考虑层与层相互作用的框架稳定分析
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摘要
本文通过分析一个简单的两层框架，表明如果采用传统计算长度系数法的理想假定，则必然会导致梁端约束在上下层柱之间的不合理分配。在放弃了传统计算长度系数法的三个不合理假定后，本文提出了两层和三层框架失稳时，考虑层间支援的框架柱计算长度的很精确的计算方法。对于两层框架，通过求解一个一元二次代数方程得到各柱柱端的转动约束；对于三层框架，通过求解一个一元三次代数方程，得到各柱柱端的转动约束。进而由传统公式或规范附表得到各柱的计算长度系数值。对于更多层的情况，先判断薄弱层，再假定薄弱层的上下层柱远端的梁端约束全部提供给与薄弱层相邻层的柱，取出薄弱层及其上下层的梁柱，按前面处理两层或三层框架的方法可以得到薄弱层柱很精确的计算长度系数，相应导得其它层柱的计算长度系数。对于更为一般的单跨不对称框架和多跨框架，本文采用梁柱合成的方法求解，精度也很理想。
Through an analysis of a simple two-story frame, this paper revealed that the assumptions used in current effective length method led to unrealistic
distribution of beam restraints among the connected columns. With three
assumptions of the conventional effective length approach discarded, a new
approach is proposed by which column effective length considering
inter-story interaction can be obtained in un-braced two-story or three-story frames. A quadratic equation with one variable for two-story frames and a cubic equation with one variable for three-story frames are derived from which the rotational restraint provided to each column may be solved and the effective length factors can then be determined by the traditional formula or tables. For frames of more than 3 stories, the weakest story is first selected and a three-story sub-assemblage including the weakest column is taken out, and the proposed method is applied, the effective length of the weakest column is thus obtained, the effective length of the remaining columns are computed through a pre-defined relations. Because the sub-assemblage included beams at far ends of the columns above and below the column under consideration, the far end condition (hinged or fixed) may be considered easily.
Through an analysis of a simple two-story frame, this paper revealed that the assumptions used in current effective length method led to unrealistic
distribution of beam restraints among the connected columns. With three
assumptions of the conventional effective length approach discarded, a new
approach is proposed by which column effective length considering
inter-story interaction can be obtained in un-braced two-story or three-story frames. A quadratic equation with one variable for two-story frames and a cubic equation with one variable for three-story frames are derived from which the rotational restraint provided to each column may be solved and the effective length factors can then be determined by the traditional formula or tables. For frames of more than 3 stories, the weakest story is first selected and a three-story sub-assemblage including the weakest column is taken out, and the proposed method is applied, the effective length of the weakest column is thus obtained, the effective length of the remaining columns are computed through a pre-defined relations. Because the sub-assemblage included beams at far ends of the columns above and below the column under consideration, the far end condition (hinged or fixed) may be considered easily.
引文
[1] 陈骥．钢结构稳定理论和应用．科学出版社．2001年北京．
[2] 饶芝英，童根树．钢结构稳定性的新诠释．建筑结构．2002．第4期．
[3] Duan, L., and Chen, W.E(1989). "Effective length factor for columns in unbraced frames." J.struct.Engrg.,ASCE, 115(1), 149-165.
[4] Duan, L., and Chen, W.F.(1989). "Effective Length factors for Columns in Braced Frames." J.Struct.Engrg.,ASCE,114(10),2357-2370.
[5] 中华人民共和国国家标准．钢结构设计规范GBJ17-88．中国计划出版社．1988．
[6] 中华人民共和国国家标准．钢结构设计规范GBJ17-88条文说明．中国计划出版社．1989．
[7] 梁启智．高层建筑结构分析和设计．华南理工大学出版社．1992年广州．
[8] N.Kishi, W.F.Chen, and Y.Goto (1997). "Effective length factor of columns in semirigid and unbraced frames." J.Struct.Engrg.,ASCE, 123(3),313-320.
[9] Salem, A.H. (1969). Discussion of "Buckling Analysis of One-Story Frames." by Alfred Zweig, F., and Albert Kahn., Journal of the Structural Division.ASCE,Vol.95,No.ST5,May,1969.
[10] Yura, J.A. (1971), "The Effective length of columns in unbraced frame",Engineering Journal, AISC,Vol.8,No.2,37-42.
[11] Yura, J.A. (1972), Discussion of"The Effective length of columns in unbraced frame", Engineering Journal, AISC,Vol.9,No.4,37-42.
[12] 陈绍蕃．钢结构设计原理(第二版)．科学出版社．1982．
[13] 夏志斌，潘有昌．结构稳定理论．高等教育出版社．1988年北京．
[14] 夏志斌，姚谏．钢结构．浙江大学出版社．1996年杭州．
[15] Bridge, R.Q., and Fraser, D.J. (1986). "Improved G-factor method for evaluating effective lengths of columns." J.Struct.Engrg.,ASCE,113(6),1341-1356.
[16] Hellesland, J., and Bjorhovde, R. (1996). "Restraint demand factors and effective lengths of braced columns." J.Struct.Engrg.,ASCE,122(10),1216-1224.
[17] Hellesland, J., and Bjorhovde, R. (1996). "Improved Frame Stability Analysis with Effective Lengths." J.Struct.Engrg.,ASCE,122(11),1275-1283.
[18] 童根树，施祖元．框架有侧移失稳的计算长度系数与D值法的关系．2003．
[19] 童根树，施祖元．非完全支撑的框架结构的稳定性．土木工程学报．第31卷，第4期．
[20] 胡达明．钢框架柱计算长度的合理确定．浙江大学硕士学位论文．1998年1月．
[21] 陈红英．弯曲型支撑框架结构的弹性稳定分析．浙江大学硕士学位论文．2002年2月．
[22] 沈永欢等编．实用数学手册．科学出版社．1992年北京．
[23] LeMessurier, WM.J. (1977), "A practical method of second order analysis, part 2,rigid frames". Engineering Journal,AISC., 14(2),49-67.
[24] Gonealves, R. (1992), "New Stability Equation for columns in braced frames", Joumal of Structural Engineering,ASCE, 118(7), 1853-1870.
[25] Dumonteil, P. (1999). Historical Note on K-Factor Equations, Engineering Joumal, Vol.36,No.2,102-103
[26] McGuire, W. (1968). Steel Structures, Prentice-Hall Inc., Englewood Cliffs,NJ.
[27] Dumonteil, P. (1992). "Simple equations for Effective Length Factors", Engineering Journal, Vol.29,No.3,111-115.
[28] Dumonteil, E, and Valley, M. (1995). Discussion of"Nrvel Design Algorithms for K Factor
Calculation and Beam-Column selection". Journal of Structural Engineering, ASCE, 384-385.
[29] Newmark, N.M.(1949), A Simple Approximate Formula for Effective End-Fixity of Columns, Journal of Aeronantical Science,Vol. 16, No.2
[30] Giulio Ballio and Federico M.Mazzolani. Theory and Design of Steel Structure. J.W. Arrowsmith Ltd., Bristol. 1983.
[31] Wood, R.H. (1974), "Effective lengths of columns in multi-storey buildings, part 1". The Structural Engineer, Vol.52,No.7,235-244.
[32] Wood, R.H. (1974), "Effective lengths of columns in multi-storey buildings, part 2". The Structural Engineer, Vol.52,No.8,295-302.
[33] Wood, R.H. (1974), "Effective lengths of columns in multi-storey buildings, part 3". The Structural Engineer, Vol. 52,No.9,341-346.
[34] Cheong-Siat-Moy, F. (1986). "K-factor paradox." J.Struct.Engrg.,ASCE,112(8),1747-1760.
[35] Cheong-Siat-Moy, F.(1988). "Discussion." J.Struct.Engrg.,ASCE, 114(9),2139-2150.
[36] Aristizabal-Ochoa, J.D. (1994). "K-factor for columns in any type of columns in any type of construction: Nonparadoxical approach." J.Struct.Engrg.,ASCE,120(4),1273-1290.
[37] Aristizabal-Ochoa, J.D. (1997). "Story stability of braced,partially braced, and unbraced frames: Classical approach." J.Struct.Engrg.,ASCE, 123(6),799-807.
[38] Cheong-Siat-Moy, F. (1999). "An improved K-factor formula." J.Struct.Engrg., ASCE,125(2), 169-174.
[39] Alfred Zweig, F., and Albert Kahn. (1968). "Buckling Analysis of One-Story Frames." Journal of the Structural Division.ASCE,Vol.94,No.ST9,2107-2134.
[40] L.Xu, and Y.Liu. (2002). "Story stability of semi-braced steel frames." Journal of Constructional Steel Research., 58,467-491.
[41] Bridge R.Q., Clarke,M.J.,etc.(1997), (Task Committee on Effective Length of The Strutural Engineering Institute of ASCE), Effective length and notional load approaches for assessing frame stability: Implications for American steel design. ASCE Publication
[2] 饶芝英，童根树．钢结构稳定性的新诠释．建筑结构．2002．第4期．
[3] Duan, L., and Chen, W.E(1989). "Effective length factor for columns in unbraced frames." J.struct.Engrg.,ASCE, 115(1), 149-165.
[4] Duan, L., and Chen, W.F.(1989). "Effective Length factors for Columns in Braced Frames." J.Struct.Engrg.,ASCE,114(10),2357-2370.
[5] 中华人民共和国国家标准．钢结构设计规范GBJ17-88．中国计划出版社．1988．
[6] 中华人民共和国国家标准．钢结构设计规范GBJ17-88条文说明．中国计划出版社．1989．
[7] 梁启智．高层建筑结构分析和设计．华南理工大学出版社．1992年广州．
[8] N.Kishi, W.F.Chen, and Y.Goto (1997). "Effective length factor of columns in semirigid and unbraced frames." J.Struct.Engrg.,ASCE, 123(3),313-320.
[9] Salem, A.H. (1969). Discussion of "Buckling Analysis of One-Story Frames." by Alfred Zweig, F., and Albert Kahn., Journal of the Structural Division.ASCE,Vol.95,No.ST5,May,1969.
[10] Yura, J.A. (1971), "The Effective length of columns in unbraced frame",Engineering Journal, AISC,Vol.8,No.2,37-42.
[11] Yura, J.A. (1972), Discussion of"The Effective length of columns in unbraced frame", Engineering Journal, AISC,Vol.9,No.4,37-42.
[12] 陈绍蕃．钢结构设计原理(第二版)．科学出版社．1982．
[13] 夏志斌，潘有昌．结构稳定理论．高等教育出版社．1988年北京．
[14] 夏志斌，姚谏．钢结构．浙江大学出版社．1996年杭州．
[15] Bridge, R.Q., and Fraser, D.J. (1986). "Improved G-factor method for evaluating effective lengths of columns." J.Struct.Engrg.,ASCE,113(6),1341-1356.
[16] Hellesland, J., and Bjorhovde, R. (1996). "Restraint demand factors and effective lengths of braced columns." J.Struct.Engrg.,ASCE,122(10),1216-1224.
[17] Hellesland, J., and Bjorhovde, R. (1996). "Improved Frame Stability Analysis with Effective Lengths." J.Struct.Engrg.,ASCE,122(11),1275-1283.
[18] 童根树，施祖元．框架有侧移失稳的计算长度系数与D值法的关系．2003．
[19] 童根树，施祖元．非完全支撑的框架结构的稳定性．土木工程学报．第31卷，第4期．
[20] 胡达明．钢框架柱计算长度的合理确定．浙江大学硕士学位论文．1998年1月．
[21] 陈红英．弯曲型支撑框架结构的弹性稳定分析．浙江大学硕士学位论文．2002年2月．
[22] 沈永欢等编．实用数学手册．科学出版社．1992年北京．
[23] LeMessurier, WM.J. (1977), "A practical method of second order analysis, part 2,rigid frames". Engineering Journal,AISC., 14(2),49-67.
[24] Gonealves, R. (1992), "New Stability Equation for columns in braced frames", Joumal of Structural Engineering,ASCE, 118(7), 1853-1870.
[25] Dumonteil, P. (1999). Historical Note on K-Factor Equations, Engineering Joumal, Vol.36,No.2,102-103
[26] McGuire, W. (1968). Steel Structures, Prentice-Hall Inc., Englewood Cliffs,NJ.
[27] Dumonteil, P. (1992). "Simple equations for Effective Length Factors", Engineering Journal, Vol.29,No.3,111-115.
[28] Dumonteil, E, and Valley, M. (1995). Discussion of"Nrvel Design Algorithms for K Factor
Calculation and Beam-Column selection". Journal of Structural Engineering, ASCE, 384-385.
[29] Newmark, N.M.(1949), A Simple Approximate Formula for Effective End-Fixity of Columns, Journal of Aeronantical Science,Vol. 16, No.2
[30] Giulio Ballio and Federico M.Mazzolani. Theory and Design of Steel Structure. J.W. Arrowsmith Ltd., Bristol. 1983.
[31] Wood, R.H. (1974), "Effective lengths of columns in multi-storey buildings, part 1". The Structural Engineer, Vol.52,No.7,235-244.
[32] Wood, R.H. (1974), "Effective lengths of columns in multi-storey buildings, part 2". The Structural Engineer, Vol.52,No.8,295-302.
[33] Wood, R.H. (1974), "Effective lengths of columns in multi-storey buildings, part 3". The Structural Engineer, Vol. 52,No.9,341-346.
[34] Cheong-Siat-Moy, F. (1986). "K-factor paradox." J.Struct.Engrg.,ASCE,112(8),1747-1760.
[35] Cheong-Siat-Moy, F.(1988). "Discussion." J.Struct.Engrg.,ASCE, 114(9),2139-2150.
[36] Aristizabal-Ochoa, J.D. (1994). "K-factor for columns in any type of columns in any type of construction: Nonparadoxical approach." J.Struct.Engrg.,ASCE,120(4),1273-1290.
[37] Aristizabal-Ochoa, J.D. (1997). "Story stability of braced,partially braced, and unbraced frames: Classical approach." J.Struct.Engrg.,ASCE, 123(6),799-807.
[38] Cheong-Siat-Moy, F. (1999). "An improved K-factor formula." J.Struct.Engrg., ASCE,125(2), 169-174.
[39] Alfred Zweig, F., and Albert Kahn. (1968). "Buckling Analysis of One-Story Frames." Journal of the Structural Division.ASCE,Vol.94,No.ST9,2107-2134.
[40] L.Xu, and Y.Liu. (2002). "Story stability of semi-braced steel frames." Journal of Constructional Steel Research., 58,467-491.
[41] Bridge R.Q., Clarke,M.J.,etc.(1997), (Task Committee on Effective Length of The Strutural Engineering Institute of ASCE), Effective length and notional load approaches for assessing frame stability: Implications for American steel design. ASCE Publication