竖向集中力作用下水平悬链线构形和张力的计算及试验验证

悬链线理论提出以来，广泛应用于电线架设、桥梁悬索和海洋拖曳等领域。目前，悬链线理论应用中主要是考虑竖向向下荷载及水平荷载作用下的工况，对于竖向向上荷载这一工况的研究却没有。本文基于补充几何假设，使悬链线问题求解更简单。从水平悬链线受均布及竖向向上荷载这一工况出发，建立了竖向集中力和均布荷载共同作用下悬链线所满足的非线性方程组。采用半显示解法对其求解，获得了悬链线构形及线内水平张力随悬链线水平距离、集中力大小和作用位置不同的变化规律；对非线性方程组求导，证明了水平张力取得极小值的条件，并给出悬链线构形对称性所需满足的条件。为了证明理论的正确性，采用不锈钢圆环链条材料进行静力构形及张力测试。结果表明，当竖向向上集中力作用在悬链线中点且大小为悬链线均布荷载的一半时，线内水平张力取得极小值，集中力作用点与悬链线两端点处于同一水平线上，此时悬链线两端水平约束力最小，受力状态最优。

Horizontal catenary configuration and tension calculation subjected to a vertical concentrated force as well as test verification

The catenary theory has been widely used in the fields of wire and bridge suspension,ship towing and so on since it was put forward.At present,the study and application of catenary theory is mainly on working conditions under the action of vertical downward load and horizontal load while the research on the condition of vertical upward load is rare.This paper tries to simplify the catenary problems based on the supplementarity of geometry assumption.Firstly it starts from the condition of horizontal catenary under the uniform and vertical upward loading,and catenary nonlinear equations under the action of vertical and uniform loads were established.Secondly,the change rules among different catenary structures,the horizontal tension in the line with the variation of the horizontal distance,concentration force and the position of the catenary are determined by using half display method.Then the minimum value of the horizontal tension is found,and the necessary conditions on the symmetry of the catenary configuration are listed through the derivation of the nonlinear equations.In order to verify this theory,the paper uses ring chains of stainless steel to test static force configuration and its tension.The results showed that the horizontal binding force of both ends of catenary is smallest and its stress state is optimal on the condition that both vertical upward binding force is acts at the midpoint of catenary,and the catenary reaches a minimum when its magnitude is half of the uniform load,and its concentrated force point is at the same level as two ends of the catenary.