Homogenized and heterogeneous limit analysis model for the pushover analysis of ancient masonry walls with irregular texture.

Two multi-step models for the pushover analysis of in-plane loaded historical masonry walls with irregular texture are presented. Both approaches are developed within an equivalent frame assumption. The first three-step model is a heuristic homogenization procedure in which the first step masonry is substituted with a macroscopic equivalent homogeneous material, with ultimate properties deduced from the solution of suitable boundary value problems on sample windows with different sizes. Masonry strength domains are evaluated through a limit analysis upper bound finite element (FE) approach. In the second step, ultimate bending moment-shear force strength domains of piers and spandrels are derived by means of a homogeneous upper bound FE limit analysis. In the last step, a frame model of an entire wall is assembled, where piers and spandrels are modeled as elastic-plastic Timoshenko beams with ultimate resistance evaluated using previous steps. The second approach is a two-step heterogeneous model, where piers and spandrels are analyzed through a FE limit analysis model, discretizing the walls “as they are”. To validate both approaches, a masonry wall arranged in irregular texture is studied in the inelastic range under increasing static loads. Results are compared with those obtained by a standard frame model and an expensive heterogeneous 2D FEM.