# Effective Assessment of Inelastic Torsional Deformation of Plan-Asymmetric Shear Wall Systems
## 1 Introduction  
Plan-asymmetric structures may undergo torsional vibration in addition to lateral oscillation if they are subjected to seismic ground motions. This induces an additional internal force, which may lead to excessive deformation in relatively flexible structural components. This excessive deformation often results in the unexpected brittle failure of structures, which has been reported during several earthquake events in the past such as the Mexico earthquake in 1985 [1], the Chile earthquake in 1985 [2], the Loma Prieta earthquake in 1989 [3], and the Kobe earthquake in 1995 [4]. The unsymmetrical distribution of mass and lateral load resisting stiffness of the plan-asymmetric structure is the primary source of the lateral torsional structural response. However, torsional deformation may occasionally be induced even in symmetric structures due to non-uniform ground motions along the foundation of the structure or the inherent torsional components of ground excitation. Details of the structural as well as non-structural members also may be sources of the torsional response. For this reason, most current seismic design codes include criteria to minimize the torsional response of building structures as well as damage caused by it. The current seismic design codes such as the International Building Code (IBC) [5], New Zealand Standards (NZS) (Standards New Zealand, 2004) [6], the National Building Code of Canada (NBCC) [7] and Eurocode [8] suggest design eccentricity based on the linear elastic state of structural components. However, the inelastic torsional response of a structure is quite different from that in the elastic range. If the main lateral force resisting components begins to yield, the eccentricity, lateral force distribution, and amount of rotation maybecome quite different from those in the elastic range. Some of the current design code provisions provide a simple solution to this problem by introducing the so-called accidental eccentricity, which is equivalent to the elastic eccentricity amplified by a certain factor. However, this accidental eccentricity may require excessive strength and stiffness for lateral force resisting components since it does not properly consider the actual torsional failure mechanism of the structure. There has been a lot of research performed to remove the limitations of the current seismic design codes and develop a proper design process. Early stage research on this issue focused on the force-based design approach, which still offers the theoretical basis to most of the current practical design codes. The main issue with this approach was the reasonable determination of design eccentricities. In [9], [PERSON] and [PERSON] first proposed a design eccentricity based on the inelastic torsional behavior of plan-asymmetric structures by considering two performance levels, i.e., serviceability and ultimate limit states. However, their approach may overestimate the strength of relative flexible wall components. To handle this issue, [PERSON] and [PERSON] [10] suggested a modified design eccentricity that provides optimal ductility requirements and overstrength factors on both flexible and stiff wall components, but it still may underestimate the design eccentricity at the intermediate inelastic stage. [PERSON] and [PERSON] [11] investigated the effect of wall components perpendicular to the excitation direction based on concepts similar to those proposed in [9; 10]. The displacement-based design approach has also been researched to properly handle this issue. Since the deformation is a better measurement of structural performance than strength or stiffness, most recently proposed design methodologies adopt this approach. In [12; 13], [PERSON] estimated the required system ductility of an asymmetric structure based on its torsional mechanism instead of proposing an effective design eccentricity. [PERSON] et al. [14] evaluated the inelastic torsional behavior in terms of strength eccentricity.