Generalised Beam Theory (GBT) for Coupled Instability Problems

  • J. M. Davies
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 379)


This paper introduces the basic principles of first- and second-order Generalised Beam Theory (GBT). It demonstrates, among other things, that there is still some life in classical structural mechanics and that this is not just a matter for academics but has practical usefulness. Indeed, ultimately, GBT may offer the most practical way to deal with the difficult problem of the distortional buckling of cold-formed sections.

All of the problems amenable to solution using GBT can also be solved by the finite element and finite strip methods. However, GBT will invariably offer the most elegant solution and, by allowing the separation of fundamental modes, it also offers possibilities that are not present in these alternative methods. In particular, in its second-order form, there are particularly attractive possibilities for dealing with problems involving coupled instabilities.

The paper shows how Generalised Beam Theory (GBT) can be advantageously used to investigate a range of practical problems in the design of cold-formed section columns and beams. Single-mode bifurcation problems, more general bifurcation problems and general buckling problems are among those which are amenable to GBT and practical examples of each are included.


Distortional Mode Elastic Foundation Virtual Work Local Buckling Section Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Schardt, R. “Verallgemeinerte Technische Biegetheorie“ (Generalised Beam Theory), Springer Verlag, Berlin, Heidelberg 1989.CrossRefGoogle Scholar
  2. 2.
    Davies, J.M. and Leach, P. “First-order Generalised Beam Theory”, J Constr. Steel Res., 31 (1994), 187–220.CrossRefGoogle Scholar
  3. 3.
    Davies, J.M., Leach, P. and Heinz, D. “Second-order Generalised Beam Theory”, J Constr. Steel Res., 31 (1994), 221–241.CrossRefGoogle Scholar
  4. 4.
    Davies, J.M. and Leach, P. “Some applications of Generalised Beam Theory”, 11th Speciality Conf. on Cold-Formed Steel Structs., St. Louis, Missouri, USA., Oct. 20–21 1992, 479–501.Google Scholar
  5. 5.
    Wlassov, W.S. “Allgemeine Schalentheorie und ihre Anwendung in der Technik”, Akademie Verlag, Berlin 1958.Google Scholar
  6. 6.
    Hetenyi, M. “Beams on Elastic Foundations”, University of Michigan Press, Ann Arbor, Michigan 1946.Google Scholar
  7. 7.
    Davies, J.M. “An exact finite element for beam on elastic foundation problems”, J.Struct.Mech., 14 (4) (1986), 489–499.CrossRefGoogle Scholar
  8. 8.
    Lau, S.C.W. and Hancock, G.J. “Inelastic buckling of channel columns in the distortional mode”, Thin-Walled Structs., 10 (1) (1990), 59–84.CrossRefGoogle Scholar
  9. 9.
    Roberts, T.M “Section properties of thin-walled bars of open cross-section,” The Structural Engineer, 43B (3) (1985).Google Scholar
  10. 10.
    Davies, J.M. “Torsion of light gauge steel members”, Chapter 6 of Design of cold-formed steel members, Ed. J Rhodes, Elsevier Science Publishers (1991).Google Scholar
  11. 11.
    Leach, P. “The calculation of modal cross-section properties for use in the Generalised Generalised Beam Theory”, Thin-Walled Structs, 19, 1994, 61–79.CrossRefGoogle Scholar
  12. 12.
    Davies, J.M. and Jiang, C. “Design of thin-walled columns for distortional buckling”, CIMS’96, 2nd Int. Conf. on Coupled Instabilities in Metal Structs., Liege, Sept. 5–7 1996.Google Scholar
  13. 13.
    Lau S.C.W. and Hancock G. J. “Distortional Buckling Formulas for Channel Columns”, J. Struct. Div., ASCE, 113 (5), 1987, 1063–1078.CrossRefGoogle Scholar
  14. 14.
    Taylor, A, Leach, P. and Davies, J. M. “The behaviour of perforated light gauge steel sections subject to combined axial load plus bending”, University of Strathclyde BiCentenary Conference, Thin-Walled Structures, December 2–4, 1996.Google Scholar
  15. 15.
    Schardt, R. “Generalised Beam Theory–An adequate method for coupled instability problems”. Thin Walled Structures, 19 (1994) 161–180.CrossRefGoogle Scholar
  16. 16.
    Buhagiar, D, Chapman, J. C, and Dowling, P. J. “Lateral torsional buckling of thin-walled beams subject to bending about the minor axis”, The Structural Engineer, 72 No. 6, March 1994, pp 93–99.Google Scholar
  17. 17.
    Chapman, J. C. et al “Development of a space frame consisting of cold-formed sections”, First world Conf. on Constructional Steel Design, Acapulco, 1992.Google Scholar
  18. 18.
    Lovell, M.H. “Lateral buckling of light gauge steel beams” MSc Thesis, University of Salford, 1983.Google Scholar
  19. 19.
    Leach, P. “The Generalised Beam Theory with finite difference applications” PhD Thesis, University of Salford, 1989.Google Scholar
  20. 20.
    Davies, J. M, Jiang, C. and Leach, P. “The analysis of restrained purlins using Generalised Beam Theory”, 12th International Speciality Conference on Cold-Formed Steel Structures, St Louis, Missouri, October 1994.Google Scholar
  21. 21.
    Jiang, C. and Davies, J. M. “Design of thin-walled purlins for distortional buckling”, University of Strathclyde BiCentenary Conference, Thin-Walled Structures, December 2–4, 1996.Google Scholar
  22. 22.
    Pekoz, T. and Soroushian, P. “Behaviour of C- and Z-purlins under wind uplift”, 6th International Speciality Conference on Cold-Formed Steel Structures, St Louis, Missouri, November 1982, pp 409–429.Google Scholar
  23. 23.
    Hancock, G. J. “Design for distortional buckling of flexural members”, Proceedings of the Third International Conference on Steel and Aluminium Structures, Istanbul 1995.Google Scholar

Copyright information

© Springer-Verlag Wien 1998

Authors and Affiliations

  • J. M. Davies
    • 1
  1. 1.University of ManchesterManchesterUK

Personalised recommendations