# Seismic Performance Evaluation of Steel Buildings with Oil Dampers Using Capacity Spectrum Method
## 4 Application of the Proposed CSM on Steel Frame Buildings
### Frame Models of Target Buildings  
The 3D frame models of the buildings were analyzed by STERA_3D software, which is a finite element-based program developed by one of the authors [32]. In the model, the steel beam element is presented by a line element with two nonlinear flexural springs at both ends, as shown in Figure 7. The steel column element is presented by a line element with nonlinear axial springs in both end sections to consider nonlinear axial-moment interaction. The steelstrength was modified 1.1 times more than the nominal strength, and the ratio of post-yield stiffness was \(\gamma=K_{0}/K_{y}=0.001\). The slab effects required to amplify the flexural stiffness of the steel beam were assumed to be 1.2. The floor slab was considered to be rigid for in-plane deformation, and free for out-of-plane deformation. The beam-column  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Building**} & \multirow{2}{*}{**Story**} & \multicolumn{2}{c}{**Longitudinal Direction**} & \multicolumn{2}{c}{**Transvers Direction**} \\ \cline{3-6}  & & **Interior Beam** & **Exterior Beam** & **Short Span** & **Long Span** \\ \hline \multirow{4}{*}{4-story} & 4 & \(550\times 200\times 9\times 16\) & \(550\times 250\times 12\times 22\) & \(700\times 300\times 12\times 22\) \\  & 3 & \(550\times 250\times 9\times 19\) & \(550\times 200\times 12  
connection was assumed to be rigid, where the rigid zone length for the beam element was set to be half of the column width.  
The bilinear-type oil damper is defined as a vertical line element with a shear spring in the middle. The shear spring consists of the Maxwell model with an elastic spring with stiffness, \(K_{D}\), and a dashpot with a bilinear-type damping coefficient, \(C\), connected in a series. The force-velocity relation of the dashpot is shown in Figure 8.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Story** & **Height (H)** & **Weight (W\({}_{\textbf{z}}\))** & **Story Stiffness** & **Damper Stiffness** & **Damping** & **Relief V. (V\({}_{\textbf{z}}\))** & \\  & & & **(K\({}_{\textbf{F}}\))** & **(K\({}_{\textbf{D}}\))** & **(C\({}_{\textbf{1}}\))** & **Relief V. (V\({}_{\textbf{z}}\))** & \\ \hline  & **m** & **kN** & **kN/mm** & **kN/mm** & **kN-s/mm** & **cm/s** & \\ \hline
10 & 4.0 & 8579.0 & 158.6 & 27.30 & 5.67 & 38.6 & 0.02 \\
9 & 4.0 & 6365.0 & 180.1 & 31.00 & 6.45 & 38.6 & 0.02 \\
8 & 4.0 & 6431.0 & 220.3 & 37.92 & 7.88 & 38.6 & 0.02 \\
7 & 4.0 & 6470.0 & 244.8 & 42.13 & 8.77 & 38.6 & 0.02 \\
6 & 4.0 & 6539.0 & 291.8 & 50.23 & 10.45 & 38.6 & 0.02 \\
5 & 4.0 & 6567.0 & 306.2 & 52.70 & 10.95 & 38.6 & 0.02 \\
4 & 4.0 & 6622.0 & 328.2 & 56.50 & 11.75 & 38.6 & 0.02 \\
3 & 4.0 & 6664.0 & 383.0 & 65.93 & 13.70 & 38.6 & 0.02 \\
2 & 4.0 & 6680.0 & 383.5 & 66.02 & 13.72 & 38.6 & 0.02 \\
1 & 6.0 & 6859.0 & 280.0 & 48.18 & 10.02 & 57.9 & 0.02 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Technical parameters of oil dampers for 10-story building.  
Figure 8: (**a**) Element model of bilinear-type oil damper, (**b**) force–velocity of oil damper.  
Figure 7: Moment–rotation relationship at bending spring of beam and column elements.  
Table 7 summarizes the natural periods and effective masses of the buildings obtained by the eigenvalue analysis. The capacity curves of the ESDOF of the buildings were obtained by the nonlinear static pushover analysis as shown in Figure 9.