New Trends in the Analysis of Masonry Structures

Abstract

The modern theory of masonry structures has been set up on the hypothesis of no-tension behaviour, with the aim of offering a reference model, independent of materials and building techniques employed. This hypothesis gives rise to inequalities which have to be satisfied by the stress tensor components and, as a dual aspect, to the kinematic behaviour characteristics of media which can be classified as lying between solids and fluids: the structure of the masonry material consists of particles reacting elastically only when in contact. An examination of the plane-stress problem leads us to define, within the prescribed domain under admissible loads, three different subdomains with null, ‘regular’, or ‘non-regular’ principal stress tensors, respectively. As the boundaries of such subdomains are not known α priori, the problem can be classified as a free boundary value problem. The analysis concerns mainly the subdomains where the stress tensor is ‘non-regular’; and a ‘non-regularity’ condition det σ = 0 is added to the equilibrium equations. This condition makes the stress problem ‘isostatic’ and leads to a violation of Saint-Venant’s compliance conditions on strains. Hence there is a need to introduce a strain tensor, not related to the stress tensor, which can be decomposed into an extensional component and a shearing component; we prove that such strains, of the class γσ c , are similar to those of the theory of plastic flow. From the point of view of computational analysis the anelastic strains are considered as given distortions; they are computed by means of the Haar-Karman principle, modified for computational purposes by an idea of Prager and Hodge.