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.
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