Interaction curves for in-plane and out-of-plane behaviors of unreinforced masonry walls

Different types of macro-elements have been proposed to simulate the behavior of unreinforced masonry (URM) structures under seismic loads. In many of these, macro-elements URM walls are replaced with beam elements with different hysteretic behaviors. The effect of out-of-plane loading or change of gravity load due to the overturning moment is usually not considered in the behavior of these macro-elements. This article presents interaction curves for bidirectional loadings of unreinforced masonry walls to investigate the importance of these factors. Two parameters are systematically changed to derive the interaction curves for a wall with specific dimensions, including compressive traction atop the wall to represent gravity loading, and loading angle that represents a combination of in-plane and out-of-plane earthquake loadings. Interaction curves are developed considering various possible failure modes for bricks and mortar, including tension, crushing and a combination of shear and compression/tension failures. The proposed interaction curves show the initiation of failure of URM walls as a function of compressive traction and loading angle. Several examples are presented for URM walls with different aspect ratios to aid in understanding the effects of various parameters on the derived interaction curves. Finally, for a specific case, the derived interaction curve is compared with nonlinear finite element results and ASCE41. The results show that, as a simplified method, the derived interaction curves can be used for the preliminary evaluation of URM walls under bidirectional loadings.