偏心支撑钢框架在循环荷载作用下的破坏机理及抗震设计对策
|
摘要
偏心支撑钢框架在弹性阶段刚度很大，能够满足高层钢结构侧移要求。在罕遇地震时，由于耗能梁段屈服进入塑性，结构有很强的耗能能力和延性，是适用于高烈度震区的一种有效的抗侧力结构体系。国内外许多学者对此进行了试验和理论研究，并将研究成果应用于工程实践。本文以工程应用为目的，研究和探索了各种典型的偏心支撑钢框架在循环荷载作用下的滞洄性能和破坏机理，并提出了抗震设计对策和建议。
本文提出了应用子结构法联合梁单元与空间退化曲壳单元分析偏心支撑钢框架耗能性能及耗能梁段破坏机理的非线性有限元分析模型。在有限元分析过程中，对于未进入塑性部分的梁、柱及支撑采用梁单元，梁单元考虑了几何非线性，对于进入塑性部分的耗能梁段采用空间退化曲壳单元，曲壳单元考虑了几何和材料的双重非线性，材料的强化采用了混合强化法则，非线性方程通过Newton-Raphson迭代结合增量法求解。在整体结构中采用两种单元较精确的分析偏心支撑钢框架的滞洄性能及破坏机理的方法，在国内外均属首次。本文编制了梁-壳元非线性有限元分析程序BSNFEM，并进行了算例分析，验证了程序的可靠性。
应用BSNFEM非线性有限元程序对偏心支撑钢框架进行了循环加载分析。对耗能梁段的长度、耗能梁段腹板的厚度、耗能梁段翼缘的厚度、耗能梁段加劲肋的间距、耗能梁段加劲肋的厚度、支撑的夹角等因素的改变对D形、K形偏心支撑钢框架耗能的影响，前人已有一些研究，本文对这些因素的影响进行了全面系统的分析，完善了理论分析的不足；而结构高跨比、支撑刚度、支撑与梁的连接形式等因素对D形、K形偏心支撑钢框架破坏机理的研究以及各种因素对Y形偏心支撑钢框架破坏机理的影响，则很少有人涉及，本文对此也进行了深入系统的分析，填补了这一研究空白。
最后，根据有限元研究结果，提出了抗震设计对策和建议。
本文全面、系统、深入地分析了三种典型偏心支撑钢框架结构在循环荷载作用下的破坏
西安建筑科技大学博士学位论文
机理，对于修订有关规范、指导工程设计有重要的参考价值，也为进一步研究偏心支撑钢框
架结构的抗震性能打下了良好的基础。
Eccentrically braced steel frames are a lateral load-resisting system which apply high intensity area and it can provide the high elastic stiffness that met higher steel building drift requirement. The links of Eccentrically braced steel frames sustain large inelastic deformation without loss of strength under severe earthquake loading which demonstrate excellent energy-dissipation capacity and ductility. It was tested and theories studied by many scholars at home and broad, and as a result, the achievements have been applied engineering practice. This p aper aim at the project application, study on collapse mechanism and design criteria of eccentrically braced steel frames under cyclic Load.
A new nonlinear finite element model which applies subsystem connect beams element and space degenerate shell element to analyze eccentric braced structural energy-dissipation and links collapse mechanism is presented in this paper. In the process of finite element analyzing, the beam, column and b race that not enter the plastic parts adopt bearn element that considered geometry nonlinear. The links entering plastic adopt space degenerate shell element that considered the nonlinear large-deformation, together with mixed hardening rule, which linearly combines isotropic and kinematic hardening. The method applied two elements to analyze the collapse mechanism and hysteretic behavior of eccentrically braced steel frames under cyclic Load in structure at first time. Computer program BSNFEM is complied. Good agreement is found between the theoretical predications and experiment result.
This paper applies nonlinear finite element program BSNFEM to analyze the behaviors of eccentrically braced steel frames under cyclic load. The study that comprehensive and systematic analyze the factor of links length, thickness of links flange, distance of links rib, thickness of links rib and angle of brace to be changed affect energy-dissipation capacity of D shape and K shape eccentrically braced steel frames have been some studied before. This paper fills the black in the filed factor of high-span ratio, brace stiffness and brace-to-beam connections to be changed affect
energy-dissipation capacity of D shape and K shape eccentrically braced steel trames and any factor to be changed affect energy-dissipation capacity of Y shape eccentrically braced steel frames.
Suggestions for seismic design based on FEM analysis are presented at last. The study that analyzing three kind of eccentrically braced steel frames is rather comprehensive and systematic, and the conclusions can be useful for revising design code, guiding design of engineering, and provide good basis for further to study seismic-resistant behavior of eccentrically braced steel frames.
本文提出了应用子结构法联合梁单元与空间退化曲壳单元分析偏心支撑钢框架耗能性能及耗能梁段破坏机理的非线性有限元分析模型。在有限元分析过程中，对于未进入塑性部分的梁、柱及支撑采用梁单元，梁单元考虑了几何非线性，对于进入塑性部分的耗能梁段采用空间退化曲壳单元，曲壳单元考虑了几何和材料的双重非线性，材料的强化采用了混合强化法则，非线性方程通过Newton-Raphson迭代结合增量法求解。在整体结构中采用两种单元较精确的分析偏心支撑钢框架的滞洄性能及破坏机理的方法，在国内外均属首次。本文编制了梁-壳元非线性有限元分析程序BSNFEM，并进行了算例分析，验证了程序的可靠性。
应用BSNFEM非线性有限元程序对偏心支撑钢框架进行了循环加载分析。对耗能梁段的长度、耗能梁段腹板的厚度、耗能梁段翼缘的厚度、耗能梁段加劲肋的间距、耗能梁段加劲肋的厚度、支撑的夹角等因素的改变对D形、K形偏心支撑钢框架耗能的影响，前人已有一些研究，本文对这些因素的影响进行了全面系统的分析，完善了理论分析的不足；而结构高跨比、支撑刚度、支撑与梁的连接形式等因素对D形、K形偏心支撑钢框架破坏机理的研究以及各种因素对Y形偏心支撑钢框架破坏机理的影响，则很少有人涉及，本文对此也进行了深入系统的分析，填补了这一研究空白。
最后，根据有限元研究结果，提出了抗震设计对策和建议。
本文全面、系统、深入地分析了三种典型偏心支撑钢框架结构在循环荷载作用下的破坏
西安建筑科技大学博士学位论文
机理，对于修订有关规范、指导工程设计有重要的参考价值，也为进一步研究偏心支撑钢框
架结构的抗震性能打下了良好的基础。
Eccentrically braced steel frames are a lateral load-resisting system which apply high intensity area and it can provide the high elastic stiffness that met higher steel building drift requirement. The links of Eccentrically braced steel frames sustain large inelastic deformation without loss of strength under severe earthquake loading which demonstrate excellent energy-dissipation capacity and ductility. It was tested and theories studied by many scholars at home and broad, and as a result, the achievements have been applied engineering practice. This p aper aim at the project application, study on collapse mechanism and design criteria of eccentrically braced steel frames under cyclic Load.
A new nonlinear finite element model which applies subsystem connect beams element and space degenerate shell element to analyze eccentric braced structural energy-dissipation and links collapse mechanism is presented in this paper. In the process of finite element analyzing, the beam, column and b race that not enter the plastic parts adopt bearn element that considered geometry nonlinear. The links entering plastic adopt space degenerate shell element that considered the nonlinear large-deformation, together with mixed hardening rule, which linearly combines isotropic and kinematic hardening. The method applied two elements to analyze the collapse mechanism and hysteretic behavior of eccentrically braced steel frames under cyclic Load in structure at first time. Computer program BSNFEM is complied. Good agreement is found between the theoretical predications and experiment result.
This paper applies nonlinear finite element program BSNFEM to analyze the behaviors of eccentrically braced steel frames under cyclic load. The study that comprehensive and systematic analyze the factor of links length, thickness of links flange, distance of links rib, thickness of links rib and angle of brace to be changed affect energy-dissipation capacity of D shape and K shape eccentrically braced steel frames have been some studied before. This paper fills the black in the filed factor of high-span ratio, brace stiffness and brace-to-beam connections to be changed affect
energy-dissipation capacity of D shape and K shape eccentrically braced steel trames and any factor to be changed affect energy-dissipation capacity of Y shape eccentrically braced steel frames.
Suggestions for seismic design based on FEM analysis are presented at last. The study that analyzing three kind of eccentrically braced steel frames is rather comprehensive and systematic, and the conclusions can be useful for revising design code, guiding design of engineering, and provide good basis for further to study seismic-resistant behavior of eccentrically braced steel frames.
引文
1-1 Egor P. Popov & Michael D. Engelhardt. Seismic Eccentrically Braced Frames. J. Construct. Steel Research, 321-354, 10, 1988
1-2 Dune K. Miller. Lessons learned from the Northridge earthquake. Engineering structures, 1998; 20 (4-6) : 249-260
1-3 崔鸿超 日本兵库县南部地区地震震害综述 建筑结构学报，Vol．17，No．1，2-13，1996
1-4 Gates W. E. & Morden M. Professional Structure Engineering Experience Related to Welded Steel Moment Frame Following The Northridge Earthquake. The structural Design of Tall buildings, Vol. 5, 1996, 29-44.
1-5 Architectural Institute of Japan. Reconnaissance Report on Damage to Steel building Structures Observed from The 1995 Hyogoken-Nanhu(Hanshin/Awaji) Earthquake May 1995.
1-6 Engelhardt M.D.&Sabot T.A. Seismic-Resistant Steel Moment Connections: Development Since the Northridge Earthquake. Construction Research Communications Limited, 1997, ISSN, 1365～1566.
1-7 Whittaker h., Gilani A.& Bertero V. Evaluation of Pre- Northridge Steel Moment-Resisting Frame Joints. The structural Design of Tall buildings, Vol. 7, 1998, 263-283.
1-8 Stefano Sorace. Seismic Assessment of Steel Frames. Journal of The Structural Engineering. Vol. 124, No. 5, May, 1998 ASCE 531-540.
1-9 陈富生，邱国桦，范重．高层建筑钢结构设计．北京：中国建筑工业出版社，2000ISBN 7-112-03766-2．
1-10 Robert Tremblay & Nathalie Robert. Seismic Design of Low and Medium-rise Chevron Braced Steel Frames. Can. J. Civ. Eng. 27:1992-1206(2000).
1-11 M. S.Medhekar & D. J. L. Kennedy. Seismic response of Two-Story Buildings with Concentrically Braced steel frames. Can. J. Civ. Eng. 26:497-509(1999).
1-12 Nariman M. Haroun and Robin Shepherd, F. ASCE. Inelastic Behavior of X-Bracing in Plane Frames. Journal of Structural Engineering, Vol. 112, No. 4, April, 1986.
1-13 Bruce F.Maison and Egor P. Popov, F. ASCE. Cyclic Response Prediction for Braced Steel Frames. Journal of the Structural Division, Vol. 106, No. ST7, July, 1980.
1-14 Addison B. Higginbotham, A. M. ASCE and Rober D. Hanson, M. ASCE. Axial Hysteretic Behavior of Steel Members. Journal of the Structural Division. Vol. 102, No. ST7, July, 1976.
1-15 K. Ikeda and S. A. Mahin, M. ASCE. Cyclic Response of Steel Braces. Journal of Structural Engineering, Vol. 112, No. 2, February, 1986.
1-16 Shouji Toma and Wai F. Chen, M. ASCE. Inelastice Cyclic Analysis of Pin-Ended Tubes. October, 17423, 1989..
1-17 Sanda Koboevic & Richard Redwood. Design and Seismic response of Shear Critical Eccentrically Braced Frames. Can. J. Civ. Eng. 24:761-771(1997)
1-18 Egor P. Popov. Recent Research on Eccentrically Braced Frames. Eng. Struct., 1983, Vol. 5, January. 3-9.
1-19 Ashok K. Jain and Subhash C. Goel, M. ASCE. Seismic Response of Eccentrically Braced Frames. Journal of the Structural Division, Vol. 106, No. ST4, April , 1980.
1-20 X. Qi, K.L. Chang &K. C. Tsai. Seismic Design of Eccentrically Braced Space Frame. Journal of The Structural Engineering. Vol. 123, No. 8, August, 1997 ASCE 997-985.
1-21 James R. Libby. Eccentrically Braced Frame Construction -A Case History. Engineering Journal/ American Institute of Steel Construction. Fourth Quarter, 1981. 149-153.
1-22 Andrew T. Merovich, M. ASCE, Joseph P. Nicoletti, F. ASCE, and Earl Hartle, M.ASCE. Eccentric Bracing in Tall Buildings. Journal of the Structural Division Vol. 108, No. ST9, September, 1982.
1-23 Keith D. Hjelmstad and Egor P. Popov, F. ASCE. Characteristices of Eccentrically Braced Frames. Journal of Structural Engineering, Vol. 112, No. 2, February , 1984.
1-24 Charles W. Roeder, A. M. ASCE and Egor P. Popov, F. ASCE. Eccentrically Braced Steel Frames for Earthquakes. Journal of the Structural Division, Vol. 104, No. ST3, March, 1978.
1-25 Keith D. Hjelmstad and Egnr P. Popv, F. ASCE. Cyclic Behavior and Design of Link Beams. Journal of Structural Engineering, Vol. 109, No. 10, October, 1983.
1-26 James o. Malley and Egor P. Popov, F. ASCE. Shear Links in Eccentrically Braced Frames. Journal of Structural Engineering, Vol. 110, No. 9, September , 1984.
1-27 Kazuhiko Kasai, S. M. ASCE and Egor P. Popov, F. ASCE. Cyclic Web Buckling Control for Shear Link Beams. Journal of Structural Engineering, Vol. 112, No. 3,March, 1986.
1-28 Kazuhiko Kasai, S. M. ASCE and Egor P. Popov, F. ASCE. General Behavior of WF Steel Shear Link Beams. Journal of Structural Engineering, Vol. l12, No. 2, February, 1986.
1-29 James M. Ricles, Member, ASCE, and Egor P. Popove, Honorary Member, ASCE. Composite Action in Eccentrically Braced Frames. Journal of Structural Engineering, Vol. 115, No. 8, August, 1989.
1-30 张斌 Y形支撑框架研究 西安建筑科技大学硕士论文 1999
1-31 M. D. Engelhardt, Associate Member, ASCE, and E. P. Popov, Honorary Member, ASCE. Experimental Performance of Long Links in Eccentrically Braced Frames. Journal of Structural
Engineering, Vol. 118, No. 11, November, 1992.
1-32 A. Ghobarah and T. Ramadan. Bolted Link-column Joints in Eccentrically Braced Frames. Engrg Struct. 1994, Volume 16, Number 1.33-41.
1-33 于安麟 EK形、 Y形支撑的抗震性能研究 西安冶金建筑学院学报vol．12．3 1990．9．
1-34 钱稼茹 陈茂盛 张天申 王明弹 偏心支撑钢框架拟动力地震反应试验分析工程抗震 1992．3．
1-35 钱稼茹 陈茂盛 张天申 偏心支撑钢框架在水平力作用下试验研究和极限分析 建筑结构1993．4．
1-36 Gilberson. M.F. Two Nonlinear Beams with Definitions of Ductility. Struct Engrg. ASCE 95 (2). 137-157.
1-37 Daniel N. Manheim, M. ASCE and Egor F. Popov, F. ASCE. Plastic Shear Hinges in Steel Frames. Journal of Structural Engineering, Vol. 109, No. 10, October, 1983
1-38 A. Ghobarah and T. Ramadan. Effect of Axial Forces on the Performance of Links in Eccentrically Braced Frames. Eng. Struct. 1990, Vol. 12, Apri. 106-113.
1-39 James M. Ricles and Egor E. P. Popov, Inelastic link element for EBF seismic analysis, ASCE. Journal of Structural Engineering, Vol. 120, No. 2, February, 1994.
1-40 T. Ramadan and A. Ghobarah. Analytical Model For Shear-Link Behavior. Journal of Structural Engineering. Vol. 121 NO. 11 November 1995. 1574-1580.
1-41 张汝清 詹先义 非线性有限元分析 重庆大学出版社 1988．
1-42 黄文 李明瑞 黄文彬 杆件结构几何非线性分析——平面问题。计算结构力学及其应用，Vol．12 NO．1 1995．2
1-43 王恒华，沈祖炎，陆瑞明．平面梁杆结构几何非线性分析的一种简便方法．计算力学学报，第14卷第1期，1992，2．
1-44 Kee Dong Kim & Michael D. Engelhardt. Beam-Cloumn Element for Nonlinear Seismic Analysis Steel Frames. Journal of Structural Engineering. Vol. 126 NO. 8 August 2000. 916-925.
1-45 Ansgar Neuenhofer and Fillip C. Filippou, Geometrically Nonlinear Flexibility-Based Frame Finite Element. Journal of Structural Engineering. Vol. 124 NO. 6 June 1998. 704-711.
1-46 S. Mukherhee, J, j, N. Reddy and C.S. Krishamoorthy. Convergence Properties and Derivative Extraction of the SuperConvergent Timoshenko Beam Finite Element. Computer Methods in Applied Mechanics and Engineering . 190(2001) 3475-3500.
1-47 Cenap Oran, M. ASCE. Tangent Stiffness in Plane Frames. Journal of The Structural Division, Vol. 99, No. ST6, June, 1973.
1-48 Cenap Oran, M. ASCE. Tangent Stiffness in Space Frames. Journal of The Structural Division, Vol. 99, No. ST6, June, 1973.
1-49 Yeong-Bin Yang, A.M. ASCE and William McGuire, F. ASCE. Stiffness Matrix for Geometric
Nonlinear Analysis. Journal of Structural Engineering, Vol. 112,No. 4, April, 1986.
1-50 Yeong-Bin Yang, A. M. ASCE and William McGuire, F. ASCE. Joint Rotation and Geometric Nonlinear Analysis. Journal of Structural Engineering, Vol. l12, No. 4, April, 1986.
1-51 YEONG-BIN YANG, JUNG-HUAI CHOU and LIANG-JENQ LEU. Rigid Body Considerations for Non-Linear Finite Element Analysis. International Journal for Numerical Methods in Engineering, Vol. 33, 1597-1610, 1992.
1-52 YEONG-BIN YANG and LIANG-JENQ LEU. Force Recovery Procedures in Nonlinear Analysis. Computers & Structures, Vol. 41, No. 6, pp. 1255-1261, 1991.
1-53 MARCELO GATTASS, JOHN F. ABEL. Equilibrium Considerations of The Updated Lagrangian Formulation of Beam-Columns with Natural Concepts. International Journal for Numerical Methods in Engineering, Vol. 24,2119-2141, 1987.
1-54 Z. FRIEDMAN and J. B. KOSMATKA. An Improved Two-Node Timoshenko Beam Finite Element. Computers &Structures, Vol. 47, No. 3, pp. 473-481, 1993.
1-55 Klaus-jurgen Bathe and Said Bolourch. Large Displacement Analysis of Three-Dimensional Beam structures. International Journal for Numerical Methods in Engineering, Vol. 14, 961-986, 1979.
1-56 YEONG-BIN YANG Theory & Analysis of nonlinear framed structures .Prentice Hall 1994.
1-57 苏明周，箱形截面钢构件在地震作用下的相关屈曲破坏机理及抗震设计对策 西安建筑科技大学博士学位论文，1999．
1-58 董永涛 张耀春，板壳结构非线性屈曲分析修正拉格朗日法， 第30卷 第2期 土木工程学报 1997年4月34-41
1-59 沈祖炎 张其林，薄壁钢构件非线性稳定问题的曲壳有限单元法，第24卷 第1期 土木工程学报 1991年2月32-43．
1-60 武振宇 张耀春，曲壳有限单元法中曲面交线处位移连续性问题的坐标转换法，第30卷 第5期 哈尔滨建筑大学学报，1997年10月 20-23
1-61 韩庆华 焊接箱形梁相互作用屈曲后性能的理论分析及试验研究 天津大学博士学位论文 1998．12
1-62 J. H. KIM and S. W. LEE. A Finite Element Formulation with Stabilization Matrix for Geometrically Non-Linear Shells. International Journal for Numerical Methods in Engineering, Vol. 33,1703-1720,1992.
1-63 YUPUGUAN, LIMIN TANG. Geometrically Non-LinearQuasi-Conforming Nine-Node Quadrilateral Degenerated Solid Shell Element. International Journal for Numerical Methods in Engineering, Vol. 38,927-942, 1995.
1-64 K. Y. SZE and H. FAN, C. L. CHOW. Elimination of Spurious Pressure and Kinematic Modes in
Biquadratic Nine-Node Plane Element. International Journal for Numerical Methods in Engineering, Vol. 38, 3911-3932, 1995.
1-65 J. J. RHIU and S. W. LEE. A Nine Node Finite Element for Analysis of Grometrically Non-Linear Sheils. International Journal for Numerical Methods in Engineering, Vol. 26, 1945-1962, 1988.
1-66 WORSAK KANOK-NUKULCBAI. A Simple and Efficient Finite Element for General Shell Analysis. International Journal for Numerical Methods in Engineering, Vol. 14, 179-200, 1979.
1-67 JUNHO JANG and PETER M. PINSKY .An Assumed Covariant Strain Based 9-Node Shell Element. International Journal for Numerical Methods in Engineering, Wol. 24, 2389-2411, 1987.
1-68 Ted BELYTSCHKO and Jame Shau-Jen ONG. A Consistent Control of Spurious Singular Modes in The 9-Node Lagrange Element for The Laplace and Mindlin Plate Equations. Computer Methods in Applied Mechanics and Engineering . 44 (1984) 269-295.
1-69 J. G. TENG and M. ROTTER. Elastic-plastic Large Deflection Analysis of Axisymmetric Shells. Computers & Structures. Vol. 31, No. 2, pp. 211-233, 1989.
1-70 TED BELYTSCHKO, WING -KAM LIU, JAME SHAU-JEN ONG § and DENNIS LAM §. Advances in Finite Element Technology Implementation and Application of A 9-Node Lagrange Shell Element with Spurious Mode Control. Computers & Structures. Vol. 20, No. 1-3, pp. 121-128, 1985.
1-71 H. PARISCH. A Critical Survey of The 9-Node Degenerated Shell Element with Special Emphasis on Thin Shell Application and Reduced Integration. Computer Methods in Applied Mechanics and Engineering . 20(1979) 323-350.
1-72 H.C. Huang & E. Hinton. A New Nine Node Degenerated Shell Element With Enhanced Membrane and Sear Interpolation. International Journal for Numerical Methods in Engineering, Vol. 22, 73-92 (1986)
1-73 Klaus-jurgen Bathe and Said Bolourch. A Geometric and Material Nonlinear Plate and Shell Element. Computers & Structures. Vol. 11, pp. 23-48, 1980.
1-74 陈骥．钢结构稳定理论与应用．北京：科学技术文献出版社，1994．9．
1-75 陈绍蕃．钢结构设计原理．北京：科学出版社，1997．
1-76 王勖成，邵敏．有限单元法基本原理和数值方法．北京：清华大学出版社，1996 ISBN 7-302-02421-9．
1-77 DAVID BUSHNELL. A Strategy for The Solution of Problems Involving Large Deflections, Plasticity and Creep. International Journal for Numerical Methods in Engineering, Vol. 11, 683-708,1977.
1-78 K. AXELSSON and A. SAMUELSSON. Finite Element Analysis of Elastic-Plastic Materials Displaying Mixed Hardening. International Journal for Numerical Methods in Engineering, Vol. 14,211-225,1979.
1-79 C. NYSSEN. An Efficient and Accurate Iterative Method, Allowing Large Incremental Steps, To Solve E1asto-Plastic Problems. Comprters &Structures, Vol. 13, pp. 63-71, 1981.
1-80 P.G. Hodge. Discussion to 'anewmethod of analysis and strains inworking hardening solids' J. App1. Mech ,Trans. ASME, 24, 1957, 481-484
1-81 [美]陈惠发 著 余天庆 王勋文 刘再华 译 刘希拉 韩大建 校译 土木工程的本构方程 华中理工大学出版社
1-82 孟凡中 著 弹塑性有限变形理论和有限元方法北京：清华大学出版社，1985年．
1-83 殷有泉 固体力学非线性有限元引论 北京大学出版社清华大学出版社1987年．
1-84 M.A.Crisfield. A Fast Incremental/Iterative Solution Procedure That Handles "Snap-Through" .Computers &structures .Vol. 13. pp. 55-62.
1-2 Dune K. Miller. Lessons learned from the Northridge earthquake. Engineering structures, 1998; 20 (4-6) : 249-260
1-3 崔鸿超 日本兵库县南部地区地震震害综述 建筑结构学报，Vol．17，No．1，2-13，1996
1-4 Gates W. E. & Morden M. Professional Structure Engineering Experience Related to Welded Steel Moment Frame Following The Northridge Earthquake. The structural Design of Tall buildings, Vol. 5, 1996, 29-44.
1-5 Architectural Institute of Japan. Reconnaissance Report on Damage to Steel building Structures Observed from The 1995 Hyogoken-Nanhu(Hanshin/Awaji) Earthquake May 1995.
1-6 Engelhardt M.D.&Sabot T.A. Seismic-Resistant Steel Moment Connections: Development Since the Northridge Earthquake. Construction Research Communications Limited, 1997, ISSN, 1365～1566.
1-7 Whittaker h., Gilani A.& Bertero V. Evaluation of Pre- Northridge Steel Moment-Resisting Frame Joints. The structural Design of Tall buildings, Vol. 7, 1998, 263-283.
1-8 Stefano Sorace. Seismic Assessment of Steel Frames. Journal of The Structural Engineering. Vol. 124, No. 5, May, 1998 ASCE 531-540.
1-9 陈富生，邱国桦，范重．高层建筑钢结构设计．北京：中国建筑工业出版社，2000ISBN 7-112-03766-2．
1-10 Robert Tremblay & Nathalie Robert. Seismic Design of Low and Medium-rise Chevron Braced Steel Frames. Can. J. Civ. Eng. 27:1992-1206(2000).
1-11 M. S.Medhekar & D. J. L. Kennedy. Seismic response of Two-Story Buildings with Concentrically Braced steel frames. Can. J. Civ. Eng. 26:497-509(1999).
1-12 Nariman M. Haroun and Robin Shepherd, F. ASCE. Inelastic Behavior of X-Bracing in Plane Frames. Journal of Structural Engineering, Vol. 112, No. 4, April, 1986.
1-13 Bruce F.Maison and Egor P. Popov, F. ASCE. Cyclic Response Prediction for Braced Steel Frames. Journal of the Structural Division, Vol. 106, No. ST7, July, 1980.
1-14 Addison B. Higginbotham, A. M. ASCE and Rober D. Hanson, M. ASCE. Axial Hysteretic Behavior of Steel Members. Journal of the Structural Division. Vol. 102, No. ST7, July, 1976.
1-15 K. Ikeda and S. A. Mahin, M. ASCE. Cyclic Response of Steel Braces. Journal of Structural Engineering, Vol. 112, No. 2, February, 1986.
1-16 Shouji Toma and Wai F. Chen, M. ASCE. Inelastice Cyclic Analysis of Pin-Ended Tubes. October, 17423, 1989..
1-17 Sanda Koboevic & Richard Redwood. Design and Seismic response of Shear Critical Eccentrically Braced Frames. Can. J. Civ. Eng. 24:761-771(1997)
1-18 Egor P. Popov. Recent Research on Eccentrically Braced Frames. Eng. Struct., 1983, Vol. 5, January. 3-9.
1-19 Ashok K. Jain and Subhash C. Goel, M. ASCE. Seismic Response of Eccentrically Braced Frames. Journal of the Structural Division, Vol. 106, No. ST4, April , 1980.
1-20 X. Qi, K.L. Chang &K. C. Tsai. Seismic Design of Eccentrically Braced Space Frame. Journal of The Structural Engineering. Vol. 123, No. 8, August, 1997 ASCE 997-985.
1-21 James R. Libby. Eccentrically Braced Frame Construction -A Case History. Engineering Journal/ American Institute of Steel Construction. Fourth Quarter, 1981. 149-153.
1-22 Andrew T. Merovich, M. ASCE, Joseph P. Nicoletti, F. ASCE, and Earl Hartle, M.ASCE. Eccentric Bracing in Tall Buildings. Journal of the Structural Division Vol. 108, No. ST9, September, 1982.
1-23 Keith D. Hjelmstad and Egor P. Popov, F. ASCE. Characteristices of Eccentrically Braced Frames. Journal of Structural Engineering, Vol. 112, No. 2, February , 1984.
1-24 Charles W. Roeder, A. M. ASCE and Egor P. Popov, F. ASCE. Eccentrically Braced Steel Frames for Earthquakes. Journal of the Structural Division, Vol. 104, No. ST3, March, 1978.
1-25 Keith D. Hjelmstad and Egnr P. Popv, F. ASCE. Cyclic Behavior and Design of Link Beams. Journal of Structural Engineering, Vol. 109, No. 10, October, 1983.
1-26 James o. Malley and Egor P. Popov, F. ASCE. Shear Links in Eccentrically Braced Frames. Journal of Structural Engineering, Vol. 110, No. 9, September , 1984.
1-27 Kazuhiko Kasai, S. M. ASCE and Egor P. Popov, F. ASCE. Cyclic Web Buckling Control for Shear Link Beams. Journal of Structural Engineering, Vol. 112, No. 3,March, 1986.
1-28 Kazuhiko Kasai, S. M. ASCE and Egor P. Popov, F. ASCE. General Behavior of WF Steel Shear Link Beams. Journal of Structural Engineering, Vol. l12, No. 2, February, 1986.
1-29 James M. Ricles, Member, ASCE, and Egor P. Popove, Honorary Member, ASCE. Composite Action in Eccentrically Braced Frames. Journal of Structural Engineering, Vol. 115, No. 8, August, 1989.
1-30 张斌 Y形支撑框架研究 西安建筑科技大学硕士论文 1999
1-31 M. D. Engelhardt, Associate Member, ASCE, and E. P. Popov, Honorary Member, ASCE. Experimental Performance of Long Links in Eccentrically Braced Frames. Journal of Structural
Engineering, Vol. 118, No. 11, November, 1992.
1-32 A. Ghobarah and T. Ramadan. Bolted Link-column Joints in Eccentrically Braced Frames. Engrg Struct. 1994, Volume 16, Number 1.33-41.
1-33 于安麟 EK形、 Y形支撑的抗震性能研究 西安冶金建筑学院学报vol．12．3 1990．9．
1-34 钱稼茹 陈茂盛 张天申 王明弹 偏心支撑钢框架拟动力地震反应试验分析工程抗震 1992．3．
1-35 钱稼茹 陈茂盛 张天申 偏心支撑钢框架在水平力作用下试验研究和极限分析 建筑结构1993．4．
1-36 Gilberson. M.F. Two Nonlinear Beams with Definitions of Ductility. Struct Engrg. ASCE 95 (2). 137-157.
1-37 Daniel N. Manheim, M. ASCE and Egor F. Popov, F. ASCE. Plastic Shear Hinges in Steel Frames. Journal of Structural Engineering, Vol. 109, No. 10, October, 1983
1-38 A. Ghobarah and T. Ramadan. Effect of Axial Forces on the Performance of Links in Eccentrically Braced Frames. Eng. Struct. 1990, Vol. 12, Apri. 106-113.
1-39 James M. Ricles and Egor E. P. Popov, Inelastic link element for EBF seismic analysis, ASCE. Journal of Structural Engineering, Vol. 120, No. 2, February, 1994.
1-40 T. Ramadan and A. Ghobarah. Analytical Model For Shear-Link Behavior. Journal of Structural Engineering. Vol. 121 NO. 11 November 1995. 1574-1580.
1-41 张汝清 詹先义 非线性有限元分析 重庆大学出版社 1988．
1-42 黄文 李明瑞 黄文彬 杆件结构几何非线性分析——平面问题。计算结构力学及其应用，Vol．12 NO．1 1995．2
1-43 王恒华，沈祖炎，陆瑞明．平面梁杆结构几何非线性分析的一种简便方法．计算力学学报，第14卷第1期，1992，2．
1-44 Kee Dong Kim & Michael D. Engelhardt. Beam-Cloumn Element for Nonlinear Seismic Analysis Steel Frames. Journal of Structural Engineering. Vol. 126 NO. 8 August 2000. 916-925.
1-45 Ansgar Neuenhofer and Fillip C. Filippou, Geometrically Nonlinear Flexibility-Based Frame Finite Element. Journal of Structural Engineering. Vol. 124 NO. 6 June 1998. 704-711.
1-46 S. Mukherhee, J, j, N. Reddy and C.S. Krishamoorthy. Convergence Properties and Derivative Extraction of the SuperConvergent Timoshenko Beam Finite Element. Computer Methods in Applied Mechanics and Engineering . 190(2001) 3475-3500.
1-47 Cenap Oran, M. ASCE. Tangent Stiffness in Plane Frames. Journal of The Structural Division, Vol. 99, No. ST6, June, 1973.
1-48 Cenap Oran, M. ASCE. Tangent Stiffness in Space Frames. Journal of The Structural Division, Vol. 99, No. ST6, June, 1973.
1-49 Yeong-Bin Yang, A.M. ASCE and William McGuire, F. ASCE. Stiffness Matrix for Geometric
Nonlinear Analysis. Journal of Structural Engineering, Vol. 112,No. 4, April, 1986.
1-50 Yeong-Bin Yang, A. M. ASCE and William McGuire, F. ASCE. Joint Rotation and Geometric Nonlinear Analysis. Journal of Structural Engineering, Vol. l12, No. 4, April, 1986.
1-51 YEONG-BIN YANG, JUNG-HUAI CHOU and LIANG-JENQ LEU. Rigid Body Considerations for Non-Linear Finite Element Analysis. International Journal for Numerical Methods in Engineering, Vol. 33, 1597-1610, 1992.
1-52 YEONG-BIN YANG and LIANG-JENQ LEU. Force Recovery Procedures in Nonlinear Analysis. Computers & Structures, Vol. 41, No. 6, pp. 1255-1261, 1991.
1-53 MARCELO GATTASS, JOHN F. ABEL. Equilibrium Considerations of The Updated Lagrangian Formulation of Beam-Columns with Natural Concepts. International Journal for Numerical Methods in Engineering, Vol. 24,2119-2141, 1987.
1-54 Z. FRIEDMAN and J. B. KOSMATKA. An Improved Two-Node Timoshenko Beam Finite Element. Computers &Structures, Vol. 47, No. 3, pp. 473-481, 1993.
1-55 Klaus-jurgen Bathe and Said Bolourch. Large Displacement Analysis of Three-Dimensional Beam structures. International Journal for Numerical Methods in Engineering, Vol. 14, 961-986, 1979.
1-56 YEONG-BIN YANG Theory & Analysis of nonlinear framed structures .Prentice Hall 1994.
1-57 苏明周，箱形截面钢构件在地震作用下的相关屈曲破坏机理及抗震设计对策 西安建筑科技大学博士学位论文，1999．
1-58 董永涛 张耀春，板壳结构非线性屈曲分析修正拉格朗日法， 第30卷 第2期 土木工程学报 1997年4月34-41
1-59 沈祖炎 张其林，薄壁钢构件非线性稳定问题的曲壳有限单元法，第24卷 第1期 土木工程学报 1991年2月32-43．
1-60 武振宇 张耀春，曲壳有限单元法中曲面交线处位移连续性问题的坐标转换法，第30卷 第5期 哈尔滨建筑大学学报，1997年10月 20-23
1-61 韩庆华 焊接箱形梁相互作用屈曲后性能的理论分析及试验研究 天津大学博士学位论文 1998．12
1-62 J. H. KIM and S. W. LEE. A Finite Element Formulation with Stabilization Matrix for Geometrically Non-Linear Shells. International Journal for Numerical Methods in Engineering, Vol. 33,1703-1720,1992.
1-63 YUPUGUAN, LIMIN TANG. Geometrically Non-LinearQuasi-Conforming Nine-Node Quadrilateral Degenerated Solid Shell Element. International Journal for Numerical Methods in Engineering, Vol. 38,927-942, 1995.
1-64 K. Y. SZE and H. FAN, C. L. CHOW. Elimination of Spurious Pressure and Kinematic Modes in
Biquadratic Nine-Node Plane Element. International Journal for Numerical Methods in Engineering, Vol. 38, 3911-3932, 1995.
1-65 J. J. RHIU and S. W. LEE. A Nine Node Finite Element for Analysis of Grometrically Non-Linear Sheils. International Journal for Numerical Methods in Engineering, Vol. 26, 1945-1962, 1988.
1-66 WORSAK KANOK-NUKULCBAI. A Simple and Efficient Finite Element for General Shell Analysis. International Journal for Numerical Methods in Engineering, Vol. 14, 179-200, 1979.
1-67 JUNHO JANG and PETER M. PINSKY .An Assumed Covariant Strain Based 9-Node Shell Element. International Journal for Numerical Methods in Engineering, Wol. 24, 2389-2411, 1987.
1-68 Ted BELYTSCHKO and Jame Shau-Jen ONG. A Consistent Control of Spurious Singular Modes in The 9-Node Lagrange Element for The Laplace and Mindlin Plate Equations. Computer Methods in Applied Mechanics and Engineering . 44 (1984) 269-295.
1-69 J. G. TENG and M. ROTTER. Elastic-plastic Large Deflection Analysis of Axisymmetric Shells. Computers & Structures. Vol. 31, No. 2, pp. 211-233, 1989.
1-70 TED BELYTSCHKO, WING -KAM LIU, JAME SHAU-JEN ONG § and DENNIS LAM §. Advances in Finite Element Technology Implementation and Application of A 9-Node Lagrange Shell Element with Spurious Mode Control. Computers & Structures. Vol. 20, No. 1-3, pp. 121-128, 1985.
1-71 H. PARISCH. A Critical Survey of The 9-Node Degenerated Shell Element with Special Emphasis on Thin Shell Application and Reduced Integration. Computer Methods in Applied Mechanics and Engineering . 20(1979) 323-350.
1-72 H.C. Huang & E. Hinton. A New Nine Node Degenerated Shell Element With Enhanced Membrane and Sear Interpolation. International Journal for Numerical Methods in Engineering, Vol. 22, 73-92 (1986)
1-73 Klaus-jurgen Bathe and Said Bolourch. A Geometric and Material Nonlinear Plate and Shell Element. Computers & Structures. Vol. 11, pp. 23-48, 1980.
1-74 陈骥．钢结构稳定理论与应用．北京：科学技术文献出版社，1994．9．
1-75 陈绍蕃．钢结构设计原理．北京：科学出版社，1997．
1-76 王勖成，邵敏．有限单元法基本原理和数值方法．北京：清华大学出版社，1996 ISBN 7-302-02421-9．
1-77 DAVID BUSHNELL. A Strategy for The Solution of Problems Involving Large Deflections, Plasticity and Creep. International Journal for Numerical Methods in Engineering, Vol. 11, 683-708,1977.
1-78 K. AXELSSON and A. SAMUELSSON. Finite Element Analysis of Elastic-Plastic Materials Displaying Mixed Hardening. International Journal for Numerical Methods in Engineering, Vol. 14,211-225,1979.
1-79 C. NYSSEN. An Efficient and Accurate Iterative Method, Allowing Large Incremental Steps, To Solve E1asto-Plastic Problems. Comprters &Structures, Vol. 13, pp. 63-71, 1981.
1-80 P.G. Hodge. Discussion to 'anewmethod of analysis and strains inworking hardening solids' J. App1. Mech ,Trans. ASME, 24, 1957, 481-484
1-81 [美]陈惠发 著 余天庆 王勋文 刘再华 译 刘希拉 韩大建 校译 土木工程的本构方程 华中理工大学出版社
1-82 孟凡中 著 弹塑性有限变形理论和有限元方法北京：清华大学出版社，1985年．
1-83 殷有泉 固体力学非线性有限元引论 北京大学出版社清华大学出版社1987年．
1-84 M.A.Crisfield. A Fast Incremental/Iterative Solution Procedure That Handles "Snap-Through" .Computers &structures .Vol. 13. pp. 55-62.