An alternative approach for limit analysis of masonry arches on moving supports in finite small displacements

Static and kinematic theorems for limit analysis of masonry arches on moving supports are herein reformulated in terms of work done by loads. These new formulations are more advantageous because they avoid having to perform the static analysis aimed at computing the reaction of the moving support. The set of statically or kinematically admissible mechanisms in which the theorems hold are identified by using the kinematic analysis approach in finite small displacements. It is demonstrated that, since a pair of “theoretical” mechanisms can be identified for a given hinge pattern, direction, sense and magnitude of movement of a support, the analyst must consider only one of them to establish whether it should be included in the set of statically or kinematically admissible mechanisms, and disregard the other, otherwise the settlement mechanism detected is incorrect. Theoretical and mathematical formulations to identify the right one are provided. Finally, the “scale-effect” on the configuration of the settlement mechanism is investigated.