Seismic capacity of purely compressed shells based on Airy stress function

Purely compressed shells are often elegant and highly efficient structural forms, but this leanness may create risk if they are subjected to unexpected patterns and magnitudes of loading, such as may arise due to seismic events. In the same way that historic masonry structures were designed to sustain loads by activating purely compressive force paths, a modern metamaterial can be designed for specific purposes following the same logic. Conventional analysis methods for compression-only shells and vaults, often developed for masonry structures, have tended not to model combined vertical and horizontal loads directly. This has created a significant challenge for engineers assessing historic vaults or designing new shells. To address this gap, this paper presents an enhanced method based on membrane equilibrium analysis (MEA) and the static theorem of limit analysis. This approach is the first application of MEA to directly consider vertical and horizontal body forces acting on a compression-only shell through a parametric formulation of an Airy stress function. The method is applied to a case study of a sail vault subjected to vertical and horizontal loads. Moreover, it is demonstrated how this approach can be used to define iso-resistant shapes that offer more sustainable design options while preserving structural capacity.