# Seismic Response Analysis of Multi-Story Steel Frames Using BRB and SCB Hybrid Bracing System
## 7 Nonlinear Time History Analysis
### Statistical Results  
As revealed by the spectral acceleration shown in Figure 4, remarkable record-to-record response deviation is noticed. Thus, the structural performance under an individual earthquake record does not necessarily stand for the central tendency when the structures are subject to a suite of ground motion records. Accordingly, the observation from the case study based on a single ground motion analysis is further examined through statistical analysis on all seismic analysis results. Figure 8 assembles the maximum story drift, maximum floor acceleration, and maximum residual story drift ratio under 20 ground motion records. Figure 7: Seismic demands under ground motion LA09: (**a**) peak story drift ratio; (**b**) peak floor acceleration; (**c**) residual story drift ratio. Figure 8a shows the scatter plot of the maximum story drift ratio for the structures under consideration. The mean values are calculated and put under the dots. Depending on the bracing configuration, the demands of hybrid braced CBFs can be larger or smaller than that of the pure BRBF. The mean values are 1.27% and 1.47% for the BRBF and the SCCBF, respectively. Although the equivalent damping ratio of SCCBF is half that of BRBF, the deformation demand is only approximately 16% higher. Compared with the BRBF, the demands of S5 and S6 are equivalent or even smaller. Thus, when the BRBs are replaced by SCBs at some stories, the corresponding frames are possible to generate improved deformation performance to a certain degree. For frames of S3 and S4, they exhibit larger deformations than original BRBF. This indicates that the BRBs and SCBs are suggested to be installed alternatively along building height. Figure 8b presents the scattered results of maximum floor accelerations along with the mean values. The BRBF shows the smallest demands of 0.66 g, due to the best energy dissipation capacity. The frames of S2 and S3 show the largest demands among all the frames with a mean value of 0.99 g, attributed to the mild damping mechanism. For the frames of S4-S6, the acceleration demands are  
Figure 8: Seismic responses under the input ground motion records: (**a**) maximum transient story drift ratio; (**b**) maximum floor acceleration; and (**c**) maximum residual story drift ratio. nearly identical, having middle values between that of BRBF and SCCBF. Thus, it can be anticipated that the engagement of SCBs would constantly increase floor acceleration demands. Figure 8c assembles the residual story drift results. The comparison between S1 and S2 is sharp because using SCBs eliminates residual deformations for the structures. This is attributed to the excellent recentering capability of SCBs. Similar observations and explanations can be found in other studies [15; 26; 35; 36; 37; 38]. The effect of combining SCBs on mitigating residual deformation is much more pronounced compared with the peak deformations and peak accelerations. As can be seen, the BRBF produces a mean residual story drift ratio over 0.5%, which violates the repairing threshold [17]. This is completely eliminated by replacing all BRBs with SCBs. For the other cases, the residual deformation is reduced to different extents by combining SCBs in different stories. The most remarkable reduction is found in the frames of S5 and S6. The corresponding reduction ratio is approximately 65%. Figure 9 examined the story-by-story seismic performance by plotting the height-wise demands. For each story or floor level, the mean values are calculated and presented. The values in Figure 9 are slightly different from that in Figure 8 because the results in Figure 8 are the mean of the maximum transient responses over all levels, while that in Figure 9 are the mean of the maximum transient responses at the specific level.