Abstract
Abstract According to Heyman’s safe theorem of the limit analysis of masonry structures, the safety of masonry arches can be verified by finding at least one line of thrust entirely laying within the masonry and in equilibrium with external loads. If such a solution does exist, two extreme configurations of the thrust line can be determined, respectively referred to as solutions of minimum and maximum thrust. In this paper it is presented a numerical procedure for determining both these solutions with reference to masonry arches of general shape, subjected to both vertical and horizontal loads. The algorithm takes advantage of a simplification of the equations underlying the Thrust Network Analysis. Actually, for the case of planar lines of thrust, the horizontal components of the reference thrusts can be computed in closed form at each iteration and for any arbitrary loading condition. The heights of the points of the thrust line are then computed by solving a constrained linear optimization problem by means of the Dual-Simplex algorithm. The MATLAB implementation of presented algorithm is described in detail and made freely available to interested users (https://bit.ly/3krlVxH). Two numerical examples regarding a pointed and a lowered circular arch are presented in order to show the performance of the method.
Highlights
The analysis of masonry arches is a classical problem of structural mechanics
According to Heyman’s safe theorem of the limit analysis of masonry structures, the safety of masonry arches can be verified by finding at least one line of thrust entirely laying within the masonry and in equilibrium with external loads
Some of them are based on the Finite Element Method (FEM) and are capable to take into account sophisticated material models [3, 32, 33, 47]
Summary
The analysis of masonry arches is a classical problem of structural mechanics. It was from the intuitions by Hooke,. Worth mentioning are recent proposals in which a fracture mechanics-based analytical method with elastic-softening of masonry is applied to analyse the structural behaviour of arch bridges and show how the arch thrust line is affected by crack formation [1, 2]. The method employed in FRS_Method, insted, computes the line of thrust by solving an optimization problem that looks for the funicular polygon closest to the geometrical axis of the arch [48] This means that a unique line of thrust is determined, which is neither one of the two limit configurations of minimum or maximum thrust, neither it obeys to the principle of least action. Results regarding the analysis of a pointed and a lowered arch are reported in order to show its performance
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