Minimum Reinforcement of Nonuniform Plates

Abstract

Considerable attention has been given to the plastic design of plates and grillages of uniform depth for minimum reinforcement material consumption, but very little has been given to nonuniform depth structures. This paper attempts to fill some of this gap. It will be shown that the optimality conditions for plates of nonuniform thickness can be derived quite simply from the Marcal-Prager-Shield “associated structure” optimization theory. These conditions are applied to an axisymmetric plate or grillage with predefined thickness variation, a square simply supported flat plate with differing reinforcement depths and to the more practical problem of an infinite flat plate with drop panels, supported on finite columns. Some remarks about the practical application of the results close the paper.