This paper explores the stiffness requirements for bracing components used in systems of parallel compression members or sub-assemblages. While rudimentary closed form equations are available to compute the threshold brace stiffness for single column systems, determining the stiffness of bracing components in multi-member systems is more complex. With the goal of developing useful multi-member stiffness models, the presented formulation is based on an equilibrium analysis of a single arbitrary column within a braced n-member system of interest. The resulting recursive relationship associated with tie-brace deformation is expanded, together with the brace-to-column shear connections and boundary conditions representing the anchor bracing, to generate a system of brace stiffness equations. Reformulating the equations as an eigenvalue problem, the minimum eigenvalue is the basis for subsequent equations derived to compute the required tie-brace stiffness in terms of the number of parallel members, and the stiffness of the shear connectors and the components of the system anchorage. Two approximations of the theoretically exact solution are also developed, providing useful alternatives for estimating system bracing requirements. Error analysis indicates that both approximate expressions sufficiently determine threshold bracing stiffness for structural systems with multiple parallel members with one or more brace points. An illustrative example is presented to demonstrate the use of the approximate expressions, and subsequent results are compared with both the derived theoretical solutions and results from finite element analyses.

本文探讨了平行受压构件或子组件系统中使用的支撑组件的刚度要求。虽然基本的封闭形式方程可用于计算单柱系统的阈值支撑刚度，但确定多杆系统中支撑组件的刚度更为复杂。为了开发有用的多构件刚度模型，所提出的公式基于支撑n内单个任意柱的平衡分析- 感兴趣的会员系统。与拉杆变形相关的递归关系被扩展，连同支撑到柱的剪切连接和代表锚杆支撑的边界条件，以生成支撑刚度方程系统。将方程重新表述为特征值问题，最小特征值是后续方程的基础，用于计算根据平行构件数量以及抗剪连接件和系统锚固部件的刚度计算所需拉杆刚度。还开发了理论上精确解的两个近似值，为估计系统支撑要求提供了有用的替代方法。误差分析表明，对于具有一个或多个支撑点的多个平行构件的结构系统，这两种近似表达式都足以确定阈值支撑刚度。提供了一个说明性示例来演示近似表达式的使用，并将随后的结果与导出的理论解决方案和有限元分析的结果进行比较。