## 2 Target Steel Building with BRB Devices
### Performance Evaluation of Target Building
#### 2.3.3 Time History Analysis under Design Earthquakes  
The target frame is analyzed under the design earthquakes and wind loads prescribed in the Japanese standard [30] to validate the design procedure and evaluate the contribution of BRBs. Five sets of earthquake ground motions are considered as listed in Table 3. Three of them are the observed earthquake ground motions scaled to Level 2 to have the maximum velocity of 50 cm/s. The other two earthquakes are artificial earthquake ground motions to have the response spectra to be compatible with the Level 2 design spectrum of the Japanese standard [31] and the phase spectra of historical earthquakes. The acceleration response spectra of selected earthquakes are illustrated in Figure 6. As for the wind load, four sets of design wind load of the different average speeds of 17, 20, 25, and 31 m/s are generated according to the AIJ recommendations [30]. Since the shape of the building is regular, the wind loads are applied at the center of gravity on each floor, while the distribution of the wind loads along the height of the building is decided according to the Japanese standard [31].  
The maximum story drift ratio of the target frame with and without BRBs under the design earthquake and wind loads is presented in Figure 7. For the design earthquake loads, the maximum story drift is controlled to satisfy the 1% design drift, while the average result indicates a 50% decrease in the critical stories compared to the target frame without BRBs. On the other hand, the maximum story drift under the wind loads also indicated an improvement of 50% in contrast to the model without BRBs, which reaches the 1.2% story drift in critical floors, in the case of a design wind load of 31 m/s. Hence, the design procedure is a straightforward tool that can determine the amount of additional stiffness to be provided by BRBs without any iteration to satisfy the design targets.  
Figure 5: Normalized mode shape of the target high-rise building with and without BRBs devices.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Categories** & **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 earthquake to be & 4 & Tohoku & 1978 & Tohoku Univ. \\ compatible with Level 2 & 5 & Tokachi Oki & 1968 & Hachinohe \\ \hline \hline \end{tabular}
\end{table}
Table 3: List of selected earthquake ground motions.  
Furthermore, in Figure 8, for the earthquake and wind loads, the maximum ductility factor and the amount of dissipated energy of each BRB along the height of the building are evaluated. For most of the earthquake loads, the ductility factor of BRBs is in the range of the pre-defined design drift, which is considered to be \(\mu=7\), except for the lower stories for which it is exceeded. In the case of design wind loads, the ductility factor is decreasing significantly in upper stories. As for the amount of dissipated energy, in both cases, the BRBs in the upper floors are less effective at dissipating the earthquake or wind loads.  
Figure 6: Response acceleration spectrum of selected ground motions (5% damping).  
Figure 7: Maximum story drift ratio of high-rise steel building with and without BRBs under design earthquake and wind loads.