Archive of Applied Mechanics

, Volume 80, Issue 4, pp 441–450 | Cite as

Nonlinear buckling analysis of simple geometrically imperfect frames

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Abstract

In this paper, the effect of geometrical imperfections due to joint angle deviations of a simple rectangular frame is thoroughly discussed. It has been found that the deviation from the right angle of the joint with respect to the center-lines of the two members of the frame affects significantly the buckling strength of the frame. It is also shown that such geometrical imperfections do not always decrease the strength of such structures but sometimes, even though loading imperfections exist, they act on the favorable side regarding its strength. The influence of various geometric parameters such as slenderness ratio as well as length and moment of inertia ratio of the members on the critical load of the imperfect frame is thoroughly discussed and representative case studies are presented.

Keywords

Nonlinear stability Moderate displacements Frame buckling Imperfections 
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References

  1. 1.
    Von Karman T., Tsien H.S.: The buckling of thin cylindrical shells under axial compression. J. Aeronaut. Sci. 8, 303–312 (1941)MATHMathSciNetGoogle Scholar
  2. 2.
    Koiter, W.T.: On the stability of elastic equilibrium. Ph.D. Thesis, Delft (1945) (translated at NASA, Tech. Trans. F10, 833, 1967)Google Scholar
  3. 3.
    Donnell L.H., Wang C.C.: Effect of imperfections on buckling of thin cylindrical shells under axial compression. J. Appl. Mech. 17, 73–83 (1950)MATHGoogle Scholar
  4. 4.
    Koiter, W.T.: The effect of axisymmetric imperfections on the buckling of cylindrical shells under axial compression. In: Proceedings of Konink Nederl. Akad. Wetensch, series B, vol. 66, pp. 265 (1963)Google Scholar
  5. 5.
    Koiter, W.T.: Elastic stability and post-buckling behavior. In: Langer, R.E. (ed.) Nonlinear Problems, pp. 257–263. The University of Wisconsin Press, Madison (1963)Google Scholar
  6. 6.
    Roorda J.: Stability of structures with small imperfections. J. Eng. Mech. (ASCE) 91(1), 87–106 (1965)Google Scholar
  7. 7.
    Koiter W.T.: Post-buckling analysis of a simple two-bar frame. In: Progress in Applied Mechanics, The Folke Odgvist Volume. Almgvist & Wiksell, Stockholm (1967)Google Scholar
  8. 8.
    Thompson J.M.T., Walker A.C.: A general theory for the branching analysis of discrete structural systems. Int. J. Solids Struct. 5, 281–288 (1969)CrossRefGoogle Scholar
  9. 9.
    Roorda J., Chilver A.H.: Frame buckling: an illustration of the perturbation technique. Int. J. Nonlinear Mech. 5, 235–246 (1970)CrossRefGoogle Scholar
  10. 10.
    Hutchinson J.W., Koiter W.T.: Postbuckling theory. Appl. Mech. Rev. 23(N12), 1353–1366 (1970)Google Scholar
  11. 11.
    Kounadis A.N., Giri J., Simitses G.J.: Nonlinear stability analysis of an eccentrically loaded two-bar frame. J. Appl. Mech. 44, 701–706 (1977)Google Scholar
  12. 12.
    Kounadis A.N., Economou A.: The effects of initial curvature and other parameters on the nonlinear buckling of simple frames. J. Struct. Mech. 12(1), 27–42 (1984)Google Scholar
  13. 13.
    Rallis N.S., Kounadis A.N.: Nonlinear sway buckling of geometrically imperfect rectangular frames. Ingenieur-Archiv 55, 90–97 (1985)CrossRefGoogle Scholar
  14. 14.
    Avraam, T.: Linear and nonlinear stability analysis of non-conservative divergence systems. Ph.D. Thesis (in Greek). The National Technical University of Athens, Athens (2004)Google Scholar
  15. 15.
    Ioannidis G.I., Raftoyiannis I.G., Kounadis A.N.: A method for the direct evaluation of buckling loads of an imperfect two-bar frame. Arch. Appl. Mech. 74(5–6), 299–308 (2005)MATHGoogle Scholar
  16. 16.
    Ioannidis, G.I., Raftoyiannis, I.G., Kounadis, A.N.: Imperfect frames exhibiting bifurcational instability. In: Proceedings of the 4th European Conf. on Steel & Composite Structures—Eurosteel 2005, June 8–10, vol. A, pp. 1.4_89–96. Maastricht, The Netherlands (2005)Google Scholar
  17. 17.
    Ioannidis, G.I., Raftoyiannis, I.G., Lignos, X.A.: Theoretical and codes buckling loads predictions of simple frames. In: Proceedings of the 7th National Congress on Mechanics, June 24–26, vol. I, pp. 275–280. Chania, Greece (2004)Google Scholar
  18. 18.
    Silvestre N., Camotim D.: Asymptotic-Numerical method to analyze the postbuckling behavior, imperfection sensitivity, and mode interaction in frames. J. Eng. Mech. ASCE 131(6), 617–632 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Civil EngineeringNational Technical University of AthensAthensGreece

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