Improved algorithm of cable force for one-time cable tensioning on steel tube arch ribs with segmental hoisting
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摘要: 为改善大跨钢管拱肋分段吊装扣索索力常用算法迭代效率低、计算时耗长, 且忽略了温变影响等不足, 建立了可考虑温变影响和提高计算效率的改进算法; 基于材料力学和几何学相关知识, 推导了吊装过程中拱肋位移变化与温变的理论关系, 并在计入温变引起索长和拱肋位移改变的情况下, 推导出扣索索力变化与温变的理论关系; 基于扣索一次张拉法和ANSYS零阶优化法, 开发了考虑温变影响且在迭代子步中对程序自动搜索实施宏观调控的扣索索力计算程序; 运用改进算法对某主跨300 m钢管混凝土拱桥开展了分段吊装施工控制分析。分析结果表明: 推导的理论公式和有限元分析结果的变化规律一致, 拱肋位移变化的最大相对误差为11%, 索力变化的最大相对误差为18%, 均能满足工程精度要求; 与原算法相比, 采用改进算法的迭代次数由26次缩减到17次, 迭代效率提高了35%, 计算索力与实测索力的最大偏差由276 kN减小到100 kN; 拱肋松索成拱位移理论值与实测值的最大偏差为7 mm, 成拱线形正常; 建立的改进算法可实现扣索一次张拉, 提高迭代效率和计算精度, 运用改进算法控制大跨钢管拱肋吊装施工可使拱肋松索成拱线形满足设计要求。Abstract: To improve the defects of low iteration efficiency, long calculation time and neglecting the influence of temperature change of common calculation methods for cable force of long-span steel tube arch ribs during the segmental hoisting, an improved algorithm considering the influence of temperature change and improving the calculation efficiency was established. Based on the knowledge of material mechanics and geometry, the theoretical relationship between the changes of arch rib displacement and temperature during the hoisting was deduced, and the theoretical relationship between the changes of cable force and temperature was deduced considering the changes of cable length and arch rib displacement caused by the temperature change. Based on the one-time cable tensioning method and the zero order optimization method in ANSYS, a calculation program of cable force was developed considering the influence of temperature change and implementing the macro-control on the automatic search in the iteration sub step. The construction control analysis of segmental hoisting for a concrete filled steel tube arch bridge with a main span of 300 m was carried out with the improved algorithm. Analysis result shows that the results of derived theoretical formula are consistent with the change rules of finite element analysis results. The maximum relative error of displacement change of arch rib is 11%, and the maximum relative error of cable force change is 18%, both can meet the engineering accuracy requirements. Comparing with the original algorithm, the iteration number reduces from 26 to 17, the iteration efficiency increases by 35%, and the maximum deviation of cable force between the calculated and measured values reduces from 276 kN to 100 kN. The maximum deviation of arch rib displacement between the theoretical and the measured values is 7 mm after loosening cables and arched, and the arched alignment is normal. The established improved algorithm can realize the one-time cable tensioning and improve the iteration efficiency and calculation accuracy. The arch rib alignment after loosening cables and arched can meet the design requirements when using the improved algorithm to control the hoisting construction of long span steel tube arch rib.
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图 11 拱肋松索成拱后的竖向变形
Figure 11. Arch rib vertical deformations after loosening cables and arched
表 1 拱肋各节段扣索体系几何参数
Table 1. Geometric parameters of cable system for each segment of arch rib
索号 1# 2# 3# 4# 5# 6# 7# 8# 9# 10# 11# 12# Lm/m 49.09 49.85 50.61 51.37 52.13 52.89 53.65 54.41 55.18 56.85 57.14 57.52 L1/m 44.88 51.07 57.90 67.03 75.96 85.31 94.92 104.69 119.47 134.67 149.58 159.54 Ln/m 17.23 40.69 52.01 64.46 75.31 85.98 96.49 106.60 122.22 137.39 152.45 164.25 α/(°) 35.94 60.86 69.40 76.34 80.58 83.59 85.72 87.20 88.74 89.14 89.60 89.62 φ/(°) 65.87 67.84 68.72 69.70 70.55 71.36 72.16 73.18 74.07 75.31 76.32 75.22 A/cm2 6.95 9.73 9.73 8.34 8.34 9.73 9.73 8.34 11.12 18.07 20.85 27.80 
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表 2 节段吊装预抬量
Table 2. Pre-cambers of segmental hoisting
mm 扣索编号 2# 3# 4# 5# 6# 7# 8# 9# 10# 11# 12# 13# 贵阳岸上游 2.56 -0.68 -0.25 -3.76 -2.13 -7.47 -2.75 -14.26 -0.07 -6.07 13.65 2.89 贵阳岸下游 2.59 -0.82 0.05 -4.16 -1.17 -8.20 -2.56 -14.93 -11.44 -7.12 17.52 2.91 遵义岸下游 1.94 -0.50 0.82 -2.77 -1.14 -5.09 -0.89 -8.84 1.87 -11.60 13.58 12.74 遵义岸上游 1.92 -0.62 0.71 -2.87 -0.60 -5.34 -1.02 -9.34 -5.17 -9.01 11.86 19.86
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