基于变形协调原理的多塔斜拉桥竖向刚度分析
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摘要
为深入探寻多塔斜拉桥的刚度特征、分析多塔斜拉桥结构力学特性,选取多塔斜拉桥的最典型形式——三塔斜拉桥,基于变形协调原理,求解单位荷载作用下多塔斜拉桥的拉索竖向弹性支承刚度公式,对推导的公式进行算例验证,并分析桥梁结构主要参数对拉索竖向支承刚度的影响.研究结果表明:对边塔非边跨和非边塔左跨分别施加单位荷载时,由该公式解求得的边塔非边跨跨中挠度值与有限元解之间的误差为6.27%,求得的非边塔跨中挠度值与有限元解之间的误差为5.79%.文中解的结果比有限元解偏大的主要原因是:公式解没有考虑斜拉索的垂度效应,单位荷载作用下所产生的水平力有一部分消耗在拉索的垂度效应中,但公式推导时没有考虑拉索垂度效应,导致主梁跨中挠度偏大.推导的拉索竖向支承刚度公式可以较真实地反映多塔斜拉桥的刚度特征,符合多塔斜拉桥概念设计的要求.
In order to explore the stiffness characteristics of multi-tower cable-stayed bridge,its structure features are analyzed by taking a three-tower cable-stayed bridge as research object,which is the simplest type of multi-tower cable-stayed bridge.This paper derives an analytic formula of cable-stayed bridges cable elastic support rigidity under unit load based on the principle of deformation coordination;a series of estimating formulae are obtained;and calculating outcomes are compared with that of a finite element model;and the influence of main structure parameters for cable support vertical stiffness are analyzed.The results show that on the non side span of side tower and the non side span of non side tower with unit load,the vertical deflection errors between the non side span of side tower and finite element are within 6.27%;the vertical deflection errors between the non side span of non side tower and finite element are within5.79%.The main reason of the result of the formula larger than finite element model is that the formula does not consider the sag effect of the cable.The horizontal force caused by the uniformly distributed load with non side tower has not full effect on it;apart of the consumption is in the sag effect of the cable.The formulae proposed can meet the requirements of the conceptual design,and it is suitable for the stiffnesscharacteristic of multi-tower cable-stayed bridge.
In order to explore the stiffness characteristics of multi-tower cable-stayed bridge,its structure features are analyzed by taking a three-tower cable-stayed bridge as research object,which is the simplest type of multi-tower cable-stayed bridge.This paper derives an analytic formula of cable-stayed bridges cable elastic support rigidity under unit load based on the principle of deformation coordination;a series of estimating formulae are obtained;and calculating outcomes are compared with that of a finite element model;and the influence of main structure parameters for cable support vertical stiffness are analyzed.The results show that on the non side span of side tower and the non side span of non side tower with unit load,the vertical deflection errors between the non side span of side tower and finite element are within 6.27%;the vertical deflection errors between the non side span of non side tower and finite element are within5.79%.The main reason of the result of the formula larger than finite element model is that the formula does not consider the sag effect of the cable.The horizontal force caused by the uniformly distributed load with non side tower has not full effect on it;apart of the consumption is in the sag effect of the cable.The formulae proposed can meet the requirements of the conceptual design,and it is suitable for the stiffnesscharacteristic 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 multispan cable-stayed bridge[J].Journal of Constructional Steel Research,2011,67:203-210.
[3] Choi Dong Ho,Gwon Sun Gil,Yoo Hoon,et al.Nonlinear static analysis of continuous multi-span suspension bridges[J].International Journal of Steel Structures,2013,13(1):103-115.
[4] Thai Huu Tai,Choi Dong Ho.Advanced analysis of multi-span suspension bridges[J].Journal of Constructional Steel Research,2013,90(8):29-41.
[5] 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.
[6] 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):291-311.
[7] 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 Venice(Italy):IABSE,2010:17-24.
[8] Fabio B,Dan M F.Bridge Maintenance,Safety,Management,Resilience and Sustainalility[M].Taylor&Francis Group,2012.
[9] Larsenkr.Dehumidification slows corrosion of forth road bridge cables[J].Materials Performance,2013,52(4):22-24.
[10]柳惠芬.斜拉桥实用简化分析[D].上海:同济大学,1995.Liu Huifen.Practically simplified analysis of cablestayed bridges[D].Shanghai:Tongji University,1995.
[11]Virlogeux M.Bridges with multiple cable-stayed spans[J].Structural Engineering and Mechanics,2001,30(1):56-58.
[12]刘丰洲.三塔斜拉桥竖向刚度解析分析[J].上海公路,2011,30(1):56-58.Liu Fengzhou.Three towers cable-stayed bridge vertical stiffness analytical analysis[J].Shanghai Highway,2011,30(1):56-58.
[13]Osamu Yoshida,Motoi Okuda,Takeo Moriya.Structural characteristics and applicability of four-span suspension bridge[J].Journal of Bridge Engineering,2004,9(5):453-463.
[14]李忠三.基于静动力特性的多塔长跨斜拉桥结构体系刚度研究[D].北京:北京交通大学,2014.Li Zhongsan.Study on rigidity of long-span cablestayed bridge with multi-tower based on the static and dynamic characteristics[D].Beijing:Beijing Jiaotong University,2014.
[15]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.
[16]李忠三,雷俊卿.多塔斜拉桥拉索支承刚度系数的求解与分析[J].长安大学学报(自然科学版),2015,35(2):83-90.Li Zhongsan,Lei Junqing.Analysis and solution of cable supporting stiffness coefficient of multi-pylon cablestayed bridges[J].Journal of Chang’an University(Natural Science Edition),2015,35(2):83-90.
[17]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.
[18]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.
[19]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.
[20]张杨永.斜拉桥近似计算与结构体系研究[D].上海:同济大学,2010.Zhang Yangyong.Approximate calculation and study of structural system in cable-stayed bridge[D].Shanghai:Tongji University,2010.
[21]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.
[22]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.
[23]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 bridges[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 multispan cable-stayed bridge[J].Journal of Constructional Steel Research,2011,67:203-210.
[3] Choi Dong Ho,Gwon Sun Gil,Yoo Hoon,et al.Nonlinear static analysis of continuous multi-span suspension bridges[J].International Journal of Steel Structures,2013,13(1):103-115.
[4] Thai Huu Tai,Choi Dong Ho.Advanced analysis of multi-span suspension bridges[J].Journal of Constructional Steel Research,2013,90(8):29-41.
[5] 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.
[6] 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):291-311.
[7] 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 Venice(Italy):IABSE,2010:17-24.
[8] Fabio B,Dan M F.Bridge Maintenance,Safety,Management,Resilience and Sustainalility[M].Taylor&Francis Group,2012.
[9] Larsenkr.Dehumidification slows corrosion of forth road bridge cables[J].Materials Performance,2013,52(4):22-24.
[10]柳惠芬.斜拉桥实用简化分析[D].上海:同济大学,1995.Liu Huifen.Practically simplified analysis of cablestayed bridges[D].Shanghai:Tongji University,1995.
[11]Virlogeux M.Bridges with multiple cable-stayed spans[J].Structural Engineering and Mechanics,2001,30(1):56-58.
[12]刘丰洲.三塔斜拉桥竖向刚度解析分析[J].上海公路,2011,30(1):56-58.Liu Fengzhou.Three towers cable-stayed bridge vertical stiffness analytical analysis[J].Shanghai Highway,2011,30(1):56-58.
[13]Osamu Yoshida,Motoi Okuda,Takeo Moriya.Structural characteristics and applicability of four-span suspension bridge[J].Journal of Bridge Engineering,2004,9(5):453-463.
[14]李忠三.基于静动力特性的多塔长跨斜拉桥结构体系刚度研究[D].北京:北京交通大学,2014.Li Zhongsan.Study on rigidity of long-span cablestayed bridge with multi-tower based on the static and dynamic characteristics[D].Beijing:Beijing Jiaotong University,2014.
[15]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.
[16]李忠三,雷俊卿.多塔斜拉桥拉索支承刚度系数的求解与分析[J].长安大学学报(自然科学版),2015,35(2):83-90.Li Zhongsan,Lei Junqing.Analysis and solution of cable supporting stiffness coefficient of multi-pylon cablestayed bridges[J].Journal of Chang’an University(Natural Science Edition),2015,35(2):83-90.
[17]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.
[18]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.
[19]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.
[20]张杨永.斜拉桥近似计算与结构体系研究[D].上海:同济大学,2010.Zhang Yangyong.Approximate calculation and study of structural system in cable-stayed bridge[D].Shanghai:Tongji University,2010.
[21]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.
[22]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.
[23]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 bridges[J].China Journal of Highway and Transport,2015,28(11):60-66.