## 6 Conclusions  
Using FE numerical simulation, the influences of the strain rate effect and earthquake sequence on the seismic responses and fragilities of a CFST frame structure with BRBs are systematically investigated in this paper. The following conclusions are drawn.  
Figure 15: Fragility curves for different damage limit states.  
(1) The strain rate can impact the structural response to a certain extent. After considering the strain rate effect of the material, the roof displacement and the ISDRs of the structure decrease.  
(2) Compared with the CFST structure without BRBs, the maximum roof displacement and ISDR of the CFST structure with BRBs decrease by 45.1% and 43.9%, respectively. Therefore, BRBs can effectively improve the seismic capacity of the CFST frame structure.  
(3) Compared with those under single mainshocks, the maximum roof displacement and the ISDR of the CFST structure with BRBs under earthquake sequences significantly increase. Under an earthquake sequence with \(\delta=0.8\), the maximum roof displacement and the maximum ISDR of the structure increase by 72.23% and 76.23%, respectively. Moreover, with an increasing scaling coefficient, the seismic response significantly increases.  
(4) The median PGA corresponding to the structure exceeding each damage limit state under an earthquake sequence decreases when compared with that under a mainshock. The fragility of the CFST structure with BRBs under an earthquake sequence is significantly greater than that under a single mainshock. Therefore, earthquake sequences should be considered in the seismic design of CFST structures. The probabilities of the structure exceeding each limit state increase with rising \(\delta\) of the earthquake sequence. The extent of the increase is more significant for severe damage and collapse limit states.  
Conceptualization, H.Z. and C.L. Methodology, H.Z. and C.L. Software, S.-M.J. Formal analysis, P.-F.L. Data curation, Q.-M.G. Writing--original draft preparation, S.-M.J. and P.-F.L. Writing--review and editing, H.Z. and C.L. Project administration, H.Z. Funding acquisition, H.Z. and C.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China (Grant No. 2018 YFD1100404, 2016 YFC0701108), the State Key Program of the National Natural Science Foundation of China (Grant No. 51738007), the Program of Guangdong Key Laboratory of Earthquake Engineering and Application Technology (Grant No. 2017B030314068), the Natural Science Foundation of Liaoning Province (Grant No. 20180550949), and the Project funded by China Postdoctoral Science Foundation (Grant No. 2018M640253).  
The authors are grateful for the financial support from the National Key R&D Program of China (2018 YFD1100404, 2016 YFC0701108) and the State Key Program of the National Natural Science Foundation of China (51738007) for carrying out this research. The support from the Program of Guangdong Key Laboratory of Earthquake Engineering and Application Technology (2017B030314068) and the Natural Science Foundation of Liaoning Province (20180550949) is also gratefully acknowledged. The second author also thanks the financial support from the project funded by China Postdoctoral Science Foundation (2018M640253).  
The authors declare no conflict of interest.