## 2 Design of Analytical Models
### Inelastic Modeling and Nonlinear Dynamic Analysis  
For nonlinear dynamic analysis, shear walls were modeled using fiber elements. Uniaxial inelastic models for concrete and rebar are represented in Figure 4, respectively. The unconfined concrete model proposed by [PERSON] and [PERSON] was used to represent the nonlinear behavior of the concrete before the maximum compressive stress of concrete [16]. In accordance with the AIK guidelines, the stress drops to the residual stress after reaching the maximum stress at the strain of 0.002. The ultimate strain at the end of stress drop is prescribed as 0.003 in the guidelines. However, the ultimate strain of 0.003 may underestimate the deformation capacity of actual unconfined concrete. Figure 4a represents the nonlinear behavior beyond the maximum compressive stress for concrete models by [PERSON], and [PERSON] and [PERSON], in which deformation capacities considerably higher than 0.003 are observed [16; 17]. Therefore, it is necessary to set an appropriate concrete deformation capacity beyond the maximum compressive stress of concrete. In this study, the ultimate strain \(\epsilon_{\mathbf{cu}}\) was determined by comparison of the test and numerical analysis results for an existing specimen tested by [PERSON] et al. [18]. A total of 1% of the maximum stress is applied to the residual stress of the unconfined concrete model. Using 0.005 for the ultimate strain, it was confirmed that the experimental results and the analytical results were in good agreement for each cycle, and the deformation at the strength drop was simulated well in Figure 5. Therefore, unconfined concrete model with the ultimate strain of 0.005 and residual strength ratio of 0.01 times the maximum stress is adopted for the analytical models in this study. The inelastic material model for reinforcing bars was determined referring to the works of [PERSON], [PERSON], and [PERSON] [19; 20; 21]. The tensile strength of the rebar was selected to be 1.5 times the yield strength, and the tensile strain at the tensile strength is 0.05. The nonlinear model of reinforcing bars was created symmetrically, but the limit of compressive strain was set to be 0.02 considering buckling as shown in Figure 4b. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Analytical Model** & **Floor** & \(f_{e}\) **(MPa)** & \(f_{y}\) **(MPa)** \\ \hline \multirow{2}{*}{Model A} & 11–25 & 21 & \multirow{2}{*}{400} \\  & 1–10 & 24 & \\ \hline \multirow{3}{*}{Model B} & 16–29 & 21 & \multirow{3}{*}{400} \\  & 6–15 & 24 & \\ \cline{1-1}  & 1–5 & 27 & \\ \hline \multirow{3}{*}{Model C} & 26–39 & 21 & \multirow{3}{*}{400} \\  & 21–25 & 24 & \\ \cline{1-1}  & 11–20 & 27 & \\ \cline{1-1}  & 6–10 & 30 & \\ \cline{1-1}  & 1–5 & 35 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material property of analytical models. All the shear walls have height-to-length ratios higher than 3.0 and are dominated by flexural behavior [19]. Therefore, the shear of those walls was modeled as linear elastic and regarded as force-controlled behavior. Uncracked stiffness was applied to the shear stiffness of the shear walls in accordance with AIK guidelines [2]. The flexural or shear behavior of coupling beams were modeled with concentrated plastic hinges of which modeling parameters were determined in accordance with the AIK guidelines. The failure mode of coupling beams is classified into flexural or shear one based on the span-to-depth ratio in the AIK guidelines [2]. All the coupled beams included in the analytical models used in this study have the span-to-depth ratio less than 4.0 for which shear failure is dominant. The nonlinear modeling parameters of a coupling beam depend on the normalized shear force determined by Equation (1) and the classification of seismic details between conforming and non-conforming details depending on whether the transverse reinforcement satisfies requirements on the boundary elements of special structural walls prescribed in KDS 14 20 80 or not [22].