Safety evaluation of masonry arches. A numerical procedure based on the thrust line closest to the geometrical axis

In this paper a numerical procedure for computing the full range of equilibrium thrust lines in masonry arches is presented. According to Heyman, the range can be obtained by shifting the thrust line upwards and downwards until it touches the upper and lower boundary of the arch. This thrust line is computed in such a way as to be the closest one to the geometrical axis. The two limit thrust lines, corresponding to the upper and lower bound of the range, are finally used to compute the degree of safety of an arch through the identification of a domain of equilibrium states and the Heymanian geometrical factor of safety, revisited in the form of a performance factor, that is more practical and immediate to understand.