Advanced Steel Construction

Vol. 11, No. 1, pp. 39-53 (2015)




Y.Y. Chen1 and G.H. Chuan2, *

Professor, State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, China

M. D. Candidate, College of Civil Engineering, Tongji University, Shanghai, China.

*(Corresponding author: E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.)

Received: 10 August 2013; Revised: 2 March 2014; Accepted: 11 April 2014




View Article   Export Citation: Plain Text | RIS | Endnote


As a crucial factor for stability calculation of frames, the effective length factor is generally determined by the traditional approaches in most current design codes, but some assumptions imposed do not reflect the real frame buckling behaviors. In this paper modified approaches are proposed based on the change of some unreasonable assumptions of the traditional approaches mainly in two aspects. Firstly, the premise that all frame columns buckle simultaneously is changed into an individual column buckling mode in braced frames, or story buckling mode in both braced and unbraced frames. Secondly, actual distribution of axial forces of columns is taken into account, so that the stability functions of columns may not be identical. Moreover, approximate formulas for calculation of the effective length factor are obtained based on the modified approaches, by which a series of numerical analysis is carried out. Numerical analysis results demonstrate that the modified approaches improve the accuracy well compared with the traditional ones.



Steel structure, Frame, Buckle, Effective length factor, Critical load, Modified approaches


[1] American Institute of Steel Construction (AISC), “Specification for Structural Steel Buildings”, ANSI/AISC 360-10, Chicago, 2010.

[2] Standards Australia Committee (SAC) BD/1, Steel Structures, “AS4100—1998, Australian Standard—Steel Structures”, Standards Australia, New South Wales, 1998.

[3] GB50017—2003, “Code for Design of Steel Structures”, Ministry of Construction, Architecture and Building Press, Beijing, 2003. (in Chinese)

[4] Kuhn, G. and Lundgren, H. R., “An Appraisal of the Effective Length Alignment Charts”, International Colloquium on Stability of Structures under Static and Dynamic Loads, ASCE, New York, 1977, pp. 212-242.

[5] Chen, W.F. and Lui, E.M., “Structural Stability—Theory and Implementation”, Elsevier, New York, 1987.

[6] Bridge, R.Q. and Fraser, D.J., “Improved G-factor Method for Evaluating Effective Lengths of Columns”, Journal of Structural Engineering, 1987, Vol. 113, No. 6, pp. 1341-1356.

[7] Essa, H.S., “Stability of Columns in Unbraced Frames”, Journal of Structural Engineering, 1997, Vol. 123, No. 7, pp. 952-957.

[8] Kishi, N., Chen, W.F. and Goto, Y., “Effective Length Factor of Columns in Semirigid and Unbraced Frames”, Journal of Structural Engineering, 1997, Vol. 123, No. 3, pp. 313-320.

[9] Kishi, N., Chen, W.F., Goto, Y. and Komuro, M., “Effective Length Factor of Columns in Flexibly Jointed and Unbraced Frames”, Journal of Constructional Steel Research, 1998, Vol. 47, No. 1-2, pp. 93-118.

[10] Tong, G.S. and Wang, J.P., “Column Effective Lengths Considering Inter-story and Inter-column Interactions in Sway-permitted Frames”, Journal of Constructional Steel Research, 2006, Vol. 62, No. 5, pp. 413-423.

[11] Yura, J.A., “The Effective Length of Columns in Unbraced Frames”, Engineering Journal, 1971, Vol. 8, No. 2, pp. 37-42.

[12] White, D.W. and Hajjar, J.F., “Buckling Models and Stability Design of Steel Frames: A Unified Approach”, Journal of Constructional Steel Research, 1997, Vol. 42, No. 3, pp. 171-207.

[13] Xu, L. and Liu, Y., “Story Stability of Semi-braced Steel Frames”, Journal of Constructional Steel Research, 2002, Vol. 58, No. 4, pp. 467-491.

[14] Choi, D.H. and Yoo, H., “Iterative System Buckling Analysis, Considering A Fictitious Axial Force to Determine Effective Length Factor for Multi-story Frames”, Engineering Structures, 2009, Vol. 31, No. 2, pp. 560-570.

[15] Galambos, T.V. and Surovek, A.E., “Structural Stability of Steel: Concepts and Applications for Structural Engineers”, John Wiley & Sons, Inc., Hoboken, New Jersey, 2008.

[16] Commission des Regles C. M. 66, “Regles de calcul des constructions en acier”, Eyrolles, Paris, 1966. (in French)

[17] Dumonteil, P., “Simple Equations for Effective Length Factors”, Engineering Journal, 1992, Vol. 29, No. 3, pp. 111-115.

[18] Dumonteil, P., “Historical Note on K-factor Equations”, Engineering Journal, 1999, Vol. 36, No. 2, pp. 102-103.