A method for the analysis of masonry arches

In this paper, a numerical method for assessing the safety of masonry arches is presented. The catenary and the thrust curve of existing arch differential equations are revised.The variational formulation of the differential equations of the catenary and of the thrust curve is presented with its finite element approximation. The optimization problem, solving the nonlinear constrained minimization which allows determining the thrust curve in equilibrium with a given load for a prescribed geometry, corresponding to the minimum value of the thrust force is discussed. Numerical examples are presented in order to assess the ability of the presented numerical procedure in solving the problem of the determination of the thrust curve, comparing the analytical, when available, with the numerical solutions. The values of the minimum and maximum allowable thrust forces are also provided.