Singular stress fields in masonry structures: Derand was right

Abstract

The idea of a no-tension (NT) material underlies the design of masonry structures since antiquity. Based on the NT model, the safety of the structure is a problem of geometry rather than of strength materials, in the same spirit of the “rules of proportion” of the medieval building tradition. The use of singular stress fields for equilibrium problems of NT materials in 2d, has been recently proposed by Lucchesi et al. to produce statically admissible stress fields; here we introduce a simple way to construct singular stresses, based on the Airy’s stress formulation. We interpret the singular part of such stress fields as axial contact forces acting on ideal 1d structures arising inside the body, in the same spirit of Strut and Tie methods. A number of simple problems of equilibrium concerning typical walls, arches and portals, is solved in terms of stress fields having regular and singular parts, by adopting the direct and the stress function formulation. The validity of the rules of proportion described by Derand and Gil is also verified.