Computational Analysis of Masonry Structures with a Funicular Model

Abstract

This paper presents a computational approach for the assessment of masonry structures based on the well known analogy between the equilibrium of arches and that of hanging strings or cables working in tension. According to the analogy, the hanging strings model the inverted shape of the equilibrium lines (or thrust lines) describing the locus of the equilibrium forces acting across the sections of the arch. The approach proposed combines two developments. First, a new cable element is proposed to numerically model the strings used to describe the equilibrium lines. The formulation proposed, obtained as a modification of the conventional equations for inextensible cables, is based on an exact analytical derivation. Compared to other available numerical approaches, it has the advantage of ensuring the exact equilibrium of the cable net after deformation. Second, complementary algorithms are proposed for the assessment of the strength of masonry structures by the application of the limit theorems of plasticity (static approach). These algorithms are intended to find optimized solutions complying with the so-called safe (or lower-bound) and uniqueness theorems. Two examples of application are described to illustrate the accuracy of the method and its ability to handle masonry structural systems.