Stability of Masonry Piers and Arches Including Sliding

Abstract

A laterally loaded masonry pier or a masonry arch under gravity loads is investigated by considering the pier or arch composed of blocks that are infinitely rigid, infinitely strong, and that transmit no tension at the joints. The constraints against interpenetration of adjacent blocks, and against sliding when prevented by a sufficient frictional force, result in a set of kinematic constraints on the system. Although the energy input to the system is nonlinear and has multiple branches, the linear part can be written as a linear program of minimizing the potential energy plus the dissipated energy of the system subject to the kinematic constraints on the system. The system is found to be stable if a statically admissible distribution of internal forces can be found in which a nonzero compressive force is transmitted at each joint, and the tangential force nowhere exceeds the normal force times the coefficient of friction. The system is shown to be unstable under a set of loads for which the virtual work is nonpositive in a kinematically admissible displacement.