Static analysis of masonry polygonal domes with membrane forces

Masonry polygonal domes are parts of several historic monuments and masonry buildings. The analysis of polygonal domes with a static approach is here presented, considering the structure made of vault cells and ribs. The vaults are portions of a cylindrical surface with single curvature in the meridian direction, and translation of the generatrix curve in the direction of the cylinder axis. The system is divided into rigid elements with interfaces. The first part of the work regards the geometry of the rigid elements, in particular the angles that characterize the shape of these. Then the equilibrium equations applied to every element are presented, with a procedure to calculate the membrane response for the self-weight in a non-redundant system, under symmetry conditions. The sum of the solution for the vaults is combined with effects of the weight of ribs and radial walls. The use of the equilibrium solution for pointed domes, domes with a lantern and oculus or additional load to the dome self-weight is shown. A limit analysis static approach is formulated calculating the maximum load relative to the equilibrium of the rigid elements considering the interfaces tensile strength and limited cohesion and friction for the shear resistance