冷弯薄壁C型构件屈曲滞回机理与简化设计方法研究
|
摘要
随着城市与新农村建设不断向前推进,尤其是国家权威部门已明确指出,新一轮GDP增长主要来源于农村的城镇化。建筑业作为城镇化的主要行业,其结构的形式与构造也须不断地改进和完善以适应建筑产业化的发展。其中,冷弯薄壁型钢结构体系作为工业化轻钢结构的一个分支倍受瞩目,其最显著的优势是施工周期短,可以提高投资效益,加快资金周转；并且施工场地占用率、建筑垃圾、建筑施工噪音等都大大降低。同时,轻钢结构建筑所用材料主要是可回收或易降解的材料,既节能、环保,又不失美观、大方,符合现代建筑发展方向理念。目前,冷弯薄壁型钢已广泛地应用于低层民用建筑中。其优点在于质轻,并且随着制造工艺的进步,屈服强度越来越高,耐久性也越来越好。同时,冷弯薄壁型钢的施工便捷性也是其它传统钢结构无法相比的,这些特点使得冷弯薄壁型钢在钢结构住宅产业化与新农村建设的大背景下,有着巨大的优势和发展前景。
本文选择应用最广泛、产业化程度最高的冷弯薄壁型钢C型构件作为研究对象,认为现有研究对相关屈曲机理、滞回性能以及适合各类截面的设计方法还存在一些值得深入的研究点。基于此,本文对以下内容展开了深入研究：
(1)借鉴Shanley模型,推导了一维杆件屈曲的全过程,深入分析了一维杆件屈曲机理与影响因素,包括初始缺陷与截面参数等。在此基础上,根据塑性区域分布不同,将塑性分为理想塑性与分布塑性,并推导了一维杆件塑性分布区域的表达式,得到了影响塑性分布区域的影响因子。同时,基于杆件屈曲模型,分析了r(塑性刚度或屈曲后刚度)与杆件屈曲、塑性行为之间的关系,为后文薄壁构件屈曲机理分析作准备。
(2)对冷弯薄壁C型构件进行了试验研究与数值模拟,包括：水平循环荷载作用下的构件滞回性能、静轴力下的屈曲行为与破坏特点,以及静力和循环荷载作用下的构件组合作用。分别得到了冷弯薄壁型钢C型构件在循环荷载作用下的恢复力模型与破坏机理、静轴力作用下构件破坏机理与偏心影响以及组合作用产生的机理,为格构机理模型的验证提供支持。
(3)分析了构件在水平循环荷载和静轴力作用下的屈曲行为与破坏机理,提出了冷弯薄壁C型构件格构机理模型,并通过数值与试验,验证了其合理性。基于格构机理模型,将薄壁构件与一维杆件屈曲机理联系起来,分析了构件初始缺陷与板组效应的影响机理,得到了构件畸变屈曲半波长计算公式,并与经典方法和数值模拟进行了对比分析。
(4)在现有的相关屈曲模式定义下,推导了畸变变形与整体变形之间的变形相关关系。从变形协调角度出发,分析了相关屈曲产生的原因与机理,指出局部与畸变屈曲对截面参数的改变,是引起与整体屈曲相关作用的根本原因。同时形心与剪心偏移也是薄壁构件特有的现象。此外,定义了新的屈曲模式,重点区分了整体屈曲与畸变-整体相关屈曲,新的模式能更准确的反映构件屈曲行为。
(5)基于模型分析了构件在水平荷载作用下的破坏机理,过早地出现局部屈曲并产生集中性的理想塑性是冷弯薄壁型钢C型构件在压弯循环荷载作用下破坏的根本原因。此外,进行了恢复力模型推导与拟合,提出了反映屈曲影响的双刚度准则,得到了影响滞回性能的重要参数。
(6)基于格构机理模型,推导畸变临界力的解析解,选择直接对转动刚度进行数值拟合的方法,得到弹性畸变临界力的简化计算表达式。定义了畸变域范围,可根据构件截面参数,直接判断构件破坏模式,简化设计过程。基于机理分析,通过对整体屈曲惯性矩进行折减来考虑畸变屈曲的相关影响,推导拟合了简化设计公式,并与原DSM设计法和试验资料作对比,具备良好的精度。
With the development of construction of city and urbanization, the National authorities have clearly pointed out that the new round of GDP growth comes from the urbanization. Building industry is the major part of industry of urbanization and its form and structure should keep on improving to adapt to it. Cold-formed steel structure system is attractive as a branch of light steel structure of building industrialization. The obvious advantage is the short construction period, which can significantly improve investment efficiency, accelerate cash-flow. In addition, the occupancy rate of the construction site, construction waste and noise are greatly reduced. At the same time, the light steel structure buildings are energy-saving and environmental. The main materials can be recycled or easily degraded. Buliding of steel structure conforms to the modern concept of Green Building and is beautiful and generous. At present, cold-formed steel are widely used during low-level civil construction as environmentally and friendly materials. Its advantages include lighter Weight, higher yield strength, and better durability. In addition, construction convenience of cold-formed steel is also obvious, which make the cold-formed steel have a huge advantage and prospect duing the steel residential industry and new rural construction.
This article researches on the C-type speciemn of cold-formed steel because it is most widely used and has the highest degree of industrialization. It is worthy of further study based on the existing research about the related buckling mechanism, hysteretic behavior and design methods suitable for all types of cross-sectional design. Thus this article studies the points as follow:
(1) Based on the Shanley model, the whole buckling process of the one-dimensional bar is derivated and the buckling mechanism and influencing factors, including the initial defection and section parameters. According to the distribution of the plastic zone, the plasticity is devided into perfect plasticity and distributed plasticity, and the plastic distribution area expression of the one-dimensional bar is deduced, and the key influencing factors are obtained. Meanwhile, based on the bar buckling model, the relationship between the r (plastic stiffness or post buckling stiffness), bar buckling and plastic behavior are analized to prepare for the study on buckling mechanism.
(2) Experimental researches and numerical simulations of C-section specimens of cold-formed steel have been done including hysteretic performance under the horizontal cyclic load, buckling behavior and destruction characteristics under static axial force and the combined effects under static and cyclic load. Restoring force model and failure mechanism of C-section specimens of cold-formed steel under the cyclic load, failure mechanism and eccentric impact under static axial force, as well as the mechanism of the combination effects are obtained to support the mechanism model.
(3) The buckling behavior and failure mechanism of the specimens under horizontal cyclic loading and static axial force are analized. The lattice mechanism model is put forward and it is verified by experimental research and numerical simulations. Based on mechanism model, it is easy to associate the thin-walled members with one-dimensional bar for buckling mechanism analysis. The influence of the initial imperfection and plate effects are analized and the formula of the distortional buckling half wave is obtained. At last, this formula is verified by the data from classical methods and numerical simulation.
(4) Based on the existing definition of the related buckling mode, the deformation relationship between the distortion deformation and overall deformation is deduced. And using the principle of deformation coordination, the causes and mechanism of the related buckling are analized and this paper indicats that the section parameters's change caused by the local and distortional buckling is the primary cause of the correlation of overall buckling. The excursion of the centroid and shear center is the peculiar phenomenon of the thin-walled specimens. In addition, a new defination of buckling mode has been made which made clear distiction between the global buckling and distortional-global buckling mode and it can show buckling behavior more accuratly.
(5) Based on the model, the failure mechanism under the horizontal cyclic loading is analized. Local buckling occurs too early and concentration plasticity are the root causes of the destruction of C-section specimens of cold-formed steel under bending cyclic loading. The restoring force model is deduced and fit, and double rigidity criterion which could reflects the buckling influence, and the important parameters which can influence the hysteretic performance are obtained.
(6) Based on the lattice mechanism model, the analytical solution of critical force of distortion buckling is deduced. The elastic critical force of distortional buckling is obtained by fitting rotational stiffness. After defining the distortion area, the failure modes can be obtained only by section parameters, which simplify the design process. Based on the mechanism analysis, the simplified design formulas considering the influence of distortional buckling by reducing moment of inertia of the overall buckling is derived and compared to the DSM and test. And it is proved to have good accuracy.
本文选择应用最广泛、产业化程度最高的冷弯薄壁型钢C型构件作为研究对象,认为现有研究对相关屈曲机理、滞回性能以及适合各类截面的设计方法还存在一些值得深入的研究点。基于此,本文对以下内容展开了深入研究：
(1)借鉴Shanley模型,推导了一维杆件屈曲的全过程,深入分析了一维杆件屈曲机理与影响因素,包括初始缺陷与截面参数等。在此基础上,根据塑性区域分布不同,将塑性分为理想塑性与分布塑性,并推导了一维杆件塑性分布区域的表达式,得到了影响塑性分布区域的影响因子。同时,基于杆件屈曲模型,分析了r(塑性刚度或屈曲后刚度)与杆件屈曲、塑性行为之间的关系,为后文薄壁构件屈曲机理分析作准备。
(2)对冷弯薄壁C型构件进行了试验研究与数值模拟,包括：水平循环荷载作用下的构件滞回性能、静轴力下的屈曲行为与破坏特点,以及静力和循环荷载作用下的构件组合作用。分别得到了冷弯薄壁型钢C型构件在循环荷载作用下的恢复力模型与破坏机理、静轴力作用下构件破坏机理与偏心影响以及组合作用产生的机理,为格构机理模型的验证提供支持。
(3)分析了构件在水平循环荷载和静轴力作用下的屈曲行为与破坏机理,提出了冷弯薄壁C型构件格构机理模型,并通过数值与试验,验证了其合理性。基于格构机理模型,将薄壁构件与一维杆件屈曲机理联系起来,分析了构件初始缺陷与板组效应的影响机理,得到了构件畸变屈曲半波长计算公式,并与经典方法和数值模拟进行了对比分析。
(4)在现有的相关屈曲模式定义下,推导了畸变变形与整体变形之间的变形相关关系。从变形协调角度出发,分析了相关屈曲产生的原因与机理,指出局部与畸变屈曲对截面参数的改变,是引起与整体屈曲相关作用的根本原因。同时形心与剪心偏移也是薄壁构件特有的现象。此外,定义了新的屈曲模式,重点区分了整体屈曲与畸变-整体相关屈曲,新的模式能更准确的反映构件屈曲行为。
(5)基于模型分析了构件在水平荷载作用下的破坏机理,过早地出现局部屈曲并产生集中性的理想塑性是冷弯薄壁型钢C型构件在压弯循环荷载作用下破坏的根本原因。此外,进行了恢复力模型推导与拟合,提出了反映屈曲影响的双刚度准则,得到了影响滞回性能的重要参数。
(6)基于格构机理模型,推导畸变临界力的解析解,选择直接对转动刚度进行数值拟合的方法,得到弹性畸变临界力的简化计算表达式。定义了畸变域范围,可根据构件截面参数,直接判断构件破坏模式,简化设计过程。基于机理分析,通过对整体屈曲惯性矩进行折减来考虑畸变屈曲的相关影响,推导拟合了简化设计公式,并与原DSM设计法和试验资料作对比,具备良好的精度。
With the development of construction of city and urbanization, the National authorities have clearly pointed out that the new round of GDP growth comes from the urbanization. Building industry is the major part of industry of urbanization and its form and structure should keep on improving to adapt to it. Cold-formed steel structure system is attractive as a branch of light steel structure of building industrialization. The obvious advantage is the short construction period, which can significantly improve investment efficiency, accelerate cash-flow. In addition, the occupancy rate of the construction site, construction waste and noise are greatly reduced. At the same time, the light steel structure buildings are energy-saving and environmental. The main materials can be recycled or easily degraded. Buliding of steel structure conforms to the modern concept of Green Building and is beautiful and generous. At present, cold-formed steel are widely used during low-level civil construction as environmentally and friendly materials. Its advantages include lighter Weight, higher yield strength, and better durability. In addition, construction convenience of cold-formed steel is also obvious, which make the cold-formed steel have a huge advantage and prospect duing the steel residential industry and new rural construction.
This article researches on the C-type speciemn of cold-formed steel because it is most widely used and has the highest degree of industrialization. It is worthy of further study based on the existing research about the related buckling mechanism, hysteretic behavior and design methods suitable for all types of cross-sectional design. Thus this article studies the points as follow:
(1) Based on the Shanley model, the whole buckling process of the one-dimensional bar is derivated and the buckling mechanism and influencing factors, including the initial defection and section parameters. According to the distribution of the plastic zone, the plasticity is devided into perfect plasticity and distributed plasticity, and the plastic distribution area expression of the one-dimensional bar is deduced, and the key influencing factors are obtained. Meanwhile, based on the bar buckling model, the relationship between the r (plastic stiffness or post buckling stiffness), bar buckling and plastic behavior are analized to prepare for the study on buckling mechanism.
(2) Experimental researches and numerical simulations of C-section specimens of cold-formed steel have been done including hysteretic performance under the horizontal cyclic load, buckling behavior and destruction characteristics under static axial force and the combined effects under static and cyclic load. Restoring force model and failure mechanism of C-section specimens of cold-formed steel under the cyclic load, failure mechanism and eccentric impact under static axial force, as well as the mechanism of the combination effects are obtained to support the mechanism model.
(3) The buckling behavior and failure mechanism of the specimens under horizontal cyclic loading and static axial force are analized. The lattice mechanism model is put forward and it is verified by experimental research and numerical simulations. Based on mechanism model, it is easy to associate the thin-walled members with one-dimensional bar for buckling mechanism analysis. The influence of the initial imperfection and plate effects are analized and the formula of the distortional buckling half wave is obtained. At last, this formula is verified by the data from classical methods and numerical simulation.
(4) Based on the existing definition of the related buckling mode, the deformation relationship between the distortion deformation and overall deformation is deduced. And using the principle of deformation coordination, the causes and mechanism of the related buckling are analized and this paper indicats that the section parameters's change caused by the local and distortional buckling is the primary cause of the correlation of overall buckling. The excursion of the centroid and shear center is the peculiar phenomenon of the thin-walled specimens. In addition, a new defination of buckling mode has been made which made clear distiction between the global buckling and distortional-global buckling mode and it can show buckling behavior more accuratly.
(5) Based on the model, the failure mechanism under the horizontal cyclic loading is analized. Local buckling occurs too early and concentration plasticity are the root causes of the destruction of C-section specimens of cold-formed steel under bending cyclic loading. The restoring force model is deduced and fit, and double rigidity criterion which could reflects the buckling influence, and the important parameters which can influence the hysteretic performance are obtained.
(6) Based on the lattice mechanism model, the analytical solution of critical force of distortion buckling is deduced. The elastic critical force of distortional buckling is obtained by fitting rotational stiffness. After defining the distortion area, the failure modes can be obtained only by section parameters, which simplify the design process. Based on the mechanism analysis, the simplified design formulas considering the influence of distortional buckling by reducing moment of inertia of the overall buckling is derived and compared to the DSM and test. And it is proved to have good accuracy.
引文
[1]中国建筑金属结构协会钢结构专家委员会.轻型钢结构房屋新技术与新产品的应用[J].北京：中国建筑工业出版社.2011：1-20.
[2]YU Wei-wen.[美].董军,夏冰青(译).冷成型钢结构设计(第三版)[M].北京：中国水利水电出版社,知识产权出版社,2002：1-10.
[3]陈骥.钢结构稳定理论与设计[M].北京：科学出版社.2001：1-15.
[4]周绪红,王世纪.薄壁构件稳定理论及其应用[M].北京：科学出版社.2009：1-11.
[5]Timoshenko.S.P. and Gere.J.M.. Theory of Elastic Stability[J].2nd. Ed. McGraw-Hill. 1961:180-189.
[6]Von Karman.T. and Sechler. E. The Strength of Thin Plates in Compression. Transactions. ASME[J]. Vol.54. APM54-5,1932:1833-1848.
[7]Bleich F.金属结构的屈曲强度[M].同济大学钢木结构教研室译.北京：科学出版社.1985
[8]Coan J M. Large-deflection theory for plates with small initial curvature loaded in edge compression[J]. Trans. AMSE.1951.73
[9]Yamaki N. Postbuckling behavior of rectangular plateswith small initial curvature loaded in edge compression[J]. J. of Appl. Mech.1956.26
[10]Rasmussen, KJR,Bifurcation Analysis of Locally Buckled Members[R]. Sydney:The University of Sydney,Research Report No. R719, December,1995
[11]Young,B,Rasmussen,KJR,Bifurcation of singly symmetric columns[J].Thin-walled Structures, 1997. vol.28(2):155-177.
[12]Young,B,Rasmussen,KJR, Inelastic Bifurcation of Cold-formed Singly Symmetric Columns[J]. Thin-walled Structures,2000.36(3):213-230.
[13]K.K.V.Devarakonda, C.W.Bert. Flexural vibration of rectangular plates subjected to sinusoidally distributed compressive loading on two opposite sides[J]. Journal of Sound and Vibration,2005, 283(3-5):749-763.
[14]高轩能,孙祖龙.槽形截面腹板非均匀受压的屈曲后强度研究[J].力学与实践,1993.Vol.5：35-39.
[15]颜少荣.薄壁槽钢受压承载力计算的有效宽厚比法[J].五邑大学学报(自然科版).2001.15(3)
[16]孟春光,张伟星.无单元法在薄板稳定问题中的应用[J].力学与实践,2004.Vol.2
[17]谈梅兰,吴光,王鑫伟.矩形薄板面内非线性分布载荷下的辛弹性力学解[J].工程力学,2008.Vol.10
[18]Cheung, YK. Finite strip method in structural analysis[D]. Oxford; New York:Pergamon Press, 1976.
[19]Cheung, YK, Fan, SC, Wu, CQ. Spline finite strip in structural analysis[M]. In:editors. Proceedings of the Proceedings of the International Conference on Finite Element Method. Shanghai, China:1982
[20]Fan, SC, Spline finite strip in structural analysis[D]. Thesis, University of Hong Kong,1982.
[21]Gierlinski, J.T.,Graves Smith, T.R. The geometric non-linear analysis of thin-walled structures by finite strips[J]. Thin-Walled Structures,1984.2:27-50
[22]Hancock, G.J.. Interaction buckling in I-section columns, Journal of tructural Engineering[J], ASCE,1981.107(1):165-179
[23]Hancock, G.J.. Distortional buckling of steel storage rack columns, Journal of Structural Engineering[J], ASCE,1985. 111(12):2770-2783
[24]Lau, SCW, Hancock, GJ. Buckling of thin flat-walled structures by a spline finite strip method[J]. Thin-Walled Structures.1986.4(4):269-294.
[25]Lau, SCW, Hancock, GJ. Inelastic buckling analysis of beams, columns and plates using the spline finite strip method[J]. Thin-Walled Structures.1989.7:213-238.
[26]Kwon, YB, Hancock, GJ. A nonlinear elastic spline finite strip analysis for thin-walled sections[J]. Thin-Walled Structures.1991.12(4):295-319.
[27]Au, FTK, Cheung, YK. Isoparametric spline finite strip for plane structures[J]. Computers & Structures.1993.48(1):23-32.
[28]Cheung, YK, Au, FTK. Isoparametric spline finite strip for degenerate shells[J]. Thin-Walled Structures.1995.21(1):65-92.
[29]Godley, MHR. Storage Racking-chapter 11. In:editors. Design of Cold Formed Steel Members[J]. Ed. Rhodes.1991.
[30]Shanmugam, NE, Thevendran, V, Tan, YH. Design formula for axially compressed perforated plates[J]. Thin-Walled Structures.1999.34(1):1.
[31]Shanmugam, NE, Thevendran, V. Lateral buckling of doubly symmetric beams containing openings[J]. Journal of Engineering Mechanics, American Society of Civil Engineers. 1991.117(7):1427-1441.
[32]Shanmugam, NE, Dhanalakshmi, M. State of art review and compilation of studies on perforated thin-walled structures[J]. International Journal of Structural Stability and Dynamics 2001.1
[33]Rhodes, J, Macdonald, M. The effect of perforation length on the behaviour of perforated elements in compression[M]. In:editors. Proceedings of the Thirthteenth International Speciality Conference on Cold-Formed Steel Structures.1996.
[34]Gabriele Eccher, Kim Rasmussen, Nadia Baldassino, Riccardo Zandonini,Isoparametric Spline Finite Strip Method for In-plane Stress Analysis[R]. Sydney:The University of Sydney, Research Report No R848, August 2005.
[35]Gabriele Eccher, Kim J. R. Rasmussen,Riccardo Zandonini,Isoparametric Spline Finite Strip Method for the Bending of Perforated Plates[R]. Sydney:The University of Sydney, Research Report No R877, February 2007.
[36]Gabriele Eccher, Kim J. R. Rasmussen,Riccardo Zandonini,Linear Elastic Isoparametric Spline Finite Strip Analysis of Perforated Thin-Walled Structures[R]. Sydney:The University of Sydney, Research Report No R878, February 2007.
[37]Gabriele Eccher, Kim J. R. Rasmussen,Riccardo Zandonini,Elastic Buckling Analysis of Perforated Thin-Walled Structures by the Isoparametric Spline Finite Strip Method[R]. Sydney: The University of Sydney, Research Report No R879, February 2007.
[38]Gabriele Eccher, Kim J. R. Rasmussen,Riccardo Zandonini,Geometric Nonlinear Isoparametric Spline Finite Strip Analysis of Perforated Thin-Walled Structures[R]. Sydney:The University of Sydney, Research Report No R880, February 2007.
[39]Zhenyu Yao, Kim JR Rasmussen,Material and Geometric Non-linear Isoparametric Spline Finite Strip Analysis of Perforated Thin-Walled Steel Structures[R]. Sydney:The University of Sydney, Research Report No R910, February 2010.
[40]Winter. G. Strength of Thin Steel Compression Flanges. Transactions[J]. ASCE.1947. Vol.112:527-576
[41]Yu,C.,Sehafer,B.W. Distortional buckling tests on cold-formed steel beams[J].ASCE, Journal of structural Engineering.2006.132(4):515-528
[42]Schafer. B.W. Cold-formed Steel Design by the Direct Strength Method:Bye-Bye Effective Width. Proceedings Annual Technical Session SSRC.2003:357-377
[43]Sehafer,B.W.,Sarawit,A.,Pek6z,T.ComPlexedgestiffenersforthin-Walled members[J]. ASCE, Journal of structural Engineering.2006.132(2):212-226.
[44]Hancock.G.J., Kwon. Y.B. and Bernard. E.S. Strength Design Curves for thin-walled Sections Undergoing Distortional Buckling[J]. Journal of Constructional Steel Reaearch.1994.Vol.31. Nos.2-3:169-186
[45]Desmond,T.P.The behavior and strength of thin-walled compression elements with longitudinal stiffeners[D]. Ph.D. Thesis. Cornell University.1977.1 thaea,New Yock.
[46]Lau, S. C. W.,Hancock, G. J. Buckling of Thin Flat-Walled Structures by a Spline Finite Strip Method[J].Thin-Walled Structures.4(4):269-294.
[47]Kwon, Y. B.,Hancock, G. J. A Nonlinear Elastic Spline Finite Strip Analysis for Thin-walled Sections[J]. Thin-Walled Structures.12(4):295-319.
[48]Papangelis, J. P.,Hancock, G. J. Computer Analysis of Thin-Walled Structural Members[J]. Computers & Structures.56(1):157-176.
[49]Hancock, G. J. Design for Distortional Buckling of Flexural Members[J]. Thin-Walled Structures.1997.27(1):3-12.
[50]Hancock, G. J., Davids, A. J., Key, P. W., Lau, S. C. W.,Rasmussen, K. J. R. Recent Developments in the Buckling and Nonlinear Analysis of Thin-walled Structural Members[J].Thin-Walled Structures.1990.9(1-4):309-338
[51]Kwon, Y. B.,Hancock, G. J. Tests of Cold-Formed Channels with Local and Distortional Buckling. Journal of Structural Engineering[J]. ASCE.117(7):1786-1803.
[52]Young, B,Rasmussen, KJR,Compression Tests of Fixed-ended and Pin-ended Cold-formed Plain Channels[R]. Sydney:The University of Sydney, Research Report No. R714, September,1995
[53]Young, B,Rasmussen, KJR,Compression Tests of Fixed Ended and Pin-ended Cold-formed Lipped Channels[R]. Sydney:The University of Sydney, Research Report No. R715, September, 1995
[54]B Young, KJR Rasmussen,Design of cold-formed singly symmetric compression members[R]. Sydney:The University of Sydney, Research Report No R759
[55]Kim JR Rasmussen,Design of Angle Columns with Locally Unstable Legs[R]. Sydney:The University of Sydney, Research Report No R830, June 2003.
[56]Demao Yang,Gregory J Hancok.Compression Tests of Cold-Reduced High Strength Steel Channel Columns failing in the Distortional Mode[R]. Sydney:The University of Sydney, Research Report No R825, January 2003.
[57]D Yang,G Hancock.Numerical Simulations of High Strength Steel Lipped-Channel Columns[R]. Sydney:The University of Sydney, Research Report No R843, November 2004.
[58]Maura Lecce. Distortional Buckling of Stainless Steel Sections[D]. Sydney:The University of Sydney,2006
[59]Kwon YB; Kim BS; Hancock, GJ. Compression tests of high strength cold-formed steel channels with buckling interaction. Journal of constrctual research[J]. ASCE,2007.65(2):278-289
[60]苏明周,陈绍蕃.卷边槽钢梁受压翼缘畸变屈曲时的屈曲系数[J].西安建筑科技大学学报.1997.29(2)
[61]柳胜华,何保康.均匀受压卷边槽形截面的畸变屈曲性能分析[J].工业建筑.2004年增刊.
[62]GB50018-2002.冷弯薄壁型钢结构技术规范[S].北京.中国计划出版社.2002
[63]蒋路.卷边槽型冷弯薄壁型钢轴压柱畸变屈曲的理论和试验研究[D].西安建筑科技大学学位论文.2007
[64]陈绍蕃.卷边槽钢的局部屈曲和畸变屈曲[J].建筑结构学报.2002.23(1).
[65]GB50018-2002.冷弯薄壁型钢结构技术规范[S].北京.中国计划出版社.2002.
[66]陈绍蕃,苏明周。冷弯型钢擦条的有效截面[J].建筑结构学报.2003.24(6).
[67]王春刚,张耀春,张状南.冷弯薄壁斜卷边槽钢受压构件的承载力实验研究[J].建筑结构学报.2006.(27)：1-9.
[68]吴金秋,童根树.不同斜卷边檩条的局部屈曲和畸变屈曲[J].钢结构.2006.21(5)：70-73.
[69]姚谏,滕锦光.冷弯薄壁卷边槽钢弹性畸变屈曲分析中的转动约束刚度[J].工程力学.2008.25(4)：65-69.
[70]姚谏.普通卷边槽钢的弹性畸变屈曲荷载[J].工程力学.2008.25(12)：30-34.
[71]杨晓痛,姚谏.加连杆的冷弯薄壁卷边槽钢受压性能实验研究与有限元分析[J].科技通报.2007.23(5)：729-735.
[72]陈骥.受压的冷弯卷边槽钢畸变屈曲强度和其相关屈曲承载力[A].钢结构工程研究(七)----中国钢结构协会结构稳定与疲劳分会2008年学术交流会论文集[C].2008.
[73]郑建灿.冷弯薄壁卷边槽钢受弯畸变屈曲及加固措施研究[D].浙江：浙江大学.2008
[74]Jurgen Becque,Kim Rasmussen,Experimental Investigation of the Interaction of Local and Overall Buckling of Stainless Steel Columnss[R]. Sydney:The University of Sydney, Research Report No R873, November 2006.
[75]Jurgen Becque, Kim Rasmussen.Numerical Investigation and Design Methods for Stainless Steel Columns failing by,Interaction of Local and Overall Bucklings[R]. Sydney:The University of Sydney, Research Report No R888, January 2008.
[76]王士奇.冷成型薄壁钢构件拉压滞回性能数值分析[D].南京：南京工业大学.2005.5.
[77]陆曦.冷成型薄壁C型钢压弯试件滞回性能研究[D].南京：南京工业大学.2006.
[78]董军,陆曦,王士奇.冷成型C型钢试件压弯滞回性能的数值分析[J],防灾减灾工程学报.2006.26(4).
[79]Yoshiaki Goto, Qingyun Wang and Makoto Obata. FEM Analysis For Hysteretic Behavior of Thin-Walled Columns[J]. Journal of Structural Engineering.1998.124:1290-1301.
[80]董永涛,张耀春.板件在单轴往复荷载作用下非线性屈曲分析的有限元法[J].哈尔滨建筑工程学院学报.1994.
[81]Goggins J.M., Broderick, B.M., Elghazouli A.Y., Lucas A.S. Behaviour of tubular steel members under cyclic axial loading[J]. Journal of Constructional Steel Research.2006.62:1-2.
[82]董永涛,张耀春.板件在单轴往复荷载作用下非线性屈曲分析的有限元法[J].哈尔滨建筑工程学院学报.1994,1.
[83]苏明周,顾强,宋振森.箱形截面钢短柱在拉压循环荷载作用下的滞回性能和翼缘宽厚比限值.[J].土木工程学报.2000.Vo1.33(5)：13-18.
[84]苏明周,顾强,郭兵.箱形截面钢压弯试件受循环弯矩作用的试验研究和理论分析.[J].建筑结构学报.2001.Vo1.22(4)：9-16.
[85]陈以一,周锋,陈城.宽肢薄腹H形截面钢柱的滞回性能[J].世界地震工程.2002.18(4).
[86]Experimental Investigation of the Interaction of Local and Overall Buckling of Stainless Steel I-Columnss[R]. Sydney:The University of Sydney, Research Report No R887, December 2007.
[87]Maura Lecce, Kim JR Rasmussen,Experimental Investigation of the Distortional Buckling of Cold-Formed Stainless Steel Sectionss[R]. Sydney:The University of Sydney, Research Report No R844, February 2005.
[88]Maura Lecce, Kim JR Rasmussen,Finite Element Modelling and Design of Cold-Formed Stainless Steel Sectionss[R]. Sydney:The University of Sydney, Research Report No R845, June 2005.
[89]刘向斌.开口双肢冷弯薄壁型钢拼合立柱轴压承载力试验与理论研究[D]长安：长安大学,2009.5.
[90]王群.开口肢冷弯薄壁型钢拼合立柱轴压承载力试验与理论研究[D]长安：长安大学,2010.2.
[91]Pi Y L;Trahair N S Lateral-distortional buckling of hollow flange beams[J]. Journal of the Struct Engrg.1997.123(6):695-702.
[92]B. Kato, W.F. Chen, M. Nakao. Effects of joint-panel shear deformation on frames[J]. Journal of Constructional Steel Research.1988.Vol 10:269-320.
[93]刘峰.新型轻钢龙骨体系整体结构有限元分析[D].武汉理工大学硕士学位论文,2006.
[94]付国宏.低层房屋风荷载特性及抗台风设计研究[D].浙江大学博士论文.2002.
[95]梁方.我国村镇低矮房屋风压数值模拟及抗风设计研究[D].河北工业大学,2006.
[96]彭雄.冷弯薄壁型钢C型构件滞回性能研究[D].北京交通大学硕士论文.2009.
[97]Ben Young, Nuno Silvestre, Dinar Camotim,. Cold-formed steel lipped channel columns influenced by local-distortional interaction:strength and DSM design[J]. Journal of Structural Engineering.2012.
[2]YU Wei-wen.[美].董军,夏冰青(译).冷成型钢结构设计(第三版)[M].北京：中国水利水电出版社,知识产权出版社,2002：1-10.
[3]陈骥.钢结构稳定理论与设计[M].北京：科学出版社.2001：1-15.
[4]周绪红,王世纪.薄壁构件稳定理论及其应用[M].北京：科学出版社.2009：1-11.
[5]Timoshenko.S.P. and Gere.J.M.. Theory of Elastic Stability[J].2nd. Ed. McGraw-Hill. 1961:180-189.
[6]Von Karman.T. and Sechler. E. The Strength of Thin Plates in Compression. Transactions. ASME[J]. Vol.54. APM54-5,1932:1833-1848.
[7]Bleich F.金属结构的屈曲强度[M].同济大学钢木结构教研室译.北京：科学出版社.1985
[8]Coan J M. Large-deflection theory for plates with small initial curvature loaded in edge compression[J]. Trans. AMSE.1951.73
[9]Yamaki N. Postbuckling behavior of rectangular plateswith small initial curvature loaded in edge compression[J]. J. of Appl. Mech.1956.26
[10]Rasmussen, KJR,Bifurcation Analysis of Locally Buckled Members[R]. Sydney:The University of Sydney,Research Report No. R719, December,1995
[11]Young,B,Rasmussen,KJR,Bifurcation of singly symmetric columns[J].Thin-walled Structures, 1997. vol.28(2):155-177.
[12]Young,B,Rasmussen,KJR, Inelastic Bifurcation of Cold-formed Singly Symmetric Columns[J]. Thin-walled Structures,2000.36(3):213-230.
[13]K.K.V.Devarakonda, C.W.Bert. Flexural vibration of rectangular plates subjected to sinusoidally distributed compressive loading on two opposite sides[J]. Journal of Sound and Vibration,2005, 283(3-5):749-763.
[14]高轩能,孙祖龙.槽形截面腹板非均匀受压的屈曲后强度研究[J].力学与实践,1993.Vol.5：35-39.
[15]颜少荣.薄壁槽钢受压承载力计算的有效宽厚比法[J].五邑大学学报(自然科版).2001.15(3)
[16]孟春光,张伟星.无单元法在薄板稳定问题中的应用[J].力学与实践,2004.Vol.2
[17]谈梅兰,吴光,王鑫伟.矩形薄板面内非线性分布载荷下的辛弹性力学解[J].工程力学,2008.Vol.10
[18]Cheung, YK. Finite strip method in structural analysis[D]. Oxford; New York:Pergamon Press, 1976.
[19]Cheung, YK, Fan, SC, Wu, CQ. Spline finite strip in structural analysis[M]. In:editors. Proceedings of the Proceedings of the International Conference on Finite Element Method. Shanghai, China:1982
[20]Fan, SC, Spline finite strip in structural analysis[D]. Thesis, University of Hong Kong,1982.
[21]Gierlinski, J.T.,Graves Smith, T.R. The geometric non-linear analysis of thin-walled structures by finite strips[J]. Thin-Walled Structures,1984.2:27-50
[22]Hancock, G.J.. Interaction buckling in I-section columns, Journal of tructural Engineering[J], ASCE,1981.107(1):165-179
[23]Hancock, G.J.. Distortional buckling of steel storage rack columns, Journal of Structural Engineering[J], ASCE,1985. 111(12):2770-2783
[24]Lau, SCW, Hancock, GJ. Buckling of thin flat-walled structures by a spline finite strip method[J]. Thin-Walled Structures.1986.4(4):269-294.
[25]Lau, SCW, Hancock, GJ. Inelastic buckling analysis of beams, columns and plates using the spline finite strip method[J]. Thin-Walled Structures.1989.7:213-238.
[26]Kwon, YB, Hancock, GJ. A nonlinear elastic spline finite strip analysis for thin-walled sections[J]. Thin-Walled Structures.1991.12(4):295-319.
[27]Au, FTK, Cheung, YK. Isoparametric spline finite strip for plane structures[J]. Computers & Structures.1993.48(1):23-32.
[28]Cheung, YK, Au, FTK. Isoparametric spline finite strip for degenerate shells[J]. Thin-Walled Structures.1995.21(1):65-92.
[29]Godley, MHR. Storage Racking-chapter 11. In:editors. Design of Cold Formed Steel Members[J]. Ed. Rhodes.1991.
[30]Shanmugam, NE, Thevendran, V, Tan, YH. Design formula for axially compressed perforated plates[J]. Thin-Walled Structures.1999.34(1):1.
[31]Shanmugam, NE, Thevendran, V. Lateral buckling of doubly symmetric beams containing openings[J]. Journal of Engineering Mechanics, American Society of Civil Engineers. 1991.117(7):1427-1441.
[32]Shanmugam, NE, Dhanalakshmi, M. State of art review and compilation of studies on perforated thin-walled structures[J]. International Journal of Structural Stability and Dynamics 2001.1
[33]Rhodes, J, Macdonald, M. The effect of perforation length on the behaviour of perforated elements in compression[M]. In:editors. Proceedings of the Thirthteenth International Speciality Conference on Cold-Formed Steel Structures.1996.
[34]Gabriele Eccher, Kim Rasmussen, Nadia Baldassino, Riccardo Zandonini,Isoparametric Spline Finite Strip Method for In-plane Stress Analysis[R]. Sydney:The University of Sydney, Research Report No R848, August 2005.
[35]Gabriele Eccher, Kim J. R. Rasmussen,Riccardo Zandonini,Isoparametric Spline Finite Strip Method for the Bending of Perforated Plates[R]. Sydney:The University of Sydney, Research Report No R877, February 2007.
[36]Gabriele Eccher, Kim J. R. Rasmussen,Riccardo Zandonini,Linear Elastic Isoparametric Spline Finite Strip Analysis of Perforated Thin-Walled Structures[R]. Sydney:The University of Sydney, Research Report No R878, February 2007.
[37]Gabriele Eccher, Kim J. R. Rasmussen,Riccardo Zandonini,Elastic Buckling Analysis of Perforated Thin-Walled Structures by the Isoparametric Spline Finite Strip Method[R]. Sydney: The University of Sydney, Research Report No R879, February 2007.
[38]Gabriele Eccher, Kim J. R. Rasmussen,Riccardo Zandonini,Geometric Nonlinear Isoparametric Spline Finite Strip Analysis of Perforated Thin-Walled Structures[R]. Sydney:The University of Sydney, Research Report No R880, February 2007.
[39]Zhenyu Yao, Kim JR Rasmussen,Material and Geometric Non-linear Isoparametric Spline Finite Strip Analysis of Perforated Thin-Walled Steel Structures[R]. Sydney:The University of Sydney, Research Report No R910, February 2010.
[40]Winter. G. Strength of Thin Steel Compression Flanges. Transactions[J]. ASCE.1947. Vol.112:527-576
[41]Yu,C.,Sehafer,B.W. Distortional buckling tests on cold-formed steel beams[J].ASCE, Journal of structural Engineering.2006.132(4):515-528
[42]Schafer. B.W. Cold-formed Steel Design by the Direct Strength Method:Bye-Bye Effective Width. Proceedings Annual Technical Session SSRC.2003:357-377
[43]Sehafer,B.W.,Sarawit,A.,Pek6z,T.ComPlexedgestiffenersforthin-Walled members[J]. ASCE, Journal of structural Engineering.2006.132(2):212-226.
[44]Hancock.G.J., Kwon. Y.B. and Bernard. E.S. Strength Design Curves for thin-walled Sections Undergoing Distortional Buckling[J]. Journal of Constructional Steel Reaearch.1994.Vol.31. Nos.2-3:169-186
[45]Desmond,T.P.The behavior and strength of thin-walled compression elements with longitudinal stiffeners[D]. Ph.D. Thesis. Cornell University.1977.1 thaea,New Yock.
[46]Lau, S. C. W.,Hancock, G. J. Buckling of Thin Flat-Walled Structures by a Spline Finite Strip Method[J].Thin-Walled Structures.4(4):269-294.
[47]Kwon, Y. B.,Hancock, G. J. A Nonlinear Elastic Spline Finite Strip Analysis for Thin-walled Sections[J]. Thin-Walled Structures.12(4):295-319.
[48]Papangelis, J. P.,Hancock, G. J. Computer Analysis of Thin-Walled Structural Members[J]. Computers & Structures.56(1):157-176.
[49]Hancock, G. J. Design for Distortional Buckling of Flexural Members[J]. Thin-Walled Structures.1997.27(1):3-12.
[50]Hancock, G. J., Davids, A. J., Key, P. W., Lau, S. C. W.,Rasmussen, K. J. R. Recent Developments in the Buckling and Nonlinear Analysis of Thin-walled Structural Members[J].Thin-Walled Structures.1990.9(1-4):309-338
[51]Kwon, Y. B.,Hancock, G. J. Tests of Cold-Formed Channels with Local and Distortional Buckling. Journal of Structural Engineering[J]. ASCE.117(7):1786-1803.
[52]Young, B,Rasmussen, KJR,Compression Tests of Fixed-ended and Pin-ended Cold-formed Plain Channels[R]. Sydney:The University of Sydney, Research Report No. R714, September,1995
[53]Young, B,Rasmussen, KJR,Compression Tests of Fixed Ended and Pin-ended Cold-formed Lipped Channels[R]. Sydney:The University of Sydney, Research Report No. R715, September, 1995
[54]B Young, KJR Rasmussen,Design of cold-formed singly symmetric compression members[R]. Sydney:The University of Sydney, Research Report No R759
[55]Kim JR Rasmussen,Design of Angle Columns with Locally Unstable Legs[R]. Sydney:The University of Sydney, Research Report No R830, June 2003.
[56]Demao Yang,Gregory J Hancok.Compression Tests of Cold-Reduced High Strength Steel Channel Columns failing in the Distortional Mode[R]. Sydney:The University of Sydney, Research Report No R825, January 2003.
[57]D Yang,G Hancock.Numerical Simulations of High Strength Steel Lipped-Channel Columns[R]. Sydney:The University of Sydney, Research Report No R843, November 2004.
[58]Maura Lecce. Distortional Buckling of Stainless Steel Sections[D]. Sydney:The University of Sydney,2006
[59]Kwon YB; Kim BS; Hancock, GJ. Compression tests of high strength cold-formed steel channels with buckling interaction. Journal of constrctual research[J]. ASCE,2007.65(2):278-289
[60]苏明周,陈绍蕃.卷边槽钢梁受压翼缘畸变屈曲时的屈曲系数[J].西安建筑科技大学学报.1997.29(2)
[61]柳胜华,何保康.均匀受压卷边槽形截面的畸变屈曲性能分析[J].工业建筑.2004年增刊.
[62]GB50018-2002.冷弯薄壁型钢结构技术规范[S].北京.中国计划出版社.2002
[63]蒋路.卷边槽型冷弯薄壁型钢轴压柱畸变屈曲的理论和试验研究[D].西安建筑科技大学学位论文.2007
[64]陈绍蕃.卷边槽钢的局部屈曲和畸变屈曲[J].建筑结构学报.2002.23(1).
[65]GB50018-2002.冷弯薄壁型钢结构技术规范[S].北京.中国计划出版社.2002.
[66]陈绍蕃,苏明周。冷弯型钢擦条的有效截面[J].建筑结构学报.2003.24(6).
[67]王春刚,张耀春,张状南.冷弯薄壁斜卷边槽钢受压构件的承载力实验研究[J].建筑结构学报.2006.(27)：1-9.
[68]吴金秋,童根树.不同斜卷边檩条的局部屈曲和畸变屈曲[J].钢结构.2006.21(5)：70-73.
[69]姚谏,滕锦光.冷弯薄壁卷边槽钢弹性畸变屈曲分析中的转动约束刚度[J].工程力学.2008.25(4)：65-69.
[70]姚谏.普通卷边槽钢的弹性畸变屈曲荷载[J].工程力学.2008.25(12)：30-34.
[71]杨晓痛,姚谏.加连杆的冷弯薄壁卷边槽钢受压性能实验研究与有限元分析[J].科技通报.2007.23(5)：729-735.
[72]陈骥.受压的冷弯卷边槽钢畸变屈曲强度和其相关屈曲承载力[A].钢结构工程研究(七)----中国钢结构协会结构稳定与疲劳分会2008年学术交流会论文集[C].2008.
[73]郑建灿.冷弯薄壁卷边槽钢受弯畸变屈曲及加固措施研究[D].浙江：浙江大学.2008
[74]Jurgen Becque,Kim Rasmussen,Experimental Investigation of the Interaction of Local and Overall Buckling of Stainless Steel Columnss[R]. Sydney:The University of Sydney, Research Report No R873, November 2006.
[75]Jurgen Becque, Kim Rasmussen.Numerical Investigation and Design Methods for Stainless Steel Columns failing by,Interaction of Local and Overall Bucklings[R]. Sydney:The University of Sydney, Research Report No R888, January 2008.
[76]王士奇.冷成型薄壁钢构件拉压滞回性能数值分析[D].南京：南京工业大学.2005.5.
[77]陆曦.冷成型薄壁C型钢压弯试件滞回性能研究[D].南京：南京工业大学.2006.
[78]董军,陆曦,王士奇.冷成型C型钢试件压弯滞回性能的数值分析[J],防灾减灾工程学报.2006.26(4).
[79]Yoshiaki Goto, Qingyun Wang and Makoto Obata. FEM Analysis For Hysteretic Behavior of Thin-Walled Columns[J]. Journal of Structural Engineering.1998.124:1290-1301.
[80]董永涛,张耀春.板件在单轴往复荷载作用下非线性屈曲分析的有限元法[J].哈尔滨建筑工程学院学报.1994.
[81]Goggins J.M., Broderick, B.M., Elghazouli A.Y., Lucas A.S. Behaviour of tubular steel members under cyclic axial loading[J]. Journal of Constructional Steel Research.2006.62:1-2.
[82]董永涛,张耀春.板件在单轴往复荷载作用下非线性屈曲分析的有限元法[J].哈尔滨建筑工程学院学报.1994,1.
[83]苏明周,顾强,宋振森.箱形截面钢短柱在拉压循环荷载作用下的滞回性能和翼缘宽厚比限值.[J].土木工程学报.2000.Vo1.33(5)：13-18.
[84]苏明周,顾强,郭兵.箱形截面钢压弯试件受循环弯矩作用的试验研究和理论分析.[J].建筑结构学报.2001.Vo1.22(4)：9-16.
[85]陈以一,周锋,陈城.宽肢薄腹H形截面钢柱的滞回性能[J].世界地震工程.2002.18(4).
[86]Experimental Investigation of the Interaction of Local and Overall Buckling of Stainless Steel I-Columnss[R]. Sydney:The University of Sydney, Research Report No R887, December 2007.
[87]Maura Lecce, Kim JR Rasmussen,Experimental Investigation of the Distortional Buckling of Cold-Formed Stainless Steel Sectionss[R]. Sydney:The University of Sydney, Research Report No R844, February 2005.
[88]Maura Lecce, Kim JR Rasmussen,Finite Element Modelling and Design of Cold-Formed Stainless Steel Sectionss[R]. Sydney:The University of Sydney, Research Report No R845, June 2005.
[89]刘向斌.开口双肢冷弯薄壁型钢拼合立柱轴压承载力试验与理论研究[D]长安：长安大学,2009.5.
[90]王群.开口肢冷弯薄壁型钢拼合立柱轴压承载力试验与理论研究[D]长安：长安大学,2010.2.
[91]Pi Y L;Trahair N S Lateral-distortional buckling of hollow flange beams[J]. Journal of the Struct Engrg.1997.123(6):695-702.
[92]B. Kato, W.F. Chen, M. Nakao. Effects of joint-panel shear deformation on frames[J]. Journal of Constructional Steel Research.1988.Vol 10:269-320.
[93]刘峰.新型轻钢龙骨体系整体结构有限元分析[D].武汉理工大学硕士学位论文,2006.
[94]付国宏.低层房屋风荷载特性及抗台风设计研究[D].浙江大学博士论文.2002.
[95]梁方.我国村镇低矮房屋风压数值模拟及抗风设计研究[D].河北工业大学,2006.
[96]彭雄.冷弯薄壁型钢C型构件滞回性能研究[D].北京交通大学硕士论文.2009.
[97]Ben Young, Nuno Silvestre, Dinar Camotim,. Cold-formed steel lipped channel columns influenced by local-distortional interaction:strength and DSM design[J]. Journal of Structural Engineering.2012.