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摘要: 在预应力混凝土(PC)斜拉桥悬臂施工中, 为了减小索力及线形误差, 分析了误差原因及其控制现状, 提出了模型误差及悬浇效应误差的控制方法。结合三维实体等参元和板壳单元的优点, 构造了适用于复杂桥梁结构空间分析的实体退化单元, 建立了离散钢筋模型。根据挂篮牵索锚固点处的变形协调条件, 推导出牵索索力随混凝土浇筑的增量计算公式, 建立了悬浇过程中各工况下挂篮前端标高控制的计算公式。应用结果表明: 在悬浇施工过程, 牵索索力控制精度达到了3%, 成桥索力控制精度达到5%, 悬臂端标高误差控制在1 cm内, 因此, 提出的控制方法可实现PC斜拉桥悬浇过程各工况下索力及线形的准确预测。Abstract: During the cantilever-casting construction of prestressed concrete(PC) cable-stayed bridge, in order to reduce the errors of cable tension and line shape, the error cause and present situation of control means were analyzed, and the control methods of model error and cantilever-casting simulation error were discussed.With the combination of 3D isoparametric element and shell element, degenerated solid element was proposed for the spatial analysis of complex PC bridge, and discrete bar model was set up.According to the deformation compatibility condition of traction cable's anchorage, the increment of cable tension during casting concrete was computed, and the calculation formula of traveler's front level was educed.Application result indicates that the control precision of trailing cable tension is within 3%, the control precision of final cable tension is within 5%, and the error of traveler's front level is within 1 cm.Therefore, the cable tension and line shape of PC cable-stayed bridge under all construction conditions can be well predicted by the proposed method.
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表 1 牵索索力控制结果
Table 1. Control result of cable tension
工况 实测值/kN 预测值/kN 差值/ kN 空挂篮 0.0 0.0 0.0 第1次牵索 1 050.0 1 050.0 0.0 浇前一半混凝土 1 397.5 1 408.5 -11.0 第2次牵索 2 100.0 2 100.0 0.0 浇后一半混凝土 2 526.0 2 514.5 11.5 表 2 相对标高控制结果
Table 2. Control result of relative elevation
工况 实测值/m 预测值/m 差值/m 空挂篮 0.000 0.000 0.000 第1次牵索 0.118 0.123 -0.005 浇前一半混凝土 -0.012 -0.003 -0.009 第2次牵索 0.048 0.054 -0.006 浇后一半混凝土 -0.046 -0.044 -0.002 注: 相对标高是以立模位置为基准点。 表 3 索力比较
Table 3. Comparison of cable tensions
索号 实测值/kN 预测值/kN 相对误差/% 1 4 367.4 4 400.0 0.74 2 3 989.7 4 197.0 -4.94 3 3 631.5 3 731.8 -2.68 4 3 387.5 3 369.9 0.52 5 3 074.5 3 164.0 -2.80 6 2 925.9 2 993.1 -2.24 表 4 索力误差比较
Table 4. Comparison of cable tension errors
误差/% > 10 9~10 8~9 7~8 6~7 5~6 平面分析 4 3 4 12 10 17 本文分析 1 0 0 4 3 12 注: 表中数据为斜拉索的根数, 全桥共152根索。 -
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