单索面曲梁悬索人行桥主缆线形分析
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摘要
提出一种非线性有限元与数值计算结合的迭代法,并拓展大型软件迈达斯悬索桥分析功能,实现单索面曲梁悬索桥空间主缆的迭代找形计算。该方法以刚性支承连续曲梁竖向支座反力控制主缆立面垂度为主,以吊索倾斜角度计算吊索横向力和轴向力控制主缆横向垂度为辅,通过迭代吊索力大小和角度实现主缆找形,最终建立单索面曲梁悬索桥成桥状态三维空间有限元模型。计算结果表明:成桥状态主缆线形顺滑,塔、主缆、吊索和主梁空间布置姿态合理,吊索内力分布均匀合理,从而验证了迭代方法的正确性,为这一复杂桥型的设计分析提供参考。
A non-linear finite element iteration method combined with numerical calculation was proposed and the suspension bridge analysis function of Midas/Civil software was extended to fulfill the main cable shape-finding analysis. The rigid roller reactions in a curved beam bridges were obtained and used as reference values of the vertical component of the tension force of the hanger to control the sag in the vertical plane. And simultaneously, the lateral force was determined by adjusting trigonometric angular relation between the hangers and main cable in each iteration to control the horizontal sag of main cable. The iteration was not stopped until the convergence was obtained. The three dimensional space finite element model of the single cable plane curved suspension bridge was finally established. The calculation results show that the main cable shape is smooth. The tower, main cable and hanger are rationally arranged and the internal force of the hanger is evenly distributed. All of these results verify the correctness of the iterative method and provide a reference for the design and analysis of these complicated bridges.
A non-linear finite element iteration method combined with numerical calculation was proposed and the suspension bridge analysis function of Midas/Civil software was extended to fulfill the main cable shape-finding analysis. The rigid roller reactions in a curved beam bridges were obtained and used as reference values of the vertical component of the tension force of the hanger to control the sag in the vertical plane. And simultaneously, the lateral force was determined by adjusting trigonometric angular relation between the hangers and main cable in each iteration to control the horizontal sag of main cable. The iteration was not stopped until the convergence was obtained. The three dimensional space finite element model of the single cable plane curved suspension bridge was finally established. The calculation results show that the main cable shape is smooth. The tower, main cable and hanger are rationally arranged and the internal force of the hanger is evenly distributed. All of these results verify the correctness of the iterative method and provide a reference for the design and analysis of these complicated bridges.
引文
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[16]Kim M,Kim D,Jung M,et al.Improved methods for determining the 3 dimensional initial shapes of cable-supported bridges[J].International Journal of Steel Structures,2014,14(1):83-102.
[17]杨孟刚,陈政清.基于UL列式的两节点悬链线索元非线性有限元分析[J].土木工程学报,2003,36(8):63-68.YANG Menggang,CHEN Zhengqing.The non-linear finite element analysis for two-node catenary element of cable structure based on UL Formulation[J].China Civil Engineering Journal,2003,36(8):63-68.
[18]朱仲毅.独塔自锚式悬索桥恒载状态下结构线形及内力分析[J].铁道科学与工程学报,2005,2(2):46-50.ZHU Zhongyi.Analysis of the geometry and inner force for self–anchored suspension bridge with single-tower under dead load[J].Journal of Railway Science and Engineering,2005,2(2):46-50.
[2]袁正国.大跨度步行桥人行激励的TMD水平向减振[J].森林工程,2015,31(2):154-158.YUAN Zhengguo.TMD horizontal vibration control of large-span foot bridge under human-induced loads[J].Forest Engineering,2015,31(2):154-158.
[3]Baus U,Schlaich M.Footbridges:construction,design,history[M].Germany:Walter de Gruyter,2008:116-120.
[4]Rosales M,Kratz A,Keil A,et al.Structural and aesthetic considerations in the design of curved cable-supported pedestrian bridges[J].Transportation Research Record Journal of the Transportation Research Board,2005(11s):571-579.
[5]Stein M.Curved pedestrian bridge-straightforward design[C]//2010 Structures Congress and the 19th Analysis and Computation Specialty Conference,2010,262-275.
[6]Brown P,Kuhendran K,Marks J.Peace bridge,Londonderry:design and construction[J].Proceedings of the Institution of Civil Engineers-Bridge Engineering,2015,168(2):163-172.
[7]孙利民,杨伟,于军峰,等.空间曲梁单边悬索桥的振动舒适性评估及减振设计[J].建筑施工,2015(12):1345-1348.SUN Liming,YANG Wei,YU Junfeng,et al.Vibration comfort evaluation and vibration reduction design of space curved beam unilateral suspension bridge[J].Building Construction,2015(12):1345-1348.
[8]Kim H K,Lee M J,Chang S P.Non-linear shape-finding analysis of a self-anchored suspension bridge[J].Engineering Structures,2002,24(12):1547-1559.
[9]李传习,姚明,柯红军,等.悬索桥空间主缆精确解析计算法[J].公路与汽运,2008(2):122-125.LI Chuanxi,YAO Ming,KE Hongjun,et al.Precise analytical calculation method for spatial cable of suspension bridge[J].Highways&Automotive Applications,2008(2):122-125.
[10]李传习,柯红军,刘海波,等.空间主缆自锚式悬索桥成桥状态的确定方法[J].工程力学,2010,27(5):137-146.LI Chuanxi,KE Hongjun,LIU Haibo,et al.Determination of finished bridge state of self-anchored suspension bridge with spatial cables[J].Engineering Mechanics,2010,27(5):137-146.
[11]李建慧,李爱群,袁辉辉,等.独柱塔空间缆索自锚式悬索桥缆索线形计算方法[J].公路交通科技,2009,26(10):66-70.LI Jianhui,LI Aiqun,YUAN Huihui,et al.Calculation method of spatial cable curve for single-pylon self-anchored suspension bridge[J].Journal of Highway and Transportation Research and Development.2009,26(10):66-70.
[12]罗喜恒,肖汝诚,项海帆.空间缆索悬索桥的主缆线形分析[J].同济大学学报(自然科学版),2004,32(10):1349-1354.LUO Xiheng,XIAO Rucheng,XIANG Haifan.Cable shape analysis of suspension bridge with spatial cables[J].Journal of Tongji University(Natural Science),2004,32(10):1349-1354.
[13]彭苗,卢哲安.空间缆索自锚式悬索桥成桥状态的确定方法[J].公路交通科技,2008,25(11):101-104.PENG Miao,LU Zhean.A method for determining dead-load state of spatial-cable self-anchored suspension bridge[J].Journal of Highway and Transportation Research and Development,2008,25(11):101-104.
[14]SUN Yuan,ZHU Hongping,XU Dong.New method for shape finding of self-anchored suspension bridges with three-dimensionally curved cables[J].Journal of Bridge Engineering,2015,20(2):1-22.
[15]郑久建,丁松,周洪彬,等.空间索面悬索桥成桥线形的Marquardt修正最小二乘法计算[J].北京交通大学学报,2016,40(1):26-30.ZHENG Jiujian,DING Song,ZHOU Hongbin,et al.Least squares calculation with marquardt correction for spatial cable shape of suspension bridge[J].Journal of Beijing Jiaotong University,2016,40(1):26-30.
[16]Kim M,Kim D,Jung M,et al.Improved methods for determining the 3 dimensional initial shapes of cable-supported bridges[J].International Journal of Steel Structures,2014,14(1):83-102.
[17]杨孟刚,陈政清.基于UL列式的两节点悬链线索元非线性有限元分析[J].土木工程学报,2003,36(8):63-68.YANG Menggang,CHEN Zhengqing.The non-linear finite element analysis for two-node catenary element of cable structure based on UL Formulation[J].China Civil Engineering Journal,2003,36(8):63-68.
[18]朱仲毅.独塔自锚式悬索桥恒载状态下结构线形及内力分析[J].铁道科学与工程学报,2005,2(2):46-50.ZHU Zhongyi.Analysis of the geometry and inner force for self–anchored suspension bridge with single-tower under dead load[J].Journal of Railway Science and Engineering,2005,2(2):46-50.