## 5 Comparison of the Pseudo-Dynamic Test and Non-Linear Dynamic Analysis Results
### Non-Linear Dynamic Analysis Results before and after Seismic Retrofitting  
The non-linear dynamic analysis conducted before and after seismic retrofitting based on the non-linear dynamic analysis method presented in Section 6.1 indicated that shear cracks occurred in the columns on the first floor at 2.1 s (3.9 mm) for the non-reinforced building. In addition, a maximum seismic response value of 3584.2 kN was observed, and the building collapsed at 3.3 s (49.1 mm). In the case of the target building retrofitted with the LLFD V-bracing system, fine bending and shear cracks occurred in the columns on the first floor at 2.82 s (3.9 mm); however, no additional maximum response occurred after showing the maximum seismic response at 3.59 s (7.5 mm), resulting in insignificant seismic damage. Figure 35 shows the load-displacement and time-displacement hysteresis curves for the first floor of the non-reinforced and LLFD-reinforced buildings when subjected to 200 cm/s\({}^{2}\). Table 18 lists the maximum response strength, maximum response displacement, and displacement ratio--important elements for seismic performance assessment--among the analysis results for the LLFD-reinforced building and non-reinforced building subjected to 200 cm/s\({}^{2}\). According to the above figure and table, compared to the non-reinforced building, the displacement of the LLFD-reinforced building was suppressed by approximately 0.15 times on the first floor, 0.23 times on the second floor, and 0.36 times on the third floor under the input ground motion of 200 cm/s\({}^{2}\), confirming the effectiveness of the seismic retrofitting design and proposed LLFD method. Meanwhile, as shown in Figures 36 and 37 and Table 19, the LLFD V-bracing system was found to share approximately 67% of the total seismic energy acting on the target R/C school building with non-seismic details as a result of its excellent energy dissipation capacity. Figures 38 and 39 show the ductility ratio (\(\mu_{s}\)) with respect to shear displacement of the columns on each floor of the non-reinforced R/C building and the building retrofitted using the LLFD V-bracing system. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Floor**} & \multirow{2}{*}{\begin{tabular}{c} **Floor Height** \\ **[mm]** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Floor Weight** \\ **W [kN]** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Yield** \\ **Displacement** \\ \(\delta_{y}\) **[mm]** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Yield Strength** \\ \(V_{y}\) **[KN]** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Failure** \\ **Mode** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Basic Seismic** \\ **Capacity Index** \\ \(E_{\mathbf{o}}\) \\ \end{tabular} } \\ \hline
1 & 3300 & 1133.4 & 24.1 & 2779.0 & Shear failure & 0.24 \\ \hline
2 & 3300 & 7556 & 27.9 & 2268.0 & Shear failure & 0.23 \\ \hline
3 & 3300 & 3778 & 18.0 & 1343.7 & Shear failure & 0.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Basic seismic capacity index (\(E_{o}\)) of non-strengthened control buildings.