Safety assessment of masonry undamaged and damaged arches subjected to gravitational loads and horizontal forces. A numeric procedure to identify the optimal thrust line

In 2019 the authors formulated a numerical procedure for assessing the safety of masonry arches based on their geometry and the shape of the thrust line. The thrust line is calculated to be nearest to the geometric axis of the arch, because it is that corresponding to the optimal inner stress state. The original procedure, which focused on the safety analysis of undamaged fixed arches subject to gravitational loads, is reformulated here to also consider arches on pinned supports as well as damaged arches, i.e. one- and two-hinged arches. The procedure is further extended to also assess safety against horizontal actions, such as those resulting from an earthquake. Finally, safety is evaluated by identifying the domain of admissible thrust lines within the thickness of the arch and by computing the degree of safety in terms of the capacity of the thrust line to be moved vertically within the domain. The reformulation and extension of the procedure exploits the technique of partitioned matrices to enable automation and easy implementation in structural calculation software.