfly shaped folded plates, single cell box girders and cylindrical shells have been analysed by the proposed method. Validity and superiority of the method as regards accuracy and economy are estab lished by comparing the analytical results obtained by the above procedure with the experimental results and/or the analytical results available in published work of various investigators. It has been shown that the proposed procedure, even when using lesser number of elements and bigger load steps, gives more accurate results. The proposed procedure also proves to be economic on computation time. These features make the procedure usable even on medium size computers like IBM 360/44.