A three-dimensional macroelement for modelling the in-plane and out-of-plane response of masonry walls

The seismic performance of unreinforced masonry buildings is commonly assessed using equivalent frame modelling. Its computational efficiency allows for a large number of analyses to be conducted, which are often required to account for epistemic and aleatoric uncertainties. To obtain a full description of the building response, in-plane and out-of-plane failure modes need to be considered, though previous elements for equivalent frame models of unreinforced masonry buildings only account for the in-plane response. This paper presents the formulation of a three-dimensional macroelement for modelling the dynamic in-plane and out-of-plane behaviour of masonry panels, which extends the approach of a previously developed macroelement to simulate the in-plane response. The proposed three-node, three-dimensional macroelement is implemented in the software OpenSees and describes the main features of the in-plane and out-of-plane behaviour of a masonry wall, including second-order geometrical effects and a coupled shear/flexural response. It also allows for the use of complex material models. The proposed element is used to simulate experimental results for in-plane shear-compression tests and out-of-plane free vibration tests of masonry panels. The implemented element, as well as the example models, is openly shared through the repository https://github.com/eesd-epfl/OpenSees/wiki.