非滑移刚度理论下的空缆线形半解析算法

为设计阶段更简洁和准确地计算悬索桥空缆线形，提出了一种锚跨水平张力-预偏量-修正水平力迭代过程的非滑移刚度理论计算方法。基于分段悬链线理论，探讨了空缆线形计算存在的三种不同情况，并以此为计算思路。在任一锚跨水平张力作用下，考虑鞍座对空缆线形的影响，以各跨无应力索长不变与鞍座两侧的力或力矩平衡为准则，推导了各跨左右鞍槽接触段和悬空段的内力与线形平衡方程，以及迭代过程中待求参数之间的影响矩阵及修正方法，以右边塔索鞍处不动点里程坐标误差为收敛条件，采用了二分法迭代出理论的左锚跨水平张力，进而得到空缆状态下各索鞍的预偏量以及各跨索段内力与线形。通过算例比对，验证了本文方法的可靠性。结果表明，在成桥状态下结构参数已知的基础上，仅需求解左锚跨水平张力一个变量参数，即可得到各跨索股线形与内力以及鞍座预偏量。相比传统的滑移刚度理论方法，本文方法迭代过程方便简洁，易收敛且精度高，无需往复固定或释放一个鞍座约束进行迭代求解，提高了计算效率，适用于任意跨对称或非对称空缆线形的计算。

Semi-analytical algorithm of cable shape under non-slip stiffness theory

In order to calculate the unloaded cable shape of a suspension bridge more concisely and accurately in the design stage, a non-slip stiffness theoretical calculation method for the iterative process of horizontal tension-predeviation-corrected horizontal force of an anchor span is proposed.Based on the segmented catenary theory, three different situations of unloaded cable shape calculation are discussed, and the calculation ideas are on this basis.Under the horizontal tension of any anchor span, considering the influence of the saddle on the shape of the empty cable, the internal force and linear balance equations of the left and right saddle groove contact section and the suspended section of each span are derived under the condition that the unstressed cable length of each span is constant and the force or moment on both sides of the saddle is balanced.The influence matrix and correction formula between the parameters to be solved in the iterative process are also derived.Taking the coordinate error of the fixed-point mileage at the right tower saddle as the convergence condition, the dichotomy is used to update the theoretical horizontal tension of the left anchor span, and then the pre-deviation of each saddle and the internal force and linear displacement of each span cable segment under the condition of empty cable are obtained.The reliability of the method is verified by the comparison of examples.The results show that on the basis of the known structural parameters in the bridge state, only one variable parameter of the horizontal tension of the left anchor span is needed to obtain the cable strand alignment and internal force of each span and the saddle pre-bias.Compared with the traditional sliding stiffness theory method, the iterative process of this method is convenient and concise, easy to converge, and has high accuracy.It does not need to fix or release a saddle constraint repeatedly for iterative solution, which improves the calculation efficiency and is suitable for the design and calculation of symmetric or asymmetric cable of any span.