A lower bound solution to the collapse of an orthotropically reinforced slab on simple supports

Abstract

Summary Although upper bounds to the collapse loads of simply supported, orthotropically reinforced concrete slabs can be readily calculated by application of the yield-line theory, corresponding lower bound solutions which must satisfy equilibrium and the yield criterion at all points in the slab are not yet available. A lower bound solution to the collapse of a simply supported, rectangular slab, orthotropically reinforced and carrying a uniformly distributed load is developed. It is based on one originally proposed by Sawczuk(4) but the distribution of twisting moments has been modified to just produce positive yield moments at all points in the slab and negative yield moments at the corners. The lower bound collapse loads calculated for a range of coefficients of orthotropy μ, and ratio of width to length of slab λ, agree extremely closely with the upper bound values derived from the yield-line theory. The yield lines, however, are quite different and are found to be an infinite set of curves in the lower bound solution. Finally, the solution is used to determine the extent of negative reinforcement required in the corners of the slab and the loads transmitted to the supporting edges.