## 4 Comparison of Pseudo-Dynamic Test Results and Non-Linear Dynamic Analysis Results
### Overview of Non-linear Dynamic Analysis  
Non-linear dynamic analysis was conducted on both the full-size two-story RC frame with no reinforcement applied, and the test frame retrofitted with the CFT-MF system shown in Figures 8 and 9 in Section 3.2. In reality, actual structures vibrate in a three-dimensional and complex manner; however, 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 (JBDPA, [29] and AJI [41]), and the segment from the center of each member, including column and beam joints, to the ends of the members, where yield hinges occur, shall be assumed to be rigid. (2) The strength of a beam shall be determined considering the effect of the slab reinforcing bars present within the effective width of the slabs that collaborate with the corresponding beam. (3) Each member shall be modelled to allow flexural springs, shear springs, and axial springs to be serially connected, as shown in Figure 20. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{**Earthquake Levels** **(cm/s\({}^{2}\))**} & \multicolumn{2}{c}{**Response Strength**} & \multicolumn{2}{c}{**Response Displacement**} \\ \cline{3-6}  & & **V\({}_{\mathbf{u}}\) a** **[kN]** & **R\({}_{\mathbf{s}}\) b** **** & \(\delta_{\mathbf{u}}\) c** & **R\({}_{\mathbf{d}}\) d**  \\ \hline PD-FR & 200 & 250.5 & 1.00 (250.5/250.5) & 58.7 & 1.00 (58.7/58.7) \\ \hline \multirow{3}{*}{PD-CFT-MF} & 200 & 432.2 & 1.72 (432.2/250.5) & 11.0 & 0.19 (11.0/58.7) \\ \cline{2-6}  & 300 & 613.3 & 2.45 (613.3/250.5) & 22.4 & 0.38 (22.4/58.7) \\ \cline{1-1} \cline{2-6}  & 400 & 773.9 & 3.09 (773.9/250.5) & 39.5 & 0.67 (39.5/58.7) \\ \hline \end{tabular}  
* Maximum response strength. b Ratio of maximum response shear strength between strengthened and reference specimens with respect to earthquake intensity. c Response displacement at maximum point. d Ratio of response displacement between strengthened and reference specimens with respect to earthquake intensity.  
\end{table} 
Table 5: Comparison of maximum seismic response load-displacement results and corresponding seismic response strength and displacement ratios. The test frame with no reinforcement applied (PD-FR) includes ground beams and walls on the foundation level. It is composed of a total of 12 nodal points, including two deck panels and branch points, as shown in Figure 20a. The test frame retrofitted with the CFT-MF system (PD-CFT-MF) includes the members that connect the existing RC frame with the CFT-MF reinforcing members in addition to the nodal points of the test frame with no reinforcement applied, as shown in Figure 20b. Thus, it is composed of a total of 20 nodal points, including branch points. The anchor bolt used to connect the existing RC members with the CFT-MF reinforcing members was modeled as a link-joint element. In non-linear dynamic analysis, the axial force was determined based on the axial load exerted on the actual existing frame (two columns), i.e., 1000-kN. Thus, each of the upper beam-column connection nodes was subjected to a constant axial force of 500-kN. Also, the additional weight of the RC frame and the CFT-MF reinforcing bars was exerted on the corresponding nodal points. Non-linear dynamic analysis was performed using CIAAY, a commercial software package developed by [PERSON] [42] to implement the three-dimensional non-linear dynamic analysis. Table 6 presents an overview of the restoring force characteristics of each member used in non-linear dynamic analysis. Figure 20: Non-linear dynamic analysis models: (**a**) control specimen (PD-FR); (**b**) PD-CFT-MF.