## 4 Analysis Results
### Comparisons with the Nonlinear Time-History Analysis
#### 4.2.2 Recorded Ground Motion  
Figures 24 and 25 show the peak relative displacement at X\({}_{3\Lambda}\)Y\({}_{3}\). The accuracy of the predicted peak displacement is satisfactory: The predicted peak approximated the envelope of the nonlinear time-history analysis results, even though some cases were overestimated (e.g., model: Model-Tf44, ground motion: UTO0416, Figure 25b). The variation of the predicted peak due to the assumed complex damping ratio (\(\beta\)) depends on the ground  
Figure 21: Comparison of the peak relative displacements at X\({}_{3\Lambda}\)Y\({}_{3}\) (Model-Tf44) for the (**a**) Art-1 and (**b**) Art-2 series. Figure 20: Comparison of the peak relative displacements at X\({}_{3\Lambda}\)Y\({}_{3}\) (Model-Tf34) for the (**a**) Art-1 and (**b**) Art-2 series. motion. In some cases, the largest peak was obtained when \(\beta\) was 0.30 (e.g., model: Model-Tf34, ground motion: UTO0416, Figure 24b), while in other cases, the largest peak was obtained when \(\beta\) was 0.10 (e.g., model: Model-Tf34, ground motion: TCU, Figure 24c). Figure 23: Comparison of the horizontal distributions of the peak displacement at level 0 (model: Model-Tf44, ground motion: Art-1 series). Figure 22: Comparison of the horizontal distributions of the peak displacement at level 0 (model: Model-Tf34, ground motion: Art-1 series). Figure 26 shows comparisons of the horizontal distribution of the peak displacement at level 0. In this figure, the Model-Tf34 results are shown, with the results for UTO0414 shown in Figure 26a and those for TCU shown in Figure 26b. Figure 26: Comparison of the horizontal distributions of the peak displacement at level 0 (model: Model-Tf34) for (**a**) UTO0414 and (**b**) TCU. Figure 25: Comparison of the peak relative displacements at X\({}_{3A}\)Y\({}_{3}\) (Model-Tf44): (**a**) UTO0414; (**b**) UTO0416; (**c**) TCU; (**d**) YPT. The predicted horizontal distribution of the peak displacement in the Y direction was notably different from the envelope of the time-history analysis in the case of UTO0414, as shown in Figure 26a. In the predicted distribution, the largest displacement occurred at X\({}_{1A}\) (the flexible side in the Y direction); meanwhile, in the envelope of the time-history analysis results, the displacement at X\({}_{1A}\) was the smallest. Conversely, the predicted horizontal distribution of the peak displacement in the Y direction fits the envelope of the time-history analysis in the case of TCU very well, as shown in Figure 26b. In the predicted distribution, the largest displacement occurred at X\({}_{1A}\), which is consistent with the envelope of the time-history analysis results. The modal displacement responses at X\({}_{1A}\) and X\({}_{6A}\) (the stiff side in the Y direction) are compared and discussed further in Section 5.5. One of the motivations of this analysis was to evaluate the seismic performance of the retrofitted building models under the recorded motions from the 2016 Kumamoto earthquake. It has already been reported in a previous study [44] that the seismic capacity evaluation of the main building of the former Uto City Hall indicate that the structure was insufficient to withstand the earthquake that occurred on 14 April 2016. Therefore, the drift of the superstructure was examined as follows. Figure 27 shows comparisons of the peak drift for the three columns in Model-Tf34 in cases with UTO0414 and UTO0416. The peak drifts for the three columns obtained from the nonlinear time-history analysis results were smaller than 0.4%. The largest peak drift occurred for column A\({}_{3}\)B\({}_{3}\) on the second story, with a value of 0.12% in the case of UTO0414 (Figure 27a) and a value of 0.30% in the case of UTO0416 (Figure 27b). Therefore, the seismic performance of Model-Tf34 was excellent for the motions recorded during the 2016 Kumamoto earthquake. Figure 28 shows comparisons of the peak drift of Model-Tf44. Similar observations can be made for Model-Tf44.