Yield-line theory and limit analysis of plates and slabs

Abstract

Synopsis The usual geometrical, statical and physical conditions for the anisotropic, perfectly plastic plate are given. It is demonstrated that the normal moment criterion usually employed in modern yield-line theory is identical with the ‘stepped’ criterion of the classical theory, and that they both correspond to a yield surface, called the upper yield surface, which satisfies the requirements of limit analysis. When the actual yield surface of the plate is different from the upper yield surface, then the yield load predicted by limit analysis can generally not be determined by yield-line theory. It is not even possible to approach the solution by successive refinement of the yield-line pattern. The common yield surfaces of metal plates are compared with the upper yield surface, and the yield surface of the arbitrarily reinforced concrete slab is derived. Finally, the relationship between yield-line theory and limit analysis is discussed, and it is concluded that the two theories are consistent in their foundation.