平面半刚性钢框架静力弹塑性分析的QR法
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摘要
钢框架梁柱连接节点的性能直接影响结构的侧移及内力,传统的钢结构设计中,梁和柱的连接一般假设为完全刚接或理想铰接,大量的试验研究表明,实际使用的连接都是介于完全刚接与理想铰接之间的半刚性连接。将半刚性连接简化为完全刚性连接将低估框架的侧移量而高估框架稳定极限承载力,使结构偏于不安全;而将半刚性连接简化为理想的铰接将使结构设计偏于保守,增加钢材用量。为了更合理的进行钢结构设计,必须考虑结构梁柱半刚性连接的影响。
本文对平面半刚性连接钢框架进行了研究,根据大位移小变形理论,采用梁柱法和稳定函数推导了梁柱结构考虑几何非线性、材料非线性及梁柱半刚性连接时的单元刚度矩阵,并用Kishi-Chen幂函数模型描述半刚性连接的特性。
本文采用QR法研究了平面钢框架考虑几何、材料、半刚性连接三重非线性的静力问题,建立了QR法的计算格式,并采用C语言编制了相应的计算程序,用典型算例的程序计算结果分析了各种非线性因素对结构的影响。结果分析表明,结构的几何非线性、材料非线性及半刚性连接相互影响,增加了结构的侧移,并对结构的内力分布及延性产生较大影响,同时降低了结构的极限承载力。本文QR法和有限元相对比,结果精度好、未知量数目少、刚度矩阵的计算过程更为简便。
The performance of beam-column connections in steel frame affects directly the sideways and internal forces of the frame. In the traditional steel structure design, beams and columns generally were assumed to be fully rigid connected or hinged ideally. Extensive tests and studies show that all connections of the steel structures in practice are between fully rigid and ideal pinned link and belong to semi-rigid connections. If the semi-rigid connections are simplified fully rigid connections, the sideways of the frame will be underestimated, the ultimate load-carrying capacity will be magnified, and the structure will lean to unsafe. If the semi-rigid connections are simplified ideal pinned connections, the design will be conservative, and the consumption of steel will increase. In order to make the design of steel frame more reasonable, the effect of semi-rigid connections must be taken account of.
This paper studies the plane semi-rigid connections steel frame, according to the big displacement theory under small deformation, uses the theory of beam-to-column and stability function to derive the element stiffness matrix which considers geometric nonlinearity, the material nonlinearity and the beam-column semi-rigid connection, and using Kishi-Chen power function to describe the nonlinear behavior of semi-rigid connections.
This paper use the QR method to study the static analysis of plane steel frame which considers triple non-linearity, has established the QR method computational scheme, has edited the corresponding computational programs by C programming language, has analyzed the influence to the structure of each kind of nonlinear factor by the program computation result of typical examples. Analysis shows that the geometry nonlinearity, the material nonlinearity and the semi-rigid connection mutual influence, and increase the sideways of the frame, influence the structure internal force and ductility, while reducing the ultimate bearing capacity. Compared with the traditional finite element method, this QR method has its advantages, such as high precision, fewer unknown quantity, and simple computational scheme.
本文对平面半刚性连接钢框架进行了研究,根据大位移小变形理论,采用梁柱法和稳定函数推导了梁柱结构考虑几何非线性、材料非线性及梁柱半刚性连接时的单元刚度矩阵,并用Kishi-Chen幂函数模型描述半刚性连接的特性。
本文采用QR法研究了平面钢框架考虑几何、材料、半刚性连接三重非线性的静力问题,建立了QR法的计算格式,并采用C语言编制了相应的计算程序,用典型算例的程序计算结果分析了各种非线性因素对结构的影响。结果分析表明,结构的几何非线性、材料非线性及半刚性连接相互影响,增加了结构的侧移,并对结构的内力分布及延性产生较大影响,同时降低了结构的极限承载力。本文QR法和有限元相对比,结果精度好、未知量数目少、刚度矩阵的计算过程更为简便。
The performance of beam-column connections in steel frame affects directly the sideways and internal forces of the frame. In the traditional steel structure design, beams and columns generally were assumed to be fully rigid connected or hinged ideally. Extensive tests and studies show that all connections of the steel structures in practice are between fully rigid and ideal pinned link and belong to semi-rigid connections. If the semi-rigid connections are simplified fully rigid connections, the sideways of the frame will be underestimated, the ultimate load-carrying capacity will be magnified, and the structure will lean to unsafe. If the semi-rigid connections are simplified ideal pinned connections, the design will be conservative, and the consumption of steel will increase. In order to make the design of steel frame more reasonable, the effect of semi-rigid connections must be taken account of.
This paper studies the plane semi-rigid connections steel frame, according to the big displacement theory under small deformation, uses the theory of beam-to-column and stability function to derive the element stiffness matrix which considers geometric nonlinearity, the material nonlinearity and the beam-column semi-rigid connection, and using Kishi-Chen power function to describe the nonlinear behavior of semi-rigid connections.
This paper use the QR method to study the static analysis of plane steel frame which considers triple non-linearity, has established the QR method computational scheme, has edited the corresponding computational programs by C programming language, has analyzed the influence to the structure of each kind of nonlinear factor by the program computation result of typical examples. Analysis shows that the geometry nonlinearity, the material nonlinearity and the semi-rigid connection mutual influence, and increase the sideways of the frame, influence the structure internal force and ductility, while reducing the ultimate bearing capacity. Compared with the traditional finite element method, this QR method has its advantages, such as high precision, fewer unknown quantity, and simple computational scheme.
引文
[1]Hadianfard,M.A.and Razani,R.Effects of semi-rigid behavior of connections in the reliability of steel frames[J].Structural Safety,2003,25(2).123-138.
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[3]王新武.钢框架梁柱连接研究[D],博士学位论文,2003,8-9.
[4]陈惠发.钢框架稳定设计[M],世界图书出版社,2001.
[5]Goverdhan,A.V.A collection of experimental moment-rotation curves and evaluation of prediction equation for Semi-Rigid connections[DB],Master's thesis,Vanderbilt University,Nashville,TN,490pp;1983.
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[7]Nethercot,D.A.Utilization of experimentally obtained connection data in assessing the performance of steel frames,in connection flexibility and steel frames(W.F.Chen,Ed.),Proceedings of a Session Sponsored by the Structural Division,ASCE,Detroit,pp.13-37;1985.
[8]Kishi,N.and Chen,W.F.Data Base of Steel Beam-column Connection.Struct[DB].Engrg.CE-STR-86-26,Purdue University,Vol.Ⅰ&Ⅱ,1986.
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[23] Hjelmstad K. D, Taciroglu E. Mixed methods and flexibility approaches for nonlinear frame analysis [J].Journal of Constructional Steel Research, 2002, 58(5-8):967-993.
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[35] Monforton, A. R. and Wu, T. S. Matrix Analysis of Semi-Rigidly Connected Frames[J]. Journal of Structural Division, ASCE, 1963,89:13-42.
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[38] Aokroyd,M. H. and Gerstle, K. H. Strength of Flexibly Connected Steel Frames[J]. Engnrg, Struct, 1983, 5(1): 31-37.
[39] Lui, E. M. and Chen, W. F. Behaviors of Braced and Unbraced Semi-rigid Frames [J]. Int. J. Solids Struct. 1988, 24(9):893-913.
[40] Haldar, A. and Nee, K. M. Elastic-Plastic Large Deformation Analysis of PR Steel Frames for LRFD[J]. Computers and Structure, 1989, 31(5):811-823.
[41] Shi,C and Atlurl,S. N. Static and Dynamic Analysis of Space Frames with Nonlinear Flexible Connections [J]. Int. J. for Numerical Methods in Engrg, 1989,28:2635-2650.
[42]Goto,Y.,Suzuki,S.and Chen,W.F.Analysis of Critical Behavior of Semi-rigid Frames with or without Load History in Connections[J].International Journal of Solids and Structures,1991,27(4):467-483.
[43]Barakat,M.and Chen,W.F.Practical Analysis of Semi-rigid Frames[J].Eng.J.AISC,1990,27(2):54-68.
[44]Barsan,G.M.and Chiorean,C.G.Computer program for large deflection elasto-plastic analysis of semi-rigid steel frameworks[J].Computers & Structures,1999,72(6):699-711.
[45]沈祖炎,丁洁民.柔性节点钢框架的二阶弹塑性极限承载力研究[J],建筑结构学报,1992,13(1):17-25.
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[2]李永泉,何若全.框架半刚性连接的研究概述[J],哈尔滨建筑工程学院学报,1994,27(3):112-118.
[3]王新武.钢框架梁柱连接研究[D],博士学位论文,2003,8-9.
[4]陈惠发.钢框架稳定设计[M],世界图书出版社,2001.
[5]Goverdhan,A.V.A collection of experimental moment-rotation curves and evaluation of prediction equation for Semi-Rigid connections[DB],Master's thesis,Vanderbilt University,Nashville,TN,490pp;1983.
[6]Nethercot,D.A.Steel beam-to-column connection A review of test data and its applicability to the evaluation of joint behavior in the performance of steel frames[DB],CIRIA Project Record,RP338;1985.
[7]Nethercot,D.A.Utilization of experimentally obtained connection data in assessing the performance of steel frames,in connection flexibility and steel frames(W.F.Chen,Ed.),Proceedings of a Session Sponsored by the Structural Division,ASCE,Detroit,pp.13-37;1985.
[8]Kishi,N.and Chen,W.F.Data Base of Steel Beam-column Connection.Struct[DB].Engrg.CE-STR-86-26,Purdue University,Vol.Ⅰ&Ⅱ,1986.
[9]王燕,彭福明.多高层刚框架梁柱半刚性连接性能[J],建筑结构,2000,30(9):18-22.
[10]施刚.钢框架半刚性端板连接的静力和抗震性能研究[D],博士学位论文,2004.
[11]郭兵,顾强,柳锋等.梁柱端板连接节点的滞回性能试验研究[J],建筑结构学报,2002,23(3):8-13.
[12]陈爱国,顾强,苏明周等.腹板双角钢梁柱连接循环荷载试验研究[J],建筑结构学报,2003,24(6):67-71.
[13]S.W Jones,P.A.Kirby and D.A.Nethercot.Columns with Simi-rigid Joints[J].J.Struct.Div,ASCE,1982,108(ST2):361-372.
[14]Frye M.J.Morris G.A.Analysis Of Flexibly Connected steel Frames[J].Canadian Journal of Civil Engineering,1975,2:280-291
[15]Kishi N,Chen W.F.Moment-rotation of Semi-rigid Connections[R].Structural Engineering Report,USA,1987,87:29-44
[16]N.Kishi,W.F.Chen and Y.Gotoetal.Design Aid of Semi-rigid Connections for Frame Analysis[J].Eng.J,AISC,1993,30(3):90-107.
[17]K.M.Ang,G.A.Morris.Analysis of Three-dimensional Frames with Flexible Beam - column Connections.Can.J.Div.Engrg.,1984,11:245-254.
[18]Lui,E.M.and Chen,W.F.Analysis and behavior of flexibly-jointed frames,Engineering Structures,1986,8;107-118.
[19]丁洁民,沈祖炎.节点半刚性对框架结构内力和位移的影响[C],第十一届全国高层会议论文集,1990.
[20]陈林,崔佳,吴惠弼.半刚性连接钢框架M—θ曲线的自适应函数法[J],重庆建筑工程学院学报,1992,14(1):48-55.
[21]Chajes A,Churchill J.E.Nonlinear frame analysis by finite element methods[J].Journal of Structural Engineering, ASCE, 1987,113(6):1221-1235.
[22] Neuenhofer A, Filippou F. C. Geometrically nonlinear flexibility-based frame finite element [J]. Journal of Structural Engineering,ASCE, 1998, 124(6):704-711.
[23] Hjelmstad K. D, Taciroglu E. Mixed methods and flexibility approaches for nonlinear frame analysis [J].Journal of Constructional Steel Research, 2002, 58(5-8):967-993.
[24] Oran C. Tangent stiffness in plane/space frame [J]. Journal of the Structural Division, 1973, 99 (ST6):973-1001.
[25] Avery P, Mahendran M. Analytical benchmark solutions for steel frame structures subjected to local buckling effects[J]. Advances in Structural Engineering, 2000, 3(3): 215-229.
[26] Chen W. F. Advanced analysis in steel frames[M] .Boca Raton :CRC Press ,1993.
[27] Attalla M. R, Deierlein G, McGuire W. Spread of plasticity:Quasi-plastic-hinge approach [J]. Journal of Structural Engineering (ASCE), 1994 ,120(8):2451-2473.
[28] Liew J Y R. Notional load plastic hinge method for frame design[J]. Journal of Structural Engineering (ASCE), 1994,120:1434-1454.
[29] King W S ,Chen W F. Practical second-order inelastic analysis of semirigid frames[J]. Journal of Structural Engineering(ASCE), 1994,120(7): 2156-2175.
[30] Liew J Y R. Implication of using refined plastic hinge analysis for load and resistance factor design[J]. Thin-Walled Structures ,1994 ,20:17-47.
[31] Chen W F,Kim S E. Design of steel structures with LRFD using advanced analysis[C]. Proceedings of the 5th International Colloquium on Stability and Ductility of Steel Structures(ed. T. Usami). Nagoya: [s. n. ], 1997, 21-32.
[32] Avery P , Mahendran M. Pseudo plastic zone analysis of steel frame structures comprising non-compact sections[R]. Brisbane:Physical Infrastructure Center, School of Civil Engineering, QUT ,1998.
[33] C. Rathbum. Elastic Properties of Riveted Connections[J]. Transactions of American Society of Civil Engineers, 1936, 101:524-563.
[34] Lightfoot, E. and Baker, A. R. The Analysis of Steel Frames with Elastic Beam-Column Connections[C]. Golden Jubilee Congress Symposium on the Design of High Buildings, Hong Kong, Hong Kong University Press.
[35] Monforton, A. R. and Wu, T. S. Matrix Analysis of Semi-Rigidly Connected Frames[J]. Journal of Structural Division, ASCE, 1963,89:13-42.
[36] Ronstad, K. M. and Subramanian, C. V. Analysis of Frames with Partial Connection Rigidity [J]. Journal of Structural Division, ASCE, 1970, 96:2283-2300.
[37] Frye, M. J. and Morris, G. A. Analysis of Flexibly Connected Steel Frames[J].Can. J. Div. Engrg, 1976,2(3): 280-291.
[38] Aokroyd,M. H. and Gerstle, K. H. Strength of Flexibly Connected Steel Frames[J]. Engnrg, Struct, 1983, 5(1): 31-37.
[39] Lui, E. M. and Chen, W. F. Behaviors of Braced and Unbraced Semi-rigid Frames [J]. Int. J. Solids Struct. 1988, 24(9):893-913.
[40] Haldar, A. and Nee, K. M. Elastic-Plastic Large Deformation Analysis of PR Steel Frames for LRFD[J]. Computers and Structure, 1989, 31(5):811-823.
[41] Shi,C and Atlurl,S. N. Static and Dynamic Analysis of Space Frames with Nonlinear Flexible Connections [J]. Int. J. for Numerical Methods in Engrg, 1989,28:2635-2650.
[42]Goto,Y.,Suzuki,S.and Chen,W.F.Analysis of Critical Behavior of Semi-rigid Frames with or without Load History in Connections[J].International Journal of Solids and Structures,1991,27(4):467-483.
[43]Barakat,M.and Chen,W.F.Practical Analysis of Semi-rigid Frames[J].Eng.J.AISC,1990,27(2):54-68.
[44]Barsan,G.M.and Chiorean,C.G.Computer program for large deflection elasto-plastic analysis of semi-rigid steel frameworks[J].Computers & Structures,1999,72(6):699-711.
[45]沈祖炎,丁洁民.柔性节点钢框架的二阶弹塑性极限承载力研究[J],建筑结构学报,1992,13(1):17-25.
[46]徐伟良,吴惠弼.半刚性连接钢框架非线性分析的修正塑性区法[J],重庆建筑大学学报,1995,17(3):35-42.
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