Computation methods of axial forces for main cables and short hangers of suspension bridges
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摘要: 为解决短吊杆轴力难以用频率法确定的问题, 提出了确定悬索桥主缆和短吊杆轴力的节点平衡法和比拟法。节点平衡法以吊点为分析对象建立以主缆轴力为未知量的超定平衡方程组, 从而获取主缆轴力的最小二乘解, 并进一步确定短吊杆轴力。比拟法基于长吊杆轴力与简支梁弯矩间关系, 建立主缆线形与长吊杆轴力的关系方程, 最终确定主缆的水平张力与短吊杆的轴力。以贵州南盘江悬索桥为例, 分别应用节点平衡法和比拟法得出主缆张力和吊杆轴力。计算结果表明: 2种方法的计算值与频率法实测值相近, 节点平衡法所得主缆张力误差为-4.3%(上游)和3.1%(下游), 比拟法所得主缆张力误差为-8.6%(上游)和-0.1%(下游); 2种方法所得长吊杆轴力最大误差约为10%, 上游吊杆轴力平均误差小于2%, 下游吊杆轴力平均误差约为9%。可见, 节点平衡法和比拟法是确定主缆和短吊杆轴力的有效方法。Abstract: To solve the problem that the axial forces of short hangers can not be measured by vibration method, nodal equilibrium method and analogy method were provided to estimate the axial forces of main cables and short hangers of suspension bridges. Nodal equilibrium method took the suspension points as analytical object to set up the over determined equilibrium equations in which the axial forces of main cables were unknown, the least squares solution of axial forces of main cables was obtained, and the axial forces of short hangers were determined. Analogy method analyzed the relationship between the axial forces of long hangers and the bending moment of equivalent beam, set up the relationship equations between the linetypes of main cables and the axial forces of long hangers to ultimately determine the horizontal tensions of main cables and the axial forces of short hangers. Guizhou Nanpan River Suspension Bridge was taken as an example, and the axial forces of main cables and hangers were estimated by using the two methods respectively. Computation result shows that calculation values by the two methods are close to the values measured by vibration method. The errors of axial forces of main cables by nodal equilibrium method are -4.3%(upstream)and 3.1%(downstream), and the errors by analogy method are -8.6%(upstream)and -0.1%(downstream). The maximum error of axial forces of long hangers by both methods is about 10%. The average errors of axial forces of upstream hangers are less than 2%, and the errors of downstream hangers are about 9%. So nodal equilibrium method and analogy method are effective to determine the axial forces of main cables and short hangers.
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表 1 中跨主缆吊点坐标
Table 1. Hanging point coordinates of main cable midspan
表 2 吊杆轴力测量结果
Table 2. Measurement results of hanger axial forces
表 3 边跨主缆轴力测量结果
Table 3. Measurement results of main cable axial forces in sidespans
表 4 主缆轴力对比
Table 4. Comparison of axial forces of main cables
表 5 部分吊杆轴力对比
Table 5. Comparison of axial forces of some hangers
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