ArchLab: a MATLAB tool for the Thrust Line Analysis of masonry arches

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.

Automated summary

This paper introduces a numerical procedure for verifying the safety of masonry arches, determining both minimum and maximum thrust solutions. The algorithm simplifies the equations of Thrust Network Analysis, calculates the heights of thrust line points through linear optimization, and is implemented in MATLAB for user access. Two numerical examples are presented to demonstrate the method's performance.