格构式压弯构件平面内稳定分析
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摘要
本文对钢结构中常用的格构式柱子和格构式压弯构件进行了平面内弹塑性稳定的研究。采用了两完全相同双轴对称工字型截面组成的缀条式构件作为研究对象。主要有三部分内容：
一是对运用ANSYS通用有限元程序中可以考虑几何和材料双重非线性的Beam189单元进行格构式柱和格构式梁柱的计算分析的正确性进行了研究，通过大量计算验证了此数值分析方法的正确性。
二是运用前述方法，引入整体和局部(柱肢)初弯曲和残余应力的影响，用考虑几何和材料双重非线性的有限元方法求得缀条柱的弹塑性极限承载力，通过对不同截面尺寸构件在不同长细比下的承载力计算，并从单肢稳定出发对结果进行拟合，得到了适应性更好的缀条柱平面内弯曲稳定系数φ的计算公式。
三是对我国各本钢结构设计规范中格构式压弯构件的平面内稳定计算公式与数值分析的结果进行了对比，定量地说明了当前格构式压弯构件平面内稳定性计算公式存在偏不安全的问题。运用前述方法，引入初弯曲和残余应力的影响，用考虑几何和材料双重非线性的有限元方法求得构件在不同轴力和弯矩比例作用下的弹塑性极限承载力，对不同截面尺寸构件在不同长细比下的承载力进行计算。根据数值分析结果，本文建议对格构式压弯构件采用与实腹式压弯构件相同的计算公式计算。
Due to structural economy, built-up members are widely used in industrial steel structures. However, the interaction of global and local buckling occurred in built-up members and its detrimental effect on the load carrying capacity have not yet been fully documented. In this thesis the in-plane inelastic stability of laced columns and beam-columns consisting of two identical doubly-symmetrical I sections are investigated.
Firstly, the validity of analyzing built-up columns and beam-columns by the general FEA program ANSYS with the Beaml89 element is studied, for the Beaml89 element can consider geometrical non-linearity and the material plasticity. Many numerical results confirm the validity of the method.
Secondly, the laced columns in plastic phase are studied with the foregoing method. The overall and local initial curvatures and the residual stresses are considered, also the material plasticity is considered in the solution process. With the program, many members with different section sizes and slenderness ratios are analyzed. A better formula calculating the
in-plane stability factor tp of laced columns is achieved by data fitting based on the stability
of a single branch.
Finally, formulae calculating the in-plane stability of built-up columns under compression and bending in various codes for steel structures are compared with numerical results, and it is found that the current formula is unsafe when the slenderness is large. The laced beam-columns worked in elastic-plastic range are studied. The initial curvatures and the residual stress are considered in the solution process. With the program, many members with different section sizes and slenderness ratios are analyzed. It is suggested that the same formula for in-plane stability of I-section beam-column be used for laced beam-columns.
一是对运用ANSYS通用有限元程序中可以考虑几何和材料双重非线性的Beam189单元进行格构式柱和格构式梁柱的计算分析的正确性进行了研究，通过大量计算验证了此数值分析方法的正确性。
二是运用前述方法，引入整体和局部(柱肢)初弯曲和残余应力的影响，用考虑几何和材料双重非线性的有限元方法求得缀条柱的弹塑性极限承载力，通过对不同截面尺寸构件在不同长细比下的承载力计算，并从单肢稳定出发对结果进行拟合，得到了适应性更好的缀条柱平面内弯曲稳定系数φ的计算公式。
三是对我国各本钢结构设计规范中格构式压弯构件的平面内稳定计算公式与数值分析的结果进行了对比，定量地说明了当前格构式压弯构件平面内稳定性计算公式存在偏不安全的问题。运用前述方法，引入初弯曲和残余应力的影响，用考虑几何和材料双重非线性的有限元方法求得构件在不同轴力和弯矩比例作用下的弹塑性极限承载力，对不同截面尺寸构件在不同长细比下的承载力进行计算。根据数值分析结果，本文建议对格构式压弯构件采用与实腹式压弯构件相同的计算公式计算。
Due to structural economy, built-up members are widely used in industrial steel structures. However, the interaction of global and local buckling occurred in built-up members and its detrimental effect on the load carrying capacity have not yet been fully documented. In this thesis the in-plane inelastic stability of laced columns and beam-columns consisting of two identical doubly-symmetrical I sections are investigated.
Firstly, the validity of analyzing built-up columns and beam-columns by the general FEA program ANSYS with the Beaml89 element is studied, for the Beaml89 element can consider geometrical non-linearity and the material plasticity. Many numerical results confirm the validity of the method.
Secondly, the laced columns in plastic phase are studied with the foregoing method. The overall and local initial curvatures and the residual stresses are considered, also the material plasticity is considered in the solution process. With the program, many members with different section sizes and slenderness ratios are analyzed. A better formula calculating the
in-plane stability factor tp of laced columns is achieved by data fitting based on the stability
of a single branch.
Finally, formulae calculating the in-plane stability of built-up columns under compression and bending in various codes for steel structures are compared with numerical results, and it is found that the current formula is unsafe when the slenderness is large. The laced beam-columns worked in elastic-plastic range are studied. The initial curvatures and the residual stress are considered in the solution process. With the program, many members with different section sizes and slenderness ratios are analyzed. It is suggested that the same formula for in-plane stability of I-section beam-column be used for laced beam-columns.
引文
[1] 夏志斌，姚谏，钢结构，浙江大学出版社，1996．
[2] 中华人民共和国国家规范，钢结构设计规范GB50017—2003，2003．
[3] ECCS. European Recommendations for Steel Construction. 1978.
[4] 童根树，格构柱的夹层梁一相关屈曲理论．西安冶金建筑学院学报，1987(3)95～104．
[5] Svensson, S.E. ,and Kragerup,J. ,Collapse Loads of Laced Columns, Journal of the Strucmral Division ASCE, Vol.108, No.ST6, June, 1982.
[6] Davies,H.T., Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, N.Y., 1962.
[7] 童根树，施祖元，李志飙，对压弯杆平面内稳定计算式及计算长度确定方法的评论，建筑结构．
[8] 门式刚架轻型房屋钢结构技术规程CECS102：2002．
[9] 中华人民共和国国家规范，冷弯薄壁型钢结构技术规范GB50018—2002．
[10] Constancio Miranda, Morris Ojalvo, Inelastic Lateral-Torsional Buclding of Beam Columns, Journal of the Engineering Mechanics Division ASCE, Vol.91, No.EM6, December, 1965.
[11] 朱俞江，童根树，箱形截面压弯构件的平面外稳定计算．钢结构，2003(5)11～15．
[12] Byskov, E., Imperfection Sensitivity in Elastic-Plastic Truss Columns, DCAMM Report No.200, The Danish Center for Applied Mathematics and Mechanics, The Technical University of Denmark, Dec., 1980.
[13] Byskov, E., Application of an Asymptotic Expansion for Elastic Buckling Problems with Mode Interaction, AIAA Journal, Vol. 17, June,1979,pp.630-633.
[14] Crawford, R.F., and Benton,M.D., Strength of Initially Wavy Lattice Columns, AIAA Journal, Vol. 18, May, 1980, pp.581-584.
[15] Crawford, R.F., and Hedgepeth, J.M., Effects of Initially Waviness on the Strength and Design of Build-up Structures, AIAA Journal, Vol.13, May, 1975, pp.672-675.
[16] Svensson, S.E. and Croll, J.G.A., Interacton Local and Overall Buclding, International Journal of Mechanical Science, vol. 17, 1975, Pergamon Press, New York, N.Y., pp. 307-321.
[17] Stein, M., Recent Advances in Shell Buckling, AIAA Paper No.68～103,1968.
[18] 饶芝英，童根树，钢结构稳定性的新诠释．建筑结构，2002(5)：12～14．
[19] 童根树，陈婷，符刚，楔形变截面压弯构件的平面内弹塑性稳定．钢结构，2003(5)8～10．
[20] 陈绍蕃，钢结构设计原理(第二版)，科学出版社，1982．
[21] 陈骥，钢结构稳定理论与设计，科学出版社，2001．
[22] 夏志斌，潘有昌，结构稳定理论，高等教育出版社，1987．
[23] 吕烈武，沈世钊，沈祖炎，胡学仁，钢结构构件稳定理论，中国建筑工业出版社，1983．
[24] 龙驭球，包世华，结构力学教程，高等教育出版社，1998．
[25] 王勖成，邵敏，有限单元法基本原理和数值方法(第二版)，清华大学出版社，1997．
[26] 郭在田，缀板式轴心受压构件的单肢计算问题，冶院科技，1984，1期．
[27] 朱林生，王英英，宋敏，钢结构偏心受压格构柱的优化设计，试验技术与试验机，第36卷，第3、4期，1996．
[28] 郑伟国，沈祖炎，缀板柱稳定极限承载力的数值积分解法，土木工程学报，第25卷，第3期，1992．
[29] 王国周，钢结构残余应力分布的若干特点，冶金工业建筑，No．8，1981．
[30] 李国跃，吕凤梧，双肢缀板钢格构立柱的整体稳定分析，土木工程学报，第35卷，第4期，2002．
[31] 沈彦韬，双肢格结构式钢柱侧移刚度的计算，广州建筑，第1期，2000．
[32] N.S.Trahair, Flexural-Torsional Buclding of Structures, E & FN SPON, London, 1993.
[33] Timoshenko S.P., Gere J.M., Theory of Elastic Stability, McGraw-Hill Co. Inc., New York, 1961.
[34] Chen W.F., Atsuta T., Theory of Beam-Columns, McGraw-Hill Co. Inc., New York, 1977.
[35] J. Roorda, Some Statistical Aspects of The Buckling of Imperfection-Sensitive Structures, J.Mech.Phys.Solids, 1969, Vol. 17, pp. 111-123.
[36] White, M. W.,and Thürlimann, B., Study of Columns with perforated Cover Plates, AREA Bull., 1956.
[37] Holt,M.,Tests on Built-up Columns of Structural Aluminum Alloys,Trans.ASCE,vol. 105, 1940.
[38] Pippard,A.J. S, The Critical Load of a Battened Column, Phil.Mag.,January 1948.
[39] Pippard,A.J.S., Battened Columns, Stud. Elastic Struct., 1952.
[40] Jones,B.D., A Theory for Structs with Lattice or Batten Bracing ,Struct.Eng. May 1952.
[41] Koenigsberger, F., and Mohsin, M.E., Design and Load Carrying Capacity of Welded and Battened Struts, Struct. Eng., June 1956.
[42] Tamayo,J.Y., and Ojalvo,M., Buckling of Three-Legged Columns with Batten Bracing, Proc.Am.Soc.Civil Eng.,Vol.91,No.ST1,February 1956.
[43] Mohsin,M.E., The Critical Load of Unsymmetrical Welded Battened Struts, Struct.Eng.,November 1965.
[44] Williamson,R.A., and Margolin,M.N., Shear Effects in Design of Guyed Towers, Journal of the Structural Division ASCE,vol.92,October, 1966.
[45] Lin,F.J., Glauser,E.C., and Johnston,B.G., Behavior of Laced and Battened Structural Members, Journal of the Structural Division ASCE,Vol.96,No.ST7,July ,1970.
[46] Full Scale Test of Aluminum Lattice Mast, Internal Report, Alcan International Ltd., Research Centre, Kingston.
[47] Guide for the Design of Aluminum Transmission Towers, by the Task Committee on Light weight Alloys of the Committee on Metals of the Structural Division, Proc.Am.Soc.Civil Eng., Vol.98,No.ST12, December, 1972.
[48] Bruce G. Johnston, ed., Structural Stability Research Council, Guide to Stability Design Criteria for Metal Structures, 3rd ed. New York: John Wiley& Sons, Inc., 1976.
[49] Friedrich Bleich, Buckling Strength of Metal Structures. New York: McGraw-Hill Book Company, Inc., 1952.
[50] R.Narayanan, Beams and Beam Columns—Stability and Strength, Applied Science Publishers, London and New York, 1983.
[51] Cyrus Omid'varan, Discrete Analysis of Latticed Columns ,Journal of Structural Division, ASCE, 94, ST1, January 1968.
[52] Adams, p.F., Segmental Design of Steel Beam Columns, Proc.Can.Struct.Eng.Conf., Toronto, 1970.
[53] Home, M.R., and Ajmani,J.L., Design of Columns Restrained by Side-Rails and the post-Buckling Behavior of Laterally Restrained Columns, Struct.Eng., Vol.49, No.8, August 1971.
[54] Omer W.Blodgett, Design of Welded Structures. Cleveland, Ohio:James F.Lincoln Arc Welding Foundation, 1966.
[55] P.J. Bredenkamp, and G.J. van den Berg, The Strength of Stainless Steel Built-up I-Section Columns, J.Construct.Steel Research, Vol.34, 1995.
[56] P.J. Bredenkamp, G.J. van den Berg, and R van der Merwe, The Behaviour of Hot-rolled and Built-up Stainless Steel Structural Members, J. Construct.Steel Res., Vol.46,Nos. 1-3,1998.
[57] Charles G.Salmon, and John E.Johnson, Steel Structures:Design and Behavior, 2rd, HARPER & ROW, PUBLISHER, New York,1980.
[58] Von K. Kl ǒ ppel, Darmstadt, and W.Ramm, Salzgitter-Thiede, Zur Stabilitǎ tsuntersuchung von mehrteiligen gitterstǎben, DER STAHLBAU, Vol. 1, 1972.
[59] Johnston, B.G., Spaced Steel Columns, Journal of the Structural Division ASCE, Vol.97, No.ST5, May, 1971.
[2] 中华人民共和国国家规范，钢结构设计规范GB50017—2003，2003．
[3] ECCS. European Recommendations for Steel Construction. 1978.
[4] 童根树，格构柱的夹层梁一相关屈曲理论．西安冶金建筑学院学报，1987(3)95～104．
[5] Svensson, S.E. ,and Kragerup,J. ,Collapse Loads of Laced Columns, Journal of the Strucmral Division ASCE, Vol.108, No.ST6, June, 1982.
[6] Davies,H.T., Introduction to Nonlinear Differential and Integral Equations, Dover Publications, New York, N.Y., 1962.
[7] 童根树，施祖元，李志飙，对压弯杆平面内稳定计算式及计算长度确定方法的评论，建筑结构．
[8] 门式刚架轻型房屋钢结构技术规程CECS102：2002．
[9] 中华人民共和国国家规范，冷弯薄壁型钢结构技术规范GB50018—2002．
[10] Constancio Miranda, Morris Ojalvo, Inelastic Lateral-Torsional Buclding of Beam Columns, Journal of the Engineering Mechanics Division ASCE, Vol.91, No.EM6, December, 1965.
[11] 朱俞江，童根树，箱形截面压弯构件的平面外稳定计算．钢结构，2003(5)11～15．
[12] Byskov, E., Imperfection Sensitivity in Elastic-Plastic Truss Columns, DCAMM Report No.200, The Danish Center for Applied Mathematics and Mechanics, The Technical University of Denmark, Dec., 1980.
[13] Byskov, E., Application of an Asymptotic Expansion for Elastic Buckling Problems with Mode Interaction, AIAA Journal, Vol. 17, June,1979,pp.630-633.
[14] Crawford, R.F., and Benton,M.D., Strength of Initially Wavy Lattice Columns, AIAA Journal, Vol. 18, May, 1980, pp.581-584.
[15] Crawford, R.F., and Hedgepeth, J.M., Effects of Initially Waviness on the Strength and Design of Build-up Structures, AIAA Journal, Vol.13, May, 1975, pp.672-675.
[16] Svensson, S.E. and Croll, J.G.A., Interacton Local and Overall Buclding, International Journal of Mechanical Science, vol. 17, 1975, Pergamon Press, New York, N.Y., pp. 307-321.
[17] Stein, M., Recent Advances in Shell Buckling, AIAA Paper No.68～103,1968.
[18] 饶芝英，童根树，钢结构稳定性的新诠释．建筑结构，2002(5)：12～14．
[19] 童根树，陈婷，符刚，楔形变截面压弯构件的平面内弹塑性稳定．钢结构，2003(5)8～10．
[20] 陈绍蕃，钢结构设计原理(第二版)，科学出版社，1982．
[21] 陈骥，钢结构稳定理论与设计，科学出版社，2001．
[22] 夏志斌，潘有昌，结构稳定理论，高等教育出版社，1987．
[23] 吕烈武，沈世钊，沈祖炎，胡学仁，钢结构构件稳定理论，中国建筑工业出版社，1983．
[24] 龙驭球，包世华，结构力学教程，高等教育出版社，1998．
[25] 王勖成，邵敏，有限单元法基本原理和数值方法(第二版)，清华大学出版社，1997．
[26] 郭在田，缀板式轴心受压构件的单肢计算问题，冶院科技，1984，1期．
[27] 朱林生，王英英，宋敏，钢结构偏心受压格构柱的优化设计，试验技术与试验机，第36卷，第3、4期，1996．
[28] 郑伟国，沈祖炎，缀板柱稳定极限承载力的数值积分解法，土木工程学报，第25卷，第3期，1992．
[29] 王国周，钢结构残余应力分布的若干特点，冶金工业建筑，No．8，1981．
[30] 李国跃，吕凤梧，双肢缀板钢格构立柱的整体稳定分析，土木工程学报，第35卷，第4期，2002．
[31] 沈彦韬，双肢格结构式钢柱侧移刚度的计算，广州建筑，第1期，2000．
[32] N.S.Trahair, Flexural-Torsional Buclding of Structures, E & FN SPON, London, 1993.
[33] Timoshenko S.P., Gere J.M., Theory of Elastic Stability, McGraw-Hill Co. Inc., New York, 1961.
[34] Chen W.F., Atsuta T., Theory of Beam-Columns, McGraw-Hill Co. Inc., New York, 1977.
[35] J. Roorda, Some Statistical Aspects of The Buckling of Imperfection-Sensitive Structures, J.Mech.Phys.Solids, 1969, Vol. 17, pp. 111-123.
[36] White, M. W.,and Thürlimann, B., Study of Columns with perforated Cover Plates, AREA Bull., 1956.
[37] Holt,M.,Tests on Built-up Columns of Structural Aluminum Alloys,Trans.ASCE,vol. 105, 1940.
[38] Pippard,A.J. S, The Critical Load of a Battened Column, Phil.Mag.,January 1948.
[39] Pippard,A.J.S., Battened Columns, Stud. Elastic Struct., 1952.
[40] Jones,B.D., A Theory for Structs with Lattice or Batten Bracing ,Struct.Eng. May 1952.
[41] Koenigsberger, F., and Mohsin, M.E., Design and Load Carrying Capacity of Welded and Battened Struts, Struct. Eng., June 1956.
[42] Tamayo,J.Y., and Ojalvo,M., Buckling of Three-Legged Columns with Batten Bracing, Proc.Am.Soc.Civil Eng.,Vol.91,No.ST1,February 1956.
[43] Mohsin,M.E., The Critical Load of Unsymmetrical Welded Battened Struts, Struct.Eng.,November 1965.
[44] Williamson,R.A., and Margolin,M.N., Shear Effects in Design of Guyed Towers, Journal of the Structural Division ASCE,vol.92,October, 1966.
[45] Lin,F.J., Glauser,E.C., and Johnston,B.G., Behavior of Laced and Battened Structural Members, Journal of the Structural Division ASCE,Vol.96,No.ST7,July ,1970.
[46] Full Scale Test of Aluminum Lattice Mast, Internal Report, Alcan International Ltd., Research Centre, Kingston.
[47] Guide for the Design of Aluminum Transmission Towers, by the Task Committee on Light weight Alloys of the Committee on Metals of the Structural Division, Proc.Am.Soc.Civil Eng., Vol.98,No.ST12, December, 1972.
[48] Bruce G. Johnston, ed., Structural Stability Research Council, Guide to Stability Design Criteria for Metal Structures, 3rd ed. New York: John Wiley& Sons, Inc., 1976.
[49] Friedrich Bleich, Buckling Strength of Metal Structures. New York: McGraw-Hill Book Company, Inc., 1952.
[50] R.Narayanan, Beams and Beam Columns—Stability and Strength, Applied Science Publishers, London and New York, 1983.
[51] Cyrus Omid'varan, Discrete Analysis of Latticed Columns ,Journal of Structural Division, ASCE, 94, ST1, January 1968.
[52] Adams, p.F., Segmental Design of Steel Beam Columns, Proc.Can.Struct.Eng.Conf., Toronto, 1970.
[53] Home, M.R., and Ajmani,J.L., Design of Columns Restrained by Side-Rails and the post-Buckling Behavior of Laterally Restrained Columns, Struct.Eng., Vol.49, No.8, August 1971.
[54] Omer W.Blodgett, Design of Welded Structures. Cleveland, Ohio:James F.Lincoln Arc Welding Foundation, 1966.
[55] P.J. Bredenkamp, and G.J. van den Berg, The Strength of Stainless Steel Built-up I-Section Columns, J.Construct.Steel Research, Vol.34, 1995.
[56] P.J. Bredenkamp, G.J. van den Berg, and R van der Merwe, The Behaviour of Hot-rolled and Built-up Stainless Steel Structural Members, J. Construct.Steel Res., Vol.46,Nos. 1-3,1998.
[57] Charles G.Salmon, and John E.Johnson, Steel Structures:Design and Behavior, 2rd, HARPER & ROW, PUBLISHER, New York,1980.
[58] Von K. Kl ǒ ppel, Darmstadt, and W.Ramm, Salzgitter-Thiede, Zur Stabilitǎ tsuntersuchung von mehrteiligen gitterstǎben, DER STAHLBAU, Vol. 1, 1972.
[59] Johnston, B.G., Spaced Steel Columns, Journal of the Structural Division ASCE, Vol.97, No.ST5, May, 1971.
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