基于变形协调原理的多塔斜拉桥非边塔纵向抗推刚度
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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这一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,求解多塔斜拉桥非边塔纵向抗推刚度,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:对非边塔左跨施加均布荷载时,本文推导公式的非边塔塔顶偏位解与已有文献有限元解间的误差在6.82%以内,说明本文推导的非边塔纵向抗推刚度公式能够反映多塔斜拉桥桥塔的刚度特征,符合多塔斜拉桥概念设计的要求;非边塔纵向抗推刚度与桥塔自身刚度、主梁刚度、拉索与主梁夹角、拉索线刚度和桥塔拉索锚固间距等因素有关.
In order to explore the stiffness characteristics of multi-tower cable-stayed bridges,the constraint to bridge towers caused by cables is compared to spring stiffness.We take the threetower cable-stayed bridge as research object,which is the most typical type of multi-tower cablestayed bridges.Firstly,the longitudinal anti-push rigidity of the non side tower of the three-tower cable-stayed bridge is solved based on the principle of deformation coordination.Secondly,the effectiveness of the derived formulas is verified by a calculation example.Finally,the influences of main parameters of the bridge structure on longitudinal anti-push rigidity of the left span of non side tower are analyzed.The results show that when imposing uniformly distributed load on thenon side tower,the errors between the deviation of non side tower roof solved by the side tower deformation formulas derived in this paper and the finite element solutions obtained from a previous study are within 6.82%.And it is illustrated that the proposed formulas is suitable for calculating the stiffness characteristics of multi-tower cable-stayed bridges,and can meet the requirements of the conceptual design.Meanwhile,the longitudinal anti-push rigidity of the non side tower for multi-tower cable-stayed bridges is related to tower stiffness,girder rigidity,angle between cable and girder,cable line stiffness and cable anchorage spacing of tower.
In order to explore the stiffness characteristics of multi-tower cable-stayed bridges,the constraint to bridge towers caused by cables is compared to spring stiffness.We take the threetower cable-stayed bridge as research object,which is the most typical type of multi-tower cablestayed bridges.Firstly,the longitudinal anti-push rigidity of the non side tower of the three-tower cable-stayed bridge is solved based on the principle of deformation coordination.Secondly,the effectiveness of the derived formulas is verified by a calculation example.Finally,the influences of main parameters of the bridge structure on longitudinal anti-push rigidity of the left span of non side tower are analyzed.The results show that when imposing uniformly distributed load on thenon side tower,the errors between the deviation of non side tower roof solved by the side tower deformation formulas derived in this paper and the finite element solutions obtained from a previous study are within 6.82%.And it is illustrated that the proposed formulas is suitable for calculating the stiffness characteristics of multi-tower cable-stayed bridges,and can meet the requirements of the conceptual design.Meanwhile,the longitudinal anti-push rigidity of the non side tower for multi-tower cable-stayed bridges is related to tower stiffness,girder rigidity,angle between cable and girder,cable line stiffness and cable anchorage spacing of tower.
引文
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[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.(in Chinese)
[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.(in Chinese)
[16]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.(in Chinese)
[17]YOSHIDA O,OKUDA M,MORIYA T.Structural characteristics and applicability of four-span suspension bridge[J].Journal of Bridge Engineering,2004,9(5):453-461.
[18]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.(in Chinese)
[19]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.(in Chinese)
[20]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 multitower suspension bridges[J].China Journal of Highway and Transport,2015,28(11):60-66.(in Chinese)
[21]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.(in Chinese)
[2]OKAMOTO Y,NAKAMURA S.Static and seismic studies on steel/concrete hybrid towers for multi-span cable-stayedbridge[J].Journal of Constructional Steel Research,2011,67(2):203-210.
[3]BIRLOGEUX M.Recent evolution of cable-stayed bridge[J].Engineering Structures,1999,21(8):737-755.
[4]CHOI D H,GWON S G,YOO H,et al.Nonlinear static analysis of continuous multi-span suspension bridges[J].International Journal of Steel Structures,2013,13(1):103-115.
[5]THAI H T,CHOI D H.Advanced analysis of multispan 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 M.Bridges with multiple cable-stayed spans[J].Structural Engineer,2001,2(22):61-82.
[8]ZHANG L W,XIAO R C,JIANG Y,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]COLFORD B R,CHIARELLO M,HENDY C,et al.Bearing replacement and strengthening of forth road bridge approach viaducts,UK[J].Bridge Maintenance,Safety,Management,Resilience and Sustainability,2012,12(6):81-92.
[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.(in Chinese)
[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.(in Chinese)
[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.(in Chinese)
[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.(in Chinese)
[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.(in Chinese)
[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.(in Chinese)
[16]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.(in Chinese)
[17]YOSHIDA O,OKUDA M,MORIYA T.Structural characteristics and applicability of four-span suspension bridge[J].Journal of Bridge Engineering,2004,9(5):453-461.
[18]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.(in Chinese)
[19]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.(in Chinese)
[20]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 multitower suspension bridges[J].China Journal of Highway and Transport,2015,28(11):60-66.(in Chinese)
[21]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.(in Chinese)