## 5 Comparison of the Pseudo-Dynamic Test and Non-Linear Dynamic Analysis Results
### Non-Linear Dynamic Analysis Overview
The variables that determined the restoring force characteristics of each column and beam shown in Table 14 (i.e., the initial flexural stiffness (\(k_{B}\)), initial shear stiffness (\(k_{s}\)), flexural crack moment (\(M_{c}\)), shear crack strength (\(V_{c}\)), flexural ultimate strength (\(M_{u}\)), and shear ultimate strength (\(V_{u}\))) were determined using Equations (9)-(17) based on the research results of JBDPA [50] and AIJ [51]. \[M_{c}=0.63\sqrt{F_{c}}Z\phi\ (\text{Beam}) \tag{9}\]  
\[M_{c}=0.63\sqrt{F_{c}}Z+ND/6\ (\text{Column}) \tag{10}\]  
\[M_{u}=0.9a_{t}\sigma_{y}d\ (\text{Beam}) \tag{11}\]  
\[M_{u}=0.8a_{t}\sigma_{y}D+0.5 ND(1-\frac{N}{bDF_{c}})\ (\text{Column}) \tag{12}\]  
\[k_{B}=6 EI/l\ (\text{Both beam and column}) \tag{13}\]  
Here, \(M_{c}\) is the flexural crack moment (N\(\cdot\)mm), \(M_{u}\) is the ultimate flexural moment (N\(\cdot\)mm), \(k_{B}\) is the initial flexural stiffness (N\(/\)mm), \(F_{c}\) is the compressive strength of the concrete (N\(/\)mm\({}^{2}\)), Z is the section modulus (mm\({}^{3}\)), \(\phi\) is the shape factor of the beam, \(N\) is the axial force (N), \(D\) is the column depth (mm), \(a_{t}\) is the total cross-sectional area of the tensile reinforcing bars (mm\({}^{2}\)), \(\sigma_{y}\) is the yield strength of the reinforcing bars (N\(/\)mm\({}^{2}\)), and d is the effective depth (mm). \[V_{c}=\{\frac{\big{(}1+\frac{\sigma_{0}}{15}\big{)}0.065k_{c}(50+F_{c})}{ \frac{M}{Vd}+1.7}\}bj\ (\text{Both beam and column, if beam, }\sigma_{0}=0) \tag{14}\]  
\[V_{u}=\Bigg{\{}\frac{0.053p_{t}^{0.023}(18+F_{c})}{\frac{M}{Vd}+0.12}+0.85 \sqrt{p_{ws}\cdot\sigma_{wy}}+0.1\sigma_{0}\Bigg{\}}bj\ (\text{Both beam and column, if beam, }\sigma_{0}=0) \tag{15}\]  
\[k_{s}=GA/\kappa\ (\text{Both beam and column}) \tag{16}\]  
Here, \(V_{c}\) is the shear crack strength (N\(\cdot\)mm); \(V_{u}\) is the ultimate shear strength (N); \(k_{B}\) is the initial shear stiffness (N\(/\)mm); \(\sigma_{0}\) is the axial stress in the column (N\(/\)mm\({}^{2}\)); \(k_{c}\) is the modification coefficient, which depends on the cross-section; \(b\) is the width (mm); \(j\) is the distance between the centroids of the tensile and compressive forces (mm); \(p_{t}\) is the tensile reinforcement ratio (percent); \(p_{ws}\) is the shear reinforcement ratio (\(p_{ws}\) = 0.012 \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Member** & \multicolumn{2}{c}{**Restoring Force Model**} & \multicolumn{2}{c}{**Model Name**} \\ \hline \multirow{2}{*}{Beam} & Flexural spring & CP3 & Cross-peak trilinear model \\ \cline{2-4}  & Shear spring & OO3 & Trilinear origin-oriented \\ \hline \multirow{4}{*}{Column} & Flexural spring & CA7 & CANNY sophisticated trilinear hysteresis model \\ \cline{2-4}  & Shear spring & OO3 & Trilinear origin-oriented \\ \cline{2-4}  & Axial spring & AS1 & Axial stiffness model \\ \hline Wall & Shear spring & OO3 & Trilinear origin-oriented \\ \hline Anchor bolt & Shear spring & EL2 & Bilinear elastic model \\ \hline LLFD & Damper spring & PP & Perfect Plastic model \\ \hline \multirow{2}{*}{Steel frame} & Flexural spring & BL2 & Degrading bilinear model \\ \cline{2-4}  & Shear spring & EL2 & Bilinear elastic model \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Restoring force characteristics of each member used in non-linear dynamic analysis. for \(p_{ws}\geq 0.012\)); \(\sigma_{wy}\) is the yield strength of the shear reinforcing bars (N/mm\({}^{2}\)); \(M/V\) is the shear span length, which had a default value of \(h_{o}/2\); \(h_{o}\) is the clear height of the column (mm). Meanwhile, the restoring force characteristics of the shear-failure-type column with non-seismic details (shear spring, OO3 in Table 14) were determined using Equation (17), proposed based on the structural testing of columns with non-seismic details in Korea [53].