A numerical method for the funicular analysis of masonry vaults accounting for stereotomy, finite strength and finite friction

Abstract

The funicular analysis of curved masonry structures is addressed, considering the stereotomy of the voussoirs, a limited compressive strength, and a limited friction coefficient. The force density method is used to handle the equilibrium of the loaded nodes of the network, whose vertices lie along vertical lines passing through the centroids of the blocks. For the resulting grid with fixed plan projection, the minimization of the horizontal thrusts is formulated in terms of the height of the restrained nodes and of any set of independent force densities. Anti-funicular networks are sought by enforcing compression-only branches of the network. Local constraints are stated at each joint addressing the hypothesis of a limited compressive strength and a finite value of the friction coefficient between two adjacent voussoirs. To enforce no-tension blocks, lower and upper bounds for the vertical coordinates of the unrestrained vertices of the network are prescribed, as well. Sequential convex programming is used to solve the arising multi-constrained minimization problem. The algorithm, which can handle networks with general topology, is assessed by comparisons with results achieved with the Durand–Claye method, a semi-analytical method for the equilibrium analysis of symmetric masonry arches and domes that accounts for the limited compressive strength of masonry, the friction coefficient and the stereotomy of the voussoirs. Numerical examples concern arches, domes and a cloister vault, considering varying mechanical parameters.