Effects of load height application and pre-buckling deflections on lateral buckling of thin-walled beams

  • Mohri, F. (IUT Nancy-Brabois, Departement Geie Civil, Universite Henri Poincare) ;
  • Potier-Ferry, M. (LPMM, UMR CNRS 7554, ISGMP, Universite Paul Verlaine-Metz)
  • Received : 2005.11.16
  • Accepted : 2006.05.23
  • Published : 2006.10.25


Based on a non-linear model taking into account flexural-torsional couplings, analytical solutions are derived for lateral buckling of simply supported I beams under some representative load cases. A closed form is established for lateral buckling moments. It accounts for bending distribution, load height application and pre-buckling deflections. Coefficients $C_1$ and $C_2$ affected to these parameters are then derived. Regard to well known linear stability solutions, these coefficients are not constant but depend on another coefficient $k_1$ that represents the pre-buckling deflection effects. In numerical simulations, shell elements are used in mesh process. The buckling loads are achieved from solutions of eigenvalue problem and by bifurcations observed on non linear equilibrium paths. It is proved that both the buckling loads derived from linear stability and eigenvalue problem lead to poor results, especially for I sections with large flanges for which the behaviour is predominated by pre-buckling deflection and the coefficient $k_1$ is large. The proposed solutions are in good agreement with numerical bifurcations observed on non linear equilibrium paths.


buckling;finite element;eigenvalue;linear stability;non linear stability;open section;pre-buckling;thin-walled beam


  1. Barsoum, R. S. and Gallagher, R. H. (1970), 'Finite element analysis of torsional and torsional-flexural stability problems', Int. J. Numer. Methods Eng., 2, 335-352
  2. Bazant, Z. P. and El Nimeiri, M. (1973), 'Large-deflection spatial buckling of thin walled beams and frames', J. Eng. Mech. Div., ASCE, 99, 1259-1281
  3. Eurocode 3, (1992), Design of steel structures, Part 1.1: General rules for buildings. European Committee for standardization, Draft Document ENV 1993-1-1, Brussels
  4. Hibbit, Karlsson and Sorensen Inc (2003), Abaqus Standard User's Manuel, Version 6.4. Abaqus, Pawtucket, RI, USA
  5. Mohri, F., Azrar, L. and Potier-Ferry, M. (2001), 'Flexural-torsional post-buckling analysis of thin-walled elements with open sections', Thin-Walled Structures, 39, 907-938
  6. Mohri, F., Azrar, L. and Potier-Ferry, M. (2002), 'Lateral post-buckling analysis of thin-walled open section beams', Thin-Walled Structures, 40, 1013-1036
  7. Mohri, F., Brouki, A. and Roth, J. C. (2003), 'Theoretical and numerical stability analyses of unrestrained monosymmetric thin-walled beams', J. Contruct. Steel Res., 59, 63-90
  8. Roberts, T. M. and Burt, C. A. (1985), 'Instability of mono symmetric beams and cantilevers', Int. J. Mech. Sci., 27(5), 313-324
  9. Ronagh, H. R., Bradford, M. A. and Attard, M. M. (2000), 'Non-linear analysis of thin-walled members of variable cross-section, Part II: Application', Comput. Struct., 77, 301-313
  10. Timoshenko, S. P. and Gere, J. M. (1961), Theory of Elastic Stability, 2nd edition, McGraw Hill, NY
  11. Trahair, N. S. (1993), Flexural-Torsional Buckling of Structures, Chapman & Hall, London
  12. Vacharajittiphan, P., Woolcock, S. T. and Trahair, N. S. (1974), 'Effect of in-plane deformation on lateral buckling', J. Struct. Mech., ASCE, 3(11), 29-60
  13. Pi, Y. L. and Bradford, M. A. (2001), 'Effects of approximations in analyses of beams of open thin-walled cross-section, Part I: Flexural-torsional stability', Int. J. Numer. Methods Eng., 51, 757-772
  14. Achour, B. and Roberts, T. M. (2000), 'Non-linear strains and stability of thin-walled bars', J. Contruct. Steel Res., 56, 237-252
  15. Laudiero, F. and Zaccaria, D. (1988), 'A consistent approach to linear stability of thin-walled beams of open section', Int. J. Mech. Sci., 30, 503-515

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