基于图形法和二分法的斜拉桥拉索参数计算方法

A method for calculating the stay-cable parameters of cable-stayed bridges based on the graphic dichotomy algorithm

运用悬链线方程对拉索线形、梁端拉索切线斜率、索长等相关参量的表达式进行了详细推导。在求解拉索参数的计算过程中,首先需要假定梁端拉索切线斜率的初始取值区间,并进行迭代运算。然而为了避开任意假定区间带来的弊处,本次研究提出了一种名为图形法的新方法,这种方法可以描绘出拉索线形与梁端拉索切线斜率的函数图,且可从图中快速准确地找出有效的取值区间;接着将得到的初始区间结合编好的二分法程序,可以更加准确地求出拉索线形方程中的梁端切线斜率,并且也可进一步求出索长、塔端拉索切线斜率、塔端和梁端拉索张拉力等相关拉索参数。最后采用铜陵长江公路大桥作为工程背景,进行实际算例研究,采用图形法和二分法结合与迭代法相比,在计算梁端切线斜率时,可将误差减少4.62%,该方法的有效性得到了验证。

The static parameter expressions such as the shape equation of stay-cable,the nonlinear equation of the beam-end tangent slope and so on,are derived according to the catenary equation.In the process of calculating the stay-cable parameters,it is needed to assume the initial interval value of the beam-end cable tangent slope.However,in order to avoid the disadvantages of an arbitrary hypothetic interval,a graphic method is presented,which can draw the cable line and the tangent slope of the beam-end cable function diagram,from which the effective interval can be quickly obtained.Further,the beam-end tangent slope in the equation of the stay-cable shape is solved more accurately by utilizing the coded program of the dichotomy algorithm.And,based on the solved beam-end tangent slope,the stay-cable parameters of cable-stayed bridge,such as the cable length,the stay-cable slope of pylons-end tangent,beam-end and pylons-end cable tension are calculated.Finally,taking the Tongling Yangtze river highway bridge as an example,compared with the iterative method,combined the graph method with the dichotomy method can reduce the error by 4.62%when calculating the tangent slope of the beam end,the effectiveness of the proposed algorithm is verified.