## 5 Comparison of the Pseudo-Dynamic Test and Non-Linear Dynamic Analysis Results
### Non-Linear Dynamic Analysis Overview  
The non-linear analysis model and method discussed in Section 5 could effectively simulate the seismic behavior of an R/C frame retrofitted with the LLFD V-bracing system. For evaluating the commercialization potential of the LLFD V-bracing system, based on the analysis model and method discussed in Section 5.1, a non-linear dynamic analysis was conducted on an R/C school building with non-seismic details (see Figure 14) retrofitted with the LLFD V-bracing system. The seismic response load and displacement characteristics of the building before and after seismic retrofitting were evaluated, with the seismic retrofitting effect verified by examining the energy dissipation capacity, seismic response load, and response displacement characteristics of the damper. As discussed in Section 5, a non-linear dynamic analysis was conducted using CANNY [52]. This analysis was conducted using the Hachinohe (EW) 200 cm/s\({}^{2}\) setting \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & **Input Ground** & \multirow{2}{*}{**Method**} & **Maximum** & **Maximum** & **Maximum** & **Maximum Load** \\  & **Acceleration** & & **Displacement** & **Deviation Ratio** & **[kN]** & **[kN]** \\ \cline{3-6}  & **[cm/s\({}^{2}\)]** & & **[mm]** & **[malysis/Test]** & **[**]** & **[**]** \\ \hline \multirow{2}{*}{PD-RC} & \multirow{2}{*}{200} & PDT & 67.3 & \multirow{2}{*}{1.07} & 251.4 & \multirow{2}{*}{1.05} \\ \cline{3-6}  & & NDA & 71.9 & & 263.1 & \\ \hline \multirow{6}{*}{PD-LLFD-V} & \multirow{2}{*}{200} & PDT & 9.5 & \multirow{2}{*}{0.99} & 439.6 & \multirow{2}{*}{0.95} \\ \cline{3-6}  & & NDA & 9.4 & & 416.5 & \\ \cline{3-6}  & & PDT & 15.7 & & 610.9 & \\ \cline{3-6}  & & NDA & 17.0 & & 553.0 & \\ \cline{3-6}  & & PDT & 27.1 & & 756.6 & \\ \cline{3-6}  & & NDA & 29.5 & & 662.6 & \\ \hline \hline \end{tabular} Note: PDT: Pseudo-dynamic test, NDA: Nonlinear dynamic analysis.  
\end{table} 
Table 15: Correlation of maximum response load and maximum response displacement based on nonlinear dynamic analysis and pseudo-dynamic test. as the input ground motion, which was the level used for the seismic design of the target building and caused the collapse of a non-reinforced frame. Figure 33 shows the modeling of the target R/C school building before and after retrofitting. The seismic reinforcement volume required for the LLFD V-bracing system was calculated using Equations (18)-(20), which could be used to determine the seismic energy absorption effect of the vibration control system based on the method proposed by the Japan seismic diagnosis standards [50], i.e., Newmark's equal energy criterion [54,55]. \[Q_{ydtp}=\frac{\left[\left(\frac{E_{Ro}}{E_{o}}\right)^{2}-1\right]\cdot\phi^{2 }\cdot(2\mu-1)\cdot\mu_{dp}}{2\beta\cdot\left(\mu\cdot\mu_{dp}-1\right)}\cdot Q_ {yst} \tag{18}\]  
\[E_{Ro}=C_{yst}\cdot\sqrt{\phi^{2}(2\mu-1)+2\beta\cdot\alpha_{c}\left(\mu- \frac{\alpha_{c}}{\alpha_{k}}\right)} \tag{19}\]  
\[E_{o}=C_{yst}\cdot\sqrt{\phi^{2}(2\mu-1)} \tag{20}\]  
Here, \(Q_{ydtp}\) is the seismic reinforcement volume required for the damper (required strength), \(Q_{yst}\) is the yield strength of the existing structural member, \(E_{Ro}\) is the target basic performance index after seismic retrofitting, \(E_{o}\) is the basic performance index of the existing structural member, \(\phi\) is the coefficient for calculating the ductility index of the existing R/C structure \((=1/0.75(1+0.05\mu)),\mu\) is the ductility ratio of the existing structure \((=\delta_{max}\delta_{yst})\), \(\mu_{dp}\) is the ductility ratio of the damper for the yield displacement of  
Figure 33: Modeling of the R/C school building before and after seismic strengthening: (**a**) Frame without strengthening; (**b**) Frame with LLFD V-typed strengthening; (**c**) Frame with LLFD V-typed strengthening (Isometric view).