斜拉索悬链线构形的伸长量解析计算方法

Analytical method for elongation of stayed-cable with catenary configuration

针对斜拉索无应力索长和张拉时伸长量控制的需求,讨论了斜拉索悬链线构形的伸长量解析计算方法。采用斜拉索的力平衡条件,获得悬链线构形的几何方程,进而通过直接积分得到给定索力时索长和伸长量计算的解析表达;利用增量索力作用时的变形协调条件,获得增量索力作用下的伸长量解析表达。基于应变等效,讨论了基于悬链线构形的弹性模量等效,明确了基于悬链线构形的等效弹性模量可以弱化为基于抛物线构形的等效弹性模量。用某叠合/混合梁斜拉桥的实际斜拉索参数,分别用数值积分、简化公式,验证了给定索力时索长和伸长量解析表达式;用Nlabs有限元、等效弹性模量方法验证了增量索力作用下伸长量计算的解析表达式。研究表明:所提解析表达式能简单直接得到精确的斜拉索伸长量,为斜拉索无应力长度和斜拉索安装时的伸长量控制提供了理论和快捷方法。

In order to meet the requirements of unstressed length and elongation control for stay cable during its installation,the analytical method for calculating the elongation of the stay cable with catenary configuration is discussed. First,the geometric equation of the stay cable with catenary configuration is obtained by applying the force equilibrium condition to the stay cable,and the analytical expressions of the cable length and its elongation under a certain given cable tension are acquired by direct integration.Moreover,the analytical expressions of the cable elongation under varying cable tension are obtained by using the deformation coordination condition. Then,the equivalent elastic modulus for stay cable with catenary configuration is discussed based on strain equivalence. It is verified that the equivalent elastic modulus for the stay cable with catenary configuration can be simplified to the equivalent elastic modulus for the stay cable with parabolic configuration. Taking the real parameters of the stay cables of a certain cable-stayed bridge with composite/hybrid girder as the case study,the analytical expressions of stay cable length and its corresponding elongation under a given cable tension are verified by numerical integration and simplified formulas respectively. Furthermore,the analytical expressions for the elongation of stay cable with varying cable tension are verified by the Nlabs finite element and equivalent elastic modulus method.The results show that the proposed analytical expressions can simply and directly figure out the exact elongation of stay cable,which provide the theory and straight forward method for the unstressed length of stay cable and the elongation control of stay cable during its installation.