Description
A large portion of current structures, including historical monuments (churches, mosques, temples, etc.) and ordinary buildings, is made of masonry. Masonry consists of blocks joined by mortar, assembled with a texture to prevent sliding through methods like Friction/Interlocking/Confinement. It is inherently heterogeneous, and the mechanical properties of the blocks, mortar, and their bond largely influence the overall masonry response. Experimental characterization remains a challenging task. The structural analysis of masonry is almost always focused on determining stress in an existing structure. Their deformation is primarily associated with fractures, it means that an elastic analysis cannot fully capture the deformation of a masonry structure. Even without considering the elastic properties of the masonry, a static analysis alone can provide dependable values for essential structural parameters. We employ a basic model for masonry known as the Rigid No-Tension Model, relying on the following Heyman's assumptions: (i) masonry cannot endure tensions; (ii) masonry possesses infinite compressive strength; (iii) elastic strains are zero; (iv) sliding is prevented by the infinite shear strength of masonry. In addition to the hypotheses described above, we assume that stress can be decomposed additively into a regular (Cauchy) part and a singular part. Specifically, we assume that the regular part is zero. In this context, the static analysis of a wall is reduced, given the forces along the boundary, to the finding of a ‘truss structure’ of compressed members within the domain (the wall itself). In two-dimensions, and with forces at the vertices of a convex polygon, the use of polytope Airy stress functions shows that this ‘truss structure’ supporting the given forces will be derived from the folds of the polyhedral function. Among all the equilibrated solutions, the envelope of tangent planes to the boundary will be chosen.
