弯梁桥的结构理论分析及支承形式研究
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摘要
随着我国公路和城市道路的迅速发展,高架道路及立体交叉工程愈来愈多,弯梁桥的运用越来越广泛。与直线梁桥相比,弯梁桥存在着弯矩和扭矩互相耦合的独特力学性质。弯梁桥不同的支承形式将直接影响到全桥的内力分布,支承形式的改变,会使弯梁桥的弯扭耦合程度也发生改变。在弯梁桥的设计中,通过选择合适的支承形式可以调整截面的受力状态,有利于弯梁桥的优化设计,可获得显著的经济效益。
本文总结了弯梁桥的四种计算理论,并在符拉索夫方程的基础上,给出了简支超静定弯梁桥的闭合解以及有限差分法数值解;详细地研究了梁格法等效模拟箱梁的基本理论,从梁格网格划分、截面特性计算及输出结果处理等方面进行了系统分析,探讨采用梁格法分析弯箱梁时较为合理的网格划分方法,以及合理的梁格刚度等效原则和计算结果的处理方法。
基于梁格法原理,运用MIDAS/Civil有限元软件建立梁格模型,分析了不同的支承形式对弯梁桥结构的影响,得出支承形式的改变对弯梁桥扭矩的影响很大,而对剪力和弯矩的影响微小的结论;提出了通过预设支座偏心、减小扭转跨径和拉大端支座间距的方法,以增强弯梁桥的抗扭能力;对具有不同中支座偏心距的弯梁桥进行分析计算,得出适当选取支座预偏心,可以使得梁端支承点不脱空、内侧支座不出现负反力,可以使得弯梁桥的扭矩满足最大值与最小值接近相等;最后总结了弯梁桥应当如何布置支承体系,以保证支承约束既能适应弯梁桥的受力和变形,又能保证结构的安全稳定;提出了施工温度不同时对支座进行偏心调整的措施,为弯梁桥的设计和同类工程的处理提供参考和借鉴。
Due to the rapid development of highways and city roads of our country, more and more elevated roads and city overhead crossings are built, which lead to the wider application of curved girder bridges. Compared to the straight beam bridges, curved girder bridges have the particular mechanical characteristic of bending moment-torsion coupling. Different supporting forms will directly affect the whole internal force distribution in curved girder bridges. The variation of the supporting form will change the degree of bending moment-torsion coupling. In the design of curved girder bridges, the force state of the section can be adjusted by selecting suitable supporting forms. It is beneficial to the optimal design of curved girder bridges and can obtain significant economic benefit.
This thesis summarized four kinds of calculation theories of curved girder bridges, in which the closed solution and finite difference method numerical solution of simple supported statically indeterminate curved girder bridges are given based on Vlasov Equation, and the basic theory of grillage analogy method to equivalently simulate box girder is studied in detail. The principles that how to divide the grillage, how to calculate the constants for longitudinal beams and transverse beams, and how to deal with the results gotten by grillage analogy in box girder bridges are analyzed systematically, and the reasonable principles are proposed.
Based on the principle of grillage analogy method, the grillage finite models with different supporting forms are built to analyze their effects to curved girder bridges by MIDAS/Civil finite element software, which come to the conclusion that the change of supporting form has great impact on the torsion and has little influence on the longitudinal shear force and bending moment. This thesis puts forward three methods to reinforce the ability of anti-torsion of curved girder bridges, which are presetting support eccentricity, reducing torsional span length and increasing the distance of beam-end supportings. By the calculation of the curved girder bridges with different internal support eccentricities, this thesis also draws the conclusions that if the support eccentricity is suitable, the beam will not disengage from supportings, the inside supportings will not appear negative counterforce and the maximum and the minimum torsion can be approximately equale. At length, the thesis provides means of arranging the supportings to ensure that they can not only adapt to the force and deformation of curved girder bridges, but also guarantee for security and stability of the structures. The thesis also provides measures to adjust supportings under different construction temperatures in hope of giving some reference for the design of curved girder bridges as well as some similar practical projects.
本文总结了弯梁桥的四种计算理论,并在符拉索夫方程的基础上,给出了简支超静定弯梁桥的闭合解以及有限差分法数值解;详细地研究了梁格法等效模拟箱梁的基本理论,从梁格网格划分、截面特性计算及输出结果处理等方面进行了系统分析,探讨采用梁格法分析弯箱梁时较为合理的网格划分方法,以及合理的梁格刚度等效原则和计算结果的处理方法。
基于梁格法原理,运用MIDAS/Civil有限元软件建立梁格模型,分析了不同的支承形式对弯梁桥结构的影响,得出支承形式的改变对弯梁桥扭矩的影响很大,而对剪力和弯矩的影响微小的结论;提出了通过预设支座偏心、减小扭转跨径和拉大端支座间距的方法,以增强弯梁桥的抗扭能力;对具有不同中支座偏心距的弯梁桥进行分析计算,得出适当选取支座预偏心,可以使得梁端支承点不脱空、内侧支座不出现负反力,可以使得弯梁桥的扭矩满足最大值与最小值接近相等;最后总结了弯梁桥应当如何布置支承体系,以保证支承约束既能适应弯梁桥的受力和变形,又能保证结构的安全稳定;提出了施工温度不同时对支座进行偏心调整的措施,为弯梁桥的设计和同类工程的处理提供参考和借鉴。
Due to the rapid development of highways and city roads of our country, more and more elevated roads and city overhead crossings are built, which lead to the wider application of curved girder bridges. Compared to the straight beam bridges, curved girder bridges have the particular mechanical characteristic of bending moment-torsion coupling. Different supporting forms will directly affect the whole internal force distribution in curved girder bridges. The variation of the supporting form will change the degree of bending moment-torsion coupling. In the design of curved girder bridges, the force state of the section can be adjusted by selecting suitable supporting forms. It is beneficial to the optimal design of curved girder bridges and can obtain significant economic benefit.
This thesis summarized four kinds of calculation theories of curved girder bridges, in which the closed solution and finite difference method numerical solution of simple supported statically indeterminate curved girder bridges are given based on Vlasov Equation, and the basic theory of grillage analogy method to equivalently simulate box girder is studied in detail. The principles that how to divide the grillage, how to calculate the constants for longitudinal beams and transverse beams, and how to deal with the results gotten by grillage analogy in box girder bridges are analyzed systematically, and the reasonable principles are proposed.
Based on the principle of grillage analogy method, the grillage finite models with different supporting forms are built to analyze their effects to curved girder bridges by MIDAS/Civil finite element software, which come to the conclusion that the change of supporting form has great impact on the torsion and has little influence on the longitudinal shear force and bending moment. This thesis puts forward three methods to reinforce the ability of anti-torsion of curved girder bridges, which are presetting support eccentricity, reducing torsional span length and increasing the distance of beam-end supportings. By the calculation of the curved girder bridges with different internal support eccentricities, this thesis also draws the conclusions that if the support eccentricity is suitable, the beam will not disengage from supportings, the inside supportings will not appear negative counterforce and the maximum and the minimum torsion can be approximately equale. At length, the thesis provides means of arranging the supportings to ensure that they can not only adapt to the force and deformation of curved girder bridges, but also guarantee for security and stability of the structures. The thesis also provides measures to adjust supportings under different construction temperatures in hope of giving some reference for the design of curved girder bridges as well as some similar practical projects.
引文
[1]邵容光,夏淦.混凝土弯梁桥[M].北京:人民交通出版设, 1992
[2]谭万忠.曲线梁桥平面变形特性和支承布置的研究[D].北京:铁道科学研究院, 2005, 5
[3]中国公路学会桥梁工程学会等. 1986年道路立交工程及弯坡斜桥学术讨论会议论文集[C]. 1986
[4]黄剑源,谢旭.城市高架桥的结构理论与计算方法[M].北京:科学出版社, 2001: 251-272
[5] V.Z.Vlasov. Thin-Walled Elastic Beams. Washington, D.C: National Science Foundation[J], 1961
[6] R.Dabrowski. Curved Thin-Walled Girders. Translation No.144. London: Cement and Concrete Association, 1968
[7]李国豪.大薄壁箱梁桥的扭转和弯曲的弯曲理论[J].土木工程学报, 1987(20)
[8]李明昭.断面可变形的矩形箱式薄壁圆弧曲杆静力分析法[J].同济大学学报, 1982(2)
[9]钱寅泉等.薄壁箱形大曲率梁桥理论分析[J].土木工程学报, 1993(10)
[10]夏淦.变曲率曲梁挠曲扭转分析[J].土木工程学报, 1991,24(2)
[11] C.P.Heins著.结构杆件的弯曲与扭转[M].常岭等译校.北京:人民交通出版社, 1981
[12]姚玲森.曲线梁桥的实用计算方法[J].土木工程学报, 1982(3)
[13]郑振飞,吴庆雄著.斜弯桥分析的广义梁格法[M].北京:人民交通出版社, 1998
[14]郑振飞,徐艳著.非径向支承弯梁桥的计算方法[M].北京:人民交通出版社, 2000
[15]项贻强.有限条在箱梁分析中的应用[J].河南交通科技, 1990
[16]赵振铭,房贞政,郭金琼.带隔板的连续箱梁有限条法分析[J].桥梁建设, 1983(4)
[17]张慕圣.连续箱梁曲桥的有限条分析法[J].土木工程学报, 1984(3)
[18]罗旗帜.薄壁箱形梁剪力滞计算的梁段有限元法[J].湖南大学学报, 1991, 18(2)
[19]钟新谷,马平,曾庆元.多室箱形梁非线性有限元分析[J].土木工程学报, 1999, 32(6): 32-39
[20] Meyer, C., Scordelis, A.C.. Computer Program for Prismatic Folded Plates with Plate andBeam Elements[J], Structural Engineering and Structural Mechanics Report No.70(3), University of California, Berkeley, 1970
[21]经柏林,邵旭东.变截面长悬臂宽箱梁桥翼缘有效宽度研究[J].中南公路工程, 1998, 23(4): 24-26
[22]彭大文,王忠.连续弯箱梁剪滞效应分析和实用计算法研究[J].中国公路学报, 1998, 11(3): 41-49
[23]谢旭,黄剑源.薄壁箱形梁桥约束扭转下翘曲、畸变和剪滞效应的空间分析[J].土木程学报, 1995, 28(4)
[24] Tesar, A.“Shear lag in the behaviour of thin-walled box bridges”Comput. Struct[J], 1996, 59(4)
[25]韦成龙,曾庆元,刘小燕等.薄壁箱梁剪力滞分析的多参数翘曲位移函数及其有限元法[J].铁道学报, 2000, 22(5): 60-63
[26]陈贞拒,程正明.连续刚构弯箱梁零号块的空间应力分析[C].第十三届全国桥梁学术会议论文集,上海, 1998(11)
[27]高岛春生著.曲线梁桥[M].张德礼译.北京:中国建筑工业出版社, 1979: 1-2
[28]范立础.桥梁工程(上册).北京:人民交通出版设, 2001, 11
[29]姜海丽,苏辉,赵伟.曲线梁桥的设计[J].黑龙江水利科技, 2006(3): 85-86
[30]韩皓,曹劲松.曲线箱梁实用设计方法的研究[J].内蒙古工业大学学报, 1997, 16(2): 23-27
[31]刘鹏.弯梁桥的评价与加固方法研究[D].西安:长安大学, 2007, 6
[32]孙向东,陈湘华.弯梁桥建模分析[J].东北公路, 2001, 24(3): 58-59
[33] E.C.汉勃利.桥梁上部结构性能[M].郭德辉译.北京:人民交通出版社, 1982: 89-100
[34] E.C. Hambly. Bridge Deck Behaviour[M]. Second edition. Champman and Hall, London, 1991
[35]戴公连,李德建.桥梁结构空间分析设计方法与应用[M].北京:人民交通出版社, 2001: 15-36
[36] Lightfoot, E. and Sawko, F. (1959),“Structural Frame Analysis by Electronic Computer: Grid Frame Works Resolved by Generalized Slop Deflection”. Engineering, PP: 18-20
[37]黄剑源,张罗溪.考虑翘曲作用的曲线格子梁理论与应用—青岛曲线斜支承格子梁桥的分析[J].土木工程学报, 1987, 20(3)
[38]陈博.异形混凝土箱梁桥静力性能研究[D].西安:长安大学, 2007, 6
[39]项海帆.高等桥梁结构理论[M].北京:人民交通出版社, 2001
[40]姚玲森.平面连续曲线梁桥支撑方式对内力的影响[C].中国土木工程学会第五届年会第二次全国桥梁学术会议论文集, 1990
[41] JTG D60―2004.公路桥涵设计通用规范[S].北京:人民交通出版社, 2004: 35
[42]梁仲林.曲线梁桥设计中支承形式的选用[J].桥梁建设, 2007(S1): 7-10
[43]朱琳.预应力混凝土曲线梁桥抗扭设计分析[D].武汉:武汉理工大学, 2006, 4
[44]冯顺剑,单德山.高速铁路曲线梁桥的合理结构形式初探[J].浙江交通职业技术学院学报, 2001, 2(4): 1-7
[45]何维利.独柱支承的曲线梁桥设计[J].北京建筑工程学院学报, 2001, 17(4): 23-28
[46]周勇,余泽新,张明武.小半径曲线梁的设计[J].中外公路, 2007, 27(2): 89-91
[47]陈维昌.福建省南同战备公路美林立交桥0#台内侧支座悬空加固处理[J].福建交通科技, 2003(2)
[48]吴玉财,吴亦嘉,邱志雄等.匝道桥预应力连续弯梁扭曲变形整治方法的安全性分析[J].中外公路, 2006, 26(2): 147-149
[49]吴玉财.预应力混凝土连续弯桥病害加固计算分析[J].交通科技, 2007(3): 31-33
[50]谢智敏,曹卫力.弯梁桥常见问题分析[J].广西交通科技, 2003(2): 49-51
[51]刘德华,金伟良,刘斌等.独柱墩曲线梁桥中的支座分析[J].南京理工大学学报, 2006, 30(1): 113-116
[2]谭万忠.曲线梁桥平面变形特性和支承布置的研究[D].北京:铁道科学研究院, 2005, 5
[3]中国公路学会桥梁工程学会等. 1986年道路立交工程及弯坡斜桥学术讨论会议论文集[C]. 1986
[4]黄剑源,谢旭.城市高架桥的结构理论与计算方法[M].北京:科学出版社, 2001: 251-272
[5] V.Z.Vlasov. Thin-Walled Elastic Beams. Washington, D.C: National Science Foundation[J], 1961
[6] R.Dabrowski. Curved Thin-Walled Girders. Translation No.144. London: Cement and Concrete Association, 1968
[7]李国豪.大薄壁箱梁桥的扭转和弯曲的弯曲理论[J].土木工程学报, 1987(20)
[8]李明昭.断面可变形的矩形箱式薄壁圆弧曲杆静力分析法[J].同济大学学报, 1982(2)
[9]钱寅泉等.薄壁箱形大曲率梁桥理论分析[J].土木工程学报, 1993(10)
[10]夏淦.变曲率曲梁挠曲扭转分析[J].土木工程学报, 1991,24(2)
[11] C.P.Heins著.结构杆件的弯曲与扭转[M].常岭等译校.北京:人民交通出版社, 1981
[12]姚玲森.曲线梁桥的实用计算方法[J].土木工程学报, 1982(3)
[13]郑振飞,吴庆雄著.斜弯桥分析的广义梁格法[M].北京:人民交通出版社, 1998
[14]郑振飞,徐艳著.非径向支承弯梁桥的计算方法[M].北京:人民交通出版社, 2000
[15]项贻强.有限条在箱梁分析中的应用[J].河南交通科技, 1990
[16]赵振铭,房贞政,郭金琼.带隔板的连续箱梁有限条法分析[J].桥梁建设, 1983(4)
[17]张慕圣.连续箱梁曲桥的有限条分析法[J].土木工程学报, 1984(3)
[18]罗旗帜.薄壁箱形梁剪力滞计算的梁段有限元法[J].湖南大学学报, 1991, 18(2)
[19]钟新谷,马平,曾庆元.多室箱形梁非线性有限元分析[J].土木工程学报, 1999, 32(6): 32-39
[20] Meyer, C., Scordelis, A.C.. Computer Program for Prismatic Folded Plates with Plate andBeam Elements[J], Structural Engineering and Structural Mechanics Report No.70(3), University of California, Berkeley, 1970
[21]经柏林,邵旭东.变截面长悬臂宽箱梁桥翼缘有效宽度研究[J].中南公路工程, 1998, 23(4): 24-26
[22]彭大文,王忠.连续弯箱梁剪滞效应分析和实用计算法研究[J].中国公路学报, 1998, 11(3): 41-49
[23]谢旭,黄剑源.薄壁箱形梁桥约束扭转下翘曲、畸变和剪滞效应的空间分析[J].土木程学报, 1995, 28(4)
[24] Tesar, A.“Shear lag in the behaviour of thin-walled box bridges”Comput. Struct[J], 1996, 59(4)
[25]韦成龙,曾庆元,刘小燕等.薄壁箱梁剪力滞分析的多参数翘曲位移函数及其有限元法[J].铁道学报, 2000, 22(5): 60-63
[26]陈贞拒,程正明.连续刚构弯箱梁零号块的空间应力分析[C].第十三届全国桥梁学术会议论文集,上海, 1998(11)
[27]高岛春生著.曲线梁桥[M].张德礼译.北京:中国建筑工业出版社, 1979: 1-2
[28]范立础.桥梁工程(上册).北京:人民交通出版设, 2001, 11
[29]姜海丽,苏辉,赵伟.曲线梁桥的设计[J].黑龙江水利科技, 2006(3): 85-86
[30]韩皓,曹劲松.曲线箱梁实用设计方法的研究[J].内蒙古工业大学学报, 1997, 16(2): 23-27
[31]刘鹏.弯梁桥的评价与加固方法研究[D].西安:长安大学, 2007, 6
[32]孙向东,陈湘华.弯梁桥建模分析[J].东北公路, 2001, 24(3): 58-59
[33] E.C.汉勃利.桥梁上部结构性能[M].郭德辉译.北京:人民交通出版社, 1982: 89-100
[34] E.C. Hambly. Bridge Deck Behaviour[M]. Second edition. Champman and Hall, London, 1991
[35]戴公连,李德建.桥梁结构空间分析设计方法与应用[M].北京:人民交通出版社, 2001: 15-36
[36] Lightfoot, E. and Sawko, F. (1959),“Structural Frame Analysis by Electronic Computer: Grid Frame Works Resolved by Generalized Slop Deflection”. Engineering, PP: 18-20
[37]黄剑源,张罗溪.考虑翘曲作用的曲线格子梁理论与应用—青岛曲线斜支承格子梁桥的分析[J].土木工程学报, 1987, 20(3)
[38]陈博.异形混凝土箱梁桥静力性能研究[D].西安:长安大学, 2007, 6
[39]项海帆.高等桥梁结构理论[M].北京:人民交通出版社, 2001
[40]姚玲森.平面连续曲线梁桥支撑方式对内力的影响[C].中国土木工程学会第五届年会第二次全国桥梁学术会议论文集, 1990
[41] JTG D60―2004.公路桥涵设计通用规范[S].北京:人民交通出版社, 2004: 35
[42]梁仲林.曲线梁桥设计中支承形式的选用[J].桥梁建设, 2007(S1): 7-10
[43]朱琳.预应力混凝土曲线梁桥抗扭设计分析[D].武汉:武汉理工大学, 2006, 4
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