悬索桥主缆找形及索鞍设计位置闭合同步解析算法

A Closure Synchronous Analytical Algorithm for Main Cable Shape Finding and Cable Saddle Design Position of Suspension Bridge

悬索桥主缆找形及索鞍设计位置是悬索桥设计阶段主要设计参数。然而,由于2类计算不能同步进行的问题,及现有文献研究关于散索鞍设计位置计算不考虑索鞍弯矩平衡而存在计算不闭合的问题,为此提出闭合同步解析算法。根据悬链线方程理论及闭合条件,建立了主缆找形解析方程组。根据索鞍几何关系及变形协调关系,建立了索鞍设计位置解析方程组。基于散索鞍力矩平衡关系建立了平衡方程组,通过求解联立的26维非线性方程组,实现了成桥状态主缆找形及索鞍设计位置闭合同步计算。为验证计算方法的可靠性,将计算结果与分段悬链线理论计算值和有限元软件计算值进行了比较分析。结果表明:成桥状态主缆线形计算值与分段悬链线理论计算值及有限元值较吻合,计算吊杆长度比分段悬链线理论计算值及有限元值偏短,相对误差值控制在1.0 mm以内;成桥状态主缆无应力长度计算值与分段悬链线理论计算值及有限元值较为吻合,中跨主缆无应力长度误差最大,分别为2.4 cm和0.8 cm,误差率在1/15 000范围内;成桥状态主缆在索鞍切点坐标与索鞍设计位置计算值与分段悬链线理论计算值误差控制在2.0 cm以内。3种计算方法结果精度吻合度较高,验证了算法的高效性及可靠性,算法可推广到悬索桥设计计算理论。

The main cable shape finding and the cable saddle design position of suspension bridge are the main design parameters in the design stage of suspension bridges.However,due to the problem that the 2 kinds of calculations cannot be carried out simultaneously,and the existing literature studies on the calculations of the design position of loose cable saddle have not considered the balance of cable saddle bending moment,which results in the unclosed calculations.For this reason,a closure synchronous analytical algorithm is put forward.According to the theory of catenary equation and the closure condition,the analytical equations of main cable shape finding are established.According to the geometric relationship and deformation coordination relationship of the cable saddle,the analytical equations of the cable saddle design position are established.Based on the equilibrium relationship of loose cable saddle moment,a set of equilibrium equations is established,and the closure synchronous calculation of main cable shape finding and cable saddle design position of completed bridge is realized by solving simultaneous 26-dimensional nonlinear equations.In order to verify the reliability of the calculation method,the calculation result is compared and analyzed with those calculated by segmental catenary theory and finite element software.The result shows that(1)the calculated values of the main cable shape finding of completed bridge closely meet those calculated by segmental catenary theory and finite element method,and the calculated length of suspender is shorter than those calculated by segmental catenary theory and finite element method,and the relative error is controlled within 1.0 mm;(2)the calculated values of the stress-free length of the main cable of completed bridge is in accordance with those calculated by segmental catenary theory and finite element method,and the errors of the stress-free length of the mid-span main cable are the largest,which are of 2.4 cm and 0.8 cm respectively,and the error rate is within the range of 1/15000;(3)the errors between the calculated values of the tangent point coordinate and the design position of the cable saddle of the main cable of the completed bridge and the calculated values by the segmental catenary theory are controlled within 2.0 cm.The results of the 3 calculation method are in good line with each other,which verified the efficiency and reliability of the algorithm,and the algorithm can be extended to the design and calculation theories of suspension bridges.