Shape Analysis of Main Cable of Single Tower Suspension Bridge with Unilateral Spatial Cable Plane and Curved Beam
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摘要:
目前空间索面悬索桥主缆成桥线形分析方法需要进行复杂的主缆微分方程求解，具有约束方程形式复杂、迭代收敛性受初值影响大等不足. 为解决主缆线形求解过程收敛性问题，本文借鉴等代梁法思路，推导得到外荷载与主缆线形的几何关联方程，并进一步构造出求解空间主缆线形的两阶段分析方法：在粗算阶段，通过解耦处理将初值要求降到最低，得到“具有足够精度且确保收敛”的结果，作为精算阶段初值；在精算阶段，采用迭代计算得到空间主缆线形精确解. 通过人行悬索桥算例验证两阶段分析方法的可行性和有效性，并使用有限元软件验证计算成果精度. 研究成果表明：本文所提出的方法对初值要求低，无需专门构造初值，迭代循环剔除了变形相容条件及无应力长度计算，求解效率更高，并且能快速收敛得到主缆线形精确解，适用于单边空间索面曲梁独塔悬索桥主缆成桥线形分析.
Abstract:The current analysis method for the main cable shape of a suspension bridge with a spatial cable plane involves solving complex differential equations for the main cable. However, this approach has certain drawbacks, such as the complicated form of constraint equations and the significant influence of initial values on iterative convergence. To address these issues and improve convergence in determining the main cable shape, the equivalent beam method was used, and geometric correlation equations between external loads and the main cable shape were derived. Subsequently, a two-stage analysis method was developed to solve the spatial main cable shape: During the rough calculation stage, decoupling processing minimized initial value requirements while obtaining accurate results with sufficient convergence. These results were then used as initial values in the precise calculation stage to iteratively calculate an exact solution for the spatial main cable shape. The feasibility and effectiveness of this two-stage analysis method were demonstrated through an example involving a pedestrian suspension bridge, and finite element software was used to verify the accuracy of calculation results. The research results demonstrate that the proposed method exhibits lower requirements for initial values and does not require the setting of initial values. The iterative process eliminates deformation compatibility conditions and stress-free length calculation, resulting in enhanced solving efficiency and rapid convergence towards obtaining an accurate solution for the main cable shape. This approach is suitable for analyzing the main cable shape of a single tower suspension bridge with a unilateral spatial cable plane.
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图 3 几何关联迭代法求解主缆线形流程
Figure 3. Flowchart of solving main cable shape using geometric correlation iteration method
表 1 精算阶段迭代计算情况
Table 1. Calculation iteration in precise calculation stage
轮次 坐标偏差
组合值/mm吊杆 x 轴向
分力差值/kN吊杆 y 轴向
分力差值/kN1 62.0 0.0197 1.1095 2 1.0 0.0194 1.1095 3 0.1 0 0.0935 4 7.1×10−3 9.7000×10−8 0.0263 5 1.6×10−3 2.6000×10−8 0.0073 
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