Asian Journal of Civil Engineering

, Volume 19, Issue 4, pp 487–499 | Cite as

The effective length factor of columns in unsymmetrical frames asymmetrically loaded

  • A. SlimaniEmail author
  • F. Ammari
  • R. Adman
Original Paper


The concept of the effective length factor represents an important parameter with regard to the elastic buckling analysis. This concept makes possible computational of the elastic critical load using a single formula for any situation of boundary conditions. We noted that substantial research has been done by many researchers in this field. The work developed in this paper, is focused on the resoluteness of the exact value of the effective length factor of columns belonging to unsymmetrical frames, with asymmetrical loading. For this purpose we chose to study an unsymmetrical frames asymmetrically loaded where the geometry and loading are set by means of a great number of a dimensionless parameters. At first, a theoretical approach is adopted to investigate the global elastic buckling of an irregular frame. This is done by considering the classical stability functions which introduce the coupling between axial loading and the bending stiffness of the columns. Thus, the governing equilibrium equations were established for the structure being studied, leading to the global nonlinear stiffness matrix of the structure. Therefore, the global elastic buckling occurs when the determinant of the nonlinear stiffness matrix vanishes. Thereafter, a wide parametrical analysis was done from the theoretical results previously obtained. In determining the effective length factor K, a marked difference was noted between the results obtained using the Eurocode 3 approach and those obtained by the current study.


Effective length factor Elastic buckling Steels frames Eurocode 3 


  1. Adman, R., & Saidani, M. (2013). Elastic buckling of columns with end restraint effects. Journal of Constructional Steel Research, 87, 1–5.CrossRefGoogle Scholar
  2. Aristizabal-Ochoa, J. D. (1994a). K-factor for columns in any type of construction: Nonparadoxical approach. Journal of Structural Engineering, 120(4), 1272–1290.CrossRefGoogle Scholar
  3. Aristizabal-Ochoa, J. D. (1994b). Slenderness K factor for leaning columns. Journal of Structural Engineering, 120(10), 2977–2991.CrossRefGoogle Scholar
  4. Aristizabal-Ochoa, J. D. (1994c). Stability of columns under uniform axial load with semirigid connections. Journal of Structural Engineering, 120(11), 3212–3222.CrossRefGoogle Scholar
  5. Aristizabal-Ochoa, J. D. (1996). Braced, partially braced and unbraced columns: Complete set of classical stability equations. Structural Engineering and Mechanics, 4(4), 365–381.CrossRefGoogle Scholar
  6. Aristizábal-Ochoa, J. D. (2002). Classic buckling of three-dimensional multicolumn systems under gravity loads. Journal of Engineering Mechanics, 128(6), 613–624.CrossRefGoogle Scholar
  7. Bridge, R. Q., & Fraser, D. J. (1987). Improved G-factor method for evaluating effective lengths of columns. Journal of Structural Engineering, 113(6), 1341–1356.CrossRefGoogle Scholar
  8. Cen, E. (2005). 1-1-Eurocode 3: Design of steel structures-part 1-1: General rules and rules for buildings. Brussels: European Committee for Standardization.Google Scholar
  9. Cheong-Siat-Moy, F. (1986). K-factor paradox. Journal of Structural Engineering, 112(8), 1747–1760.CrossRefGoogle Scholar
  10. Cheong-Siat-Moy, F. (1999). An improved K-factor formula. Journal of Structural Engineering, 125(2), 169–174.CrossRefGoogle Scholar
  11. Gantes, C. J., & Mageirou, G. E. (2005). Improved stiffness distribution factors for evaluation of effective buckling lengths in multi-story sway frames. Engineering Structures, 27(7), 1113–1124.CrossRefGoogle Scholar
  12. Girgin, K., Ozmen, G., & Orakdogen, E. (2006). Buckling lengths of irregular frame columns. Journal of Constructional Steel Research, 62(6), 605–613.CrossRefGoogle Scholar
  13. Hellesland, J. (2012). Evaluation of effective length formulas and applications in system instability analysis. Engineering Structures, 45, 405–420.CrossRefGoogle Scholar
  14. Hellesland, J., & Bjorhovde, R. (1996). Improved frame stability analysis with effective lengths. Journal of Structural Engineering, 122(11), 1275–1283.CrossRefGoogle Scholar
  15. Horne, M. (1975). An approximate method for calculating the elastic critical loads of multi-storey plane frames. The Structural Engineer, 53(6), 242–248.Google Scholar
  16. Kalochairetis, K. E., & Gantes, C. J. (2012). Elastic buckling load of multi-story frames consisting of Timoshenko members. Journal of Constructional Steel Research, 71, 231–244.CrossRefGoogle Scholar
  17. Kashdan, L., Conner Seepersad, C., Haberman, M., & Wilson, P. S. (2012). Design, fabrication, and evaluation of negative stiffness elements using SLS. Rapid Prototyping Journal, 18(3), 194–200.CrossRefGoogle Scholar
  18. Kishi, N., Chen, W.-F., & Goto, Y. (1997). Effective length factor of columns in semirigid and unbraced frames. Journal of Structural Engineering, 123(3), 313–320.CrossRefGoogle Scholar
  19. Li, Q., Zou, A., & Zhang, H. (2016). A simplified method for stability analysis of multi-story frames considering vertical interactions between stories. Advances in Structural Engineering, 19(4), 599–610.CrossRefGoogle Scholar
  20. Livesley, R. K., & Chandler, D. B. (1956). Stability functions for structural frameworks. Manchester: Manchester University Press.Google Scholar
  21. Load, A. (1999). Resistance factor design (LRFD) specification for structural steel buildings. Chicago: American Institute of Steel Construction Inc.Google Scholar
  22. Mageirou, G. E., & Gantes, C. J. (2006). Buckling strength of multi-story sway, non-sway and partially-sway frames with semi-rigid connections. Journal of Constructional Steel Research, 62(9), 893–905.CrossRefGoogle Scholar
  23. Raftoyiannis, I. G. (2005). The effect of semi-rigid joints and an elastic bracing system on the buckling load of simple rectangular steel frames. Journal of Constructional Steel Research, 61(9), 1205–1225.CrossRefGoogle Scholar
  24. Teh, L. H., & Gilbert, B. P. (2016). A buckling model for the stability design of steel columns with intermediate gravity loads. Journal of Constructional Steel Research, 117, 243–254.CrossRefGoogle Scholar
  25. Webber, A., Orr, J., Shepherd, P., & Crothers, K. (2015). The effective length of columns in multi-storey frames. Engineering Structures, 102, 132–143.CrossRefGoogle Scholar
  26. Wood, R. H. (1974). Effective lengths of columns in multi-storey buildings. Building Research Establishment, Building Research Station.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Civil EngineeringUniversity of Science and Technology Houari Boumediene (USTHB)AlgiersAlgeria

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