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.