Abstract
A masonry arch is considered as an assembly of rigid blocks with deformable joints. The joint deformations are characterized by linear hardening plasticity under axial thrust and moment. The activation of four hinges in the arch results in a mechanism. Two types of mechanisms are considered in evaluating a structure: mortar controlled and block controlled. The mortar controlled mechanism is considered by Maier's theory of piecewise linear interacting yield surfaces with linear hardening. The hardening constants and their interactions may be found experimentally. It is found that stable and unstable mechanisms exist, which are predicted by applying first- and second-order optimality conditions to energy functions on a constrained state space. Bounds on the loads activating a mechanism may be determined using bounding theorems similar to the bounding theorems of plasticity. The block controlled behaviour of the system is predicted using Heyman's application of rigid plastic analysis and the bounding theorems of plasticity.
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