An iterative procedure for collapse analysis of reinforced concrete plates

Abstract

An iterative procedure is proposed for evaluating the ultimate load of a laterally loaded plate discretized by finite elements. The procedure regards reinforced concrete plates, but it can be extended to metallic plates without any conceptual change. The stress and displacement fields are approximated by means of a finite element model with constant stress and linear displacement fields. Consequently, any load distribution is represented by the equivalent system of nodal forces for a given mesh. In the set of mechanisms compatible with the assumed discretization the best upper bound to the collapse multiplier of the actual load is obtained via linear programming. By dualization a sequence of linear programming problems is obtained which allows an evaluation of a lower bound of the collapse multiplier for the equivalent load system. When the mesh gets finer and finer, the value obtained does not change substantially anymore. This value can be regarded as an estimate of the collapse multiplier for the original load system. Some numerical examples of plates subjected to uniform pressure confirm the reliability of this approximate multiplier.