Reinforced Concrete (RC) walls are often used as coupled systems in construction of multi-story buildings because of their advantages in comparison with individual walls such as higher lateral stiffness, lower bending moments on each individual wall, and higher energy dissipation because of the inelastic deformations of coupling beams (El Tawil et al., 2010). These elements have been extensively utilized in medium-rise and high-rise building structures within the past decades. Nowadays, RC coupled shear walls are popular lateral force resisting systems, especially in high-risk seismic zones (Farhidzadeh et al., 2013). The reason behind this trend is that RC coupled walls are significantly capable of controlling the inter story drift ratio, which has been frequently used as a performance indicator in design of structures (Carrillo and Alcocer, 2012). Similarly, these structural systems are quite efficient in reducing the associated implication of non-structural elements damage.
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The expected energy dissipation mechanism of a ductile RC wall system under lateral deformations is flexural yielding (i.e. plastic hinges) at the base of both the cantilever and coupled wall systems, and at both ends of each coupling beam in a coupled wall system (Boivin and Paultre, 2012). Series of design provisions are specified in the current codes to confine the inelastic response at the wall base. These are aimed at ensure enough strength against undesirable modes of failure like brittle shear failure(Ghorbanirenani et al., 2012).
Many researchers have conducted both experimental and analytical investigations to identify the behavior of coupled walls, and to improve the performance of these systems. The C-shaped coupled wall system (i.e. core wall) is one of the simplest and is a popular arrangement used in practice. Despite their popularity, however, there have been relatively few studies on the seismic behavior of these RC structures (Beyer et al. 2008), necessitating research on the seismic performance of C-shaped cores. One of the most important characteristics of these nonplanar wall systems is their response when the structure is subjected to torsional efforts due to the eccentricity of lateral forces. This will be more significant when the structural system is asymmetric in plan regarding the lateral stiffness and strength distribution. Such a configuration in plan of a building is prone to have large torsional response during a severe earthquake. Reports and field observations after the past earthquakes showed severe structural damages because of torsional effects (Hart, 1975; Esteva, 1987). A recent investigation by Dizhur et al. (2011) reported significant structural damages, which was apparently caused by a “torsionallysensitive response”, after the Christchurch earthquake in 2011.
Most of the researches carried out in the past focused on the behavior of planar RC walls, including various proposed approaches for predicting their nonlinear flexure-shear interaction behavior (Colotti, 1993; Elwood, 2002; Massone et al., 2006 and 2009; Mullapudi and Ayoub, 2009; Zhang and Xu, 2009; Jiang and Kurama, 2010; Beyer et al., 2011; Panagiotou and Restrepo, 2011; Fischinger et al., 2012). These approaches were mostly based on fiber-section elements such as multiple-vertical-line-elements (MVLE) proposed by Vulcano et al. (1988). Biaxial behavior of concrete material (e.g. modified compression field theory; Vecchio and Collins, 1986) were also considered in some of these approaches.
On the contrary, experimental researches on the performance of non-planar (e.g. C-shaped) RC walls subjected to lateral loads are very limited. In one of the first attempts, Ile and Reynouard (2005) examined three full scale U-shaped RC walls under thecyclic lateral loading. The purpose of the study wasto study the behavior of U-shaped walls against uniaxial and biaxial bending and shear, and to compare the design provisions required by two versions of Eurocode 8. A shell model was also developed for simulation of non-planar RC walls. Beyer et al. (2008-a) investigated the bi-directional quasi-static cyclic response of ductile U-shaped RC walls by conducting experimental tests on two half-scale specimens with different thicknesses. The tests mainly focused on the flexural behavior of walls, considering different directions of loading (two orthogonal as well as diagonal). Results showed the diagonal direction as the most critical direction, in which the maximum moment resisted by the wall was less than the corresponding value calculated by the plastic hinge analysis. Moreover, the displacement capacity of the wall in diagonal direction was found to be smaller than the other two orthogonal directions. A simplified numerical model was also developed by Beyer et al. (2008-b), and a practical approach was proposed for implementation and analysis of of U-shaped walls. The numerical approach was based on wide-column analogy, and has been shown to produce reasonable estimation of the inelastic displacement response for slender walls. Constantin and Beyer (2012) used a 3D multilayered shell element model for U-shaped walls to capture their local as well as the global behavior under diagonal loading. The model was developed using the software VecTor4 developed at the University of Toronto (Wong and Vecchio, 2003), and was found to be accurate in terms of loading capacity of the wall, but not for its displacement ductility.
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Lowes et al. (2013) examined three 1/3 scale C-shaped wall specimens, representing a part of a coupled RC core system, under biaxial loading protocols. Results of cyclic tests showed that bidirectional loading significantly affected the response for displacement cycles in excess of the yield displacement. At these displacement levels, bidirectional loading resulted in a significant reduction in the stiffness of the wall in the direction parallel to the web of the wall (loading activating strongâ€axis bending).
Recently, Lu and Panagiotou (2014) presented a three-dimensional (3D) cyclic model for non-planar RC walls, based on beam-truss analogy. The model was able to predict the effects of flexure-shear interaction, considering biaxial behavior of concrete material, and account for mesh-size effects. Although the proposed model has been revised several times and they validated the model for three reinforced concrete T-shaped, C-shaped, and I-shaped section wall specimens, the modeling approach was found to be complicated in terms of calibration of truss members and material properties (Kolozvari, 2013). The results were also sensitive for precisely tracking the displacement responses of walls in a wide-amplitude.
In design of RC shear walls, the fundamental design equations are mainly based on the “plane sections remain plane” assumption, which is unable to capture the shear lag effects related to flexure and warping torsion. Such effects can be substantial in non-planar (C-, I- or T-shaped) wall configurations, and might affect the response of structural system in seismic excitations. A study Boivin and Paultre (2010) was shown that the seismic provisions proposed by NBCC 2005 and the CSA standard A23.3-04 (2014) for design of ductile RC shear walls buildings could considerably underestimate the shear demand, especially at the base of the shear wall system. This issue would be due to the fact that the amplification effects from the higher modes of vibration cannot be efficiently taken into account by the current capacity design methods. In seismic design of a multi-story ductile RC wall, this can produce design strength envelopes that largely underestimate the seismic force demand. Hence, more studies need to be conducted on the seismic performance of these structural systems and effectiveness of available retrofitting methods, both of which were investigated in the current study. A recent research (Pelletier, 2015) showed that the dynamic shear amplification factor newly introduced in CSA A23.3-14 (2014) allows a more realistic seismic shear force demand to be obtained for RC shear walls. This factor should be applied to prevent brittle shear failure and to account for the inelastic effects of higher modes. However, RC shear wall systems that are designed based on the CSA A23-04 need to be controlled for shear demands. Moreover, CSA A23.3-14 excludes the coupled and partially coupled walls from the clause specified for “accounting for inelastic effects of higher modes”. Furthermore, NBCC 2015 provides a higher mode factor Mv which is equal to 1.0 for coupled shear walls except in very occasional cases, Ta=2.0 seconds and S0.2/S5=65, in which the Mv is equal to 1.03. On the contrary, it was found by Boivin and Paultre (2010) that the shear envelope calculated based on the capacity design method is significantly unconservative in either the cantilever or coupled wall directions. Therefore, more accurate evaluations for the future designs and retrofit options for existing building are essential.
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