# A Study on the Effects of Vertical Mass Irregularity on Seismic Behavior of BRBFs and CBFs
## 1 Introduction  
Buckling restrained braces (BRBs) are seismic elements that comprise an axially yielding core and an axially decoupled restraining mechanism, which suppress the overall buckling. BRBs generally comprise of a mortar-filled steel section that encloses a yielding core wrapped in a thin debonding layer or gap between the core and mortar or all-steel restrainer. As a low-friction interface, this layer limits the axial load transferred to the restrainer in BRBs through accommodating the core lateral expansion caused by the Poisson impact [1]. Given the significant energy dissipation capacity of BRBs compared to that of other completely ductile systems, properly designed BRBs could serve as hysteretic dampers with adequate fatigue capacity for safely withstanding earthquakes of different magnitudes without suffering noticeable damage [1]. In 2017, [PERSON] and [PERSON] proposed the main criteria for the modern design of BRBs and discussed their applications in high-rise buildings [2]. Numerous seismic resistant members employed to decrease the probability of structural collapse during earthquakes include concrete-filled steel tubes, shear walls, braces and structures confined with high-strength concrete [3; 4; 5; 6; 7; 8; 9]. Given their significantly higher seismic performance compared to that of conventional braced frames (CBFs), buckling-restrained braced frames (BRBFs) are growingly used today as efficient seismic load resistant frames in regions with high seismic hazard levels. The main difference between these two types of frames lies in the free bucking characteristic of BRBFs [10; 11]. Steel BRBFs were also found to significantly increase the energy dissipation capacity, ductility, and hysteretic stability of structures [12]. The seismic performance of buildings can be improved by increasing post-yield energy dissipation and elastic stiffness using BRBFs in their design [13]. Many experimental, numerical, and analytical studies have investigated the incorporation of BRBFs as dampers into the outrigger system [14; 15; 16; 17; 18; 19; 20; 21; 22]. [PERSON] et al. [21] recommended using BRBs as diagonal web members in steel outrigger trusses and found this outrigger configuration to significantly dissipate energy in rare earthquakes. Torsional and mass irregularity and weak story are among the factors that may result in inaccurate prediction of seismic response of irregular structures. Heavier stories need larger and heavier structural elements, which result in unavoidable stiffness and strength irregularity. Depending on the location of irregularity, appropriate structural models and analytical methods should be used to examine its effects [22]. According to the Iranian code of practice for seismic resistant design of buildings [23], building irregularities involve both height and plan. Vertical irregularities caused by changes in the dynamic properties of structures along their height, e.g., strength, stiffness, and mass, were referred in literature as nongeometric irregularities [24]. A large body of literature is also devoted to the impact of vertical irregularities on the seismic performance of structures [25; 26; 27; 28; 29]. Because of the existence of aesthetic consideration and city regulation, irregular configurations, in plan and elevation of buildings, are inevitable. However, these buildings may have to withstand large earthquakes in the future; therefore, their behavior, when subjected to earthquakes, needs to be evaluated. It is believed that vertical irregularities are one of the important causes of structure failures under seismic load. In the past earthquakes, majority of the collapsed structures had irregular distribution of mass. Excess mass might cause rapid increase in lateral inertia forces, ductility reduction in column, and increase of collapse tendency because of P-delta effects [30]. It is worthwhile to note that large structures or high-rise buildings were more affected due to the long duration and narrow band nature of far-field excitation [31].