## 5 Comparison of the Pseudo-Dynamic Test Results and Nonlinear Dynamic Analysis Results
### Overview of the Nonlinear Dynamic Analysis  
Nonlinear dynamic analysis was conducted on both the full-size two-story RC frame with no reinforcement applied and the test frame retrofitted with the NBSD system shown in Figure 11 in Section 4.4. In reality, actual structures vibrate in a three-dimensional and complex manner, but, in the present study, it was assumed that the used columns, beams, and walls were wire-type materials so that the test frame was modeled as a plane frame, in which only the seismic force in the horizontal direction was considered. The floor-specific structural evaluation was conducted at the member level, and the following assumptions were applied in the analysis: (1) The position of each member's yield hinges was determined based on references [7; 39], and the segment from the center of each member, including column and beam joints, to the ends of the members, where yield hinges occur, should be assumed to be rigid. (2) The strength of a beam should be determined considering the effect of the slab reinforcing bars present within the effective width of the slabs that collaborate with the corresponding beam. Each member should be modeled to allow flexural springs, shear springs, and axial springs to be serially connected, as shown in Figure 22a. The modified Ramberg-Osgood (MRO) model was employed as a hysteresis model for the NBSD-based seismic control system because the model is suitable to simulate the hysteric behavior of steel slit dampers. The hysteric characteristics of the MRO model with respect to the stiffness can be represented by the primary stiffness (\(\alpha\)-\(K_{0}\)) and secondary stiffness (\(\beta\)-\(K_{0}\)), which can be obtained by applying the stiffness coefficient (\(\alpha\), \(\beta\)) to the initial stiffness (\(K_{0}\)). The unloading and reloading hysteresis loops were characterized based on the curve number (\(\lambda d\)). Table 11 summarizes the parameters used in the MRO model for the NBSD system. The nonlinear analysis results obtained based on Table 11 were then compared with the NBSD material test results obtained during the cyclic loading tests described in Section 4, as shown in Figure 23. The results showed that the simulated hysteric behavior was largely consistent  
\begin{table} \begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{\begin{tabular}{c} **Specimen** \\ **Name** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Input Seismic** \\ **Ground** \\ **Motion** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Degree of** \\ **Acceleration** \\ **(cm/s\({}^{2}\))** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Maximum** \\ **Load** \\ **(cm/s\({}^{2}\))** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Maximum** \\ **Load** \\ **(kN)** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Maximum** \\ **Ratios** \\ **\(s_{s}\)*1** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **Displacement** \\ **(k\({}_{u}\) **mm)** \\ \end{tabular} } \\ \hline \multirow{2}{*}{PD-FR} & Hachinohe & \multirow{2}{*}{200} & \multirow{2}{*}{272.5} & 1.00 & \multirow{2}{*}{70.2} & 1.00 \\  & & & & (272.5/272.5) & & (70.2/70.2) \\ \hline \multirow{4}{*}{PD-NBSD-WSCS} & \multirow{4}{*}{
\begin{tabular}{c} Hachinohe \\ (EW) \\ \end{tabular} } & \multirow{4}{*}{200} & \multirow{2}{*}{419.5} & 1.53 & \multirow{2}{*}{23.8} & 0.33 \\  & & & & (419.5/272.5) & & (23.8/70.2) \\ \cline{1-1} \cline{3-4} \cline{6-6}  & & \multirow{2}{*}{300} & \multirow{2}{*}{592.9} & 2.17 & \multirow{2}{*}{46.6} & 0.66 \\  & & & & (592.9/272.5) & & (46.6/70.2) \\ \cline{1-1} \cline{3-4} \cline{6-6}  & & \multirow{2}{*}{400} & \multirow{2}{*}{711.9} & 2.61 & \multirow{2}{*}{85.6} & 1.21 \\  & & & & (592.9/272.5) & & (46.6/70.2) \\ \hline \hline \end{tabular}   
* *with the experimental results, except that the energy dissipation exhibited an error of about 1%. Figure 23: Comparison of the nonlinear analysis and material test results of NBSD.