Some Aspects on the Statics of Masonry Arches

The paper deals with the analysis of masonry arches. The differential equation defining the line of thrust is reviewed. Then, the equilibrium equations for the arch subjected to a distribution of point-wise forces acting on nodes lying on the line of thrust are written. The equilibrated force distributions for given curves of thrust are deduced and several numerical examples for circular and parabolic arches are presented. The problem of the determination of the line of thrust for prescribed arch geometry and loading distribution is approached by formulating a suitable nonlinear constrained minimization problem. The proposed numerical technique is used to derive the profile of the line of thrust for circular and parabolic arches subjected to uniform and non-uniform loading distributions. Then, the problem of the elastic arch is formulated and solved making use of the method of consistent deformations (the force method). The effects of the horizontal settlement of the impost of the arch, which induces a modification of the position of the line of thrust, and of the increasing horizontal distributed load, which can lead to the collapse of the arch, are investigated.