# Effective Assessment of Inelastic Torsional Deformation of Plan-Asymmetric Shear Wall Systems
## 5 Conclusions  
In this paper, we proposed a simple method that can accurately assess the inelastic lateral displacement and rotation of plan-asymmetric wall structures. The relationship between the lateral displacement and rotation was obtained by considering the inelastic behavior of asymmetric structures. This relationship was presented and interpreted in the displacement-rotation (D-R) coordinate system. This coordinate system was first introduced in this paper and very conveniently describes the inelastic torsional behavior of the asymmetric structure. The validity of the proposed method was verified by comparing its predictions and inelastic time-history analysis results for a model problem. The main conclusions of this paper are as follows:  
1. Most of the current seismic design codes such as IBC, NZS, NBCC and Eurocode are based on the force-based design approach and introduce the concept of the design eccentricity consisting of static and accidental eccentricities. They do not properly consider the inelastic deformation and actual failure mechanism of plan-asymmetric structures. As a result, they may require excessive strength and stiffness for lateral force resisting components. 2. The inelastic torsional response assessment procedure proposed in this paper shows that the linear elastic approach may both underestimate the torsional rotation at the initial yielding stage and overestimate it at the post yielding stage, resulting in inaccurate estimation of the torsional response over the entire inelastic range. 3. The stiffness of the transverse wall may affect the overall yielding procedure of asymmetric structures. As a result, first yielding may occur even in the stiff side wall if the transverse wall stiffness and yield displacement are determined mainly by its length. This effect is not considered by any of the current code provisions such as IBC and Eurocode, while the procedure proposed in this study can handle it properly. 4. A comparison between the results of the time history analysis and the predictions of the proposed method for the model problem under three different seismic excitations (El Centro, Kobe and Northridge) shows that the relative error averages of the proposed method range approximately from 10.0% to 13.7% and are considerably smaller than those of the linear elastic response. It also indicates that the proposed method is able to provide more accurate solutions if the level of plan-asymmetry is higher. Figure 20: Comparison between the relative errors of the flexible side wall maximum displacement computed by the two methods with respect to \(\beta\). In general, the proposed method underestimates the flexible side wall displacement as it is based on simple static analytical procedure and has some limitations in accurately capturing the effect of complex dynamic behavior. Therefore, some safety margin needs to be introduced, if it is applied to the design of an actual plan-asymmetric structure. Currently, we are extending the inelastic torsional response assessment approach proposed in this paper and developing an iterative method utilizing the secant stiffness of each wall for the effective estimation of the inelastic torsional behavior of complex plan-asymmetric structures. This approach also can be incorporated into the adaptive push-over analysis discussed in [31; 32; 33; 34] that explicitly considers the nonlinear torsional and higher-mode effects for the analysis of multi-story structures. In this paper, [PERSON] and [PERSON] proposed the main concept of the new inelastic torsional deformation assessment; [PERSON], [PERSON] and [PERSON] developed all the mathematical equations of the proposed method; [PERSON] prepared all the seismic excitation data required for the time-history analysis; [PERSON] performed the time-history analysis to verify the effectiveness of the proposed method; [PERSON] and [PERSON] compared and analyzed the results of the time history analysis and the proposed method; [PERSON] wrote the entire manuscript.