An equilibrated macro-element for nonlinear analysis of masonry structures

A new macro-element based on the equivalent frame approach is presented to analyze the nonlinear in-plane structural response of masonry panels under lateral loadings. A nonlinear elastic response is assumed for the masonry material, limiting the focus to the case of monotonic loading condition, typical of push-over analysis. The sectional response of the beam is determined performing analytical integration, without resorting to a fiber approach. A two-node force-based (FB) beam finite element (FE) is formulated, where the resultant stress components are exactly interpolated along the beam axis. The beam FE is composed of a central flexible element, characterized by a no-tension constitutive relationship, and a lumped nonlinear shear hinge arranged in series. Hence, it is possible to capture the main flexural and shear nonlinear mechanisms typical of a masonry panel response. An efficient solution algorithm is developed, based on a consistent element state determination procedure. Some applications on simple panels and on experimental walls with openings are presented, showing a very satisfactory agreement between the numerical and the experimental results, both in terms of global push-over curves and local distributions of damaging paths.