###### Abstract
Based on the previous numerical and experimental studies conducted on TnT BRBs, it is recommended that the diameter-to-thickness ratio of the load-bearing tube (i.e., inner tube) should satisfy the highly ductile member requirement to avoid premature local buckling. In fact, the optimal parameters to achieve high energy dissipation capacity with a virtually symmetrical inelastic cyclic response are to use an outer tube thicker than the inner tube, providing a small gap amplitude to accommodate  
Figure 2: Schematic representation of a tube-in-tube buckling restrained brace. the lateral movement of the inner tube and reducing the friction force transfer between the two tubes as much as possible [24; 25; 26; 27]. In a study by [PERSON] and [PERSON] [24], the TnT BRB was conceptualized and subjected to tests involving a series of specimens under cyclic loads. Each specimen featured a steel brace, termed the inner tube, which was enveloped by a larger hollow steel section that functioned as the buckling restrainer, referred to as the outer tube. An intentional small annular gap, measuring just a few millimeters, was incorporated to allow the inner brace to bear nearly all the axial load while the outer tube provided essential lateral support to avert buckling phenomena. Throughout their experiments, [PERSON] and [PERSON] [24] analyzed various design parameters, including the size of the gap, the stiffness of the outer tube (determined by its thickness), and the structural details of the gusset plates. The braces underwent quasi-static reversed cyclic loading, conforming to an adapted AISC loading standard involving multiple cycles at escalating drift amplitudes. The findings indicated that the TnT BRBs produced stable and symmetrical hysteresis loops at story drift ratios reaching approximately 3.5% to 4.0%, with no observable degradation in strength (Figure 3). Conversely, traditional HSS tube braces subjected to the same testing conditions exhibited buckling and subsequent fracture at approximately 2% drift. The TnT mechanism effectively prolonged the brace's fracture endurance, enhancing the ductility capacity from an estimated 6 to 8 in conventional braces to a range of 14 to 20 in the BRBs. To assess the effect of the coefficient of friction (COF) between the contact surfaces of the inner and outer tubes on the hysteretic behavior, [PERSON] et al. [27] performed a series of cyclic simulations on TnT BRBs under identical loading protocols using various COFs between the contact surfaces where shear force transfer due to friction could be significant at high demand levels. Their results indicated that as the coefficient of friction reduced, cyclic stability and symmetry improved. This can be attributed to the reduction in the shear stress transferred from the outer tube to the inner tube, which seems to expedite the formation of local deformations. Researchers have investigated the potential of utilizing steel channels as buckling restrainers in addition to TnT BRBs, which presents a valuable solution for retrofitting applications. [PERSON] et al. [25] proposed the concept of channel-encased BCBs, wherein an existing brace is enveloped by two steel channel segments. These channels are fillet-welded together, often supplemented with intermittent \"stitch\" welds or plates, thereby creating a closed section that surrounds the brace. This design effectively forms a composite tube around the brace by using basic, easily sourced shapes. The spacing between the brace and  
Figure 3: Inelastic cyclic response of a typical TnT BRB (adapted from [PERSON] et al. [24]). the channels can be adjusted through small separators or variations in welding geometry, permitting the brace to slide until it makes contact with the channels under buckling conditions. [PERSON] et al. [26] evaluated channel-encased braces featuring circular HSS braces, as these are prevalent in contemporary construction practices.