Static Behavior and Key Influencing Factors of Double-Cable Suspension Bridge
-
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.
-
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 
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
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
下载: 导出CSV
-
肖汝诚. 桥梁结构体系[M]. 北京: 人民交通出版社, 2013: 307-313. 王忠彬,万田保. 泰州长江公路大桥三塔两跨悬索桥结构行为特征[J]. 桥梁建设,2008(2): 38-40, 59.WANG Zhongbin, WAN Tianbao. Characteristics of structural behavior of three-tower and two-span suspension bridge of Taizhou Changjiang river highway bridge[J]. Bridge Construction, 2008(2): 38-40, 59. 肖世国,赵琳智. 悬索桥隧道式锚碇侧摩阻力近似解析算法[J]. 西南交通大学学报,2018,53(5): 974-981.XIAO Shiguo, ZHAO Linzhi. Approximate analytical method for skin friction of tunnel-type anchorage used in suspension bridge engineering[J]. Journal of Southwest Jiaotong University, 2018, 53(5): 974-981. OSAMU Y, MOTOI O, TAKEO M. Structural characteristics and applicability of four span suspension bridge[J]. Journal of Bridge Engineering, 2004, 9(5): 453-463. doi: 10.1061/(ASCE)1084-0702(2004)9:5(453) JAEHO J, JAEHONG K, JONGGYUN B, et al. Practical design of continuous two main-span suspension bridge in Korea[C]//34th International Symposium on Bridge and Structural Engineering. Venice: IABSE, 2010: 62-69. 何婧. 大跨度双缆悬索桥结构体系及其受力特性研究[D]. 成都: 西南交通大学, 2016. GIMSING N J. Cable supported bridges[M]. 2nd ed. Chichester: John Wiley, 1997: 183-185. 陈艾荣, 陈文明. 多塔悬索桥的性能[C]//中国公路学会桥梁和结构工程学会, 桥梁学术研讨会论文集. 北京: 人民交通出版社, 2001: 561-566. 肖恩源. 再论悬挂索的重力刚度—双索、多跨[J]. 公路,2001(7): 67-72. doi: 10.3969/j.issn.0451-0712.2001.07.017XIAO Enyuan. Discussing gravity stiffness of suspension bridge gravity stiffness of suspended cable— double cables and multispan[J]. Highway, 2001(7): 67-72. doi: 10.3969/j.issn.0451-0712.2001.07.017 柴生波,肖汝诚,孙斌. 双缆悬索桥体系的力学特性(I)[J]. 华南理工大学学报(自然科学版),2011,39(12): 159-163. doi: 10.3969/j.issn.1000-565X.2011.12.027CHAI Shengbo, XIAO Rucheng, SUN Bin. Mechanical characteristics of double-cable suspension bridge(I)[J]. Journal of South China University of Technology (Natural Science Edition), 2011, 39(12): 159-163. doi: 10.3969/j.issn.1000-565X.2011.12.027 柴生波,肖汝诚,孙斌. 双缆悬索桥体系的力学特性(II)[J]. 华南理工大学学报(自然科学版),2012,40(2): 23-28. doi: 10.3969/j.issn.1000-565X.2012.02.005CHAI Shengbo, XIAO Rucheng, SUN Bin. Mechanical characteristics of double-cable suspension bridge(II)[J]. Journal of South China University of Technology (Natural Science Edition), 2012, 40(2): 23-28. doi: 10.3969/j.issn.1000-565X.2012.02.005 柴生波,肖汝诚. 双缆悬索桥体系的力学特性(III)[J]. 华南理工大学学报(自然科学版),2013,41(8): 120-125. doi: 10.3969/j.issn.1000-565X.2013.08.020CHAI Shengbo, XIAO Rucheng. Mechanical characteristics of double-cable suspension bridge(III)[J]. Journal of South China University of Technology (Natural Science Edition), 2013, 41(8): 120-125. doi: 10.3969/j.issn.1000-565X.2013.08.020 WANG Xiulan, CHAI Shengbo, XU Yue. Deformation characteristics of double-cable multispan suspension bridges[J]. Journal of Bridge Engineering, 2016, 21(4): 1-7. doi: 10.1061/(ASCE)BE.1943-5592.0000858 WANG Xiulan, CHAI Shengbo, XU Yue. Sliding resistance of main cables in double-cable multispan suspension bridges[J]. Journal of Bridge Engineering, 2017, 22(3): 1-7. doi: 10.1061/(ASCE)BE.1943-5592.0001018 WANG Xiulan, CHAI Shengbo. Determining the middle tower stiffness value in an in-plane double-cable triple-tower suspension bridge[J]. Journal of Bridge Engineering, 2018, 23(7): 1-6. 张清华,韩少辉,贾东林,等. 新型装配式UHPC华夫型上翼缘组合梁受力性能[J]. 西南交通大学学报,2019,54(3): 445-452,442.ZHANG Qinghua, HAN Shanhui, JIA Donglin, et al. Mechanical performance of novel perfabricated composite girder with top flange of ultra hight performance concrete waffle deck panel[J]. Journal of Southwest Jiaotong University, 2019, 54(3): 445-452,442. 张清华,李乔. 悬索桥主缆鞍座间摩擦特性试验研究[J]. 土木工程学报,2013,46(4): 85-92.ZHANG Qinghua, LI Qiao. Studies on cable-saddle frictional characteristics for long-span suspension bridges[J]. China Civil Engineering Journal, 2013, 46(4): 85-92. 张清华,李乔,周凌远. 悬索桥主缆与鞍座摩擦问题理论分析方法研究[J]. 中国公路学报,2014,27(1): 44-50. doi: 10.3969/j.issn.1001-7372.2014.01.007ZHANG Qinghua, LI Qiao, ZHOU Lingyuan. Theoretical analysis of cable-saddle frictional characteristics for suspension bridges[J]. China Journal of Highway and Transport, 2014, 27(1): 44-50. doi: 10.3969/j.issn.1001-7372.2014.01.007 ZHANG Qinghua, CHENG Zhenyu, CUI Chuang, et al. Analytical model for frictional resistance between cable and saddle of suspension bridges equipped with vertical friction plates[J]. Journal of Bridge Engineering, 2017, 22(1): 1-12. doi: 10.1061/(ASCE)BE.1943-5592.0000986 CHENG Zhenyu, ZHANG Qinghua, JIA Donglin, et al. Analytical study on frictional resistance between cable and saddle equipped with friction plates for multispan suspension bridges[J]. Journal of Bridge Engineering, 2018, 23(1): 1-13. doi: 10.1061/(ASCE)BE.1943-5592.0001176 张清华,程震宇,贾东林,等. 悬索桥主缆与鞍座抗滑移安全系数的确定方法[J]. 中国公路学报,2017,30(7): 41-49. doi: 10.3969/j.issn.1001-7372.2017.07.006ZHANG Qinghua, CHENG Zhenyu, JIA Donglin, et al. Method for determining anti-slip safety factors between main cable and saddle in suspension bridge[J]. China Journal of Highway and Transport, 2017, 30(7): 41-49. doi: 10.3969/j.issn.1001-7372.2017.07.006 沈锐利,王路,王昌将,等. 悬索桥主缆与索鞍间侧向力分布模式的模型试验研究[J]. 土木工程学报,2017,50(10): 75-81.SHEN Ruili, Wang Lu, Wang Changjiang, et al. Experimental study on distribution pattern of lateral force between main cable and cable saddle for suspension bridge[J]. China Civil Engineering Journal, 2017, 50(10): 75-81. 王路,沈锐利,王昌将,等. 悬索桥主缆与索鞍间侧向力理论计算方法与公式研究[J]. 土木工程学报,2017,50(12): 87-96.WANG Lu, SHEN Ruili, WANG Changjiang, et al. Experimental study on distribution pattern of lateral force between main cable and cable saddle for suspension bridge[J]. China Civil Engineering Journal, 2017, 50(12): 87-96. -
下载:
点击查看大图
图(9) / 表(9)
计量
- 文章访问数: 675
- HTML全文浏览量: 341
- PDF下载量: 24
- 被引次数: 0