Limit analysis of structures formed from rigid blocks

Abstract

In this paper a technique previously developed for the analysis of rigid‐plastic structural frames is adapted to provide a formal procedure for finding the limit load of any structure formed from rigid blocks. In this procedure the load factor is maximized subject to the euilibrium equations of the structure and linear constraints imposed by criteria of failure at the block interfaces. In part I of the paper it is assumed that the limiting shear force associated with sliding at a block interface is independent of the normal component of force across the interface. This assumption means that the normality rule is satisfied, so that the upper‐ and lower‐bound theorems of classical limit analysis apply. This part includes a description of computer program for the collapse analysis of masonry arches with joints incapable of carrying tension. In part II the limit on the Shear force at a block interface is assumed to be that associated with Coulomb friction. It is not difficult to extend the computational algorithm described in part I to deal with this situation. However, the failure mechanism computed by the algorithm will not necessarily satisfy the normality rule. The corresponding limit load may therefore be an over‐estimate of the true failure load, even though it is computed by a lower‐bound (equilibrium) approach. A criterion is established for testing the validity of a failure load computed in these circumstances. Copyright © 1978 John Wiley & Sons, Ltd