Generalized thrust network analysis for the safety assessment of vaulted masonry structures

Abstract

A generalized thrust network analysis is proposed for the safety assessment of vaulted masonry structures under their self-weight. The method requires introducing a 3D network of beams as a discretization of the vault mid-surface. The stress state in each beam is given by an internal thrust acting in the vertical plane containing the beam. By using three suitable statical descriptors per beam to represent those thrusts, the equilibrium equations of the network nodes and the static admissibility conditions of the stress state in the network beams are formulated consistently with the classical Heyman’s assumptions on masonry. As crucial merit of the formulation, those conditions result to be linear equalities and inequalities, respectively, in the unknown statical descriptors. It is then proven that the proposed method generalizes the classical thrust network analysis, which is recovered by imposing the further nonlinear constraint that the thrusts associated with the beams attached to a node converge into a single point. The minimum thrust problem for masonry vaults is formulated within the proposed framework, taking the form of a straightforward linear programming problem. On such a basis, the minimum thickness problem is also addressed. An extensive campaign of numerical results is presented, dealing with the safety assessment of masonry spherical domes, ogival domes and cross vaults. Compared to the classical thrust network analysis, the proposed method (i) overcomes computational issues related to the solution of nonlinear/non-convex optimization problems; (ii) accounts for more general stress states; and (iii) explicitly provides the settlement mechanism associated with the minimum thrust state.