A significant proportion of existing buildings worldwide are unreinforced brick or stone masonry constructions, in addition to those with invaluable cultural significance. URM is known to have negligible tensile capacity and hence shows brittle behaviour under lateral action (e.g., earthquakes). Satisfactory seismic performance depends on integral action of the masonry load-bearing walls and roof/floor structural systems, which are influenced not only by the strength and stiffness of the individual components but also on the quality of their interconnections. Therefore, seismic assessment of URM buildings should be carried out by identifying potential weak links in the inertial load path, before carrying out any retrofitting measures to strengthen and/or stiffen any of the components or their connections. A reliable numerical model of the URM building is essential to carry out a detailed assessment. Many nonlinear models (micro, meso and macro-level) have been developed in the past. Although the accuracy of micro- and meso-models are adequately demonstrated in the previous research, they are less preferred over macro-models because of difficulty involved in obtaining reliable material properties and of high computational demand. Alternatively, simplified macro-element models using the Equivalent Frame Modelling (EFM) approach are useful for a quicker estimation of global responses.
EFM is a popular approach among practitioners, and even with several approximations it satisfactorily captures the global responses and failure mechanisms, although there are several areas of improvement. Currently available macro-elements in the EFM approach consider in-plane (IP) and out-of-plane (OOP) responses of masonry walls in a decoupled manner, whereas in reality, interactions can be expected. Such an assumption results in the global response being completely dependent on the in-plane capacity of masonry walls and necessitates additionally seismic verification for OOP failure through local mechanism checks (for e.g., using limit analysis). Such decoupling of interaction is justifiable under the assumption that the OOP failure mechanism is not expected to occur in the presence of proper wall-wall/wall-floor connections and rigid diaphragm action of slabs, which may be a valid assumption for new masonry constructions. However, in existing structures, OOP failure is likely to happen since the connections are not ideal, and rigid diaphragm action is typically not achievable for most structural typologies of floor and roofs. Additionally, due to randomness in earthquake ground motion, masonry piers can experience a combination of in-plane and out-of-plane effects. Any damage in out-of-plane direction in a URM wall can compromise its capacity in the in-plane direction, and the reverse is also true. Hence, decoupling such interaction in URM macro-modelling can potentially lead to overestimation of its lateral strength capacity. Therefore, the present study aims to address the interaction of IP and OOP behaviour of a URM wall panel (pier) through the development of a 3D nonlinear macro-element, compatible with the EFM approach for seismic modelling and analysis of masonry structures.