拉索线形参数的解析解研究

Study on Analytical Solution of Cable Shape Parameters

为确定斜拉桥拉索的精确无应力索长、等效弹性模量、拉索在梁端和塔端的锚固角度及拉索的垂度等参数,需要先精确地确定拉索的线形方程,但是传统的计算方法或精度不足,或计算繁琐。为了满足工程应用及学术研究的要求,确定了一种计算简便且精度较高的拉索线形计算公式。通过利用自重作用下拉索上任意一微段的静力平衡条件,构造出拉索线形相关的微分方程。以梁端锚点和塔端锚点的坐标作为微分方程的边界条件,采用通用数学计算软件Maple求解,得到了拉索的理论线形公式。以此为基础,进一步推导出拉索的曲线索长、无应力索长、等效弹性模量、锚固角度以及拉索垂度等参数。使用推导所得的理论公式以及Ernst公式分别计算出某斜拉桥拉索的无应力索长、等效弹性模量等关键参数,并将计算结果进行对比。结果表明,使用Ernst公式计算得出的无应力索长较实际偏长,而利用本研究计算方法得到的无应力索长等计算结果则相对准确。从而证明了本研究推导出的线形理论公式的准确性,减少了近似计算带来的误差,为大跨度斜拉桥的精确设计和施工提供了理论支撑,也为相关研究提供一定的参考。

In order to determine the precise unstressed cable length,equivalent elastic modulus,anchoring angles of the cables at the beam end and pylon end,and the sag of the cables,the equation of cable shape needs to be accurately determined at first,however,traditional calculation methods have either insufficient precision or complicated calculations.For the sake of meeting the requirements of engineering applications and academic researches,a calculation formula of cable shape with simple calculation and high accuracy is determined.The static equilibrium condition of any micro segment on the cable under the action of self-weight is adopted to construct a related differential equation of cable shape.Taking the coordinates of the beam end anchor point and the pylon end anchor point as the boundary conditions of the differential equation,the theoretical formula of the cable shape is obtained by using the general mathematical calculation software Maple.On this basis,the parameters such as deflection of cable length,unstressed cable length,equivalent elastic modulus,anchor angle and sag of the stay cable are further derived.The key parameters such as unstressed cable length and equivalent elastic modulus of a cable-stayed bridge are calculated by using the derived theoretical formula and the Ernst equation and then compared.The result shows that(1)the unstressed cable length calculated by the Ernst equation is longer than the actual one,while the unstressed cable length obtained by the proposed calculation method is relatively accurate.This proves the accuracy of the derived theoretical formula of cable shape,it reduces the error caused by approximate calculation and provide theoretical support for the accurate design and construction of long-span cable-stayed bridges,and also provides a certain reference for related research.