基于CR列式的斜拉桥几何非线性分析
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摘要
斜拉桥几何非线性分析目前主要采用等效模量考虑索垂度效应,稳定函数或几何刚度阵考虑梁柱效应、拉格朗日增量列式(TL列式或UL列式)考虑大位移。由于斜拉桥跨度范围涵盖广,多大跨径考虑或不考虑结构几何非线性影响没有明确的界定,对于400～600m跨径斜拉桥多数研究者只采用等效模量考虑索垂度效应,简化地考虑几何非线性。本文则采用改进的CR-UL列式,悬链线索单元模拟拉索方法对400～600m跨径斜拉桥几何非线性作精细化分析,主要研究内容如下:
1.总结TL列式、UL列式和CR列式的特点,从3种列式的公式推导上说明其各自的优缺点。验证CR-UL列式在计算几何非线性上的准确性,指出UL列式在计算大位移几何非线性问题上误差较大,为斜拉桥非线性有限元分析提供理论基础。
2.对比基于线性二阶理论的P-Delta分析与非线性分析的计算原理,并以实例证明,在结构位移相对较小的情况时P-Delta分析能得出与非线性分析很接近的结果。
3.回顾悬链线索单元的基本方程和切线刚度矩阵的推导过程,验证悬链线索单元在计算索垂度效应方面的精准性,为用悬链线索单元模拟斜拉索提供了理论基础。
4.以400、600米级两座结构相似的钢箱斜拉桥为例,基于CR-UL列式理论,悬链线索单元模拟拉索,通过全桥仿真建模,计算了全部施工阶段和使用阶段斜拉桥几何非线性的影响,并与另外4种不同几何非线性分析方法进行对比。主要结论为:①斜拉桥大位移几何非线性影响较小,采用线性二阶的P-Delta分析或基于CR列式的几何非线性分析考虑梁柱非线性均能满足工程要求;②400米级斜拉桥采用等效模量法考虑垂度效应,线性二阶计算梁柱效应和大位移即能得到满足工程需要的结果;但随着跨度增加,几何非线性影响增加,600米级斜拉桥建议采用悬连线索单元模拟斜拉索,几何刚度阵非线性计算梁柱效应和大位移的方法。
Geometric nonlinearity analysis of cable-stayed bridges mainly considered the equivalent modulus to cable sag effect,stability function or the geometric stiffness matrix to beam-column effect,the Lagrangian Incremental formulation(TL or UL formulation)to large displacement.Because of wide-span cable-stayed bridge,how long-span structures should consider the effects of geometric non-linearity is not clearly defined。When calculation the cable-stayed bridge for span between 400～600m,most of researchers only using the equivalent modulus method to consider effect of cable sag and simplify consideration of geometric nonlinearity.This paper,used the improved CR-UL formation and catenary cable element to simulat the cable-stayed,accurate analysis the geometrically nonlinear problem of the 400～600m span cable-stayed bridge.The main research contents are as follows:
1.Summarizing the characteristics of TL,UL and CR formulation,Indicating their respective advantages and disadvantages from Formula Derivation.Authenticating accuracy of CR-UL formulation on geometric nonlinear analysis,and validating that there ie a Larger error on UL formulation for Calculation of geometric non-linear.Providing the theoretical basis for Nonlinear Finite Element analysis of cable-stayed bridge.
2.Comparing P-Delta analysis principle with non-linear analysis principle then proved that,when the structure have small displacement,the results from the P-Delta analysis is similar to the results from non-linear analysis.
3.Reviewing the basic equation of catenary cable element and derivation process of tangent stiffness matrix.Verified it is accuracy that use the cable element to simulate stay cable when analysis the cable sag effect.It provides a theoretical basis for use the cable element to simulate stay cable.
4.Taking Two similar cable-stayed bridges of steel box as an example,based on CR-UL formulation,the catenary cable element was used to simulate stay cable,through the Simulation of full-bridge,Calculating the effects of geometric non-linear on cable-stayed bridge in the construction phase and use phase.And compareing with other four methods, obtaining the main conclusions:①The influence of geometric non-linear of cable-stayed bridge is small,so use linear second order P-Delta analysis or geometric nonlinear analysis based on the CR formation to consider the nonlinear beam-column will be able to meet the engineering requirements;②400-meter cable-stayed bridge using the equivalent modulus method to consider effect of sag,calculation of linear second-order effect and the large displacement beam-column will be able to meet the engineering requirements;However,as the span increased the impact of geometric nonlinearity is also increased,600-meter cable-stayed bridge suggest to using catenary cable element to simulation the cable-stayed,and using uonlinear geometric stiffness matrix to calculat the beam-column effect and the large displacement.
1.总结TL列式、UL列式和CR列式的特点,从3种列式的公式推导上说明其各自的优缺点。验证CR-UL列式在计算几何非线性上的准确性,指出UL列式在计算大位移几何非线性问题上误差较大,为斜拉桥非线性有限元分析提供理论基础。
2.对比基于线性二阶理论的P-Delta分析与非线性分析的计算原理,并以实例证明,在结构位移相对较小的情况时P-Delta分析能得出与非线性分析很接近的结果。
3.回顾悬链线索单元的基本方程和切线刚度矩阵的推导过程,验证悬链线索单元在计算索垂度效应方面的精准性,为用悬链线索单元模拟斜拉索提供了理论基础。
4.以400、600米级两座结构相似的钢箱斜拉桥为例,基于CR-UL列式理论,悬链线索单元模拟拉索,通过全桥仿真建模,计算了全部施工阶段和使用阶段斜拉桥几何非线性的影响,并与另外4种不同几何非线性分析方法进行对比。主要结论为:①斜拉桥大位移几何非线性影响较小,采用线性二阶的P-Delta分析或基于CR列式的几何非线性分析考虑梁柱非线性均能满足工程要求;②400米级斜拉桥采用等效模量法考虑垂度效应,线性二阶计算梁柱效应和大位移即能得到满足工程需要的结果;但随着跨度增加,几何非线性影响增加,600米级斜拉桥建议采用悬连线索单元模拟斜拉索,几何刚度阵非线性计算梁柱效应和大位移的方法。
Geometric nonlinearity analysis of cable-stayed bridges mainly considered the equivalent modulus to cable sag effect,stability function or the geometric stiffness matrix to beam-column effect,the Lagrangian Incremental formulation(TL or UL formulation)to large displacement.Because of wide-span cable-stayed bridge,how long-span structures should consider the effects of geometric non-linearity is not clearly defined。When calculation the cable-stayed bridge for span between 400～600m,most of researchers only using the equivalent modulus method to consider effect of cable sag and simplify consideration of geometric nonlinearity.This paper,used the improved CR-UL formation and catenary cable element to simulat the cable-stayed,accurate analysis the geometrically nonlinear problem of the 400～600m span cable-stayed bridge.The main research contents are as follows:
1.Summarizing the characteristics of TL,UL and CR formulation,Indicating their respective advantages and disadvantages from Formula Derivation.Authenticating accuracy of CR-UL formulation on geometric nonlinear analysis,and validating that there ie a Larger error on UL formulation for Calculation of geometric non-linear.Providing the theoretical basis for Nonlinear Finite Element analysis of cable-stayed bridge.
2.Comparing P-Delta analysis principle with non-linear analysis principle then proved that,when the structure have small displacement,the results from the P-Delta analysis is similar to the results from non-linear analysis.
3.Reviewing the basic equation of catenary cable element and derivation process of tangent stiffness matrix.Verified it is accuracy that use the cable element to simulate stay cable when analysis the cable sag effect.It provides a theoretical basis for use the cable element to simulate stay cable.
4.Taking Two similar cable-stayed bridges of steel box as an example,based on CR-UL formulation,the catenary cable element was used to simulate stay cable,through the Simulation of full-bridge,Calculating the effects of geometric non-linear on cable-stayed bridge in the construction phase and use phase.And compareing with other four methods, obtaining the main conclusions:①The influence of geometric non-linear of cable-stayed bridge is small,so use linear second order P-Delta analysis or geometric nonlinear analysis based on the CR formation to consider the nonlinear beam-column will be able to meet the engineering requirements;②400-meter cable-stayed bridge using the equivalent modulus method to consider effect of sag,calculation of linear second-order effect and the large displacement beam-column will be able to meet the engineering requirements;However,as the span increased the impact of geometric nonlinearity is also increased,600-meter cable-stayed bridge suggest to using catenary cable element to simulation the cable-stayed,and using uonlinear geometric stiffness matrix to calculat the beam-column effect and the large displacement.
引文
[1]范立础.桥梁工程[M].人民交通出版社.2000
[2]林元培.斜拉桥[M].人民交通出版社.1996
[3]O'Briem WT.Francis AJ.Cable movements under two-dimensional load[J].Journal of Structural Division,ASCE,1964,90(ST3):89-123.
[4]Emst.Der E-Modul-von-Soilenunter Berucksiehtigung-des-Durehhangers[J].Der Bauingenieur.1965,40(2):52-55
[5]O'Briem WT.General solution of suspended cable problems[J].Jounrnal of Structural Division,ASCE,1967,93(ST1):1-26.
[6]Peyrot AH.Goulois AM.Analysis of flexible transmission lines[J].Jounrnal of Structural,Division,ASCE,1978,104(ST5):763-779
[7]Jayararnan HB,Knudson WC.A curved element for the analysis of cable Structures[J].Computers and Structures,1981,14(3-4):325-333.
[8]Irvine HM.Cable Structures[M].Combrige:The MIT Press,1981.
[9]张震陆,陈本贤.柔索分析的“悬链段”方法研究[J].工程力学,1990,7(4).
[10]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.
[11]罗喜恒.复杂悬索桥施工过程精细化分析研究[D].上海:同济大学,2004.
[12]Brotton DM.A general computer programme for the solution of suspension bridge problems.The Structural Engineer,1966,44(5):161-167.
[13]Saafan SA.Theoratieal Analysis of SusPension Bridges[J].Proc.ASCE,1966,92(ST4),1-1
[14]FlemingJF.Nonlinear Static Analysis of Cable-stayed Bridge Structures[J].ComPuters and Structures,1979,10:621-635.
[15]Bathe KJ,Bolourehi S.Large disPlaeement analysis of three-dimensional beam struetures[J].International Journal for Numerical Methods in Engineerin.1979,14:961-986
[16]Nazmy,Ahmed M.Abdel-Ghaffar.Three dimensional Nonlinear StatieAnalysis of Cablestayed Bridges.ComPuters&Structures.1990,34(2):PP.257-27
[17]陈德伟.斜拉桥的非线性分析及工程控制[D].上海:同济大学
[18]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
[19]潘永仁.悬索桥结构分析理论与方法[M].人命交通出版社.2004
[20]梁鹏.超大跨度斜拉桥几何非线性及随机过程分析[D].上海:同济大学.2004
[21]刘人通.弹性力学[M].西北工业大学出版社.2002
[22]杨炳成,陈偕民.结构有限元素法[M].1996
[23]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
[24]殷有泉.非线性有限元基础[M].北京大学出版社.2007
[25]项海帆.高等桥梁结构理论[M].人民交通出版社.2007
[26]宋天霞,郭建生,杨元明.非线性固体计算力学[M].华中科技大学出版社.2005
[27]华孝良,徐光辉.桥梁结构非线性分析[M].人民交通出版社.1997
[28]颜东煌.斜拉桥合理设计状态确定与施工控制[D].长沙:湖南大学.2001
[29]颜东煌、田仲初、钟正强.桥梁施工仿真计算程序设计方法[J].公路工程计算机应用论文集,1996
[30]蔺鹏臻,刘世忠.桥梁结构有限元分析[M].科学出版社.2008
[31]MidasIT(Beijing) Corporation.MIDAS/CIVIL Analys for Civilstmeture.2006
[32]郑凯锋,陈宁,张晓翘.桥梁结构仿真分析技术研究[J].桥梁建设,1998,(02):10-15
[33]贺栓海.桥梁结构理论与计算方法[M].人民交通出版社.2003
[34]张晓壳,陈宁,王应良等.斜拉桥的数学建模[J].国外桥梁,1998,2:52-5
[35]唐茂林.大跨度悬索桥空间几何非线性分析及软件开发[D].成都:西南交通大学.2003
[36]李乔,唐亮.悬臂拼装桥梁制造与安装线形的确定[c].中国土木学会桥梁分会 2004年桥梁年会论文集,北京:人民交通出版社,2004
[37]李乔.斜拉桥悬臂施工时安装标高的计算方法[C].四川省公路学会桥梁学术会议论文集.2001
[38]秦顺全.斜拉桥安装的无应力状态控制法[C].中国土木学会桥梁分会2004年桥梁年 会论文集,北京:人民交通出版社,2004
[39]秦顺全.桥梁施工控制—无应力状态法理论与实践[D].北京:人民交通出版社,2007
[40]王勇等.杭州湾跨海大桥工程总结[M].北京:人民交通出版社,2008
[41]南京长江第三大桥建设指挥部.南京长江第三大桥主桥技术总结[M].北京:人民交通出版社,2005
[42]苏通大桥建设指挥部.苏通大桥论文集第一辑[M].北京:中国科学技术出版社,2004
[43]JTG/T D65-01-2007.公路斜拉桥设计细则[S].北京:人民交通出版社,2007
[44]陈政清,颜全胜.大跨度斜拉桥的非线性分析[J].长沙铁道学院学报,1991,9(3):29-33
[45]梁鹏,秦建国,袁卫军.超大跨度斜拉桥活载几何非线性分析[J].公路交通科技.2006(04):60-62
[2]林元培.斜拉桥[M].人民交通出版社.1996
[3]O'Briem WT.Francis AJ.Cable movements under two-dimensional load[J].Journal of Structural Division,ASCE,1964,90(ST3):89-123.
[4]Emst.Der E-Modul-von-Soilenunter Berucksiehtigung-des-Durehhangers[J].Der Bauingenieur.1965,40(2):52-55
[5]O'Briem WT.General solution of suspended cable problems[J].Jounrnal of Structural Division,ASCE,1967,93(ST1):1-26.
[6]Peyrot AH.Goulois AM.Analysis of flexible transmission lines[J].Jounrnal of Structural,Division,ASCE,1978,104(ST5):763-779
[7]Jayararnan HB,Knudson WC.A curved element for the analysis of cable Structures[J].Computers and Structures,1981,14(3-4):325-333.
[8]Irvine HM.Cable Structures[M].Combrige:The MIT Press,1981.
[9]张震陆,陈本贤.柔索分析的“悬链段”方法研究[J].工程力学,1990,7(4).
[10]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.
[11]罗喜恒.复杂悬索桥施工过程精细化分析研究[D].上海:同济大学,2004.
[12]Brotton DM.A general computer programme for the solution of suspension bridge problems.The Structural Engineer,1966,44(5):161-167.
[13]Saafan SA.Theoratieal Analysis of SusPension Bridges[J].Proc.ASCE,1966,92(ST4),1-1
[14]FlemingJF.Nonlinear Static Analysis of Cable-stayed Bridge Structures[J].ComPuters and Structures,1979,10:621-635.
[15]Bathe KJ,Bolourehi S.Large disPlaeement analysis of three-dimensional beam struetures[J].International Journal for Numerical Methods in Engineerin.1979,14:961-986
[16]Nazmy,Ahmed M.Abdel-Ghaffar.Three dimensional Nonlinear StatieAnalysis of Cablestayed Bridges.ComPuters&Structures.1990,34(2):PP.257-27
[17]陈德伟.斜拉桥的非线性分析及工程控制[D].上海:同济大学
[18]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
[19]潘永仁.悬索桥结构分析理论与方法[M].人命交通出版社.2004
[20]梁鹏.超大跨度斜拉桥几何非线性及随机过程分析[D].上海:同济大学.2004
[21]刘人通.弹性力学[M].西北工业大学出版社.2002
[22]杨炳成,陈偕民.结构有限元素法[M].1996
[23]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
[24]殷有泉.非线性有限元基础[M].北京大学出版社.2007
[25]项海帆.高等桥梁结构理论[M].人民交通出版社.2007
[26]宋天霞,郭建生,杨元明.非线性固体计算力学[M].华中科技大学出版社.2005
[27]华孝良,徐光辉.桥梁结构非线性分析[M].人民交通出版社.1997
[28]颜东煌.斜拉桥合理设计状态确定与施工控制[D].长沙:湖南大学.2001
[29]颜东煌、田仲初、钟正强.桥梁施工仿真计算程序设计方法[J].公路工程计算机应用论文集,1996
[30]蔺鹏臻,刘世忠.桥梁结构有限元分析[M].科学出版社.2008
[31]MidasIT(Beijing) Corporation.MIDAS/CIVIL Analys for Civilstmeture.2006
[32]郑凯锋,陈宁,张晓翘.桥梁结构仿真分析技术研究[J].桥梁建设,1998,(02):10-15
[33]贺栓海.桥梁结构理论与计算方法[M].人民交通出版社.2003
[34]张晓壳,陈宁,王应良等.斜拉桥的数学建模[J].国外桥梁,1998,2:52-5
[35]唐茂林.大跨度悬索桥空间几何非线性分析及软件开发[D].成都:西南交通大学.2003
[36]李乔,唐亮.悬臂拼装桥梁制造与安装线形的确定[c].中国土木学会桥梁分会 2004年桥梁年会论文集,北京:人民交通出版社,2004
[37]李乔.斜拉桥悬臂施工时安装标高的计算方法[C].四川省公路学会桥梁学术会议论文集.2001
[38]秦顺全.斜拉桥安装的无应力状态控制法[C].中国土木学会桥梁分会2004年桥梁年 会论文集,北京:人民交通出版社,2004
[39]秦顺全.桥梁施工控制—无应力状态法理论与实践[D].北京:人民交通出版社,2007
[40]王勇等.杭州湾跨海大桥工程总结[M].北京:人民交通出版社,2008
[41]南京长江第三大桥建设指挥部.南京长江第三大桥主桥技术总结[M].北京:人民交通出版社,2005
[42]苏通大桥建设指挥部.苏通大桥论文集第一辑[M].北京:中国科学技术出版社,2004
[43]JTG/T D65-01-2007.公路斜拉桥设计细则[S].北京:人民交通出版社,2007
[44]陈政清,颜全胜.大跨度斜拉桥的非线性分析[J].长沙铁道学院学报,1991,9(3):29-33
[45]梁鹏,秦建国,袁卫军.超大跨度斜拉桥活载几何非线性分析[J].公路交通科技.2006(04):60-62