## 6 Conclusions  
In this study, two types of innovative enhancements are proposed to protect buckling-restrained braces from bulging failure of the restrainer, and they are validated experimentally. The first approach involves adding inner restrainers composed of a bent steel plate, and the other approach is the use of a partially thickened unbonding material for the outward force to bypass the centerline of the cross-section. Cyclic loading tests were performed to investigate the behavioral characteristics of the buckling-restrained braces with one or both types of enhancements, and the effects of the enhancements were evaluated in terms of the strength and deformation capacity. The experimental results and findings are summarized as follows:  
1. The inner restrainer is more efficient for BRBs with relatively thin outer restrainers. For an outer restrainer of 6 mm thickness, the compressive strength increases by 20%, the maximum deformation increases by 8-20%, and the cumulative deformation increases by 25% upon inserting the inner restrainer. However, for an outer restrainer of 9 mm thickness, the compressive strength increases by only 10%, and there is no significant improvement in the maximum and cumulative deformations. The effect on the tensile strength is minimal.
2. The outward force from the steel core increases in correspondence with the resistance enhanced by the inner restrainer, accompanied by an increase in the compressive force in the steel core. Thus, the compression strength adjustment factor increases to the range of 1.26-1.5 and exceeds the acceptable threshold depending on the applicable  
Figure 16: Comparison of bent steel plate in R-T9S2 at different sections: (**a**) A-A’; (**b**) B-B’.  
Figure 17: Deformed shape and buckling wavelength of steel core in R-T9S2 (Numbers are half wavelength in the unit of mm).  
standard. Therefore, efforts are required to improve the proposed inner restrainer to alleviate the compression-hardening effect.
3. Even when the inner restrainer is installed, bulging failure eventually occurs. Bulging failure most often occurs at the location where the inner restrainer is terminated, and, accordingly, a strengthening effect is hard to achieve.
4. An analytical formula for estimating the outward-force-resisting capacity of the inner restrainer was proposed based on the yield-line theory for the flange element and the inelastic shear deformation of the web element. The proposed theoretical outward-force-resisting capacity conservatively predicts the demand-to-capacity ratio for most of the strengthened specimens. An unconservative prediction for the two specimens with thicker outer and inner restrainers is inferred to be caused by the location of the bulging failure close to the end of the inner restrainer.
5. Upon observing the cross-section of a strengthened specimen, it is found that cracks do not appear in the mortar filler where bulging failure does not occur, implying the effectiveness of the proposed inner restrainer. However, it is necessary to improve the details such that the inner restrainer is sufficiently extended or the steel core is stiffened at the vulnerable location.
6. The effective buckling wavelength of the steel core cut from the specimen is lower than the value predicted in previous studies by approximately 50%. Shorter wavelengths result in a higher outward force from the steel core. Therefore, in-depth research in this respect is necessary in the future.  
Conceptualization, J.-H.P.; methodology, J.-H.P.; validation, B.-H.K.; formal analysis, B.-H.K.; investigation, B.-H.K.; writing--original draft preparation, S.-J.A.; writing--review and editing S.-J.A.; supervision, J.-H.P. All authors have read and agreed to the published version of the manuscript.  
This work is supported by the Korea Agency for Infrastructure Technology Advancement (KAIA) grant funded by the Ministry of Land, Infrastructure and Transport (Grant RS-2021-KA163162).  
Not applicable.  
The authors declare no conflict of interest.