Journal of Earthquake Engineering, 19:60–84, 2015 Copyright © A. S. Elnashai ISSN: 1363-2469 print / 1559-808X online DOI: 10.1080/13632469.2014.946571 Interaction Curves for In-Plane and Out-of-Plane Behaviors of Unreinforced Masonry Walls KIARASH M. DOLATSHAHI 1 , AMJAD J. AREF 2 , and ANDREW S. WHITTAKER 2 1 Department of Civil Engineering, Sharif University of Technology, Tehran, Iran 2 Department of Civil, Structural and Environmental Engineering, University at Buffalo – State University of New York, New York, USA 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 behav- ior 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 sys- tematically 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 inter- action 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. Keywords Unreinforced Masonry; Interaction Curves; Bidirectional Loadings; Finite Element Validations 1. Introduction A number of computational approaches [Park et al., 2009; Dolatshahi, 2012; Dolatshahi and Aref, 2011; Calderini and Lagomarsino, 2008; Casolo, 2004; Casolo and Pena, 2007; Chen et al., 2008; Page, 1978; Stavridis and Shing, 2010; Lourenco, 1996; Oliveira and Lourenco, 2004] have been used to assess the behavior of masonry structures under static and dynamic loadings. These computational methods are mainly categorized in three groups, namely, micro-, meso-, and macro-scale. In micro-scale modeling the detailed behavior of each part of the structure is incorporated and the resulting analysis of this modeling approach offers high level of accuracy compared to meso- and macro- models. The main challenge with micro-scale analysis is the high computational demand required to build the numerical model and to run the analysis. Despite the advantages of micro-scale Received 8 November 2013; accepted 15 July 2014 Address correspondence to Kiarash M. Dolatshahi, Department of Civil Engineering, Sharif University of Technology, E-mail: dolatshahi@sharif.edu Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ueqe. 60 Downloaded by ["University at Buffalo Libraries"] at 07:43 24 January 2015