Impacts of initial internal force and geometric nonlinearity of suspension bridge on bridge-rail interaction
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摘要: 依据梁轨相互作用原理, 提出了基于悬索桥成桥变形状态重构道床纵向阻力位移-力曲线的方法, 并从存在初始位移的5×32 m简支梁桥上无缝线路钢轨受力和变形两方面验证了重构方法的可行性; 结合多单元建模方法与U.L.列式法, 建立了考虑悬索桥初始内力和几何非线性的线-梁-索-缆-塔空间计算模型, 以某(2×84+1 092+2×84) m大跨悬索桥为例, 对比分析了不同工况下悬索桥初始内力与几何非线性对梁轨相互作用的影响。分析结果表明: 提出的道床纵向阻力重构方法能够避免桥梁初始变形对梁轨相互作用的影响, 使悬索桥上无缝线路计算模型能考虑初始内力的影响; 主缆垂度效应对各工况下梁轨相互作用的影响不足1%, 计算中可忽略该因素; 悬索桥初始内力主要影响挠曲、制动及断轨工况, 可使挠曲力、制动力及断缝值分别降低22.4%、12.7%和9.3%;大变形效应不仅可以改变挠曲力分布规律, 还可大幅减小断缝值, 降幅达22.4%;建议悬索桥上无缝线路在挠曲、制动及断轨工况下应考虑初始内力与大变形效应的影响, 伸缩工况下可将悬索桥简化为同等跨度的跨中纵向约束、梁端自由的连续梁桥进行计算; 建立的计算模型可为悬索桥上无缝线路设计提供精确的仿真结果。Abstract: Based on the theory of bridge-rail interaction, an approach to reconstruct the displacement-force curve of ballast longitudinal resistance was put forward according to the deformation of suspension bridge under the completed bridge state. A feasibility study on the reconstructing approach was conducted via two aspects of the force and deformation of continuous welded rail(CWR) on a 5×32 m simply supported beam bridge with initial deformation. With the multi-element modelling method and the U.L. formulation method, a rail-girder-hanger-cable-pylon spatial calculation model was established considering the initial internal force and geometric nonlinearity of suspension bridge. Taking a(2×84+1 092+2×84) m long-span suspension bridge as an example, the impacts of initial internal force and geometric nonlinearity of suspension bridge on the bridge-rail interaction under different working conditions were comparatively analyzed. Analysis result shows that the approach put forward to reconstruct the ballast longitudinal resistance can avoid the impact of initial deformation of bridge on the bridge-rail interaction, and make it possible to consider the effect of initial internal force on the bridge-rail interaction. The impact of main cable sag effect on the bridge-rail interaction is less than 1% under each working condition, so the factor can be neglected. The initial internal force of suspension bridge plays an important role under the bending, braking and rail breaking conditions. It can reduce the bending force, braking force and rail broken gap by 22.4%, 12.7% and 9.3%, respectively. The large displacement effect can not only change the distribution law of bending force, but also can significantly reduce the rail broken gap by 22.4%. It is suggested to consider the initial internal force and large displacement effect of suspension bridge under the bending, braking and rail breaking conditions of CWR on suspension bridges. The suspension bridge can be simplified as a continuous beam bridge with a longitudinal constraint at the mid-span and expandable beam ends at both sides under the expansion and contraction condition. The established calculation model can provide accurate simulation results for the design of CWR on suspension bridges.
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图 4 线-梁-索-缆-塔空间计算模型
Figure 4. Rail-girder-hanger-cable-pylon spatial calculation model
表 1 恒载结果
Table 1. Results of dead loads
拉力类别 主缆拉力 吊索平均拉力 最大 最小 设计值/kN 730 513.0 668 219.0 5 501.5 仿真值/kN 696 727.1 638 347.1 5 350.5 相对误差/% 4.6 4.5 2.7 
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表 2 分析状态
Table 2. Analysis states
工况编号 状态介绍 FCD 考虑初始内力、主缆垂度效应及大变形效应 CD 考虑主缆垂度效应及大变形效应 D 仅考虑大变形效应 N 按线性理论计算
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表 3 断轨及伸缩工况结果
Table 3. Results of rail breaking condition and expansion and contraction condition
对比项目 伸缩工况(降温) FCD CD D N 相对伸缩工况左侧位移/mm 17.5 35.8 35.8 76.7 钢轨纵向力峰值/kN 左侧梁缝 2 311.7 2 233.2 2 137.4 2 137.4 1 877.0 右侧梁缝 2 314.6 2 485.0 2 577.3 2 577.3 2 775.6
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