The Safety of Masonry Arches Subject to Vertical and Horizontal Forces. A Numerical Method Based on the Thrust Line Closest to the Geometrical Axis

In this paper the topic of the safety assessment of masonry arches based upon their geometry is investigated. The theoretical background is the Heymanian master safe theorem along with the no-tension assumption of masonry. The continuous arch is analyzed considering a discrete pattern of vertical loads, such as those of the self-weight and superimposed loads. Among all the lines of thrust contained within the profile of the arch, the one closest to the geometrical axis can be considered to be the best one thanks to the minimum bending moment and shear force present in each cross section. A numerical procedure for computing the line of thrust closest to the geometrical axis of an arch subject to its self-weight has been recently formulated by the authors. This procedure accounts for this line of thrust by minimizing the distances between the geometrical axis of the arch and the thrust line. In order to consider the action of both vertical loads and horizontal forces proportional to the vertical ones, such as those provoked by an earthquake, an extension of this procedure is herein presented. The safety of the arch is finally assessed by computing a domain of equilibrium thrust lines within the profile of the arch which provides, in analogy with the Heymanian geometrical factor of safety, the full range factor of safety. The procedure is described in the paper and illustrated with regards to the analysis of arches subject only to vertical loads and arches subject to also horizontal forces.