Capacity of Masonry Arches and Spatial Frames

Abstract

A numerical model for the study of spatial structures consisting of curved, three-dimensional members with variable cross sections is presented, together with its application to the nonlinear geometric and material analysis of skeletal masonry constructions. Nonlinear material behavior is included in the model by means of elastoplastic constitutive equations under shear and compressive stresses, while a linear-elastic perfectly brittle behavior is assumed in tension. The dependency of shear strength upon the applied compression is taken into account by means of the Mohr-Coulomb failure criterion. Nonlinear geometric effects caused by the imposition of the equilibrium condition upon the deformed configuration of the structure are considered, but it is assumed that the increments of both displacements and sectional rotations are moderately small. Three examples are presented. The first is a circular helicoid formerly studied by Young and Scordelis (1958). A very good agreement and accuracy level were obtained, even though a very small number of elements, two or three, were used. The second example deals with the analysis of a masonry arch up to failure including nonlinear material and geometric effects. Finally, the advantage of the presented formulation in the analysis of large structures is shown through the study of a Gothic vault.