# Seismic Design of Steel Moment-Resisting Frames with Damping Systems in Accordance with KBC 2016
## 4 Design Example
### Six-Story Steel Moment Frames with Viscoelastic Dampers (6F-SMRF-VED)
#### 4.3.2 Design of Velocity-Dependent Damping Devices
Nonlinear response history analysis was performed using the final stiffness and damping coefficient of the damping devices. It is unnecessary to examine design base shear because the damping correction factor was set to 1.0. The base shear reduction factor was 0.92 which is smaller than 1.0. The peak story drifts of the final design are summarized in Table 8. Compared to Table 6, the maximum peak story drift was reduced to 0.90%, which is slightly lower than the allowable story drift ratio of 1.0%. As a result, the proposed design methodology can design damping systems with a sufficiently accurate prediction of performance. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Structure without Damping**} & \multirow{2}{*}{**Iteration**} & \multirow{2}{*}{**Added**} & \multirow{2}{*}{**Target**} & \multirow{2}{*}{**Frequency**} & \multirow{2}{*}{**Period**} \\
**Devices** & & & & & \\ \hline
**Fundamental** & **Fundamental** & & & & \\
**Period** & **Frequency** & & & \\
**\(T\) (sec)** & **\(\omega\) (rad/sec)** & & & & \\ \hline \multirow{4}{*}{2.09} & \multirow{4}{*}{3.00} & - & 0.050 & 0.000 & 3.00 & 2.09 \\ \cline{3-5}  & & 1 st & 0.200 & 0.150 & 3.47 & 1.81 \\ \cline{3-5}  & & 2 nd & 0.142 & 0.092 & 3.26 & 1.93 \\ \cline{3-5}  & & 3 rd & 0.166 & 0.116 & 3.34 & 1.88 \\ \cline{3-5}  & & 4 th & 0.156 & 0.106 & 3.31 & 1.90 \\ \cline{3-5}  & & \multicolumn{2}{c}{Fin} & 0.161 & 0.111 & 3.33 & 1.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Target damping ratio and frequency. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Seismic Design**} & \multirow{2}{*}{**Story**} & \multirow{2}{*}{**Story Drift**} & \multicolumn{2}{c}{**Member Section (DCR)**} & \multirow{2}{*}{**Weight (kN)**} \\ \cline{3-5}
**Model** & & & **Beam** & **Column or Brace** \\ \hline \multirow{4}{*}{6-SMRF-VED** **(with damping systems)**} & **6** & **0.51** & \(\text{H}\text{-}354\times 176\times 8/13\) & Column: H-414 \(\times\) 405 \(\times\) 18/28 (0.19) & \\ \cline{2-4}  & 5 & 0.68 & (0.75) & Brace: H-244 \(\times\) 252 \(\times\) 11/1 (0.43) & \\ \cline{2-4}  & 4 & 0.83 & \(\text{H}\text{-}450\times 200\times 9/14\) & \\ \cline{2-4}  & 3 & 0.90 & (0.79) & \\ \cline{2-4}  & 2 & 0.85 & \(\text{H}\text{-}496\times 199\times 9/14\) & \\ \cline{2-4}  & 1 & 0.51 & (0.78) & \\ \hline \multirow{4}{*}{6-SMRF-SD** **(without damping systems)**} & **6** & 0.62 & \(\text{H}\text{-}506\times 201\times 11/19\) & \\ \cline{2-4}  & 5 & 0.77 & (0.36) & \\ \cline{1-1} \cline{2-4}  & 4 & 0.90 & \(\text{H}\text{-}606\times 201\times 12/20\) & \\ \cline{1-1} \cline{2-4}  & 3 & 0.97 & (0.47) & \\ \cline{1-1} \cline{2-4}  & 2 & 0.88 & \(\text{H}\text{-}606\times 201\times 12/20\) & \\ \cline{1-1} \cline{2-4}  & 1 & 0.48 & (0.45) & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of peak drift ratio and structural weight. As with the displacement-dependent damping system design, the structural elements comprising the damping system must be both elastic against the loads including seismic loads and forces induced by damping devices for design earthquake. Braces to install damping devices transmitting damping device force to the seismic-force-resisting force and the column at the right-hand side of the first story damping device transmitting vertical component of damping device force to the foundation comprises the damping system of the structure. DCRs for the frame members and panel zones were computed in terms of rotation angle ductility from nonlinear response history analysis for design earthquake and represented in Figure 14. In the case of columns and braces, higher DCR between bending moment DCR and axial force DCR is given in Figure 14a. All the members that belong to the damping system in the central bay remain elastic with DCRs lower than 1.0. Finally, damping device safety subjected to the maximum considered earthquake was checked. The maximum shear strain of damping devices was 0.455 from the response analysis for the maximum considered earthquake.