## 5 Comparison of the Pseudo-Dynamic Test and Non-Linear Dynamic Analysis Results
### Non-Linear Dynamic Analysis Overview  
The target specimens used in the non-linear dynamic analysis were the non-reinforced two-story R/C frame, with the frame retrofitted with the LLFD V-tracing system shown in Figures 15 and 16 in Section 4.4. While the actual structures vibrate in three dimensions, in this study, they were modeled as plane frames that considered only horizontal seismic forces by replacing columns, beams, and walls with linear elements. The floor characteristics of the structure were evaluated based on the member level, with the following assumptions made for the analysis: (1) The location of the yield hinge of each member was determined by referring to the literature [50; 51], with the section from the center of each member to its end where the yield hinge occurred assumed to be rigid; and (2) The strength of the beams also considered the influence of slab reinforcing bars within the effective width of the slab, which was the scope of the cooperation with the beams. In addition, each member was modeled as serially connected flexural, shear, and axial springs, as shown in Figure 24.  
Figure 24: Nonlinear dynamic analysis model: (**a**) Non-strengthened frame (PD-RC); (**b**) LLFD V-typed strengthening frame (PD-LLFD-V). As for the restoring force model of the LLFD vibration control system, the perfect plastic (PP) model was applied based on the LLFD member test results shown in Section 3. In the case of the hysteretic characteristics of the PP model, the characteristics of the unloading and reloading hysteresis curves were determined by the initial stiffness (\(K_{0}\)) and yield strength of the LLFD (\(V_{d,y}\)). Table 13 lists the parameters of the PP model used for the LLFD, while Figure 25 shows the LLFD restoring force characteristics for the non-linear dynamic analysis based on Table 13. The LLFD was the GS-LLFD used in the pseudo-dynamic test. The torque pressure was \(T_{0}=200\)kN\(\cdot\)m and the yield strength (\(V_{d,y}\)) was 125 kN, obtained using regression Equation (4) for the member test. The yield displacement (\(\delta_{d,y}\)) was 0.08 mm, as measured in the member test (see Table 4). The non-reinforced frame specimen, with ground beams and walls at the foundation (Figure 24a), comprised 12 nodes, including two bottom plates and ground points. Meanwhile, the frame specimen retrofitted with the LLFD V-bracing system (PD-LLFD-V) consisted of nodes that connected the additional steel frame to the existing R/C frame, LLFD, and V-shaped steel member for the LLFD installation, as shown in Figure 24b. The PD-LLFD-V frame had 24 nodes, including ground points. The joint between the existing R/C member and steel frame was modeled with a link joint element. For the axial force in the non-linear dynamic analysis, the axial load applied to the actual existing frame (two columns) used in the pseudo-dynamic test shown in Figures 14 and 15 (i.e., 1000 kN) was distributed to the upper beam-column joint nodes, and a constant axial force of 500 kN was applied. The additional weight of the R/C frame and LLFD reinforcement was also applied to the corresponding nodes. The non-linear dynamic analysis was conducted using CANNY (Version C11), a general-purpose software program for three-dimensional non-linear dynamic analysis developed by [PERSON] [52]. Table 14 provides an overview of the restoring force characteristics \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Member** & \(\mathbf{T_{0}}\) & \(\delta_{d,y}\) & \(\mathbf{V_{d,y}}\) & \(\mathbf{K_{0}}\) \\  & (kN\(\cdot\)m) & [mm] & [kN] & [kN/mm] \\ \hline LLFD & 200 & 0.08 & 125 & 15,625 \\ \hline \(T_{0}\): Torque, \(\delta_{d,y}\): Yield displacement, \(V_{d,y}\): Yield strength, \(K_{0}\): Initial stiffness. & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Parameters of perfect plastic model used in LLFD. Figure 25: Hysteresis model of LLFD for nonlinear dynamic analysis. of each member used in the non-linear dynamic analysis.