UNIFIED APPROACH FOR THE CADD OF R.C. SLABS USING YIELD-LINE THEORY

Abstract

Yield-line analysis is a well established method of calculating the upper bound failure load of reinforced concrete slabs, for which no general computerised method of solution has so far been developed. In the work presented, a simple computer program is described for the yield line solution of isotropic and orthotropic reinforced concrete slabs based on a nonlinear simplex routine. The determination of the critical yield line pattern for the reinforced concrete slabs is a trial and error process which involves a lot of efforts for the search of the optimal value of the ultimate load i.e. the value of critical collapse load. In order to overcome this mathematical jugglary, the direct search methods for the optimisation of non linear functions are employed so as to make the process fully automated. The present work includes analysis and design of the RC slabs subjected to any combination of loading whether uniform, point or line loads and having any set of support conditions at the edge.The slabs supported along free edges by edge beams, are also considered. Apart from the edge supported slabs, the cases of the slabs provided with a column support and slab with a partially.unsupported edge are also incorporated. The algorithm is based on both the methods of determining the yeild-line solution viz. Equations of equilibrium and Principle of virtual work. Future extensions to include slabs with re-entrant corners, skew slabs and slabs provided with two column supports in addition to more sophisticated methods of inputting data are discussed. The design of slabs is done by Limit State Method incorporating the recommendations of IS:456-1978. The critical yield line pattern and the details of the reinforcement are plotted and demonstrated by the typical examples classified under different categories.