Force-based macro-element formulation for the analysis of structural masonry shear walls
Abstract The equivalent frame method is widely used for the structural analysis of masonry buildings subjected to lateral loads. In this approach, masonry structural components are idealized as macro-elements, which consist of reticulated finite elements formulated to simulate the quasi-brittle behavior of masonry and its typical failure mechanisms. This study investigates a macro-element with a mixed force-based formulation applied to the modeling of structural masonry shear walls. The study is based on a previously developed macro-element for unreinforced masonry panels, using the Timoshenko beam theory, which adopts a uniaxial constitutive model for masonry and incorporates a non-linear shear hinge. The cross-sectional stiffness matrix is obtained through analytical integration, without fiber discretization. This macro-element is capable of reproducing the failure mechanisms of rocking, bed joint sliding, and diagonal cracking. The present study focuses on the enhancement of the macro-element through extensions to the original formulation and modifications to the non-linear solution procedure. The main contributions include the introduction of a tensile branch into the masonry constitutive law, as well as the incorporation of reinforcement through a fiber-based approach. In addition, modifications were introduced in the matrix representation of the cross-section force-deformation relationship, resulting in a more robust numerical scheme with improved convergence. The macro-element was applied to the numerical simulation of experimentally tested unreinforced and reinforced masonry shear walls, yielding results consistent with data reported in literature.