Skip to main content
SpringerLink
Log in

Flexural–torsional postbuckling analysis of beams of arbitrary cross section

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In this article, the postbuckling analysis of axially compressed elements of arbitrary cross section is presented taking into account moderately large displacements, moderately large angles of twist and employing nonlinear relationships between bending moments and curvatures. The elements are supported by the most general boundary conditions including elastic support or restraint. Based on Galerkin’s method and approximating the displacement field of the element by polynomial expressions the governing differential equations lead to a nonlinear algebraic system. The geometric, inertia, torsion and warping constants of the arbitrary beam cross section are evaluated employing the boundary element method. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint–Venant’s torsional constant. Both the Wagner’s coefficients and the shortening effect are taken into account, while their influence is examined and discussed. Numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Vlasov V.Z.: Thin-Walled Elastic Beams. Israel Program for Scientific Translations, Jerusalem (1961)

    Google Scholar 

  2. Timoshenko S.P., Gere J.M.: Theory of Elastic Stability. McGraw-Hill, Tokyo (1961)

    Google Scholar 

  3. Barsoum R.S., Gallagher R.H.: Finite element analysis of torsional and torsional–flexural stability problems. Int. J. Numer. Methods Eng. 2, 335–252 (1970)

    Article  MATH  Google Scholar 

  4. Barsoum R.S.: Finite element method applied to the problem of stability of non-conservative system. Int. J. Numer. Eng. 3, 63–87 (1971)

    Article  MATH  Google Scholar 

  5. Grimaldi A., Pignataro M.: Postbuckling behavior of thin-walled open cross-section compression members. Mech. Based Des. Struct. Machines 7(2), 143–159 (1979)

    Article  Google Scholar 

  6. Szymczak C.: Buckling and initial post-buckling behavior of thin-walled I columns. Comput. Struct. 11, 481–487 (1980)

    Article  MATH  Google Scholar 

  7. Kitipornchai S., Wang C.M.: Buckling of monosymmetric I-beams under moment gradient. J. Struct. Eng. 112(4), 781–799 (1986)

    Article  Google Scholar 

  8. Wang C.M., Kitipornchai S.: On stability of monosymmetric cantilevers. Eng. Struct. 8, 169–180 (1986)

    Article  Google Scholar 

  9. Attard M.M.: Lateral buckling analysis of beams by the FEM. Comput. Struct. 23(2), 217–231 (1986)

    Article  MATH  Google Scholar 

  10. Laudiero F., Zaccaria D.: A consistent approach to linear stability of thin-walled beams of open section. Int. J. Mech. Sci. 30(7), 315–503 (1988)

    Article  Google Scholar 

  11. Laudiero F., Zaccaria D.: Finite element analysis of stability of thin-walled beams of open section. Int. J. Mech. Sci. 30(8), 543–557 (1988)

    Article  MATH  Google Scholar 

  12. Trahair N.S.: Flexural–Torsional Buckling of Structures. Chapman and Hall, London (1993)

    Google Scholar 

  13. Kounadis A.N., Ioannidis G.I.: Lateral post-buckling analysis of beam columns. J. Eng. Mech., ASCE 120(4), 695–706 (1994)

    Article  Google Scholar 

  14. Ioannidis G.I., Kounadis A.N.: Lateral post-buckling analysis of monosymmetric I-beams under uniform bending. J. Construct. Steel Res. 30, 1–12 (1994)

    Article  Google Scholar 

  15. Kounadis A.N.: Postbuckling analysis of bars with thin-walled cross sections under simultaneous bending and torsion due to central thrust. J. Construct. Steel Res. 45, 17–37 (1998)

    Article  Google Scholar 

  16. Mohri F., Azrar L., Potier-Ferry M.: Flexural–torsional post-buckling analysis of thin-walled elements with open sections. Thin Walled Struct. 39, 907–938 (2001)

    Article  Google Scholar 

  17. Mohri F., Azrar L., Potier-Ferry M.: Lateral post-buckling analysis of thin-walled open section beams. Thin Walled Struct. 40, 1013–1036 (2002)

    Article  Google Scholar 

  18. Mohri F., Damil N., Potier-Ferry M.: Large torsion finite element model for thin-walled beams. Comput. Struct. 86, 671–683 (2008)

    Article  Google Scholar 

  19. Attard M.M.: Nonlinear theory of non-uniform torsion of thin-walled open beams. Thin Walled Struct. 4, 101–134 (1986)

    Article  Google Scholar 

  20. Attard M.M.: Nonlinear shortening and bending effect under pure torque of thin-wailed open beams. Thin Walled Struct. 4, 165–177 (1986)

    Article  Google Scholar 

  21. Ronagh H.R., Bradford M.A., Attard M.M.: Nonlinear analysis of thin-walled members of variable cross-section. Part I: theory. Comput. Struct. 77, 285–299 (2000)

    Article  Google Scholar 

  22. Ronagh H.R, Bradford M.A., Attard M.M.: Nonlinear analysis of thin-walled members of variable cross-section part II: applications. Comput. Struct. 77, 301–313 (2000)

    Article  Google Scholar 

  23. Sapountzakis E.J., Mokos V.G.: Warping shear stresses in nonuniform torsion by BEM. Comput. Mech. 30(2), 131–142 (2003)

    Article  MATH  Google Scholar 

  24. Ramm E., Hofmann T.J.: Stabtragwerke, Der Ingenieurbau. In: Mehlhorn, G.(eds) Band Baustatik/Baudynamik, Ernst & Sohn, Berlin (1995)

    Google Scholar 

  25. Rothert H., Gensichen V.: Nichtlineare Stabstatik. Springer, Berlin (1987)

    MATH  Google Scholar 

  26. Sapountzakis E.J., Tsiatas G.C.: Flexural–torsional buckling and vibration analysis of composite beams. Comput. Mater. Cont. 6(2), 103–115 (2007)

    Google Scholar 

  27. Sapountzakis E.J.: Solution of nonuniform torsion of bars by an integral equation method. Comput. Struct. 77, 659–667 (2000)

    Article  Google Scholar 

  28. Lawson C.L., Hanson R.J.: Solving Least Squares Problems. Prentice-Hall, Inc., New Jersey (SIAM Edition 1995) (1974)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering, Institute of Structural Analysis and Aseismic Research, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece

    Evangelos J. Sapountzakis & John A. Dourakopoulos

Authors
  1. Evangelos J. Sapountzakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John A. Dourakopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Evangelos J. Sapountzakis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sapountzakis, E.J., Dourakopoulos, J.A. Flexural–torsional postbuckling analysis of beams of arbitrary cross section. Acta Mech 209, 67–84 (2010). https://doi.org/10.1007/s00707-009-0140-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-009-0140-0

Keywords

Search

Navigation