Form-finding algorithm for masonry arches subjected to in-plane earthquake loading

This paper presents the first form finding method for masonry arches subjected to self-weight and in-plane horizontal loading due to earthquakes. New material-efficient arch shapes are obtained by considering both horizontal and gravitational acceleration in the form finding process. By interpreting the obtained forms, insights into the influence of form on the earthquake resistance of the arches are presented. The form finding algorithm relies on two simplified, first-order equilibrium methods: thrust line analysis and kinematic limit state analysis, which present respectively a lower- and upper-bound approach to the analytic problem of arch stability under gravity and horizontal loading. Through a methodological application of a series of geometric manipulations of the thrust line, shapes are obtained that can resist the design acceleration by guaranteeing a compression-only load path. Forms are obtained for horizontal accelerations of 0.15, 0.3 and 0.45g, as well as for arches of different rise-to-span ratios (1/2, 1/4 and 1/8). The obtained shapes require up to 65% less material than circular arches with constant thickness that are designed to withstand the same horizontal acceleration and self-weight, regardless of acceleration magnitude. The findings of this research will thus allow more material-efficient design of masonry arches in seismic areas.