Static Behavior and Key Influencing Factors of Double-Cable Suspension Bridge
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摘要: 双缆悬索桥体系是一种适用于大跨度多塔悬索桥的结构体系，为了对该类悬索桥体系的受力特性开展深入研究，基于有限元方法对其静力特性以及关键设计参数的影响效应进行对比分析. 首先以一座典型的单缆多塔悬索桥为参照，选定双缆多塔悬索桥的关键设计参数，建立两类多塔悬索桥的有限元模型；其次基于所建立的有限元模型，对比分析两类多塔悬索桥体系的竖向刚度差异；最后研究双缆悬索桥体系，边主跨比、中塔刚度、恒载分配比和矢跨比等关键设计参数对于中塔塔顶主缆总的不平衡力、中塔塔顶最大纵向位移以及主梁跨中最大挠度的影响效应. 研究结果表明：相比单缆多塔悬索桥，双缆多塔悬索桥能够有效提高结构的竖向刚度，同时大幅减小中塔塔顶主缆总的不平衡力；减小边主跨比对双缆结构体系竖向刚度和塔顶主缆总的不平衡力的影响较小；增大中塔刚度可以显著提高双缆结构体系的竖向刚度，但是中塔塔顶主缆总的不平衡力有较大幅度的增加；恒载分配比例取为1.0～2.0时，双缆结构体系的中塔塔顶位移及主梁跨中挠度较小；减小顶缆矢高或者增大底缆矢高均可以显著提高双缆结构体系的竖向刚度，有效减小主梁跨中挠度和中塔塔顶位移.Abstract: Double-cable suspension bridge system is one of structural systems suitable for long-span multi-tower suspension bridges. In order to study the mechanical properties of the bridge system, the finite element method is used to analyze its static behavior and the effect of key design parameters. First, the main design parameters of a double-cable multi-tower suspension bridge are determined according to a typical single-cable multi-tower suspension bridge, and finite element models of the two types of suspension bridges are established. Based on the models, the vertical stiffness values of the two suspension bridges are then compared. Finally, the influence of key design parameters such as the ratio of side to main span, stiffness of middle tower, dead load distribution ratio, and rise-span ratio on the total unbalanced force of the main cable, vertical displacement at top tower, and the maximum mid-span deflections of the main beam are studied. The results show that compared with the single-cable bridge, the double-cable bridge can effectively improve the vertical stiffness of the bridge system and greatly reduce the total unbalanced force of the main cable. Reducing the ratio of side to main span has little effect on the vertical stiffness of the double-cable bridge and the total unbalanced force of the main cable. On the contrary, increasing the middle tower stiffness can improve the vertical stiffness of the double-cable bridge significantly, but simultaneously resulting in a large increase in the unbalanced force of the main cable. When the dead load distribution ratio ranges from 1.0 to 2.0, the displacement at middle tower top and mid-span deflections of main beams are smaller in the double-cable bridge. In addition, decreasing the rise-span ratio of top cable or increasing the rise-span ratio of bottom cable can significantly improve the vertical stiffness of the double cable bridge, and thus effectively reduce the maximum mid-span deflections of the main beam and the displacement at the middle tower top.
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图 2 单双缆多塔悬索桥立面布置图（单位：m）
Figure 2. Elevation layout of single- and double-cable multi-tower suspension bridges (unit：m)
图 3 单双缆多塔悬索桥空间有限元模型
Figure 3. Spatial finite element model of single and double-cable multi-tower suspension bridges
表 1 单双缆多塔悬索桥的主要构件参数
Table 1. Parameters of main components of single and double-cable multi-tower suspension bridges
构件 弹模
/GPa容重
/（kN•m–3）面积
/m2惯性矩
/m4单双缆吊索 205.0 78.5 0.004 3 单双缆加劲梁 210.0 77.0 1.600 0 2.3 单缆主缆 205.0 78.5 0.250 2 双缆顶底缆 205.0 78.5 0.125 1 单缆边桥塔 34.5 25.0 21.200 0 118.6 25.200 0 231.9 双缆边桥塔 34.5 25.0 24.000 0 175.8 28.100 0 343.7 单缆中塔 钢截段 210.0 77.0 2.100 0 11.0 3.100 0 29.4 混凝土
截段34.5 25.0 89.200 0 2 471.6 117.600 0 4 053.7 双缆中塔 钢截段 210.0 77.0 2.300 0 15.3 3.500 0 40.7 混凝土
截段34.5 25.0 89.200 0 2 471.6 117.600 0 4 053.7 
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表 2 单双缆多塔悬索桥主要设计参数
Table 2. Main design parameters of single and double-cable multi-tower suspension bridges
结构形式 参数 数值 跨度 主缆 （220 + 850 + 850 + 220）m 加劲梁 （200 + 850 + 850 + 200）m 单缆主缆
（2根）矢高 85.00 m 矢跨比 1/10 面积 0.250 2 m2 双缆顶缆
（2根）矢高 70.83 m 矢跨比 1/12 面积 0.125 1 m2 恒载分配比 0.5 双缆底缆
（2根）矢高 106.25 m 矢跨比 1/8 面积 0.125 1 m2 恒载分配比 0.5 虚拟缆 矢跨比 1/10
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表 3 单双缆多塔悬索桥受力及变形对比
Table 3. Comparison of force and deformation between single and double-cable multi-tower suspension bridges
参数 单缆
体系双缆体系 虚拟缆 顶缆 底缆 塔顶不平衡力/（× 106 N） 10.19 8.52 –10.13 18.65 塔顶纵向位移/m 1.450 1.125 主梁跨中挠度/m 3.69 2.99
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表 4 边主跨比对主缆内力的影响
Table 4. Influence on ratio of side to main span to internal force of main cable
× 107 N 边主跨比 加载跨 非加载跨 顶缆 底缆 顶缆 底缆 0.235 7.462 6.932 8.475 5.067 0.3 7.472 6.926 8.474 5.069 0.35 7.483 6.915 8.463 5.078 0.4 7.494 6.911 8.460 5.080 0.45 7.510 6.900 8.452 5.086
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表 5 中塔刚度对主缆内力的影响
Table 5. Influence on middle tower to internal force of main cable
× 107 N 中塔刚度比 加载跨 非加载跨 顶缆 底缆 顶缆 底缆 0.5 7.249 7.004 8.701 4.990 0.7 7.345 6.971 8.598 5.025 1.0 7.462 6.932 8.475 5.067 1.5 7.605 6.884 8.326 5.118 2.0 7.707 6.848 8.220 5.157 4.0 7.989 6.754 8.048 5.258
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表 6 顶、底缆恒载及面积取值
Table 6. Load and area value of the top and bottom cables
λ 顶缆 底缆 qt/（kN•m−1） At/m2 qb/（kN•m−1） Ab/m2 1/2 122.98 0.187 6 61.49 0.062 6 1 92.24 0.150 1 92.24 0.100 1 2 61.49 0.107 2 122.98 0.143 0 3 46.11 0.083 4 138.36 0.166 8 4 36.89 0.068 2 147.58 0.182 0
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表 7 恒载分配比对主缆内力的影响
Table 7. Influence on dead load distribution ratio to internal force of main cable
× 107 N λ 加载跨 非加载跨 顶缆 底缆 顶缆 底缆 1/2 10.720 4.537 11.278 3.128 1 7.885 6.611 8.806 4.840 2 5.129 8.607 6.176 6.685 3 3.787 9.571 4.788 7.667 4 2.997 10.135 3.925 8.281
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表 8 顶、底缆恒载及面积取值
Table 8. Load and area of the top and bottom cables
矢高 f/L 顶缆 底缆 总面积/m2 ft/m At/m2 fb/m Ab/m2 顶缆矢高 1/10 85.00 0.104 106.25 0.125 0.229 1/12 70.83 0.125 0.250 1/14 60.71 0.146 0.271 1/16 53.13 0.166 0.291 1/18 47.22 0.187 0.312 1/20 42.50 0.208 0.333 底缆矢高 1/9 70.83 0.125 94.44 0.140 0.265 1/8.5 100.00 0.132 0.258 1/8 106.25 0.125 0.250 1/7.5 113.33 0.117 0.242 1/7 121.43 0.109 0.234
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表 9 矢跨比对主缆内力的影响
Table 9. Influence of rise-span ratio to internal force of main cable
× 107 N 失高 f/L 加载跨 非加载跨 顶缆 底缆 顶缆 底缆 顶缆矢高 1/10 5.347 7.571 5.795 6.098 1/12 6.222 7.818 7.250 5.930 1/14 7.320 7.922 8.633 5.887 1/16 8.569 7.960 10.014 5.895 1/18 9.931 7.967 11.430 5.992 1/20 11.380 7.962 12.901 5.888 底缆矢高 1/9 6.337 8.549 7.139 6.821 1/8.5 6.269 8.191 7.204 6.360 1/8 6.222 7.818 7.250 5.930 1/7.5 6.198 7.429 7.275 5.534 1/7 6.160 7.081 7.295 5.182
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