## 1 Introduction  
Steel-braced frames can efficiently achieve a higher stiffness and strength compared to steel moment-resisting frames. However, the buckling of braces limits the ductility of steel-braced frames. To improve the ductility of braced frames, special concentrically braced frames, in which the brace members have lower slenderness and width-to-thickness ratios, or eccentrically braced frames, in which inelastic deformation is concentrated on the links, are used [1]. As an efficient alternative, innovative details of braced frames have been developed to achieve a more robust behavior, such as the utilization of a specially detailed mid-height gusset plate as an energy-dissipating fuse [2, 3]. Furthermore, a buckling-restrained brace (BRB) is used to obtain a more robust and ductile behavior of the concentrically braced frames. The BRB is a type of brace designed to ensure compressive strength and deformation capacity comparable to tensile strength and deformation capacity, thereby preventing premature buckling failure. Seismic-force-resisting systems that incorporate BRBs can behave in a ductile manner and dissipate energy stably by preventing a sudden decrease in the lateral resistance owing to buckling [4]. In a typical BRB, a restrainer is installed around the perimeter of the steel core to prevent buckling. Researchers have developed different types of restrainers and steel cores to prevent premature buckling efficiently [5, 6]. One of the simplest BRBs constitutes the combination of a plate-shaped steel core and a restrainer composed of a rectangular steel tube filled with mortar. In such a BRB, the thickness of the restrainer can be reduced to save the steel material that does not resist external loads directly, as long as sufficient flexural stiffness of the restrainer is retained. However, the reduced thickness makes the restrainer vulnerable to bulging because the steel core, which has undergone flexural deformation inside the restrainer, exerts an outward force on the mortar filler as the compressive force increases. Bulging is a typical failure mode of the BRB [7; 8]. [PERSON] et al. (2016) and [PERSON] et al. (2018) derived a formula for the capacity of a restrainer with a rectangular tube section resisting outward forces by applying the yield line theory based on the results of finite element analysis [9; 10]. [PERSON] et al. (2010), [PERSON] et al. (2012), and [PERSON] (2017) idealized the perimeter wall of a restrainer with a rectangular or circular tube section resisting outward forces as an effective beam [11; 12; 13]. They proposed a resistance capacity based on a plastic mechanism and compared the calculation results with cyclic loading test results. [PERSON] et al. (2019) proposed local bulging criteria for BRBs with a steel core of a triangular cross-section and compared the calculation results with experimental results [14]. [PERSON] et al. (2022) observed numerous bulging failure modes in a timber restrainer and derived the capacity of the timber restrainer [15]. [PERSON] et al. (2021, 2023) theoretically presented the bulging resistance of a circular restrainer based on an experiment and a finite element analysis of BRBs with a corrugated core bar [16; 17]. According to these studies, bulging can be prevented by increasing the thickness of the restrainer because most of the outward force resistance is proportional to the square of the restrainer thickness. However, in this process, more steel than that required to prevent only flexural buckling may be consumed. In this study, two types of enhancements are proposed for BRBs with a rectangular tube section restrainer to prevent bulging failure in the restrainer. First, bent steel plates, serving as inner restrainers, were inserted to increase the outward-force-resisting capacity against steel core deformation. Second, a gap was formed where the steel core contacted the mortar filler for the outward force to bypass the longitudinal center plane of the restrainer.