# Seismic Performance Evaluation of Steel Buildings with Oil Dampers Using Capacity Spectrum Method
## 4 Application of the Proposed CSM on Steel Frame Buildings
### Comparison Results between CSM and THA  
The maximum responses of the target buildings under the earthquake ground motions were estimated by the proposed CSM, and compared with the results of nonlinear THA. Figures 11-14 show the story drifts and story shear forces obtained by the proposed CSM and the nonlinear THA for the selected ground motions along the height of the target buildings.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Eategories** & **No.** & **Event** & **Year** & **Station** \\ \hline Scaled earthquake to be & 1 & Imperial Valley & 1940 & El Centro \\ compatible of 50 cm/s & 2 & Kern County & 1952 & Taft \\  & 3 & Kobe & 1995 & JMA \\ \hline Artificially generated & 4 & Tohoku & 1978 & Tohoku Univ. \\ earthquake to be & 5 & Tokachi Oki & 1968 & Hachinohe \\ compatible of L2 & 6 & Kobe & 1995 & JMA \\ \hline \hline \end{tabular}
\end{table}
Table 8: List of selected earthquake ground motions.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Building** & **Parameter** & **1 st Mode** & **2 nd Mode** & **3 rd Mode** \\ \hline \multirow{2}{*}{4-story} & Natural period (s) & 1.40 & 0.49 & 0.25 \\  & Effective mass (\%) & 91.2 & 7.90 & 0.60 \\ \hline \multirow{2}{*}{10-story} & Natural period (s) & 2.03 & 0.75 & 0.44 \\  & Effective mass (\%) & 82.8 & 11.3 & 3.40 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Dynamic characteristics of target buildings.  
Figure 9: Capacity curve of the ESDOF of target buildings: (**a**) 4-story building, (**b**) 10-story building.  
For the 4-story building, the average ratio of THA to proposed CSM (for story drift and story shear force) was 0.95 for the scaled 50 cm/s earthquakes. The ratio for the artificially generated earthquakes compatible with Level-2 design earthquake was about 0.90. Similarly, the ratios for the proposed CSM and the THA for story drift and story shear force, in the 10-story building, were 1.10 and 1.20 for the scaled and artificially generated ground motions, respectively. It was also noted that, for the 4-story building, the proposed CSM method overestimated the story shear force of the structure, although the story drift was underestimated for the 10-story building. Furthermore, the correlation between the performance results obtained from the proposed CSM method and THA is estimated as given in Figure 15. The estimated correlation was about 0.9 for the selected earthquakes in terms of story drift and story shear force for both of the steel buildings with oil dampers. The estimated correlation indicates that the proposed CSM can be used as a practical  
Figure 11: Comparison of story drifts between proposed CSM and time history analysis (THA) for 4-story building.  
Figure 10: Response spectra of selected ground motions and design response spectrum of Level-2 earthquake with 5% damping factor.  
procedure to estimate the maximum responses of passively controlled buildings equipped with bilinear oil damping devices.  
Figure 12: Comparison of story shear forces between proposed CSM and THA for 4-story building.  
Figure 13: Comparison of story drifts between proposed CSM and THA for 10-story building.