Abstract Truss-confined buckling-restrained braces (TC-BRBs) are composed of conventional double steel tube BRBs and additional installation of external truss-confining systems. The truss-confining systems make TC-BRBs fulfil the need of the long-span bracing and enable economic and rational design. The previous experimental and numerical investigation of TC-BRBs suggested that the lower limit of the restraining ratio to ensure a stable cyclic behaviour was an empirical value of 3.0 for preliminary and conservative design. This paper aims to propose more rigorous design formulas for estimating the lower limit of the restraining ratio based on the numerical and theoretical analyses of typical TC-BRBs, triple- and quadruple-TC-BRBs (TTC- and QTC-BRBs). First, the formulas of the elastic buckling load of TC-BRBs are derived. Then, the load-carrying behaviour of TC-BRBs with the initial geometric imperfection is investigated with consideration of the most disadvantageous bending direction. The internal force variation of the external restraining members is discussed with increasing the restraining ratio, and it is found that the failure of TC-BRBs is governed by the compressive chord at the mid span. Furthermore, according to the criterion that the external restraining members do not fail before the core reaches the required axial displacement, the rigorous formulas for predicting the lower limit of the restraining ratio are derived. The formulas assure more rational and economic design of the load-carrying capacity of TC-BRBs.

中文翻译：

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桁架约束屈曲约束支撑承载机理：数值与理论分析

摘要 桁架约束屈曲约束支撑（TC-BRBs）由传统的双钢管BRBs和外部桁架约束系统组成。桁架约束系统使TC-BRBs满足大跨度支撑的需要，实现经济合理的设计。先前对 TC-BRB 的实验和数值研究表明，确保稳定循环行为的约束比的下限是初步和保守设计的经验值 3.0。本文旨在基于典型 TC-BRB、三重和四重 TC-BRB（TTC-和 QTC-BRB）的数值和理论分析，提出更严格的设计公式来估计约束比的下限。首先，推导了TC-BRBs弹性屈曲载荷的计算公式。然后，考虑到最不利的弯曲方向，研究了具有初始几何缺陷的 TC-BRB 的承载行为。讨论了外约束构件内力随约束比增加的变化，发现TC-BRBs的失效受跨中受压弦杆的控制。此外，根据外约束构件在芯部达到所需轴向位移之前不会失效的准则，推导出约束比下限的严格预测公式。该公式保证了TC-BRBs承载能力的更合理和经济的设计。讨论了外约束构件内力随约束比增加的变化，发现TC-BRBs的失效受跨中受压弦杆的控制。此外，根据外约束构件在芯部达到所需轴向位移之前不会失效的准则，推导出约束比下限的严格预测公式。该公式保证了TC-BRBs承载能力的更合理和经济的设计。讨论了外约束构件内力随约束比增加的变化，发现TC-BRBs的失效受跨中受压弦杆的控制。此外，根据外约束构件在芯部达到所需轴向位移之前不会失效的准则，推导出约束比下限的严格预测公式。该公式保证了TC-BRBs承载能力的更合理和经济的设计。根据外约束构件在芯部达到所需轴向位移前不会失效的准则，推导出约束比下限的严格预测公式。该公式保证了TC-BRBs承载能力的更合理和经济的设计。根据外约束构件在芯部达到所需轴向位移前不会失效的准则，推导出约束比下限的严格预测公式。该公式保证了TC-BRBs承载能力的更合理和经济的设计。