# A Study on the Effects of Vertical Mass Irregularity on Seismic Behavior of BRBFs and CBFs
## 1 Introduction
### Literature Review  
Conventional steel braces were initially mounted in steel frames to increase the seismic capacity [32]. [PERSON] et al. [33] reported a higher resistance to earthquake for BRBs compared to that of conventional braces. [PERSON] et al. [34], using a novel model, investigated the buckling response of conventional steel braces. Analyzing BRBFs by employing different gaps between core and external sheath, [PERSON] and [PERSON] [35] reported the significant effect of bending stiffness of all-steel BRBFs on their global buckling behavior. [PERSON] and [PERSON] [36] found all-steel BRBFs to protect structures under seismic loads within life safety levels by comparing their behavior for different gaps between core and steel casing with that of regular convergent cross bracings. According to [PERSON] et al. [37], the deformed BRB web can enhance resistance to out-of-plane buckling and raise buckling strength against high quake loads. In contrast to regular steel braces, a novel all-steel BRBF introduced by different researchers [38; 39; 40; 41], was found to increase the formability and energy absorbability at a high formability and maintain the performance of tall structures within their service life.  
Previous researches suggest that employing the techniques commonly used for regular structures cannot accurately obtain inelastic seismic response of irregular structures and its difference from that of regular structures [42; 43; 44]. Furthermore, different analytical methods for irregular structures compared to those applied to regular structures are provided by seismic codes [45]. The equivalent lateral force method is not applicable to analyzing irregular structures, although modal response spectrum analysis, linear response history analysis and nonlinear response history analysis are allowed owing to their use of higher mode effects.  
In 2015, [PERSON] and [PERSON] [46] explored the effects of far-field earthquakes on the seismic response of single degree of freedom systems considering soil-structure interactions. Numerous studies have also examined the responses of buildings to far-field earthquakes [46; 47; 48; 49; 50; 51]. [PERSON] and [PERSON] [52]assessed the accuracy of the improved modal pushover analysis for asymmetric plan structures. In addition, [PERSON] et al. [53] modified the multimodal pushover method, and [PERSON] et al. [54] appraised the precision of static nonlinear analysis using a tested reinforced concrete frame. [PERSON] et al. [55] studied the seismic behavior of special moment frames (SMFs) with special ductility undergoing near- and far-field earthquakes by considering different modes, including the effects of soil-structure interaction, permanent displacement (Fling step), and forward directivity in near-field earthquake records, as well as vertical component of near-field earthquakes. It was demonstrated that near-field earthquakes impose more damage on the structure than far-field earthquakes [56; 57; 58].  
Undoubtedly, the existence of vertical irregularities, opting for sort of braces, and the distance of the structure from the active fault, are three important and decisive factors in analyzing the seismic performance of the structures. Hence, in the present study, effects of the aforementioned factors have been evaluated simultaneously.