FE limit analysis meso-mechanical model for the pushoveranalysis of 2D masonry frames

A numerical model for the pushover analysis of in-plane loaded unreinforced masonry walls is presented. An “equivalent frame” approach is adopted for the inelastic analysis of the walls, which are modeled by means of vertical piers and horizontal deformable beams (masonry spandrels) interconnected with rigid links. A two steps procedure is adopted: in Step I, ultimate bending moment-shear force strength domains of the masonry spandrels are derived by means of a heterogeneous upper bound FE limit analysis. Suitable static and kinematic boundary conditions are imposed on spandrels to account for the complex interaction of internal forces and deformed shapes of the spandrels at failure. Results are finally stored in a database. In Step II, spandrels failure surfaces are implemented in an equivalent frame, where spandrels are modeled through elastic Timoshenko beams and nodal plastic hinges with finite ductility. The piers are modeled in a similar manner, but their shear and bending moment capacity are estimated according to the Italian Design Code. A full scale three storey three bay masonry wall subjected to seismic excitation is analyzed in order to test the reliability of the procedure proposed when compared with alternative approaches based on (i) standard equivalent frames and (ii) complex 2D nonlinear heterogeneous FE analyses.