具有侧向弹性支撑钢梁的稳定性能研究
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摘要
稳定问题是钢结构设计中的突出问题，对于受压、受弯和受剪等存在受压区的构件，屈曲一旦发生，结构随即崩溃，因此稳定问题往往比强度问题显得更为重要。虽然在过去近几百年中，对稳定问题己经进行了很多研究，取得了很大成就，但由于稳定问题本身的复杂性，这方面的研究仍在进行。
然而梁的屈曲可以用侧向或者扭转约束来防止。本文拟采用在双跨连续梁跨中、悬臂梁端部设置侧向弹性支撑，以提高其稳定性，但由于带有侧向弹性支撑梁的屈曲研究尚少，本文的目的在于对现有理论进行完善和发展。本文基于连续化模型，采用能量变分法给出一些复杂问题的解析解，并给出相应问题的高精度数值解；同时采用有限元建立模型计算分析，应用理论与有限元模拟结合的方法，得到的数据结果真实可靠，为后续的研究提供依据，为实际工程的应用奠定了基础。
本文采用理论与数值模拟相结合的方法，主要研究工作为：
1.具有侧向弹性支撑钢梁的稳定问题理论分析
根据现有的总势能表达式，分别针对集中荷载作用下具有侧向弹性支撑双跨连续梁的屈曲问题、集中荷载作用下具有侧向弹性支撑悬臂梁的屈曲问题以及均布荷载作用下具有侧向弹性支撑悬臂梁的屈曲问题，采用能量变分法，引入无量纲参数，基于最小势能原理给出相应问题的高精度数值解。并通过大量计算回归出高精度的临界屈曲弯矩计算公式。
2.具有侧向弹性支撑钢梁稳定问题的有限元验证
首先运用已有文献验证有限元模型的正确性，然后选择两种国标H型钢截面建立有限元模型，通过有限元分析验证本文理论解的正确性。
Buckling of steel beam is the most important problem for designing of steel structure.Once buckling appeared in compressed member、flexural member or shear member, structureimmediately collapsed, so the stability problem is more important than strength problem.Although the stability problem has been vast researched and made great achievements in thepast hundreds of years, but because of the complexity of stability problem, the research ofthis aspect is still on.
However，buckling of steel beam can be prevented by lateral or torsional braces. In orderto improve the stability of steel beam, this paper adopt to set lateral elastic brace in midspanof double-span beam and cantilever beam ends. Because of the research on the bucklingbehaviors of steel beam with lateral elastic brace is very little，the purpose of this paper is toimprove and develop the existing theories, which is based on continuous model, using theenergy variational method give some complex analytical solution of the problem, at the sametime give the corresponding high accuracy of numerical solution; at the same time using thefinite element model for calculation and analysis, application of theory and finite elementsimulation method, the data which abtained is ture and reliable, and provide a basis for followstudy and establish the foundation formula for the pratical project.
This paper adopt to a method that the theory is combined with numerical simulation. Itconsists of two parts as follows：
1. the theory analysis on the stability problem of steel beam with lateral elastic brace
Based on the existing of the total potential energy expression，separately analyzed theproblems of buckling，such as double-span beam with lateral elastic brace under concentratedload，cantilever beam with lateral elastic brace under concentrated load and uniform load.This paper is based on the principle of minimum potential energy give high-precisionnumerical solution by using the energy variational method and introducing of dimensionlessparameters. Obtained the high-precision and reliable formula by substantial calculating forcalculating the critical buckling moment.
2. the finite element analysis on the stability problem of steel beam with lateral elasticbrace
Firstly, using the existing literature to verify the finite element model，and then select twokinds of GB H-shaped steel section to stablish finite lement model.and verifing the theoreticalsolution of this paper through finite element analysis.
然而梁的屈曲可以用侧向或者扭转约束来防止。本文拟采用在双跨连续梁跨中、悬臂梁端部设置侧向弹性支撑，以提高其稳定性，但由于带有侧向弹性支撑梁的屈曲研究尚少，本文的目的在于对现有理论进行完善和发展。本文基于连续化模型，采用能量变分法给出一些复杂问题的解析解，并给出相应问题的高精度数值解；同时采用有限元建立模型计算分析，应用理论与有限元模拟结合的方法，得到的数据结果真实可靠，为后续的研究提供依据，为实际工程的应用奠定了基础。
本文采用理论与数值模拟相结合的方法，主要研究工作为：
1.具有侧向弹性支撑钢梁的稳定问题理论分析
根据现有的总势能表达式，分别针对集中荷载作用下具有侧向弹性支撑双跨连续梁的屈曲问题、集中荷载作用下具有侧向弹性支撑悬臂梁的屈曲问题以及均布荷载作用下具有侧向弹性支撑悬臂梁的屈曲问题，采用能量变分法，引入无量纲参数，基于最小势能原理给出相应问题的高精度数值解。并通过大量计算回归出高精度的临界屈曲弯矩计算公式。
2.具有侧向弹性支撑钢梁稳定问题的有限元验证
首先运用已有文献验证有限元模型的正确性，然后选择两种国标H型钢截面建立有限元模型，通过有限元分析验证本文理论解的正确性。
Buckling of steel beam is the most important problem for designing of steel structure.Once buckling appeared in compressed member、flexural member or shear member, structureimmediately collapsed, so the stability problem is more important than strength problem.Although the stability problem has been vast researched and made great achievements in thepast hundreds of years, but because of the complexity of stability problem, the research ofthis aspect is still on.
However，buckling of steel beam can be prevented by lateral or torsional braces. In orderto improve the stability of steel beam, this paper adopt to set lateral elastic brace in midspanof double-span beam and cantilever beam ends. Because of the research on the bucklingbehaviors of steel beam with lateral elastic brace is very little，the purpose of this paper is toimprove and develop the existing theories, which is based on continuous model, using theenergy variational method give some complex analytical solution of the problem, at the sametime give the corresponding high accuracy of numerical solution; at the same time using thefinite element model for calculation and analysis, application of theory and finite elementsimulation method, the data which abtained is ture and reliable, and provide a basis for followstudy and establish the foundation formula for the pratical project.
This paper adopt to a method that the theory is combined with numerical simulation. Itconsists of two parts as follows：
1. the theory analysis on the stability problem of steel beam with lateral elastic brace
Based on the existing of the total potential energy expression，separately analyzed theproblems of buckling，such as double-span beam with lateral elastic brace under concentratedload，cantilever beam with lateral elastic brace under concentrated load and uniform load.This paper is based on the principle of minimum potential energy give high-precisionnumerical solution by using the energy variational method and introducing of dimensionlessparameters. Obtained the high-precision and reliable formula by substantial calculating forcalculating the critical buckling moment.
2. the finite element analysis on the stability problem of steel beam with lateral elasticbrace
Firstly, using the existing literature to verify the finite element model，and then select twokinds of GB H-shaped steel section to stablish finite lement model.and verifing the theoreticalsolution of this paper through finite element analysis.
引文
[1]陈骥．钢结构稳定理论与设计（第三版）[M]．北京：科学出版社，2006．
[2]钟善桐.钢结构稳定设计[M].中国建筑工业出版社,1991.
[3] Salvadori M G．Lateral buckling of beams of rectangular cross-section under bendingand shear[C]．1st US National Congress of Applied Mechanics，1951：403．
[4] Hartmann A J．Elastic lateral buckling of continuous beams[J]．Journal of StructuralDivision，ASCE，1967，93(4)：11-26．
[5] Masur E F．Discussion of Elastic Lateral Buckling of Continuous Beams[J]．byHartmann A J，Journal of Structural Division，ASCE，1967，93(6)：283．
[6] Trahair N S．Discussion of Elastic Lateral Buckling of Continuous Beams[J]．byHartmann A J，Journal of Structural Division，ASCE，1968，94(3)：845．
[7] Trahair N S．Elastic stability of continuous beams[J]．Journal of Structural Division，ASCE,1969，95(6)：1295-1312．
[8] Nethercot D A，Trahair N S．Lateral buckling approximations for elastic beams[J]．TheStructural Engineering，1976，54(6)：197-204．
[9] Dux F，Kitipornchai S．Elastic buckling of laterally continuous I-beams[J]．Journal ofStructural Division，ASCE，1969，108(9)：2099-2116．
[10]郭耀杰，方山峰.钢结构构件弯扭屈曲问题的计算和分析[J].建筑结报.1990,11(3):38-43.
[11]郭耀杰，方山峰.论Timoshenko总势能的不完备性.力学与实践[J].1999,21(2):56-58.
[12]陈士林，方山峰.钢结构构件非线性屈曲问题的样条有限条分析[J].建筑结构.1995,25(5):9-13.
[13]高丽亚.国产H型钢梁整体稳定性能的理论与试验研究[D].西安建筑科技大学硕士论文.2003:8-64.
[14]高丽亚，邓长根，郝际平.国产轧制H型钢整体稳定性能研究—稳定系数计算原理对国产热轧H型钢梁的适用性分析[J].工业建筑.2006,36(10):75-78.
[15]张壮南，张耀春.双跨连续工字形梁的弹性屈曲分析[J].钢结构增刊.2004:112-116.
[16]张磊，童根树．两跨连续梁的弹性稳定[C]．中国钢协结构稳定与疲劳分会2004年学术交流会论文集，钢结构，2004(增刊)：310-321．
[17] Lei ZHANG，Gengshu TONG．Elastic Stability of Two-Span Continuous Beams underMoveing Loads[J]．Advances in structural Engineering2005，8(2)．
[18]童根树，张磊.薄壁钢梁稳定性计算的争议及其解决[J].建筑结构学报.2002,23(3):44-51.
[19]童根树，张磊.薄壁钢梁中的横向应力及其对强度和稳定性的影响[J].土木工程学报.2003,36(4):59-64.
[20]张磊，童根树.薄壁构件弯扭失稳的一般理论[J].建筑结构学报.2003,24(3):16-24.
[21]辛克贵，姜美兰.薄壁杆件稳定分析的样条有限杆元法[J].清华大学学报（自然科学版）.2001,41(4/5):235-239.
[22]杜咏.工字钢梁弯扭屈曲的计算模型和屈曲方程的求解[J].南京建筑工程学院学报.1997,3:30-34.
[23]吴秀水，辛克贵，姜美兰.横向荷载作用下薄壁杆件稳定分析的有限杆元法[J].工程力学.2001,18(1):47-55.
[24]戴国欣，王浩科，刘海鑫等.国产轧制H型钢整体稳定几何控制条件[J].钢结构.2004,19(73):62-64.
[25]张磊，童根树.两跨连续梁的弹性稳定[J].钢结构增刊.2004:310-322.
[26]张磊.薄壁构件稳定新理论及其应用[D].浙江大学博士论文.2005:180-207.
[27]张壮南.单轴对称工字形单悬伸梁和双跨连续梁整体稳定性能研究[D].哈尔滨：哈尔滨工业大学.2007.
[28]张孝芳.单轴对称工字型截面双跨连续钢梁整体稳定性研究[D].湘潭：湘潭大学.2011.
[29]柳凯议．双跨钢梁的屈曲分析与应用[D].大庆：大庆石油学院，2009．
[30]张磊.考虑横向正应力影响的薄壁构件稳定理论及其应用[D].浙江:浙江大学，2005.3.
[31]童根树.钢结构的平面外稳定[M].北京:中国建筑工业出版社，2007.2.
[32] Woolcoek, S.T, Trahair, N.S. Post-Buckling Behavior of Determinate Beams[J]. Journalof the Engineering Mechanics Division, Vol.100, No.EM2,1974:151-171.
[33] Ings, N,L, Trahair，N.S. Beam and Column Buckling under Directed Loading[J]. Journalof Structural Engineering, ASCE, Vol.113, No.6,1987:1251-1263.
[34] Attard, M.M, Bradford, M.A. Bifurcation Experiments on MonosymmetricCantilevers[C].12th Australasion Conference on the Mechanics of Structures andMaterials1990:207-213.
[35]秦桦.单轴对称工字形等截面悬臂梁的整体稳定性[D].西安：西安建筑科技大88学.2007
[36]张磊，童根树.工字形截面悬臂梁的稳定性能研究[J].工程力.2003,20(4):176-182.
[37]郑昌坝，张洪海.工字形截面悬臂钢梁的稳定性研究[J].力学与实践.2007,29(6):56-59.
[38]董诗忆.单轴对称楔形工字钢梁的弹性弯扭屈曲[D].浙江:浙江大学.
[39] Trahair N.S., Nethercot D.A. Bracing requirements in thin-walled structures,Developments in Thin-walled Structures,-2,Edited by J. Rhodes&A.C.Walker,London, Elsevier Applied Science Publishers,1984:93-130.
[40] Taylor A.C., Ojalvo M., Torsional restraint of lateral buckling,Journal of the StructuralDivision,ASCE,1966,92(2):115-129.
[41] Nethercot D.A., Buckling of laterally or torsionally restrained beams,Journal of theStructural Division, ASCE,1973,99(4):773-791.
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[43] Valentino J., Trahair, N.S., Torsional restraint against elastic lateral buckling, Journal ofthe Structural Engineering, ASCE,1988,124(4):1217-1224.
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[47]吴勇军.支撑位置对钢构件稳定承载力的影响[D].南京：河海大学.
[48]周红钦.支撑位置对轻型工资钢梁侧向稳定性的影响[D].郑州：郑州大学.2009.
[49]沈祖炎，陈扬骥等.钢结构基本原理[M].北京：中国建筑工业出版社，2005.
[50]吕烈武，沈世钊，沈祖炎，胡学仁.钢结构构件稳定理论[M].中国建筑工业出版社，1982.
[51]夏志斌.结构稳定理论[M].北京：高等教育出版社，1988.
[52]童根树.钢结构的平面外稳定[M].中国建筑工业出版社.2007.
[53] Zhang Lei，Tong Gengshu．Elastic buckling of inter-braced parallel beamsystems[J]．Advances in Structural Engineering, Vol.7, No.4,2004, pp.171-182.
[54]童根树，张磊．薄壁钢梁稳定性计算的争议及解决[J]．建筑结构学报，2002，23(3):44-51．
[55] Clark J W，Hill H N．Lateral buckling of beams[J]．Journal of Structural Division,ASCE,1960，127：180-201．．
[2]钟善桐.钢结构稳定设计[M].中国建筑工业出版社,1991.
[3] Salvadori M G．Lateral buckling of beams of rectangular cross-section under bendingand shear[C]．1st US National Congress of Applied Mechanics，1951：403．
[4] Hartmann A J．Elastic lateral buckling of continuous beams[J]．Journal of StructuralDivision，ASCE，1967，93(4)：11-26．
[5] Masur E F．Discussion of Elastic Lateral Buckling of Continuous Beams[J]．byHartmann A J，Journal of Structural Division，ASCE，1967，93(6)：283．
[6] Trahair N S．Discussion of Elastic Lateral Buckling of Continuous Beams[J]．byHartmann A J，Journal of Structural Division，ASCE，1968，94(3)：845．
[7] Trahair N S．Elastic stability of continuous beams[J]．Journal of Structural Division，ASCE,1969，95(6)：1295-1312．
[8] Nethercot D A，Trahair N S．Lateral buckling approximations for elastic beams[J]．TheStructural Engineering，1976，54(6)：197-204．
[9] Dux F，Kitipornchai S．Elastic buckling of laterally continuous I-beams[J]．Journal ofStructural Division，ASCE，1969，108(9)：2099-2116．
[10]郭耀杰，方山峰.钢结构构件弯扭屈曲问题的计算和分析[J].建筑结报.1990,11(3):38-43.
[11]郭耀杰，方山峰.论Timoshenko总势能的不完备性.力学与实践[J].1999,21(2):56-58.
[12]陈士林，方山峰.钢结构构件非线性屈曲问题的样条有限条分析[J].建筑结构.1995,25(5):9-13.
[13]高丽亚.国产H型钢梁整体稳定性能的理论与试验研究[D].西安建筑科技大学硕士论文.2003:8-64.
[14]高丽亚，邓长根，郝际平.国产轧制H型钢整体稳定性能研究—稳定系数计算原理对国产热轧H型钢梁的适用性分析[J].工业建筑.2006,36(10):75-78.
[15]张壮南，张耀春.双跨连续工字形梁的弹性屈曲分析[J].钢结构增刊.2004:112-116.
[16]张磊，童根树．两跨连续梁的弹性稳定[C]．中国钢协结构稳定与疲劳分会2004年学术交流会论文集，钢结构，2004(增刊)：310-321．
[17] Lei ZHANG，Gengshu TONG．Elastic Stability of Two-Span Continuous Beams underMoveing Loads[J]．Advances in structural Engineering2005，8(2)．
[18]童根树，张磊.薄壁钢梁稳定性计算的争议及其解决[J].建筑结构学报.2002,23(3):44-51.
[19]童根树，张磊.薄壁钢梁中的横向应力及其对强度和稳定性的影响[J].土木工程学报.2003,36(4):59-64.
[20]张磊，童根树.薄壁构件弯扭失稳的一般理论[J].建筑结构学报.2003,24(3):16-24.
[21]辛克贵，姜美兰.薄壁杆件稳定分析的样条有限杆元法[J].清华大学学报（自然科学版）.2001,41(4/5):235-239.
[22]杜咏.工字钢梁弯扭屈曲的计算模型和屈曲方程的求解[J].南京建筑工程学院学报.1997,3:30-34.
[23]吴秀水，辛克贵，姜美兰.横向荷载作用下薄壁杆件稳定分析的有限杆元法[J].工程力学.2001,18(1):47-55.
[24]戴国欣，王浩科，刘海鑫等.国产轧制H型钢整体稳定几何控制条件[J].钢结构.2004,19(73):62-64.
[25]张磊，童根树.两跨连续梁的弹性稳定[J].钢结构增刊.2004:310-322.
[26]张磊.薄壁构件稳定新理论及其应用[D].浙江大学博士论文.2005:180-207.
[27]张壮南.单轴对称工字形单悬伸梁和双跨连续梁整体稳定性能研究[D].哈尔滨：哈尔滨工业大学.2007.
[28]张孝芳.单轴对称工字型截面双跨连续钢梁整体稳定性研究[D].湘潭：湘潭大学.2011.
[29]柳凯议．双跨钢梁的屈曲分析与应用[D].大庆：大庆石油学院，2009．
[30]张磊.考虑横向正应力影响的薄壁构件稳定理论及其应用[D].浙江:浙江大学，2005.3.
[31]童根树.钢结构的平面外稳定[M].北京:中国建筑工业出版社，2007.2.
[32] Woolcoek, S.T, Trahair, N.S. Post-Buckling Behavior of Determinate Beams[J]. Journalof the Engineering Mechanics Division, Vol.100, No.EM2,1974:151-171.
[33] Ings, N,L, Trahair，N.S. Beam and Column Buckling under Directed Loading[J]. Journalof Structural Engineering, ASCE, Vol.113, No.6,1987:1251-1263.
[34] Attard, M.M, Bradford, M.A. Bifurcation Experiments on MonosymmetricCantilevers[C].12th Australasion Conference on the Mechanics of Structures andMaterials1990:207-213.
[35]秦桦.单轴对称工字形等截面悬臂梁的整体稳定性[D].西安：西安建筑科技大88学.2007
[36]张磊，童根树.工字形截面悬臂梁的稳定性能研究[J].工程力.2003,20(4):176-182.
[37]郑昌坝，张洪海.工字形截面悬臂钢梁的稳定性研究[J].力学与实践.2007,29(6):56-59.
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