基于变形协调原理的多塔斜拉桥边塔纵向抗推刚度
|
摘要
为深入探寻多塔斜拉桥刚度特征,将斜拉索对桥塔的约束比作弹簧刚度的理念引入多塔斜拉体系。选取多塔斜拉桥的最典型形式——三塔斜拉桥建立弹簧刚度等效模型,基于变形协调原理,求解多塔斜拉桥边塔纵向抗推刚度,对推导的公式进行算例验证,并分析结构主要参数对桥塔纵向抗推刚度的影响。研究结果表明:对边塔非边跨施加均布荷载时,本文推导的塔顶偏位公式与有限元解之间的误差在7.8%以内。文中解的结果比有限元解偏大的主要原因是:文中公式解没有考虑斜拉索的垂度效应,均布荷载满布边塔非边跨时所产生的水平力实际上没有完全作用在边塔,有一部分消耗在拉索的垂度效应中。本文推导的边塔纵向抗推刚度公式可以较真实地反映多塔斜拉桥边塔的刚度特征,符合多塔斜拉桥概念设计的要求。
In order to explore the stiffness characteristic of multi-tower cable-stayed bridge, this paper introduces an idea to multi-tower cable-stayed bridge with the cable constraint the tower as spring stiffness. The three tower cable-stayed bridge was taken as research object, which is the simplest type of multi-tower cable-stayed bridge. Based on the principle of deformation coordination, longitudinal restraint stiffness of the side tower for multi-tower cable-stayed bridge was solved out, and a series of estimating formulae are provided and calculating outcomes are compared with that of a finite element model. Besides the influence of main structure parameters for longitudinal restraint stiffness of the side tower were also analyzed. The results show that on the side tower with uniformly distributed load, the errors between the side tower deformation formula in this paper and finite element are within 7.8%. The main reason of the result of the formula in this paper bigger than finite element model is the formula does not consider the sag effect of the cable. The horizontal force caused by the uniformly distributed load with side tower has not full effect at the side tower, and a part of the consumption is in the sag effect of the cable. The presented theoretical can meet the requirements of the conceptual design, and it is suitable for thestiffness requirements of multi-tower cable-stayed bridge.
In order to explore the stiffness characteristic of multi-tower cable-stayed bridge, this paper introduces an idea to multi-tower cable-stayed bridge with the cable constraint the tower as spring stiffness. The three tower cable-stayed bridge was taken as research object, which is the simplest type of multi-tower cable-stayed bridge. Based on the principle of deformation coordination, longitudinal restraint stiffness of the side tower for multi-tower cable-stayed bridge was solved out, and a series of estimating formulae are provided and calculating outcomes are compared with that of a finite element model. Besides the influence of main structure parameters for longitudinal restraint stiffness of the side tower were also analyzed. The results show that on the side tower with uniformly distributed load, the errors between the side tower deformation formula in this paper and finite element are within 7.8%. The main reason of the result of the formula in this paper bigger than finite element model is the formula does not consider the sag effect of the cable. The horizontal force caused by the uniformly distributed load with side tower has not full effect at the side tower, and a part of the consumption is in the sag effect of the cable. The presented theoretical can meet the requirements of the conceptual design, and it is suitable for thestiffness requirements of multi-tower cable-stayed bridge.
引文
[1]Niles J.Cable supported bridges:concept&design[M].3rd ed.John Wiley&Sons Ltd,2012.
[2]Yutaka Okamoto,Shunichi Nakamura.Static and seismic studies on Steel/Concrete hybrid towers for multi-span cable-stayed bridge[J].Journal of Constructional Steel Research,2011,67:203-210.
[3]Birlogeux M.Recent evolution of cable-stayed bridge[J].Engineering Structures,1999,21(8):737-755.
[4]Dong-Ho Choi,Sun-Gil Gwon,Hoon Yoo,et al.Nonlinear static analysis of continuous multi-span suspension bridges[J].International Journal of Steel Structures,2013,13(1):103-115.
[5]Thai Huu-Tai,Choi Dong-Ho.Advanced analysis of multi-span suspension bridges[J].Journal of Constructional Steel Research,2013,90(1):29-41.
[6]GE Y J,XIANG H F.Extension of bridging capacity of cable-supported bridges using double main spans or twin parallel decks solutions[J].Structure and Infrastructure Engineering,2011,7(7-8):551-567.
[7]Birlogeux Michel.Bridges with multiple cable-stayed spans[J].Structural Engineer,2001,2(22):61-82.
[8]ZHANG Liwen,XIAO Rucheng,JIANG Yang,et al.The characteristics of the multi-span suspension bridge with double main cables in the vertical plane[J].Structural Engineer,2012,42(3):291-302.
[9]Yoshimura T,Kawahara M.Aerodynamic stability of large suspension bridge using cable frames[C]//Proceeding of the 34th International Symposium on Bridge and Structural Engineering,2010.
[10]曹珊珊,雷俊卿,李忠三,等.多塔斜拉桥刚度分析[J].世界桥梁,2012,12(1):55-58.CAO Shanshan,LEI Junqing,LI Zhongsan,et al.Analysis of rigidity of multi-pylon cable-stayed bridges[J].The World Bridge,2012,12(1):55-58.
[11]喻梅,李乔,廖海黎.多塔斜拉桥的刚度配置[J].四川建筑科学研究,2010,36(4):67-71.YU Mei,LI Qiao,LIAO Haili.Stiffness configuration of multi-pylon cable-stayed bridges[J].Sichuan Building Science,2010,36(4):67-71.
[12]陶能迁,王福敏.提高PC三塔斜拉桥整体刚度研究[J].重庆交通学院学报,2007,26(2):14-20.TAO Nengqian,WANG Fumin.Study on improving the whole rigidity of prestressed concrete three-pylon cable-stayed bridge[J].Journal of Chongqing Jiaotong University,2007,26(2):14-20.
[13]李鹏程.多塔斜拉桥刚度分析[D].重庆:重庆交通大学,2009.LI Pengcheng.Multi-tower cable-stayed bridge stiffness analysis[D].Chongqing:Chongqing Jiaotong University,2009.
[14]金立新,郭慧乾.多塔斜拉桥发展综述[J].公路,2010(7):24-29.JIN Lixin,GUO Huiqian.Summary of multi-tower cable-stayed bridge[J].Highway,2010(7):24-29.
[15]林道锦,李忠三,王仁贵.多塔斜拉桥力学性能研究[J].公路,2013(7):317-321.LIN Daojin,LI Zhongsan,WANG Rengui.Analysis of mechanical properties of multi-pylon cable-stayed bridges[J].Highway,2013(7):317-321.
[16]郑春,刘晓东.论多塔斜拉桥的刚度[J].公路,2002(6):98-100.ZHENG Chun,LIU Xiaodong.Rigidity of multi-tower cable-stayed bridge[J].Highway,2002(6):98-100.
[17]宋涛.矮塔斜拉桥设计关键问题研究[D].西安:长安大学,2016.SONG Tao.Study on design theory of extradosed cable stayed bridge[D].Xi’an:Chang’an University,2016.
[18]Osamu Yoshida,Motoi Okuda,Takeo Moriya.Structural characteristics and applicability of four-span suspension bridge[J].Journal of Bridge Engineering,2004,9(5):453-461.
[19]柴生波,肖汝诚,张学义,等.多跨悬索桥中塔纵向刚度研究[J].中国公路学报,2012,25(2):67-71.CHAI Shengbo,XIAO Rucheng,ZHANG Xueyi,et al.Study of longitudinal stiffness of middle pylon in Multi-span suspension bridge[J].China Journal of Highway and Transport,2012,25(2):67-71.
[20]张学义,谭红梅,肖汝诚,等.主缆为悬链线的多塔悬索桥的中塔刚度计算[J].华中科技大学学报(自然科学版),2014,42(10):124-127.ZHANG Xueyi,TAN Hongmei,XIAO Rucheng,et al.Calculation of longitudinal stiffness of Mid-tower in Multi-span suspension bridges based on catenary equation[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2014,42(10):124-127.
[21]孙斌,胡志坚,张立文,等.多塔悬索桥活载效应简化分析[J].中国公路学报,2015,28(11):60-66.SUN Bin,HU Zhijian,ZHANG Liwen,et al.Simplified analysis of live load responses in Multi-tower suspension bridge[J].China Journal of Highway and Transport,2015,28(11):60-66.
[2]Yutaka Okamoto,Shunichi Nakamura.Static and seismic studies on Steel/Concrete hybrid towers for multi-span cable-stayed bridge[J].Journal of Constructional Steel Research,2011,67:203-210.
[3]Birlogeux M.Recent evolution of cable-stayed bridge[J].Engineering Structures,1999,21(8):737-755.
[4]Dong-Ho Choi,Sun-Gil Gwon,Hoon Yoo,et al.Nonlinear static analysis of continuous multi-span suspension bridges[J].International Journal of Steel Structures,2013,13(1):103-115.
[5]Thai Huu-Tai,Choi Dong-Ho.Advanced analysis of multi-span suspension bridges[J].Journal of Constructional Steel Research,2013,90(1):29-41.
[6]GE Y J,XIANG H F.Extension of bridging capacity of cable-supported bridges using double main spans or twin parallel decks solutions[J].Structure and Infrastructure Engineering,2011,7(7-8):551-567.
[7]Birlogeux Michel.Bridges with multiple cable-stayed spans[J].Structural Engineer,2001,2(22):61-82.
[8]ZHANG Liwen,XIAO Rucheng,JIANG Yang,et al.The characteristics of the multi-span suspension bridge with double main cables in the vertical plane[J].Structural Engineer,2012,42(3):291-302.
[9]Yoshimura T,Kawahara M.Aerodynamic stability of large suspension bridge using cable frames[C]//Proceeding of the 34th International Symposium on Bridge and Structural Engineering,2010.
[10]曹珊珊,雷俊卿,李忠三,等.多塔斜拉桥刚度分析[J].世界桥梁,2012,12(1):55-58.CAO Shanshan,LEI Junqing,LI Zhongsan,et al.Analysis of rigidity of multi-pylon cable-stayed bridges[J].The World Bridge,2012,12(1):55-58.
[11]喻梅,李乔,廖海黎.多塔斜拉桥的刚度配置[J].四川建筑科学研究,2010,36(4):67-71.YU Mei,LI Qiao,LIAO Haili.Stiffness configuration of multi-pylon cable-stayed bridges[J].Sichuan Building Science,2010,36(4):67-71.
[12]陶能迁,王福敏.提高PC三塔斜拉桥整体刚度研究[J].重庆交通学院学报,2007,26(2):14-20.TAO Nengqian,WANG Fumin.Study on improving the whole rigidity of prestressed concrete three-pylon cable-stayed bridge[J].Journal of Chongqing Jiaotong University,2007,26(2):14-20.
[13]李鹏程.多塔斜拉桥刚度分析[D].重庆:重庆交通大学,2009.LI Pengcheng.Multi-tower cable-stayed bridge stiffness analysis[D].Chongqing:Chongqing Jiaotong University,2009.
[14]金立新,郭慧乾.多塔斜拉桥发展综述[J].公路,2010(7):24-29.JIN Lixin,GUO Huiqian.Summary of multi-tower cable-stayed bridge[J].Highway,2010(7):24-29.
[15]林道锦,李忠三,王仁贵.多塔斜拉桥力学性能研究[J].公路,2013(7):317-321.LIN Daojin,LI Zhongsan,WANG Rengui.Analysis of mechanical properties of multi-pylon cable-stayed bridges[J].Highway,2013(7):317-321.
[16]郑春,刘晓东.论多塔斜拉桥的刚度[J].公路,2002(6):98-100.ZHENG Chun,LIU Xiaodong.Rigidity of multi-tower cable-stayed bridge[J].Highway,2002(6):98-100.
[17]宋涛.矮塔斜拉桥设计关键问题研究[D].西安:长安大学,2016.SONG Tao.Study on design theory of extradosed cable stayed bridge[D].Xi’an:Chang’an University,2016.
[18]Osamu Yoshida,Motoi Okuda,Takeo Moriya.Structural characteristics and applicability of four-span suspension bridge[J].Journal of Bridge Engineering,2004,9(5):453-461.
[19]柴生波,肖汝诚,张学义,等.多跨悬索桥中塔纵向刚度研究[J].中国公路学报,2012,25(2):67-71.CHAI Shengbo,XIAO Rucheng,ZHANG Xueyi,et al.Study of longitudinal stiffness of middle pylon in Multi-span suspension bridge[J].China Journal of Highway and Transport,2012,25(2):67-71.
[20]张学义,谭红梅,肖汝诚,等.主缆为悬链线的多塔悬索桥的中塔刚度计算[J].华中科技大学学报(自然科学版),2014,42(10):124-127.ZHANG Xueyi,TAN Hongmei,XIAO Rucheng,et al.Calculation of longitudinal stiffness of Mid-tower in Multi-span suspension bridges based on catenary equation[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2014,42(10):124-127.
[21]孙斌,胡志坚,张立文,等.多塔悬索桥活载效应简化分析[J].中国公路学报,2015,28(11):60-66.SUN Bin,HU Zhijian,ZHANG Liwen,et al.Simplified analysis of live load responses in Multi-tower suspension bridge[J].China Journal of Highway and Transport,2015,28(11):60-66.