## 1 Introduction
This method has been adopted widely for seismic retrofitting of existing structures and for new designs intended to withstand seismic action, applicable to both engineered and heritage buildings. BRBs are energy-dissipating components that restrain elastic and plastic deformation, effectively controlling buckling. They dissipate vibration energy and reduce the structure's natural period via hysteretic behavior instead of relying on physical impacts. Key advantages of BRB systems over conventional bracing include (a) high energy dissipation, (b) superior ductility and symmetrical hysteretic responses, (c) adjustable energy dissipation through core tube modification, (d) resistance to residual buckling and minimal structural damage after severe loading, and (e) early warning of potential failure indicated by localized pinching in hysteresis loops [16; 17]. Tube-in-Tube braces consist of two concentric tubes: a main brace and an outer tube. The main brace contracts the inner tube. During seismic events, the outer tube prevents buckling by providing support, ensuring stabilization [18]. It resists forces on the structure and enhances lateral stability. The main tube handles tension and compression, increasing the brace's resistance. A key advantage of the Tube-in-Tube system is its compatibility with standard lateral frames and diagonal bracing, offering higher resistance values. The outer tubes can take various shapes for architectural design, providing benefits for diaphragm wall systems and accommodating significant construction variations. A significant number of researchers have focused on experimental studies evaluating the efficacy of BRB systems [19; 20; 21; 22; 23; 24; 25] and their potential failure mechanisms. This emphasis on experimental methods stems from their reliability in substantiating research outcomes in structural engineering and guiding design standards. Accumulating experimental data is crucial for developing and maintaining these standards, forming the basis of performance-based engineering and validating nonlinear response history analysis models. While numerical models can be backed by various experimental data types, small-scale structural tests offer the clearest validation. Recent investigations have provided significant insights in experimental studies. [PERSON] et al. [8] executed shake table experiments on a portal reinforced concrete frame with rubber cylinders to improve load-bearing capabilities, revealing that these braces enhanced seismic performance. [PERSON] et al. [26] conducted shake table tests on a concrete frame retrofitted with a brace beam, finding that it markedly increased stiffness and reduced lateral story drift. [PERSON] et al. [27] examined the seismic response of a poorly designed frame retrofitted with a novel brace system, concluding that it significantly lowered inter-story drift ratios and exhibited stable hysteretic behavior, thus improving older buildings' seismic responses in prone regions. [PERSON] et al. [28] performed quasi-static tests to investigate failure mechanisms of conventional braces, proposing a double-stage brace design that verified gradual failure instead of catastrophic. [PERSON] et al. [29] tested two reinforced concrete column piers--one with braces and one without--demonstrating that braces curtailed displacement and curvature by effectively dissipating seismic energy. [PERSON] and [PERSON]'s [30] testing program with Bidirectional Ductile Diaphragms showed a reliable hysteretic response when using V-configuration braces. Lastly, [PERSON] et al. [31] analyzed composite frames, finding that those with braces enhanced lateral resistance by up to 142% and had an initial stiffness at least 8.4 times greater. [PERSON] et al. [32] examined a replaceable coupling beam with hybrid energy dissipation devices, showing it effectively reduced inter-story drifts and mitigated damage to nearby elements.