大跨径悬索桥索鞍处主缆长度计算方法

Calculation method for length of main cable at saddle in long-span suspension bridge

摘要:

为了充分考虑索鞍对主缆长度的影响,兼顾操作便捷性与计算准确性,提出大跨径悬索桥索鞍处主缆长度解析计算方法. 首先,根据主缆与索鞍的几何关系,推导了索鞍处主缆曲线修正算法；然后,利用牛顿-拉菲森迭代法,对所得二元非线性方程组进行求解；最后,选取常见的主索鞍与散索鞍两组算例,验证该方法的可靠性. 结果表明:相比于传统算法,减少了6个方程与6个初始输入参数,表达形式更加明确；仅需输入两个参数,且对参数初始值设置没有严格要求,均可达到快速收敛的效果,增强了其可操作性；迭代次数减少50%,计算时间不足传统算法的10%,大大提高了计算效率,且计算精度可满足工程要求. 所提出的算法可方便地应用于建设期间主缆曲线长度以及索鞍位置的确定,使大跨径悬索桥的施工控制更为精准,进而确保其成桥状态满足设计要求.

Abstract:

Taking into account the influence of saddle on the length of main cable and considering the convenience of operation as well as the calculation accuracy, an analytical calculation method for the length of main cable at the saddle of long-span suspension bridge was proposed. First, according to the geometric relationship between the main cable and the saddle, the main cable curve correction algorithm was derived. Then, the Newton-Raphson iterative method was used to solve the obtained binary nonlinear equations. Finally, the reliability of the method was verified using main cable saddle and loose cable saddle as examples. Results show that compared with traditional algorithm, six equations and six initial input parameters were reduced, which made the expression form clearer. Only two parameters were needed to be input and there was no strict requirement for the setting of the initial values of the parameters, which led to fast convergence and thus enhanced the operability. The number of iterations was reduced by 50%, and the calculation time was less than 10% of the traditional algorithm, which greatly improved the calculation efficiency and met the engineering requirements. The algorithm proposed in this paper can be easily applied to the determination of the length of main cable curve and the position of cable saddle during construction, which can make the construction control of the long-span suspension bridge more accurate so as to ensure that the state of the accomplished bridge meets the design requirements.