## 3 Tube-in-Tube Buckling-Restrained Braces  
According to the post-earthquake reconnaissance reports [39; 40; 41; 42; 43; 44], most of the RC buildings collapsed or heavily damaged during the 2023 Kahramanmaras earthquakes mainly due to the global deficiencies, either stiffness or strength or both. Therefore, the RC frame included in the present study was designed to represent such stiffness and strength deficiencies simultaneously. Among all the external bracing systems in seismic retrofitting to overcome global deficiencies, BRBs are one of the most popular ones for their large stiffness, strength, and stable inelastic response [45]. Despite their large energy dissipation capacity, traditional concrete-encased BRBs are relatively heavy compared with their all-steel counterparts and costly, which prevents their use for ordinary buildings. To address the aforementioned issues related to conventional buckling bracings and existing traditional BRBs, [PERSON] et al. [46] proposed Tube-in-Tube (TnT) BRBs, which are a new type of all-steel BRB with no formal design standards. The outer tube (jacket) helps prevent local and overall buckling in the inner tube (core) while enhancing structural strength. With their high strength, stiffness, reliability, and energy dissipation capacity, TnT BRBs are seen as better alternatives to traditional concrete encased BRB designs. [PERSON] et al. [35] initially presented all-steel TnT BRBs as a solution to the challenges of diminished strength and stiffness resulting from buckling, which is frequently encountered with conventional buckling braces. Also, TnT BRBs are less labor-intensive due to their simplicity in fabrication and much lighter because of the absence of concrete encasing. Furthermore, unlike concrete-encased BRBs, TnT BRBs impose smaller demands on the surrounding members because of their small compression overstrength and cyclic hardening tendency, as reported in [PERSON] and [PERSON] [47]. The TnT BRB configuration utilized for the retrofitting of the substandard RC frame being analyzed is depicted in Figure 2. The load-bearing inner tube, characterized by its anticipated substantial inelastic axial deformation, is constructed using widely utilizedcircular or square hollow structural sections (HSS). Surrounding this load-bearing tube is the buckling restrainer, which consists of a two-segment outer tube that is fillet welded to a central stopper located in the mid-section. To facilitate fabrication and enable the load-bearing tube to laterally deform without imposing significant compressive loads on the outer tube, a small gap is incorporated between the load-bearing and the buckling restrainer tubes. The stopper, represented as a ring-shaped plate in the mid-section, is fillet welded to both the load-bearing and buckling restrainer tubes. This component serves to stabilize the two-segment outer tube while allowing the load-bearing inner tube to deform in an axial manner unrestrictedly. The connector plates, located at each end, function to transfer the axial load exerted on the load-bearing tube to the end connection assembly. These plates are interconnected via pretensioned high-strength bolts, ensuring a secure transfer of forces. Meanwhile, the end connection assembly comprises a reinforced gusset plate that links with the connector plate, adeptly transferring the axial loads from the load-bearing tube to the adjacent structural members, such as girders or columns, at both ends. This assembly is meticulously designed to restrict both in-plane and out-of-plane end rotations, which could potentially introduce global stability challenges. It is critical to note that such end rotations can lead to significant flexural demands, negatively affecting the overall performance of TnT braces, as supported by references [18; 48]. Figure 2: Tube-in-Tube Buckling-Restrained brace scheme used in the study.