# Seismic Response Analysis of Multi-Story Steel Frames Using BRB and SCB Hybrid Bracing System
## 7 Nonlinear Time History Analysis  
### Case Study  
To have a preliminary understanding of the seismic responses of the CBFs using hybrid bracing system, this subsection conducts nonlinear time history analysis on BRBF, SCCBF, and hybrid braced CBFs upon a single ground motion record by a case study. The ground motion record LA09 is artificially selected to demonstrate the effect of using hybrid bracing system. Figure 6 plots the time-history responses of roof drift ratios and roof accelerations for the frames under consideration. In the initial stage, the structures exhibit similar behavior until the ground motion excites the structures into serious nonlinearity. The peak roof drift ratios are approximately 0.66% and 1.05% for BRBF and SCCBF, respectively, which is primarily due to the fact that BRBF has much higher damping capacity than SCCBF. In terms of using hybrid braces, the corresponding deformation demands are between the BRBF and SCCBF, lying in the range from 0.91% to 1.01%. However, as will be shown in the statistical results, the average peak story drift ratio shows a different observation, which will be discussed later on. Figure 5: Cyclic pushover results of the steel frames: (**a**) S1; (**b**) S2; (**c**) S3; (**d**) S4; (**e**) S5; and (**f**) S6. The residual deformation demands are also a key index determining the seismic performance of seismic-resisting structures. This response parameter directly determines the repair cost and downtime duration after earthquakes. It is clear that the BRBF tends to produce biased deformation in a single side after being yielded, causing significant residual deformation at the end of the earthquake with 0.3% residual roof drift ratio. The SCCBF is found with entirely eliminated residual roof drift ratio at the end of vibration, thanks to the excellent recentering capability given by SCBs. Regarding the CBFs with hybrid bracing systems, the corresponding residual deformations are well reduced, compared with the BRBF. Therefore, the involvement of SCBs in a BRBF system may amplify the deformation demand to a certain degree but it remarkably decreases residual deformation demand. Besides with the peak and residual deformation demands, the floor acceleration response is also examined. The results at the roof level are presented. It is interesting to note that, except for the frame S4, all the other frames suffer from nearly identical demands. This is because the yielding mechanism of the braces well caps the force demand in the entire structural system and consequently limits the increase of acceleration demand. The relatively large outcome generated in frame S4 is caused by  
Figure 6: Response time history under ground motion LA09: (**a**) roof deformation; (**b**) roof acceleration. higher mode effect. It means the significant nonlinearity of frame S4 involves the contribution from the 2 nd or even higher modes. This phenomenon is similar to that noticed in a prior study [49]. Figure 7 plots the level-by-level responses throughout building height, including the peak story drift ratio, peak floor acceleration, and residual story drift ratio. This plot not only exhibits the magnitudes of considered demands but also displays the response deviation among different stories. Figure 7a shows that the SCCBF and BRBF exhibit similar peak deformation patterns over building height but that the former experiences higher demand by approximately 70%. When some of BRBs are replaced by SCBs, the deformation demands will be increased. Taking frames S5 and S6 for example, both of which use BRBs and SCBs alternatively over all stories, they show similar deformation patterns. Although the peak story drift ratios are approximately 50% larger than the BRBF, they are well within the design targets of 1.5% as prescribed by the American Society of Civil Engineers (ASCE) code [50]. For peak floor accelerations, the smallest values are associated with the BRBF.