## 1 Introduction  
Recent studies on the seismic retrofitting of reinforced concrete columns have placed a notable emphasis on the utilization of high-performance materials, including high-strength concrete and fiber-reinforced polymers (FRPs). Furthermore, there is a growing focus on the development of effective techniques for retrofitting existing structures. The introduction of advanced techniques, including rapid and cost-effective repairs of earthquake-damaged buildings, as well as numerical modeling and simulation techniques for more accurate assessment of a building's seismic performance, is also a trend in current research [1; 2; 3; 4; 5]. [PERSON] et al. [1] conducted experimental research on reinforcing concrete structures using FRPs. [PERSON] et al. [1] investigated the deformability of the specimens after reinforcement, with a view to enhancing the seismic performance of reinforced concrete beam-column joints. [PERSON] et al. [2] studied the seismic performance of corroded RC columns reinforced by textile-reinforced concrete. [PERSON] et al. [3] proposed a seismic reinforcement method using viscoelastic dampers to prevent shear deformation. [PERSON] et al. [4] fabricated a 1/5 scale model of an RC frame reinforced with RC infill walls with mega-braces (RCIWMB) and evaluated its seismic performance through shaking table tests. They compared the seismic performance by producing specimens with RCIWMB arranged vertically and intersected. [PERSON] et al. [5] proposed a design method for the seismic retrofit of reinforced concrete buildings using aluminum multi-stiffened shear panels as dampers, and its effectiveness has been validated using nonlinear response-history analysis. Seismic design has allowed inelastic deformation in structures, using hysteretic behavior to dissipate seismic energy. However, this leads to damage and permanent deformations in structures, resulting in high repair costs. As an alternative, recent seismic designs have implemented the use of structural fuses [5]. In the seismic design and the retrofitting of structures, considering structural fuses means sacrificing these members to disperse seismic energy while maintaining the performance of the structural elements. Structural fuses enter the inelastic region before other structural members, absorbing seismic energy and concentrating damage during earthquakes. After an earthquake, only these fuse elements need replacement, making repairs easier and more cost-effective. In the seismic retrofitting of reinforced concrete structures, structural fuses often use metallic materials for dampers or buckling-restrained braces (BRBs), with the main advantage being their quick repair. Consequently, research on the seismic retrofitting of reinforced concrete structures is focused on evaluating the dynamic behavior of structures with retrofitting members to assess whether they can function as structural fuses [6; 7; 8; 9; 10]. Structures with structural fuses involve complex parameters, requiring nonlinear time history analysis in the design. Therefore, studies on the analysis techniques of structural fuses are also prevalent. [PERSON] and [PERSON] [6] presented a simple and reliable design procedure for structures using BRBs as structural fuses. [PERSON] et al. [7] applied BRBs, commonly used as structural fuses, to a 2/3-scale model and conducted quasi-static tests to observe their effect on the seismic performance of a complete bridge. The experiments confirmed that adding structural fuses increased the system's strength and stiffness and effectively dissipated seismic energy. [PERSON] and [PERSON] [8] noted that, in moment-resisting frames (MRF), the beam span-depth ratio should be designed to allow sufficient length of plastic hinges at the beam ends. They highlighted the issue of over-designing the structure and foundation in the current design procedures for steel MRFs. To overcome this issue, they introduced a new shear structural fuse for MRFs.