###### Abstract  
This study investigates the cumulative damage of a 20-story high-rise steel building equipped with buckling-restrained braces (BRB) under the likely occurrence of earthquake and wind events in the design life of the building. The objective of this research is to introduce a method for evaluating the cumulative damage of BRBs under multi-hazard events that are expected to occur during the service life of a high-rise building in order to achieve a safer building. A methodology is proposed using a Poisson point process to estimate the timeline of earthquake and wind events, wherein the events are assumed to be independent in nature. The 20-story high-rise steel building with BRBs is designed according to the Japanese standard and analyzed using the finite element approach, considering nonlinearities in the structural elements and BRBs. The building is analyzed consecutively using the timeline of earthquakes and winds, and the results are compared with those under individual earthquakes and winds. In addition to the responses of the frame such as the floor displacement and acceleration, the damage of BRBs in terms of the damage index, the energy absorption, the plastic strain energy, and the maximum and cumulative ductility factor are evaluated. It is observed that the BRB's fatigue life under multi-hazard scenarios is a multi-criteria issue that requires more precise investigation. Moreover, the overall building's performance and BRB's cumulative damage induced by the sequence of events in the design life of the building is significantly larger than that under an individual event. steel structure; buckling-restrained brace; cumulative damage; multi-hazard; wind +
Footnote †: journal: Applied Sciences  
17 September 2021  
30 September 2021  
5 October 2021  
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**1. Introduction**  
The buckling-restrained brace (BRB) is an energy-absorbing device that consists of a detached steel core brace inside a steel restrainer infilled with concrete mortar. This unique combination enables the BRB to exhibit stable hysteresis behavior both in compression and tension. The BRB was originally invented in Japan, and the first practical application was reported by [PERSON] et al. in 1988 [1]. Since the first successful application of BRB for 10- and 15-story steel frame buildings in 1989, the device has gained popularity in seismically active regions around the world [2]. The excellent performance of BRB as an energy-absorbing device has been proved by many experimental tests [3, 4, 5, 6, 7, 8, 9, 10]. The use of BRB has become one of the efficient measures to minimize the effect of seismic loadings in low- to high-rise buildings [11, 12]. Moreover, the BRB is extensively employed to retrofit the existing buildings to increase the building strength and energy dissipation capacity [13, 14, 15, 16, 17]. The use of BRBs is common in Japan for high-rise buildings [18] to mitigate their performance since the high-rise buildings experience a large amplitude shaking due to the effect of resonance with the long period component of earthquake ground motions. Since Japan is a country that experiences frequent earthquakes and typhoons [19], the performance of the high-rise building with BRBs must be examined under the multi-hazardscenario of earthquakes and long-duration winds. Although the performance of BRBs in high-rise buildings under either earthquake and wind loads is extensively studied in Japan and worldwide, limited studies had been conducted to evaluate the cumulative damage of BRBs in the successful application of wind and earthquakes. It is because most of the seismic provisions and design guidelines specify the design method for the single event of earthquakes and winds [20]. Under the multi-hazard scenario, high-rise buildings are exposed to a series of high-cycle low-strength dynamic wind loads and low-cycle high-strength earthquake loads.