An automatic computational method for predicting the collapse load of slabs and plates was proposed by Munro and Da Fonseca, based on a triangular mesh covering the surface. If the collapse mechanism is assumed to consist of plastic hinges forming only along edges of this mesh, an upper bound on the collapse load can be found by solving a linear programming problem. The approach was improved by a number of workers, who developed computational methods of modifying an initially arbitrary mesh so as to generate more realistic collapse mechanisms.

This paper describes work currently in progress which applies closely similar methods directly to the optimal design of concrete slabs for minimum volume of reinforcing steel. If the assumption is made that, for a given effective depth, the plastic hinge moment is proportional to the volume of steel used, the design problem for orthotropic slabs can be stated as follows: given a fixed shape and loading for the slab, determine the minimum design moment in two orthogonal directions, for both sagging and hogging, so that the load can safely be carried. The amount of reinforcement may be allowed to differ in different (given) regions of the slab, but is constant within each region. In this paper the simpler case of constant reinforcement throughout the slab will be used.

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