斜拉—悬索协作体系桥的结构体系研究及其弹性地基梁算法
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摘要
斜拉-悬索协作体系桥作为一种集斜拉桥和悬索桥于一体的缆索承重桥梁,兼具二者的优势,扬长避短,且结构新颖、工程造价低,因此受到越来越多的重视。随着研究的一步步深入,人们对这种桥型的静动力学性能的了解越来越深入。但是由于真正建成的实桥甚少,对这种桥型的尝试主要还停留在方案设计阶段,大部分设计工作者对该桥型缺乏总体性的把握,设计经验不足,导致这种桥型的推广应用存在很大障碍。现在摆在桥梁工作者面前一个很重要的任务就是为这种桥型的推广应用创造更多的机会,让更多的人在设计方案中想到并熟练的应用这种桥型。这就需要全面了解这种桥梁结构体系较之其他桥型的优缺点并能从总体上把握它的结构受力特性,而且需要有一些简单实用的计算方法来对这种桥型进行初步分析。为此,本文做了如下工作：
(1)对斜拉-悬索协作体系桥的结构体系进行了研究,并分析了矢跨比、吊跨比和边跨辅助墩这几个因素对结构力学性能的影响。进行了斜拉-悬索协作体系桥与斜拉桥、悬索桥的对比研究；进行了自锚式斜拉-悬索协作体系桥与地锚式斜拉-悬索协作体系桥之间的对比研究,并分析总结了产生差别的原因。
(2)推导了三跨支承等刚度梁、单跨简支等刚度梁和单跨简支混合梁三种不同形式斜拉-悬索协作体系桥的索梁活载比计算公式,并归纳为一个统一的计算式,每种情况通过不同的系数取值来表征主梁支承形式及刚度分布的不同。研究了斜拉-悬索协作体系桥索梁活载比与拉索倾角、拉索面积、主缆面积、主缆矢跨比、吊跨比及主梁刚度等参数之间的变化关系；研究了索梁活载比的变化对斜拉-悬索协作体系桥的弯矩、挠度和索力变幅的影响规律,有助于在初步设计阶段把握结构的总体特性。
(3)基于温克尔假定,推导了求解弹性地基梁的传递矩阵新解法,推导时计入了轴向力的影响,在边界条件、荷载形式、刚度、弹性地基系数等因素发生变化时都能对弹性地基梁进行求解,其本质上是一种离散的解析计算方法,具有很高的精度。推导了斜拉-悬索协作体系桥的重力刚度,包括恒载状态下水平方向的刚度以及在活载作用下的竖向刚度；推导了斜拉索对主梁的弹性支承刚度。
(4)将弹性地基梁法应用于斜拉-悬索协作体系桥的活载内力和位移计算中,并通过一个算例验证了该方法的有效性和精确度。对利用弹性地基梁法来进行实用简化分析的优缺点进行了总结,为这种方法在缆索承重桥梁中的应用提供建议。
As a new type of cable-supported bridge, cable-stayed suspension has merits of both suspension bridge and cable-stayed bridge, and avoiding the shortcomings of them. Moreover, with the new structure and low costing, it has being more and more attention. With the further research, people have more and more understanding of the static dynamic performance of this type of bridge. However, due to the real bridge of this type built very little, the attempting to this type of bridge still remains in the process of program designing. The most design workers lack of the general certainty and design experience on it, leading to a big obstacle to popularization and application. A very important task for bridge workers now is to create more opportunities in promoting the use of this bridge and let more people think and use this bridge in the design of programs with skilled application. Compared with the other types of advantages and disadvantages, this bridge requires a comprehensive understanding of the structure system which not only from the grasp of its overall force structure properties, but also from the preliminary analysis in some simple and practical way of calculation. The main research work covers the following aspects:
(1) This paper has researched the structure system of cable-stayed suspension, and discussed the effects of the ratio of rise to span, ratio of suspension span to main span, and the location of assistant pier on the mechanic behavior of this type of bridge. Comparison between cable-stayed bridge and cable-stayed suspension bridge, and comparison between suspension bridge and cable-stayed suspension bridge have been conducted. Moreover, a comparative study on the mechanical behavior of the earth-anchored and self-anchored cable-stayed bridges was also conducted, and the causes of the differences between the two patterns of bridges are analyzed.
(2) Under uniform live load, the formulations of cable/beam live-load ratio for three different types of cable-stayed suspension bridges are deduced, and whose result is verified by that of FEM. Moreover, these formulations are grouped into a united form of formula which could be distinguished by coefficients according to the different boundary conditions and different distribution of the main beam stiffness. Lately the correlation for cable/beam live-load ratio and structure parameters is discussed. It is proved that the cable/beam live-load ratio reflects structure trait and is helpful for holding mechanic characteristic at concept design stage.
(3) Based on the Winkler assumption, the united form of transfer matrix suitable for different beams on the elastic foundation is obtained by derivation from basic differential equation for beam. This method takes into account the impact of axial force. Moreover, when the boundary conditions, the main beam stiffness, elastic foundation coefficient are not constants, the method of transfer matrix is still applicable to solve the beam on the elastic foundation. The gravity stiffness the cable-stayed suspension bridge is deduced including the axial stiffness under dead load condition and the vertical stiffness under the action of live load. And the elastic support stiffness of the stay cables to the main beam is also deduced too.
(4) The elastic foundation beam method is applied to calculate the internal force and deformation of the main beam of the cable-stayed suspension bridge under live load. And the results are compared by that of FEM through a numerical example. Finally, the strengths and weaknesses of the elastic foundation beam method are summarized to provide guidance recommendations for the application of this practical simplify calculation method in the cable-suspension bridges.
(1)对斜拉-悬索协作体系桥的结构体系进行了研究,并分析了矢跨比、吊跨比和边跨辅助墩这几个因素对结构力学性能的影响。进行了斜拉-悬索协作体系桥与斜拉桥、悬索桥的对比研究；进行了自锚式斜拉-悬索协作体系桥与地锚式斜拉-悬索协作体系桥之间的对比研究,并分析总结了产生差别的原因。
(2)推导了三跨支承等刚度梁、单跨简支等刚度梁和单跨简支混合梁三种不同形式斜拉-悬索协作体系桥的索梁活载比计算公式,并归纳为一个统一的计算式,每种情况通过不同的系数取值来表征主梁支承形式及刚度分布的不同。研究了斜拉-悬索协作体系桥索梁活载比与拉索倾角、拉索面积、主缆面积、主缆矢跨比、吊跨比及主梁刚度等参数之间的变化关系；研究了索梁活载比的变化对斜拉-悬索协作体系桥的弯矩、挠度和索力变幅的影响规律,有助于在初步设计阶段把握结构的总体特性。
(3)基于温克尔假定,推导了求解弹性地基梁的传递矩阵新解法,推导时计入了轴向力的影响,在边界条件、荷载形式、刚度、弹性地基系数等因素发生变化时都能对弹性地基梁进行求解,其本质上是一种离散的解析计算方法,具有很高的精度。推导了斜拉-悬索协作体系桥的重力刚度,包括恒载状态下水平方向的刚度以及在活载作用下的竖向刚度；推导了斜拉索对主梁的弹性支承刚度。
(4)将弹性地基梁法应用于斜拉-悬索协作体系桥的活载内力和位移计算中,并通过一个算例验证了该方法的有效性和精确度。对利用弹性地基梁法来进行实用简化分析的优缺点进行了总结,为这种方法在缆索承重桥梁中的应用提供建议。
As a new type of cable-supported bridge, cable-stayed suspension has merits of both suspension bridge and cable-stayed bridge, and avoiding the shortcomings of them. Moreover, with the new structure and low costing, it has being more and more attention. With the further research, people have more and more understanding of the static dynamic performance of this type of bridge. However, due to the real bridge of this type built very little, the attempting to this type of bridge still remains in the process of program designing. The most design workers lack of the general certainty and design experience on it, leading to a big obstacle to popularization and application. A very important task for bridge workers now is to create more opportunities in promoting the use of this bridge and let more people think and use this bridge in the design of programs with skilled application. Compared with the other types of advantages and disadvantages, this bridge requires a comprehensive understanding of the structure system which not only from the grasp of its overall force structure properties, but also from the preliminary analysis in some simple and practical way of calculation. The main research work covers the following aspects:
(1) This paper has researched the structure system of cable-stayed suspension, and discussed the effects of the ratio of rise to span, ratio of suspension span to main span, and the location of assistant pier on the mechanic behavior of this type of bridge. Comparison between cable-stayed bridge and cable-stayed suspension bridge, and comparison between suspension bridge and cable-stayed suspension bridge have been conducted. Moreover, a comparative study on the mechanical behavior of the earth-anchored and self-anchored cable-stayed bridges was also conducted, and the causes of the differences between the two patterns of bridges are analyzed.
(2) Under uniform live load, the formulations of cable/beam live-load ratio for three different types of cable-stayed suspension bridges are deduced, and whose result is verified by that of FEM. Moreover, these formulations are grouped into a united form of formula which could be distinguished by coefficients according to the different boundary conditions and different distribution of the main beam stiffness. Lately the correlation for cable/beam live-load ratio and structure parameters is discussed. It is proved that the cable/beam live-load ratio reflects structure trait and is helpful for holding mechanic characteristic at concept design stage.
(3) Based on the Winkler assumption, the united form of transfer matrix suitable for different beams on the elastic foundation is obtained by derivation from basic differential equation for beam. This method takes into account the impact of axial force. Moreover, when the boundary conditions, the main beam stiffness, elastic foundation coefficient are not constants, the method of transfer matrix is still applicable to solve the beam on the elastic foundation. The gravity stiffness the cable-stayed suspension bridge is deduced including the axial stiffness under dead load condition and the vertical stiffness under the action of live load. And the elastic support stiffness of the stay cables to the main beam is also deduced too.
(4) The elastic foundation beam method is applied to calculate the internal force and deformation of the main beam of the cable-stayed suspension bridge under live load. And the results are compared by that of FEM through a numerical example. Finally, the strengths and weaknesses of the elastic foundation beam method are summarized to provide guidance recommendations for the application of this practical simplify calculation method in the cable-suspension bridges.
引文
[1]孙淑红.大跨度吊拉组合体系及计算方法研究[D].重庆：重庆交通学院,1999.
[2]王会利.自锚式斜拉—悬索协作体系桥结构性能分析与试验研究[D].大连：大连理工大学,2007.
[3]杜高明.大跨度自锚式斜拉—悬索协作体系桥结构性能分析[D].大连：大连理工大学,2006.
[4]吴宏业.自锚式斜拉—悬索协作体系桥静力性能分析[D].大连：大连理工大学,2007.
[5]万国朝.大贝尔特悬索桥设计[J].国外公路.1995,15(1)：11-17.
[6]王伯惠.斜拉—悬索协作体系桥[J].辽宁省交通高等专科学校学报.2000,2(3)：1-6.
[7]王伯惠.伶仃洋三大航道桥桥型方案探讨(一)伶仃西桥[C].厦门：1999.
[8]王伯惠.伶仃洋三大航道桥桥型方案探讨(二)伶仃东桥[C].厦门：1999.
[9]大连理工大学土木建筑设计研究院桥梁研究所,大连庄河建设大桥初步设计图[Z].2005.
[10]张哲,朱巍志,王会利.自锚式斜拉—悬索协作体系桥的方案设计[J].桥梁建设.2009(04).
[11]周念先.对特大跨径索桥若干问题的商榷：答严国敏高级工程师[J].江苏交通工程.1993(003)：1-5.
[12]Chen J, Zhang Z, Wang H. Research on the Combined Cable-Stayed and Self-Anchored Suspension Bridge[J]. Pacific Science Review.2005(7):107-111.
[13]周孟波,刘自明,王邦楣.斜拉桥手册[M].北京：人民交通出版社,2004.
[14]孙斌,肖汝诚,贾丽君,等.斜拉-悬吊协作体系桥经济性能研究[C].南京：同济大学出版社,2000.
[15]颜娟.自锚式悬索桥[J].国外桥梁.2002(001)：19-22.
[16]张哲,窦鹏,石磊,等.自锚式悬索桥的发展综述[J].世界桥梁.2003(1)：5-9.
[17]张元凯,肖汝诚.自锚式悬索桥的概念设计[J].公路.2002(11)：46-49.
[18]邱文亮.自锚式悬索桥非线性分析与试验研究[D].大连：大连理工大学,2004.
[19]张新军,张丹.吊拉组合体系桥的研究进展[J].浙江工业大学学报.2007,35(5)：553-558.
[20]Mal J. Nonlinear models of suspension bridges[J]. Journal of Mathematical Analysis and Applications.2006,321(2):828-850.
[21]Karoumi R. Some modeling aspects in the nonlinear finite element analysis of cable supported bridges[J]. Computers and Structures.1999,71(4):397-412.
[22]周上君.大跨度斜拉桥非线性分析[J].桥梁建设.1982(4)：11-24.
[23]张翔.大跨径悬索桥的几何非线性分析[C].第十二届全国桥梁学术会议论文集：1992.
[24]李德寅.钢悬索桥非线性计算基本理论一[J].国外桥梁.1994(3)：204-216.
[25]潘永仁.悬索桥结构非线性分析理论与方法[M].北京：人民交通出版社,2004.
[26]潘家英,吴亮明,高路彬.大跨度斜拉桥活载非线性研究[J].土木工程学报.1993,26(1)：31-37.
[27]辛克贵,杨国平.大跨度斜拉桥恒载非线性静力分析[J].清华大学学报：自然科学版.2002,42(6)：818-821.
[28]华孝良,徐光辉.桥梁结构非线性分析[M].北京：人民交通出版社,1997.
[29]林少恒,陈启.悬索桥结构几何非线性分析方法[J].山西建筑.2009(22).
[30]肖汝诚,周念先.走向21世纪的斜张桥(二)：斜张桥的计算理论[J].铁道标准设计.1998(005)：1-2.
[31]肖汝诚,周念先.走向21世纪的斜张桥(三)[J].铁道标准设计.1998(012)：27-33.
[32]周念先,肖汝诚.走向21世纪的斜张桥(一)[J].铁道标准设计.1998(001)：6-9.
[33]Wenzel H. Cable stayed bridges:history, design, application[M]. Northern Gate,1998.
[34]Wang P H, Tseng T C, Yang C G. Initial shape of cable-stayed bridges[J]. Computers & structures.1993,47(1):111-123.
[35]Bruno D, Leonardi A. Natural periods of long-span cable-stayed bridges[J]. Journal of Bridge Engineering.1997,2(3):105-115.
[36]柳惠芬.斜拉桥的实用简化分析[D].上海：同济大学,1995.
[37]华孝良,张惠峰.斜拉桥几何非线性简化分析法及其应用[J].中国土木工程学会桥梁及结构工程学会第11届年会论文集.1994.
[38]柳惠芬,姚玲森.斜拉桥梁非线性实用简化分析[J].同济大学学报：自然科学版.2001,29(1)：118-121.
[39]MS特罗伊茨基著,王学汶程庆国等译.斜拉桥理论与设计[M].北京：中国铁道出版社,1980.
[40]黄琼.钢—混凝土混合梁自锚式悬索桥受力性能与计算方法研究[D].长沙：中南大学,2007.
[41]郭永强,崔远.悬索桥的初步分析[J].中外公路.2005,25(002)：54-60.
[42]雷俊卿,郑明珠,徐恭义.悬索桥设计[M].北京：人民交通出版社,2002.
[43]周孟波,刘自明,王邦楣.悬索桥手册[M].北京：人民交通出版社,2003.
[44]Irvine H M. Cable structures[M]. New York:Dover,1992.
[45]Ochsendorf J A, Billington D P. Self-anchored suspension bridges[J]. Journal of bridge engineering.1999,4(3):151.
[46]檀永刚,石磊,张哲.一种悬索桥静力分析的解析元法[J].武汉理工大学学报(交通科学与工程版).2009(05).
[47]吕丹,盛洪飞,郑传峰,等.自锚式悬索桥主梁面内稳定实用简化计算方法探索[J].华东公路.2008(01).
[48]黄琼,叶梅新.自锚式悬索桥简化计算方法研究[J].铁道学报.2008(01).
[49]肖海波,俞亚南,高庆丰.自锚式悬索桥主缆成桥线形分析[J].浙江大学学报(工学版).2004(11).
[50]周孟波,文武松.悬索桥的简化数值分析方法[J].国外桥梁.2000(02).
[51]程翔云.“悬索桥按二阶理论的实用计算”法的推广应用探讨[J].公路.2000(06).
[52]Wollmann G P. Preliminary analysis of suspension bridges[J]. Journal of Bridge
Engineering.2001,6(4):227-233.
[53]Clemente P, Nicolosi G, Raithel A. Preliminary design of very long-span suspension bridges[J]. Engineering Structures.2000,22(12):1699-1706.
[54]Cobo A D, Aparicio A C. Preliminary static analysis of suspension bridges[J]. Engineering Structures.2001,23(9):1096-1103.
[55]Virlogeux M. Recent evolution of cable-stayed bridges[J]. Engineering structures. 1999,21 (8):737-755.
[56]Ahmed N U. A general mathematical framework for stochastic analysis of suspension bridges[J]. Nonlinear Analysis:Real World Applications.2000,1(4):457-483.
[57]李国豪.桥梁与结构理论研究[M].上海科学技术文献出版社,1983.
[58]徐君兰,向中富.关于悬索桥的重力刚度[J].重庆交通学院学报.2000,19(2)：71-74.
[59]陈仁福.大跨悬索桥理论[M].成都：西南交通大学出版社,1994.
[60]龙驭球.弹性地基梁的计算[M].北京：人民教育出版社,1982.
[61]尹刚,朱渝春,冯贤桂.弹性地基梁的积分变换解法[J].重庆工学院学报.2005,19(5)：12-14.
[62]陈天愚,张克绪.弹性地基梁的修正刚度矩阵解法[J].哈尔滨建筑大学学报.2000,33(2)：44-48.
[63]刘庆潭,倪国荣.弹性地基梁的传递矩阵法求解[J].长沙铁道学院学报.1992,10(2)：92-102.
[64]尼尔斯J,吉姆辛,姚铃森,等.缆索承重桥梁[M].北京：人民交通出版社,1992.
[65]Gimsing N J. Cable supported bridges:Concepts and design[M].1983.
[66]严国敏.现代斜拉桥[M].成都：西南交通大学出版社,2000.
[67]严国敏,周世忠.现代悬索桥[M].北京：人民交通出版社,2002.
[68]陈明宪.斜拉桥的发展与展望[J].中外公路.2006,26(4)：76-86.
[69]Virola J, Ing-feani E, Helsinki F. Long-span cable-supported bridges:general review [J]. The IES Journal Part A:Civil & Structural Engineering.2009,2(4):304-308.
[70]Niels J G. Cable Supported Bridges:Concept and Design[M]. New York:John Wiley & Sons,1997.
[71]王伯惠.斜拉桥结构发展和中国经验[M].北京：人民交通出版社,2003.
[72]肖汝诚,项海帆.拉吊协作桥的施工控制与吊索疲劳控制研究[J].同济大学学报.1999,27(2)：234-238.
[73]黎祖华.超大跨度桥梁形式的探讨[J].国外桥梁.1992(4)：13-15.
[74]尼尔斯J,吉姆辛,姚林森,等.缆索承重桥梁构思与设计[M].北京：人民交通出版社,1992.
[75]许福友,张哲,黄才良,等.斜拉-悬吊协作体系桥工程应用及特点分析[J].中外公路.2009,29(1)：98-101.
[76]孙淑红,蒙云.吊拉组合桥交接区域吊杆的疲劳问题研究[J].重庆交通学院学报.1999,18(4)：13-18.
[77]蒙云,刘东,孙淑红.大跨度P.F.C.吊拉组合桥设计研究[J].重庆交通学院学报.1999,18(4)：8-12.
[78]张哲,王会利,黄才良,等.自锚式斜拉-悬索协作体系桥梁设计与分析[J].公路.2006(7)：44-48.
[79]贾丽君.大跨度悬索桥体系及其性能研究[D].上海：同济大学,2009.
[80]陈从春.矮塔斜拉桥设计理论核心问题研究[D].上海：同济大学,2006.
[81]Tang M. Design of cable-stayed girder bridges [J]. Journal of the Structural Division. 1972,92(8):1789-1802.
[82]Zellnet W. Discussion of Cable-Stayed Bridges:Degrees of Anchoring[J]. Journal of Structural Engineering.1984,110(4):910-914.
[83]Brozzetti J. Design development of steel-concrete composite bridges in France[J]. Journal of Constructional Steel Research.2000,55(1-3):229-243.
[84]李方东.钢—砼箱形结合梁在斜拉桥中的应用[J].公路与汽运.2003(6)：56-59.
[85]陈开利,余天庆,习刚.混合梁斜拉桥的发展与展望[J].桥梁建设.2005(2)：1-4.
[86]肖汝诚,贾丽君,薛二乐.斜拉—悬吊协作体系的设计探索[J].土木工程学报.2000,33(5)：46-51.
[87]刘钊,刘厚军.悬索桥主缆变形及重力刚度新算法[J].工程力学.2009(6)：127-132.
[88]张志国,邹振祝,赵玉成,等.悬索桥主缆线形解析方程解及应用[J].工程力学.2005,22(003)：172-176.
[89]胡隽.大跨度吊拉组合索桥的理论研究[D].北京：北方交通大学,2000.
[90]苗家武.超大跨度斜拉桥设计理论研究[D].上海：同济大学,2006.
[91]周念先.特大跨斜张桥与悬索桥的对比[J].江苏交通工程.1993(1)：16-20.
[92]蒋永林,卢伟.斜拉桥和悬索桥跨越效率的比较[J].国外桥梁.1998(4)：10-11.
[93]肖汝诚,项海帆.斜拉-悬吊协作体系桥力学特性及其经济性能研究[J].中国公路学报.1999.
[94]Starossek U. Cable-stayed bridge concept for longer spans[J]. Journal of Bridge Engineering.1996,1(3):99-103.
[95]Manabu I. Cable-supported steel bridge:design problem and solutions[J]. Journal of construct steel research.1996,39(1):69-84.
[96]Cluley N C, Shepherd R. Analysis of concrete cable-stayed bridges for creep, shrinkage and relaxation effects[J]. Computers and Structures.1996,58(2):337-350.
[97]姚玲森.混凝土斜张桥的徐变与收缩内力计算[J].中南公路工程.1982,1(5)：54-73.
[98]胡建华,唐茂林,刘蓉,等.自锚式悬索桥收缩徐变效应分析[J].重庆交通大学学报：自然科学版.2007,26(005)：5-8.
[99]夏国平,张哲,王骞.混凝土收缩徐变对斜拉-悬索协作体系桥的影响[C].大连：中国建筑工业出版社,2008.
[100]李熠,于磊.收缩徐变对混凝土斜拉桥成桥状态的影响分析[J].国防交通工程与技术.2009(06).
[101]陆从飞.大跨度斜拉桥施工阶段几何非线性静力分析[J].四川建筑.2009(05).
[102]夏国平,张哲,叶毅.斜拉-悬索协作体系桥的温度效应分析[J].武汉理工大学学报(交通科学与工程版).2009(05).
[103]XiaoqingS, Yongshui Z, Yuanfu Z. Influence Research of Temperature on Suspension Bridge Anchor Span Strand Tension [J] [J]. Transportation Science & Technology.2009,4.
[104]中交公路规划设计院.公路桥涵设计通用规范(JTGD60—2004)[M].北京：人民交通出版社,2004.
[105]陈从春.矮塔斜拉桥索梁活载比的特性研究[J].公路交通科技.2009,16(1)：99-103.
[106]Spyrakos C C, Kemp E L, Venkatareddy R. Validated analysis of wheeling suspension bridge[J]. Journal of Bridge Engineering.1999,4(1):1-7.
[107]徐君兰,姚玲森.悬索桥[M].北京：人民交通出版社,2001.
[108]潘永仁,杜国华.悬索桥恒载结构几何形状及内力的精细计算[J].中国公路学报.2000,13(4)：33-36.
[109]Plan S, Committees S, Committees P, et al. Suspension Bridge Cable Strength Equation Modifications[J]. Transportation Research.2009,6:55AM.
[110]项海帆,姚玲森.高等桥梁结构理论[M].北京：人民交通出版社,2001.
[111]李正良.变刚度梁的计算[M].北京：人民交通出版社,1996.
[112]李国豪,石洞.公路桥梁荷载横向分布计算[M].北京：人民交通出版社,1987.
[113]柳红霞.共轭梁法在梁变形计算中的运用[J].长沙大学学报.2002,16(02)：63-66.
[114]冯健,吕志涛.次弯矩计算的共轭梁法[J].东南大学学报：自然科学版.1997,27(A11)：71-75.
[115]柳惠芬,姚玲森,易建国.双塔斜拉桥的实用简化分析[J].上海公路.2001,29(1)：118-121.
[116]孙训方,方孝淑,关来泰.材料力学[M].北京：高等教育出版社,1994.
[117]胡锡恒.实用拉普拉斯变换与Z变换手册[M].北京：电子工业出版社,1988.
[118]肖恩源.索的特性(连载)[J].公路.1997(05)：1-7.
[119]肖恩源.索的特性(续)[J].公路.1997(06)：2-6.
[120]肖恩源.索的特性(续)[J].公路.1998(04)：24-31.
[121]吴恒立.关于悬索桥的重力刚度一文的讨论[J].重庆交通学院学报.2001,20(001)：118-119.
[122]Jennings A. Gravity stiffness of classical suspension bridges[J]. Journal of Structural Engineering.1983,109(1):16-36.
[123]Yang D. Modeling on gravity stiffness of suspension bridges by finite element method of geometric nonlinearity[C].上海：上海大学出版社,2007.
[124]郑凯锋,栗怀广,胥润东.连续超大跨悬索桥的刚度特征[J].西南交通大学学报.2009,44(3)：342-346.
[125]王京杭,夏咏明,蒋湘成.南京白果桥主缆长度计算[J].现代交通技术.2009(05).
[126]王鹏.悬索桥空缆线形分析综述[J].工程与建设.2009(04).
[127]杨益.悬索桥空缆状态下结构参数计算[J].科技信息.2008(32).
[128]hegab H I A,周先雁,朱之基.用能量法分析斜拉桥[J].世界桥梁.1987,4：63-71.
[129]吴红林,黄侨,金秀辉.斜拉桥施工控制调索方法研究及应用[J].公路交通科技(应用技术 版).2007(04).
[130]易鹏.大跨度公铁两用斜拉桥计算模型简化的探讨[J].铁道标准设计.2003(09).
[131]郭卓明,李国平,袁万城.独塔单索面斜拉桥主塔稳定简化分析[J].同济大学学报(自然科学版).2000(02).
[132]王勋文,辛学忠,潘家英,等.确定PC斜拉桥合理恒载索力方法的探讨[J].桥梁建设.1996(04).
[133]罗开红,岳平,王清.数值模拟在悬索桥中的应用[J].科技风.2009(13).
[134]周云开,郑子恒.自锚式悬索桥恒载吊索力设计方法探讨[J].广东建材.2009(06).
[135]李乔.斜拉桥的受力特征分析[C].昆明：1999.
[136]贺栓海.桥梁结构理论与计算方法[M].北京：人民交通出版社,2003.
[137]张雪松,梁鹏,贾丽君,等.非线性因素对超大跨度斜拉桥活载内力的影响[J].重庆交通学院学报.2005,24(1)：5-8.
[138]李晓莉.独塔斜拉桥的设计理论研究[D].上海：同济大学,2006.
[2]王会利.自锚式斜拉—悬索协作体系桥结构性能分析与试验研究[D].大连：大连理工大学,2007.
[3]杜高明.大跨度自锚式斜拉—悬索协作体系桥结构性能分析[D].大连：大连理工大学,2006.
[4]吴宏业.自锚式斜拉—悬索协作体系桥静力性能分析[D].大连：大连理工大学,2007.
[5]万国朝.大贝尔特悬索桥设计[J].国外公路.1995,15(1)：11-17.
[6]王伯惠.斜拉—悬索协作体系桥[J].辽宁省交通高等专科学校学报.2000,2(3)：1-6.
[7]王伯惠.伶仃洋三大航道桥桥型方案探讨(一)伶仃西桥[C].厦门：1999.
[8]王伯惠.伶仃洋三大航道桥桥型方案探讨(二)伶仃东桥[C].厦门：1999.
[9]大连理工大学土木建筑设计研究院桥梁研究所,大连庄河建设大桥初步设计图[Z].2005.
[10]张哲,朱巍志,王会利.自锚式斜拉—悬索协作体系桥的方案设计[J].桥梁建设.2009(04).
[11]周念先.对特大跨径索桥若干问题的商榷：答严国敏高级工程师[J].江苏交通工程.1993(003)：1-5.
[12]Chen J, Zhang Z, Wang H. Research on the Combined Cable-Stayed and Self-Anchored Suspension Bridge[J]. Pacific Science Review.2005(7):107-111.
[13]周孟波,刘自明,王邦楣.斜拉桥手册[M].北京：人民交通出版社,2004.
[14]孙斌,肖汝诚,贾丽君,等.斜拉-悬吊协作体系桥经济性能研究[C].南京：同济大学出版社,2000.
[15]颜娟.自锚式悬索桥[J].国外桥梁.2002(001)：19-22.
[16]张哲,窦鹏,石磊,等.自锚式悬索桥的发展综述[J].世界桥梁.2003(1)：5-9.
[17]张元凯,肖汝诚.自锚式悬索桥的概念设计[J].公路.2002(11)：46-49.
[18]邱文亮.自锚式悬索桥非线性分析与试验研究[D].大连：大连理工大学,2004.
[19]张新军,张丹.吊拉组合体系桥的研究进展[J].浙江工业大学学报.2007,35(5)：553-558.
[20]Mal J. Nonlinear models of suspension bridges[J]. Journal of Mathematical Analysis and Applications.2006,321(2):828-850.
[21]Karoumi R. Some modeling aspects in the nonlinear finite element analysis of cable supported bridges[J]. Computers and Structures.1999,71(4):397-412.
[22]周上君.大跨度斜拉桥非线性分析[J].桥梁建设.1982(4)：11-24.
[23]张翔.大跨径悬索桥的几何非线性分析[C].第十二届全国桥梁学术会议论文集：1992.
[24]李德寅.钢悬索桥非线性计算基本理论一[J].国外桥梁.1994(3)：204-216.
[25]潘永仁.悬索桥结构非线性分析理论与方法[M].北京：人民交通出版社,2004.
[26]潘家英,吴亮明,高路彬.大跨度斜拉桥活载非线性研究[J].土木工程学报.1993,26(1)：31-37.
[27]辛克贵,杨国平.大跨度斜拉桥恒载非线性静力分析[J].清华大学学报：自然科学版.2002,42(6)：818-821.
[28]华孝良,徐光辉.桥梁结构非线性分析[M].北京：人民交通出版社,1997.
[29]林少恒,陈启.悬索桥结构几何非线性分析方法[J].山西建筑.2009(22).
[30]肖汝诚,周念先.走向21世纪的斜张桥(二)：斜张桥的计算理论[J].铁道标准设计.1998(005)：1-2.
[31]肖汝诚,周念先.走向21世纪的斜张桥(三)[J].铁道标准设计.1998(012)：27-33.
[32]周念先,肖汝诚.走向21世纪的斜张桥(一)[J].铁道标准设计.1998(001)：6-9.
[33]Wenzel H. Cable stayed bridges:history, design, application[M]. Northern Gate,1998.
[34]Wang P H, Tseng T C, Yang C G. Initial shape of cable-stayed bridges[J]. Computers & structures.1993,47(1):111-123.
[35]Bruno D, Leonardi A. Natural periods of long-span cable-stayed bridges[J]. Journal of Bridge Engineering.1997,2(3):105-115.
[36]柳惠芬.斜拉桥的实用简化分析[D].上海：同济大学,1995.
[37]华孝良,张惠峰.斜拉桥几何非线性简化分析法及其应用[J].中国土木工程学会桥梁及结构工程学会第11届年会论文集.1994.
[38]柳惠芬,姚玲森.斜拉桥梁非线性实用简化分析[J].同济大学学报：自然科学版.2001,29(1)：118-121.
[39]MS特罗伊茨基著,王学汶程庆国等译.斜拉桥理论与设计[M].北京：中国铁道出版社,1980.
[40]黄琼.钢—混凝土混合梁自锚式悬索桥受力性能与计算方法研究[D].长沙：中南大学,2007.
[41]郭永强,崔远.悬索桥的初步分析[J].中外公路.2005,25(002)：54-60.
[42]雷俊卿,郑明珠,徐恭义.悬索桥设计[M].北京：人民交通出版社,2002.
[43]周孟波,刘自明,王邦楣.悬索桥手册[M].北京：人民交通出版社,2003.
[44]Irvine H M. Cable structures[M]. New York:Dover,1992.
[45]Ochsendorf J A, Billington D P. Self-anchored suspension bridges[J]. Journal of bridge engineering.1999,4(3):151.
[46]檀永刚,石磊,张哲.一种悬索桥静力分析的解析元法[J].武汉理工大学学报(交通科学与工程版).2009(05).
[47]吕丹,盛洪飞,郑传峰,等.自锚式悬索桥主梁面内稳定实用简化计算方法探索[J].华东公路.2008(01).
[48]黄琼,叶梅新.自锚式悬索桥简化计算方法研究[J].铁道学报.2008(01).
[49]肖海波,俞亚南,高庆丰.自锚式悬索桥主缆成桥线形分析[J].浙江大学学报(工学版).2004(11).
[50]周孟波,文武松.悬索桥的简化数值分析方法[J].国外桥梁.2000(02).
[51]程翔云.“悬索桥按二阶理论的实用计算”法的推广应用探讨[J].公路.2000(06).
[52]Wollmann G P. Preliminary analysis of suspension bridges[J]. Journal of Bridge
Engineering.2001,6(4):227-233.
[53]Clemente P, Nicolosi G, Raithel A. Preliminary design of very long-span suspension bridges[J]. Engineering Structures.2000,22(12):1699-1706.
[54]Cobo A D, Aparicio A C. Preliminary static analysis of suspension bridges[J]. Engineering Structures.2001,23(9):1096-1103.
[55]Virlogeux M. Recent evolution of cable-stayed bridges[J]. Engineering structures. 1999,21 (8):737-755.
[56]Ahmed N U. A general mathematical framework for stochastic analysis of suspension bridges[J]. Nonlinear Analysis:Real World Applications.2000,1(4):457-483.
[57]李国豪.桥梁与结构理论研究[M].上海科学技术文献出版社,1983.
[58]徐君兰,向中富.关于悬索桥的重力刚度[J].重庆交通学院学报.2000,19(2)：71-74.
[59]陈仁福.大跨悬索桥理论[M].成都：西南交通大学出版社,1994.
[60]龙驭球.弹性地基梁的计算[M].北京：人民教育出版社,1982.
[61]尹刚,朱渝春,冯贤桂.弹性地基梁的积分变换解法[J].重庆工学院学报.2005,19(5)：12-14.
[62]陈天愚,张克绪.弹性地基梁的修正刚度矩阵解法[J].哈尔滨建筑大学学报.2000,33(2)：44-48.
[63]刘庆潭,倪国荣.弹性地基梁的传递矩阵法求解[J].长沙铁道学院学报.1992,10(2)：92-102.
[64]尼尔斯J,吉姆辛,姚铃森,等.缆索承重桥梁[M].北京：人民交通出版社,1992.
[65]Gimsing N J. Cable supported bridges:Concepts and design[M].1983.
[66]严国敏.现代斜拉桥[M].成都：西南交通大学出版社,2000.
[67]严国敏,周世忠.现代悬索桥[M].北京：人民交通出版社,2002.
[68]陈明宪.斜拉桥的发展与展望[J].中外公路.2006,26(4)：76-86.
[69]Virola J, Ing-feani E, Helsinki F. Long-span cable-supported bridges:general review [J]. The IES Journal Part A:Civil & Structural Engineering.2009,2(4):304-308.
[70]Niels J G. Cable Supported Bridges:Concept and Design[M]. New York:John Wiley & Sons,1997.
[71]王伯惠.斜拉桥结构发展和中国经验[M].北京：人民交通出版社,2003.
[72]肖汝诚,项海帆.拉吊协作桥的施工控制与吊索疲劳控制研究[J].同济大学学报.1999,27(2)：234-238.
[73]黎祖华.超大跨度桥梁形式的探讨[J].国外桥梁.1992(4)：13-15.
[74]尼尔斯J,吉姆辛,姚林森,等.缆索承重桥梁构思与设计[M].北京：人民交通出版社,1992.
[75]许福友,张哲,黄才良,等.斜拉-悬吊协作体系桥工程应用及特点分析[J].中外公路.2009,29(1)：98-101.
[76]孙淑红,蒙云.吊拉组合桥交接区域吊杆的疲劳问题研究[J].重庆交通学院学报.1999,18(4)：13-18.
[77]蒙云,刘东,孙淑红.大跨度P.F.C.吊拉组合桥设计研究[J].重庆交通学院学报.1999,18(4)：8-12.
[78]张哲,王会利,黄才良,等.自锚式斜拉-悬索协作体系桥梁设计与分析[J].公路.2006(7)：44-48.
[79]贾丽君.大跨度悬索桥体系及其性能研究[D].上海：同济大学,2009.
[80]陈从春.矮塔斜拉桥设计理论核心问题研究[D].上海：同济大学,2006.
[81]Tang M. Design of cable-stayed girder bridges [J]. Journal of the Structural Division. 1972,92(8):1789-1802.
[82]Zellnet W. Discussion of Cable-Stayed Bridges:Degrees of Anchoring[J]. Journal of Structural Engineering.1984,110(4):910-914.
[83]Brozzetti J. Design development of steel-concrete composite bridges in France[J]. Journal of Constructional Steel Research.2000,55(1-3):229-243.
[84]李方东.钢—砼箱形结合梁在斜拉桥中的应用[J].公路与汽运.2003(6)：56-59.
[85]陈开利,余天庆,习刚.混合梁斜拉桥的发展与展望[J].桥梁建设.2005(2)：1-4.
[86]肖汝诚,贾丽君,薛二乐.斜拉—悬吊协作体系的设计探索[J].土木工程学报.2000,33(5)：46-51.
[87]刘钊,刘厚军.悬索桥主缆变形及重力刚度新算法[J].工程力学.2009(6)：127-132.
[88]张志国,邹振祝,赵玉成,等.悬索桥主缆线形解析方程解及应用[J].工程力学.2005,22(003)：172-176.
[89]胡隽.大跨度吊拉组合索桥的理论研究[D].北京：北方交通大学,2000.
[90]苗家武.超大跨度斜拉桥设计理论研究[D].上海：同济大学,2006.
[91]周念先.特大跨斜张桥与悬索桥的对比[J].江苏交通工程.1993(1)：16-20.
[92]蒋永林,卢伟.斜拉桥和悬索桥跨越效率的比较[J].国外桥梁.1998(4)：10-11.
[93]肖汝诚,项海帆.斜拉-悬吊协作体系桥力学特性及其经济性能研究[J].中国公路学报.1999.
[94]Starossek U. Cable-stayed bridge concept for longer spans[J]. Journal of Bridge Engineering.1996,1(3):99-103.
[95]Manabu I. Cable-supported steel bridge:design problem and solutions[J]. Journal of construct steel research.1996,39(1):69-84.
[96]Cluley N C, Shepherd R. Analysis of concrete cable-stayed bridges for creep, shrinkage and relaxation effects[J]. Computers and Structures.1996,58(2):337-350.
[97]姚玲森.混凝土斜张桥的徐变与收缩内力计算[J].中南公路工程.1982,1(5)：54-73.
[98]胡建华,唐茂林,刘蓉,等.自锚式悬索桥收缩徐变效应分析[J].重庆交通大学学报：自然科学版.2007,26(005)：5-8.
[99]夏国平,张哲,王骞.混凝土收缩徐变对斜拉-悬索协作体系桥的影响[C].大连：中国建筑工业出版社,2008.
[100]李熠,于磊.收缩徐变对混凝土斜拉桥成桥状态的影响分析[J].国防交通工程与技术.2009(06).
[101]陆从飞.大跨度斜拉桥施工阶段几何非线性静力分析[J].四川建筑.2009(05).
[102]夏国平,张哲,叶毅.斜拉-悬索协作体系桥的温度效应分析[J].武汉理工大学学报(交通科学与工程版).2009(05).
[103]XiaoqingS, Yongshui Z, Yuanfu Z. Influence Research of Temperature on Suspension Bridge Anchor Span Strand Tension [J] [J]. Transportation Science & Technology.2009,4.
[104]中交公路规划设计院.公路桥涵设计通用规范(JTGD60—2004)[M].北京：人民交通出版社,2004.
[105]陈从春.矮塔斜拉桥索梁活载比的特性研究[J].公路交通科技.2009,16(1)：99-103.
[106]Spyrakos C C, Kemp E L, Venkatareddy R. Validated analysis of wheeling suspension bridge[J]. Journal of Bridge Engineering.1999,4(1):1-7.
[107]徐君兰,姚玲森.悬索桥[M].北京：人民交通出版社,2001.
[108]潘永仁,杜国华.悬索桥恒载结构几何形状及内力的精细计算[J].中国公路学报.2000,13(4)：33-36.
[109]Plan S, Committees S, Committees P, et al. Suspension Bridge Cable Strength Equation Modifications[J]. Transportation Research.2009,6:55AM.
[110]项海帆,姚玲森.高等桥梁结构理论[M].北京：人民交通出版社,2001.
[111]李正良.变刚度梁的计算[M].北京：人民交通出版社,1996.
[112]李国豪,石洞.公路桥梁荷载横向分布计算[M].北京：人民交通出版社,1987.
[113]柳红霞.共轭梁法在梁变形计算中的运用[J].长沙大学学报.2002,16(02)：63-66.
[114]冯健,吕志涛.次弯矩计算的共轭梁法[J].东南大学学报：自然科学版.1997,27(A11)：71-75.
[115]柳惠芬,姚玲森,易建国.双塔斜拉桥的实用简化分析[J].上海公路.2001,29(1)：118-121.
[116]孙训方,方孝淑,关来泰.材料力学[M].北京：高等教育出版社,1994.
[117]胡锡恒.实用拉普拉斯变换与Z变换手册[M].北京：电子工业出版社,1988.
[118]肖恩源.索的特性(连载)[J].公路.1997(05)：1-7.
[119]肖恩源.索的特性(续)[J].公路.1997(06)：2-6.
[120]肖恩源.索的特性(续)[J].公路.1998(04)：24-31.
[121]吴恒立.关于悬索桥的重力刚度一文的讨论[J].重庆交通学院学报.2001,20(001)：118-119.
[122]Jennings A. Gravity stiffness of classical suspension bridges[J]. Journal of Structural Engineering.1983,109(1):16-36.
[123]Yang D. Modeling on gravity stiffness of suspension bridges by finite element method of geometric nonlinearity[C].上海：上海大学出版社,2007.
[124]郑凯锋,栗怀广,胥润东.连续超大跨悬索桥的刚度特征[J].西南交通大学学报.2009,44(3)：342-346.
[125]王京杭,夏咏明,蒋湘成.南京白果桥主缆长度计算[J].现代交通技术.2009(05).
[126]王鹏.悬索桥空缆线形分析综述[J].工程与建设.2009(04).
[127]杨益.悬索桥空缆状态下结构参数计算[J].科技信息.2008(32).
[128]hegab H I A,周先雁,朱之基.用能量法分析斜拉桥[J].世界桥梁.1987,4：63-71.
[129]吴红林,黄侨,金秀辉.斜拉桥施工控制调索方法研究及应用[J].公路交通科技(应用技术 版).2007(04).
[130]易鹏.大跨度公铁两用斜拉桥计算模型简化的探讨[J].铁道标准设计.2003(09).
[131]郭卓明,李国平,袁万城.独塔单索面斜拉桥主塔稳定简化分析[J].同济大学学报(自然科学版).2000(02).
[132]王勋文,辛学忠,潘家英,等.确定PC斜拉桥合理恒载索力方法的探讨[J].桥梁建设.1996(04).
[133]罗开红,岳平,王清.数值模拟在悬索桥中的应用[J].科技风.2009(13).
[134]周云开,郑子恒.自锚式悬索桥恒载吊索力设计方法探讨[J].广东建材.2009(06).
[135]李乔.斜拉桥的受力特征分析[C].昆明：1999.
[136]贺栓海.桥梁结构理论与计算方法[M].北京：人民交通出版社,2003.
[137]张雪松,梁鹏,贾丽君,等.非线性因素对超大跨度斜拉桥活载内力的影响[J].重庆交通学院学报.2005,24(1)：5-8.
[138]李晓莉.独塔斜拉桥的设计理论研究[D].上海：同济大学,2006.