Abstract This paper proposes a theoretical solution for multi-span continuous sliding cable structures, which were usually analyzed by numerical simulations. Firstly, the analytical equation for the unstressed length of single-span cable based on the undeformed configuration is derived, in which the tension forces at the ends can be accurately calculated. Then, according to the tension balance condition at sliding joints and the assumption of invariant total unstressed cable length (ITUL method), multivariate transcendental equations for the sliding analysis of multi-span cable structures with and without considering friction are established and solved by multiple Newton-Raphson iterations. Moreover, a theoretical method based on the assumption of invariant total cable length (ITL method) is also proposed and the applicability of the ITL method is investigated. Finally, four typical examples are analyzed by the ITUL method, and the accuracy of the ITL method as well as some existing numerical simulations is evaluated. The result shows that the ITUL method proposed in this paper is more accurate and reliable than the ITL method. The ITUL method can provide a theoretical basis for the design and analysis of multi-span sliding cable structures.

中文翻译：

---

考虑滑动的多跨连续索结构的理论解

摘要 本文提出了多跨连续滑动索结构的理论解决方案，通常通过数值模拟进行分析。首先，推导了基于未变形构型的单跨索无应力长度解析方程，可以准确计算端部拉力。然后，根据滑动节点处的张力平衡条件和无应力总索长不变的假设（ITUL法），建立了考虑摩擦力和不考虑摩擦力的多跨索结构滑动分析的多元超越方程，并采用多元牛顿法求解。 -Raphson 迭代。而且，提出了一种基于电缆总长不变假设的理论方法（ITL方法），并研究了ITL方法的适用性。最后，通过ITUL方法对4个典型实例进行了分析，并对ITL方法的准确性以及现有的一些数值模拟进行了评价。结果表明，本文提出的 ITUL 方法比 ITL 方法更准确可靠。ITUL方法可为多跨滑索结构的设计与分析提供理论依据。