大跨度钢箱梁斜拉桥几何非线性分析
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摘要
斜拉桥由于其桥型美观、跨越能力强以及施工方便在近年来得到了快速发展。作为一种高次超静定柔性受力体系,与连续梁和桁架梁相比较,斜拉桥特别是大跨度斜拉桥,几何非线性影响较为突出,而且影响因素也较多。主要表现在：首先,随着斜拉索长度的增加,垂度效应渐渐明显,即索的伸长量与索拉力不成正比关系,这主要是由斜拉索自重引起的。其次,由于结构本身为柔性体系,承受外荷载时整个结构的变形较大,大位移问题突出。这种影响改变了荷载对结构上其它节点产生的弯矩。如果位移量过大,则会严重影响荷载对结构的效应。最后,由于轴力与弯矩的相互作用,斜拉桥特别是大跨度斜拉桥几何非线性的分析非常复杂。可以说,几何非线性对斜拉桥受力性能带来的影响已成为目前斜拉桥发展的重要制约因素。
目前认为,影响斜拉桥几何非线性的因素主要包括三个方面：垂度效应、大变形效应、弯矩—轴力组合效应。
本文首先介绍了斜拉桥的起源及发展历史,然后对斜拉桥的几何非线性研究方法进行了全面评述。最后以重庆丰都长江二桥设计方案为依托进行了实例分析。具体的研究内容和取得的成果如下：
(1)介绍斜拉桥几何非线性分析理论及其在实际计算中的应用,分析斜拉桥各种非线性因素产生的原因及其影响。
(2)针对丰都长江二桥设计方案建立有限元模型,模拟丰都长江二桥的施工过程,对其进行施工过程和成桥后的几何非线性分析。
(3)几何非线性对主梁弯矩的影响以斜拉索垂度的影响最大,大位移影响次之,弯矩与轴力组合效应影响最小,而且不同的施工阶段影响程度也不同。
(4)考虑温度荷载时,车辆荷载作用下,斜拉桥几何非线性较为明显,不可忽略。
Recently, Cable-stayed bridge has been rapidly developed because of beautiful appearance, long-span capacity and convenient construction. As a kind of flexible structure with high static indetermination, compared with continuous beam and truss beam bridges, the effect of geometrical nonlinearity of cable-stayed bridge is more outstanding and the influence factors are also more, especially for long-span cable-stayed bridge. These factors mainly manifested in the following aspects:Firstly, with the increase of the length of the cable, the sag generated by self-weight of the structure increase also, at the same time, the elongation and the tension of the cable is not in proportional relation. Secondly, the geometric deformation of the whole structure is larger, performed as a notable large displacement, that is when the load in cable-stayed bridge structure effect just for a node, the node will occur displacement, the load will also move. This displacement will change the bending moment on the other node produced by the load. If the displacement amount is large, it will seriously affect the effects of the load on the structure. Coupled with the axial force and bending moment interaction effects, it will make the geometrical nonlinear of long span cable-stayed bridge analysis more and more complex. Geometric nonlinearity of cable-stayed bridge has become the important restriction factor to the development of cable-stayed bridge.
The effect of geometrical nonlinearity of cable-stayed bridge includes three aspects:, cable-sage effects,combined effects of bending moment and axial force and large displacement.
First, this dissertation introduces the history and development of cable-stayed bridge, and then describes the research status of the theory of geometric nonlinearity for cable-stayed bridge. Lastly, taking the2th changjiang river bridge of chongqing fengdu as research background the author did some instance. The main contents and conclusions of the research are listed as follows:
Firstly, there is a introduction of the geometrical nonlinear analysis of cable-stayed bridge and its application in actual calculation, then, the author analysis the reasons and effects which caused by various nonlinear factors.
(1) Based on the design scheme of the2th fengdu changjiang river, we established a finite element model to simulate the actual construction process, and then analysis the geometric nonlinearity of construction stage and completed stage.
(2) Geometrical nonlinearity which affect the bending moment of the main girder, cable-sag has the most obvious effect and nonlinear of large displacement has greater effect, while the combined effect of moment and axial force has the least influence. Further, the effect degree is different in different construction phase.
(3) Taking account of the temperature load, geometric nonlinear of vehicle load is obvious, so it can not be ignored.
目前认为,影响斜拉桥几何非线性的因素主要包括三个方面：垂度效应、大变形效应、弯矩—轴力组合效应。
本文首先介绍了斜拉桥的起源及发展历史,然后对斜拉桥的几何非线性研究方法进行了全面评述。最后以重庆丰都长江二桥设计方案为依托进行了实例分析。具体的研究内容和取得的成果如下：
(1)介绍斜拉桥几何非线性分析理论及其在实际计算中的应用,分析斜拉桥各种非线性因素产生的原因及其影响。
(2)针对丰都长江二桥设计方案建立有限元模型,模拟丰都长江二桥的施工过程,对其进行施工过程和成桥后的几何非线性分析。
(3)几何非线性对主梁弯矩的影响以斜拉索垂度的影响最大,大位移影响次之,弯矩与轴力组合效应影响最小,而且不同的施工阶段影响程度也不同。
(4)考虑温度荷载时,车辆荷载作用下,斜拉桥几何非线性较为明显,不可忽略。
Recently, Cable-stayed bridge has been rapidly developed because of beautiful appearance, long-span capacity and convenient construction. As a kind of flexible structure with high static indetermination, compared with continuous beam and truss beam bridges, the effect of geometrical nonlinearity of cable-stayed bridge is more outstanding and the influence factors are also more, especially for long-span cable-stayed bridge. These factors mainly manifested in the following aspects:Firstly, with the increase of the length of the cable, the sag generated by self-weight of the structure increase also, at the same time, the elongation and the tension of the cable is not in proportional relation. Secondly, the geometric deformation of the whole structure is larger, performed as a notable large displacement, that is when the load in cable-stayed bridge structure effect just for a node, the node will occur displacement, the load will also move. This displacement will change the bending moment on the other node produced by the load. If the displacement amount is large, it will seriously affect the effects of the load on the structure. Coupled with the axial force and bending moment interaction effects, it will make the geometrical nonlinear of long span cable-stayed bridge analysis more and more complex. Geometric nonlinearity of cable-stayed bridge has become the important restriction factor to the development of cable-stayed bridge.
The effect of geometrical nonlinearity of cable-stayed bridge includes three aspects:, cable-sage effects,combined effects of bending moment and axial force and large displacement.
First, this dissertation introduces the history and development of cable-stayed bridge, and then describes the research status of the theory of geometric nonlinearity for cable-stayed bridge. Lastly, taking the2th changjiang river bridge of chongqing fengdu as research background the author did some instance. The main contents and conclusions of the research are listed as follows:
Firstly, there is a introduction of the geometrical nonlinear analysis of cable-stayed bridge and its application in actual calculation, then, the author analysis the reasons and effects which caused by various nonlinear factors.
(1) Based on the design scheme of the2th fengdu changjiang river, we established a finite element model to simulate the actual construction process, and then analysis the geometric nonlinearity of construction stage and completed stage.
(2) Geometrical nonlinearity which affect the bending moment of the main girder, cable-sag has the most obvious effect and nonlinear of large displacement has greater effect, while the combined effect of moment and axial force has the least influence. Further, the effect degree is different in different construction phase.
(3) Taking account of the temperature load, geometric nonlinear of vehicle load is obvious, so it can not be ignored.
引文
[1]邹循华.大跨径钢箱梁斜拉桥的静力几何非线性分析研究.南昌大学硕士学位论文,2008
[2]陈明宪.斜拉桥建造技术.北京.人民交通出版社,2003
[3]辛克贵 刘钺强 杨国平.大跨度斜拉桥恒载非线性分析[D],清华大学学报,2002
[4]李传习.夏桂云.大跨度桥梁结构计算理论.北京.人民交通出版社,2003
[5]胡文辉.润扬长江公路大桥北汊斜拉桥施工控制.东南大学硕士学位论文。2004
[6]严国敏.现代斜拉桥[M].西南交通大学出版社,1996
[7]魏科.基于CR列式的斜拉桥几何非线性分析,长安大学硕士学位论文,2009
[8]林元培.斜拉桥[M].人民交通出版社,1996
[9]王华林.斜拉桥非线性分析与施工控制.武汉理工大学硕士学位论文,2002
[10]姚玲森.桥梁工程.北京：人民交通出版社,1990
[11]邵旭东.桥梁工程[桥梁工程]人民交通出版社,2007
[12]朱晞,王克海.几何非线性对大跨度斜拉桥的影响.92全国桥梁结构学术大会,武汉,1992
[13]周凌远.斜拉桥非线性理论及极限承载力研究.西南交通大学博士论文,2007
[14]Seif SP, Dilger WH. Nonlinear Analysis and Collapse Load of P/C Cable-Ctayed Bridges [J] Journal of Structural Engineering.1990, 116(3):829-849
[15]Virlogeux M. Erection of Cable-Stayed Bridges [A].Proceedings of the Seminar of Cable- Stayed Bridges, Recent Developments and Their Future[C].JaPan:Yokohama.1991.77-106
[16]Ottosen N.S. Constitutive Model for Short-Time Loading of Concrete[J]. Journal of the Engineering, Mechanics Division. 1979, 105(1):127-141
[17]Wempner GA. Discrete Approximations Related to Nonlinear Theories of Solids[J]. International Journal of Solids and Structures,1971,7:1581-1599
[18]Man Chung Tang. Analysis of Cable-Stayed Girder Bridges. Journal of Structural Division [J], ASCE. May 1971
[19]尹超.大跨度斜拉桥几何非线性分析.西南交通大学硕士学位论文.2005
[20]Fleming JF. Nonlinear Static Analysis of Cable-Stayed Bridge Structures[J].Computers and Structures,1979
[21]Fleming JF. Egeseli EA. Dynamic Behavior of a Cable-Stayed Bridge [J].Earthquake Engineering and structural Dynamics, 1980
[22]Fleming JF. Computer Analysis of Structure System [M].New York:McGraw-Hill Book Co. 1989
[23]Nazmy A.S, Abdel-Ghaffar A.M. Three-dimensional Nonlinear Static Analysis of Cable-Stayed Bridges[J].Computers and Structures,1990
[24]Wang PH, Tseng TC, Yang GG Initial Shape of Cable-Stayed Bridges[J]. Computers and Structures 1993,46:1095-1106
[25]Wang PH, Yang GG Parametric Studies on Cable-Stayed Bridges [J]. Computers and Structures 1996
[26]Wang PH, Lin HT, Tang TY. Study on Nonlinear Analysis of a Highly Redundant Cable-Stayed Bridge[J].Computers and Structures, 2002, 80:165-182
[27]Wang PH, Tang TY, Zheng HN. Analysis of Cable-Stayed Bridges During Construction by Cantilever Methods [J].Computers and Structures, 2004, 82:329-346
[28]Wang YC. Geometric Nonlinear Behavior of Cable-Stayed Bridges[D].USA:University of Colorado at Boulder. 1994
[29]潘家英.吴亮明.高路彬等.关于大跨度斜拉桥几何非线性问题.全国桥梁结构学术大会论文集.同济大学出版社,1992
[30]李平利.大跨度斜拉桥施工阶段几何非线性静力分析.西南交通大学硕士论文,2004
[31]华孝良.徐光辉.桥梁结构非线性分析[M].人民交通出版社.1997
[32]O'Briem WT. General Solution of Suspended Cable Problems [J]. Journal of Structural Division, ASCE,1967,93(STl):1-26
[33]刘人通.弹性力学[M].西北工业大学出版社,2002
[34]蒋友谅.非线性有限元法.北京：北京工业学院出版社,1988
[35]杨炳成,陈偕民.结构有限元素法[M],1996
[36]赵均海.王敏强,魏雪英.高等有限元[M].武汉理工大学出版社,2004
[37]殷有泉.非线性有限元基础[M].北京大学出版社,2007
[38]项海帆.高等桥梁结构理论[M].人民交通出版社,2007
[39]宋天霞,郭建生,杨元明.非线性固体计算力学仁M].华中科技大学出版社,2005
[40]叶芳芳.大悬挑悬挂混合结构的施工控制.中南大学硕士学位论文.2009
[41]沈锐利.桥梁结构分析理论.西南交通大学工学硕士教学讲义,2009
[42]潘永仁.悬索桥结构分析理论与方法[M].人民交通出版社,2004
[43]颜东煌.斜拉桥合理设计状态确定与施工控制[D].湖南大学,2001
[44]廖元裳.钢筋混凝土桥.中国铁道出版社,1997
[45]徐金良.钢管混凝土拱桥施工过程及地震响应分析,西南交通大学硕士学位论文,2008
[46]徐凯燕,魏德敏,刘灿.大跨度斜拉桥几何非线性静力计算分析[J].工程抗震与加固改造,2008
[47]《桥梁设计常用数据手册》编写委员会编.北京：人民交通出版社,2005
[48]于应良.大跨度斜拉桥考虑几何非线性的静、动力分析和钢箱梁的第二体系应力研究.西南交通大学博士学位论文,2000
[49]北京Midas技术有限公司Midas使用手册,2000
[50]李乔.斜拉桥的受力特征分析[C].四川省公路学会桥梁专委会,1998年桥梁学术讨论会, 成都：西南交通大学出版社,1998：57-60
[51]周上君.斜拉桥非线性静力分析.桥梁建设.1982
[2]陈明宪.斜拉桥建造技术.北京.人民交通出版社,2003
[3]辛克贵 刘钺强 杨国平.大跨度斜拉桥恒载非线性分析[D],清华大学学报,2002
[4]李传习.夏桂云.大跨度桥梁结构计算理论.北京.人民交通出版社,2003
[5]胡文辉.润扬长江公路大桥北汊斜拉桥施工控制.东南大学硕士学位论文。2004
[6]严国敏.现代斜拉桥[M].西南交通大学出版社,1996
[7]魏科.基于CR列式的斜拉桥几何非线性分析,长安大学硕士学位论文,2009
[8]林元培.斜拉桥[M].人民交通出版社,1996
[9]王华林.斜拉桥非线性分析与施工控制.武汉理工大学硕士学位论文,2002
[10]姚玲森.桥梁工程.北京：人民交通出版社,1990
[11]邵旭东.桥梁工程[桥梁工程]人民交通出版社,2007
[12]朱晞,王克海.几何非线性对大跨度斜拉桥的影响.92全国桥梁结构学术大会,武汉,1992
[13]周凌远.斜拉桥非线性理论及极限承载力研究.西南交通大学博士论文,2007
[14]Seif SP, Dilger WH. Nonlinear Analysis and Collapse Load of P/C Cable-Ctayed Bridges [J] Journal of Structural Engineering.1990, 116(3):829-849
[15]Virlogeux M. Erection of Cable-Stayed Bridges [A].Proceedings of the Seminar of Cable- Stayed Bridges, Recent Developments and Their Future[C].JaPan:Yokohama.1991.77-106
[16]Ottosen N.S. Constitutive Model for Short-Time Loading of Concrete[J]. Journal of the Engineering, Mechanics Division. 1979, 105(1):127-141
[17]Wempner GA. Discrete Approximations Related to Nonlinear Theories of Solids[J]. International Journal of Solids and Structures,1971,7:1581-1599
[18]Man Chung Tang. Analysis of Cable-Stayed Girder Bridges. Journal of Structural Division [J], ASCE. May 1971
[19]尹超.大跨度斜拉桥几何非线性分析.西南交通大学硕士学位论文.2005
[20]Fleming JF. Nonlinear Static Analysis of Cable-Stayed Bridge Structures[J].Computers and Structures,1979
[21]Fleming JF. Egeseli EA. Dynamic Behavior of a Cable-Stayed Bridge [J].Earthquake Engineering and structural Dynamics, 1980
[22]Fleming JF. Computer Analysis of Structure System [M].New York:McGraw-Hill Book Co. 1989
[23]Nazmy A.S, Abdel-Ghaffar A.M. Three-dimensional Nonlinear Static Analysis of Cable-Stayed Bridges[J].Computers and Structures,1990
[24]Wang PH, Tseng TC, Yang GG Initial Shape of Cable-Stayed Bridges[J]. Computers and Structures 1993,46:1095-1106
[25]Wang PH, Yang GG Parametric Studies on Cable-Stayed Bridges [J]. Computers and Structures 1996
[26]Wang PH, Lin HT, Tang TY. Study on Nonlinear Analysis of a Highly Redundant Cable-Stayed Bridge[J].Computers and Structures, 2002, 80:165-182
[27]Wang PH, Tang TY, Zheng HN. Analysis of Cable-Stayed Bridges During Construction by Cantilever Methods [J].Computers and Structures, 2004, 82:329-346
[28]Wang YC. Geometric Nonlinear Behavior of Cable-Stayed Bridges[D].USA:University of Colorado at Boulder. 1994
[29]潘家英.吴亮明.高路彬等.关于大跨度斜拉桥几何非线性问题.全国桥梁结构学术大会论文集.同济大学出版社,1992
[30]李平利.大跨度斜拉桥施工阶段几何非线性静力分析.西南交通大学硕士论文,2004
[31]华孝良.徐光辉.桥梁结构非线性分析[M].人民交通出版社.1997
[32]O'Briem WT. General Solution of Suspended Cable Problems [J]. Journal of Structural Division, ASCE,1967,93(STl):1-26
[33]刘人通.弹性力学[M].西北工业大学出版社,2002
[34]蒋友谅.非线性有限元法.北京：北京工业学院出版社,1988
[35]杨炳成,陈偕民.结构有限元素法[M],1996
[36]赵均海.王敏强,魏雪英.高等有限元[M].武汉理工大学出版社,2004
[37]殷有泉.非线性有限元基础[M].北京大学出版社,2007
[38]项海帆.高等桥梁结构理论[M].人民交通出版社,2007
[39]宋天霞,郭建生,杨元明.非线性固体计算力学仁M].华中科技大学出版社,2005
[40]叶芳芳.大悬挑悬挂混合结构的施工控制.中南大学硕士学位论文.2009
[41]沈锐利.桥梁结构分析理论.西南交通大学工学硕士教学讲义,2009
[42]潘永仁.悬索桥结构分析理论与方法[M].人民交通出版社,2004
[43]颜东煌.斜拉桥合理设计状态确定与施工控制[D].湖南大学,2001
[44]廖元裳.钢筋混凝土桥.中国铁道出版社,1997
[45]徐金良.钢管混凝土拱桥施工过程及地震响应分析,西南交通大学硕士学位论文,2008
[46]徐凯燕,魏德敏,刘灿.大跨度斜拉桥几何非线性静力计算分析[J].工程抗震与加固改造,2008
[47]《桥梁设计常用数据手册》编写委员会编.北京：人民交通出版社,2005
[48]于应良.大跨度斜拉桥考虑几何非线性的静、动力分析和钢箱梁的第二体系应力研究.西南交通大学博士学位论文,2000
[49]北京Midas技术有限公司Midas使用手册,2000
[50]李乔.斜拉桥的受力特征分析[C].四川省公路学会桥梁专委会,1998年桥梁学术讨论会, 成都：西南交通大学出版社,1998：57-60
[51]周上君.斜拉桥非线性静力分析.桥梁建设.1982