Parametric analysis of structures from flat vaults to reciprocal grids

We propose a parametric analysis of a class of structural systems stemming from the 17th century invention of Joseph Abeille usually called flat vault and reaching the field of reciprocal grids. Our purpose is to understand the load descent paths taking place in the various specimens of this class and their relations with basic structural principles such as that of the inverted catenary, useful to deal with vaults, or that of the lever, more appropriate for grids.The analysis is performed on changes of the geometry and of the topology that preserve the logic of the bonding of stone blocks characterizing Abeille’s invention. Shown results concern the distribution of the elastic energy, the reactions, the chirality and the stress and displacement maps.Our findings support the idea that the structures belonging to this class of structures (and having reasonable proportions) are rather to be considered as deflected grids than as compressed vaults. Furthermore, a local bending interests the blocks, for because of the bonding, in a way that is typical of reciprocal structures.