# Seismic Design of Steel Moment-Resisting Frames with Damping Systems in Accordance with KBC 2016
## 4 Design Example
### Three-Story Steel Moment-Resisting Frames with Metallic Yielding Dampers (3F-OMRF-MD)
#### 4.2.2 Design of Displacement-Dependent Damping Devices
However, the damping performance obtained from the results of the nonlinear response history analysis is 0.79, which mean that the expected damping performance goal was achieved with a sufficiently accurate prediction of performance. The average maximum story drift ratios for seven ground motion records representing design earthquake were 0.66%, 0.65% and 0.48% for the first, second, and third story, respectively, as summarized in Table 5 and all of those values are much smaller than the allowable story drift ratio 1.0%. This is because the base shear reduction factor 0.79 for seismic-force-resisting system governs the design rather than story drift reduction in this design example. The average maximum TADAS damping device deformation for seven ground motion records representing the maximum considered earthquake was maximum at the first story and calculated to be 41.2 mm. The deformation capacity of the example TADAS damping device is 60.3 mm. Therefore, damping devices can maintain the damping performance even under the maximum considered earthquake. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(\beta_{v}\)} & \multirow{2}{*}{**Floor**} & \multirow{2}{*}{
\begin{tabular}{c} **Story Force** \\ **Ratio** \\ \end{tabular} } & \(\begin{array}{c}V_{y}\\ (\textbf{kN})\end{array}\) & \(\begin{array}{c}V_{u}\\ (\textbf{kN})\end{array}\) & \(\begin{array}{c}\delta_{y}\\ (\textbf{mm})\end{array}\) & \(\begin{array}{c}\delta_{u}\\ (\textbf{mm})\end{array}\) \\ \hline \multirow{2}{*}{0.141} & 3 & 0.56 & 140 & 147 & 4.6 & 17.2 \\ \cline{2-7}  & 2 & 0.82 & 204 & 223 & 4.6 & 24.8 \\ \cline{2-7}  & 1 & 1.00 & 249 & 270 & 5.9 & 30.4 \\ \hline \multirow{2}{*}{0.120} & 3 & 0.57 & 145 & 152 & 4.6 & 15.7 \\ \cline{2-7}  & 2 & 0.81 & 209 & 226 & 4.6 & 22.6 \\ \cline{2-7}  & 1 & 1.00 & 255 & 274 & 5.9 & 28.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Characteristics of TADAS damping devices to achieve target damping ratio. KBC 2016 requires structural elements comprising a damping system to remain elastic subjected to both seismic loads and forces induced by damping devices for design earthquake. DCRs for the frame members and panel zones were computed in terms of rotation angle ductility from nonlinear response history analysis and represented in Figure 11. In the case of columns and braces, higher DCR among bending moment DCR and axial force DCR in a member is given in Figure 11. All the members that belong to the damping system at the central bay remain elastic since DCRs are lower than 1.0. Therefore, the design result obtained by the proposed procedure satisfies all the requirements of KBC 2016. To examine the effect of structural steel material reduction by damping devices, a bare ordinary moment resisting frame is designed to achieve story drifts similar to the frame with damping devices. Steel sections and story drifts of two models with and without damping devices are summarized with the respective total weights in Table 5, where 3F-OMRF-SD represents the seismically designed bare frame. The total weight of steel sections for the frame with damping devices is 149 kN, which is 67% of 221 kN for the frame without damping devices. Thus, the proposed procedure can yield efficient structural material-saving design. [PERSON] et al. [5] provide similar design example, in which three-story and three-bay frames are designed without and with metallic yielding damping devices using equivalent lateral force procedure although the seismic-force-resisting system is a special moment-resisting frame and target story drift ratio is set to 2% differently from this study. In the comparative design example, the frame with damping devices has 76% of the weight for frames without damping devices. In spite of several different conditions, this comparison supports the ability of the proposed design procedure to reduce seismic demand on the seismic-force-resisting system with supplementary energy dissipation relying on more accurate response prediction by nonlinear response history analysis.