This paper presents the first form finding method for masonry arches subjected to self-weight and inplane
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.