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Lateral-torsional buckling of prismatic and tapered thin-walled open beams: assessing the influence of pre-buckling deflections

  • Andrade, A. (Department of Civil Engineering, FCT, University of Coimbra) ;
  • Camotim, D. (Department of Civil Engineering, ICIS/IST, Technical University of Lisbon)
  • 투고 : 2004.03.24
  • 심사 : 2004.07.27
  • 발행 : 2004.08.25

초록

The paper begins by presenting a unified variational approach to the lateral-torsional buckling (LTB) analysis of doubly symmetric prismatic and tapered thin-walled beams with open cross-sections, which accounts for the influence of the pre-buckling deflections. This approach (i) extends the kinematical assumptions usually adopted for prismatic beams, (ii) consistently uses shell membrane theory in general coordinates and (iii) adopts Trefftz's criterion to perform the bifurcation analysis. The proposed formulation is then applied to investigate the influence of the pre-buckling deflections on the LTB behaviour of prismatic and web-tapered I-section simply supported beams and cantilevers. After establishing an interesting analytical result, valid for prismatic members with shear centre loading, several elastic critical moments/loads are presented, discussed and, when possible, also compared with values reported in the literature. These numerical results, which are obtained by means of the Rayleigh-Ritz method, (i) highlight the qualitative differences existing between the LTB behaviours of simply supported beams and cantilevers and (ii) illustrate how the influence of the pre-buckling deflections on LTB is affected by a number of factors, namely ($ii_1$) the minor-to-major inertia ratio, ($ii_2$) the beam length, ($ii_3$) the location of the load point of application and ($ii_4$) the bending moment diagram shape.

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참고문헌

  1. Achour, B. and Roberts, T.M. (2000),"Non-linear strains and instability of thin-walled bars", J. Const. Steel Res., 56(3), 237-252. https://doi.org/10.1016/S0143-974X(99)00072-3
  2. Andrade, A. (2003),"Lateral-torsional buckling of tapered beams", M.A.Sc. Thesis (Structural Engineering), Civil Eng. Dept., IST/TU Lisbon. (in Portuguese)
  3. Andrade, A. and Camotim, D. (2002),"Lateral-torsional stability behaviour of arbitrary singly symmetric tapered steel beams: a variational formulation", Procs. of Third European Conference on Steel Structures (EUROSTEEL'02 - Coimbra, 19-20/9), A. Lamas, L.S. Silva (eds.), 107-118 (vol. 1).
  4. Andrade, A. and Camotim, D. (2003),"Lateral-torsional buckling of singly symmetric tapered beams: theory and applications", J. Eng. Mech. (ASCE), accepted for publication.
  5. Attard, M. (1986a),"Non-linear theory of non-uniform torsion of thin-walled open beams", Thin-Walled Structures, 4(2), 101-134.
  6. Attard, M. (1986b),"Lateral buckling analysis of beams by the FEM", Comput. Struct., 23(2), 217-232. https://doi.org/10.1016/0045-7949(86)90214-2
  7. Baker, J.F., Horne, M.R. and Heyman, J. (1956), The Steel Skeleton (Vol. 2), Cambridge University Press, Cambridge.
  8. Bazant, Z.P. and Cedolin, L. (1991), Stability of Structures - Elastic, Inelastic, Fracture and Damage Theories, Oxford University Press, New York.
  9. Boissonnade, N. and Muzeau, J.P. (2001),"New beam finite element for tapered members", Procs. 8th Int. Conference on Civil and Structural Engineering Computing (Vienna, 19-21/9), B. Topping (ed.), Civil-Comp Press, 73-74. (CD-ROM paper #27).
  10. Ciarlet, P.G. (1988), Mathematical Elasticity (Vol. 1: Three-Dimensional Elasticity), Studies in Mathematics and its Applications 20, Elsevier Science Publishers B. V., Amsterdam.
  11. Clark, J.W. and Knoll, A.H. (1958),"Effect of deflection on lateral buckling strength", J. Eng. Mech., (ASCE), 84(2), Paper 1596, 1-18.
  12. Comite Europeen de Normalisation (1992), Eurocode 3: Design of Steel Structures, Part 1-1: General Rules and Rules for Buildings (ENV 1993-1-1), Brussels.
  13. Courant, R. and Hilbert, D. (1953), Methods of Mathematical Physics (Vol. 1), Interscience Publishers, New York.
  14. Davidson, J.F. (1952),"The elastic stability of bent I-section beams", Proceedings of the Royal Society of London, 212A, 80-95.
  15. Green, A.E. and Zerna, W. (1968), Theoretical Elasticity, Oxford University Press, London.
  16. Michell, A.G. (1899),"Elastic stability of long beams under transverse forces", The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, 48, 5th Series, 298-309. https://doi.org/10.1080/14786449908621336
  17. Mohri, F., Azrar, L. and Potier-Ferry, M. (2002),"Lateral post-buckling analysis of thin-walled open section beams", Thin-Walled Structures, 40(12), 1013-1036. https://doi.org/10.1016/S0263-8231(02)00043-5
  18. Mollmann, H. (1986),"Theory of thin-walled elastic beams with finite displacements", Finite Rotations in Structural Mechanics - Euromech Colloquium 197 (Jablonna, 1985), W. Pietraszkiewics (ed.), Springer-Verlag, Berlin, 195-209.
  19. Pettersson, O. (1952),"Combined bending and torsion of beams of monosymmetrical cross-section", Bulletin N. 10, Division of Building Statics and Structural Engineering, Royal Institute of Technology, Stockholm.
  20. Pi, Y.L. and Trahair, N.S. (1992a),"Prebuckling deflections and lateral buckling. Part I: Theory", J. Struct. Eng., (ASCE), 118(11), 2949-2966. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:11(2949)
  21. Pi, Y.L. and Trahair, N.S. (1992b),"Prebuckling deflections and lateral buckling. Part II: Applications", J. Struct. Eng., (ASCE), 118(11), 2967-2985. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:11(2967)
  22. Rajasekaran, S. (1994),"Equations for tapered thin-walled beams of generic open section", J. Eng. Mech., (ASCE), 120(8), 1607-1629. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:8(1607)
  23. Reis, A.J. and Camotim, D. (2001), Structural Stability, McGraw-Hill, Lisbon. (in Portuguese)
  24. Roberts, T.M. (1981),"Second order strains and instability of thin-walled bars of open cross-section", Int. J. Mech. Sciences, 23(5), 297-306. https://doi.org/10.1016/0020-7403(81)90033-3
  25. Roberts, T.M. and Azizian, Z.G. (1983),"Influence of pre-buckling displacements on the elastic critical loads of thin-walled bars of open cross-section", Int. J. Mech. Sciences, 25(2), 93-104. https://doi.org/10.1016/0020-7403(83)90003-6
  26. Roberts, T.M. and Burt, C.A. (1985),"Instability of monosymmetric I-beams and cantilevers", Int. J. Mech. Sciences, 27(5), 313-324. https://doi.org/10.1016/0020-7403(85)90021-9
  27. Ronagh, H.R. and Bradford, M.A. (1999),"Non-linear analysis of thin-walled members of open cross-section", Int. J. Numer. Methods Eng., 46(4), 535-552. https://doi.org/10.1002/(SICI)1097-0207(19991010)46:4<535::AID-NME686>3.0.CO;2-Q
  28. Ronagh, H., Bradford, M. and Attard, M. (2000a),"Nonlinear analysis of thin-walled members of variable crosssection. Part I: Theory", Comput. Struct., 77(3), 285-299. https://doi.org/10.1016/S0045-7949(99)00223-0
  29. Ronagh, H., Bradford, M. and Attard, M. (2000b),"Nonlinear analysis of thin-walled members of variable crosssection. Part II: Application", Comput. Struct., 77(3), 301-313. https://doi.org/10.1016/S0045-7949(99)00224-2
  30. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability, McGraw-Hill, New York.
  31. Trahair, N.S (1993), Flexural-Torsional Buckling of Structures, E & FN Spon (Chapman & Hall), London.
  32. Trahair, N.S. and Woolcock, S.T. (1973),"Effect of major axis curvature on I-beam stability", J. Eng. Mech., (ASCE), 99(1), 85-98.
  33. Vacharajittiphan, P., Woolcock, S. and Trahair, N.S. (1974),"Effect of in-plane deformation on lateral buckling", J. Struct. Eng., (ASCE), 3(1), 29-60.
  34. Van Erp, G.M., Menken, C.M. and Veldpaus, F.E. (1988),"The non-linear flexural-torsional behaviour of straight slender elastic beams with arbitrary cross sections", Thin-Walled Structures, 6(5), 385-404. https://doi.org/10.1016/0263-8231(88)90019-5
  35. Ville de Goyet, V. (1989),"Non-linear finite element static analysis of 3D structures formed by members with non-symmetric cross-sections", Ph.D. Thesis, University of Liege. (in French)
  36. Vlassov, B. (1961), Thin-Walled Elastic Bars, Israel Program for Scientific Translations, Jerusalem.
  37. Wilde, P. (1968),"The torsion of thin-walled bars with variable cross-section", Archiwum Mechaniki Stosowanej, 4(20), 431-443.
  38. Yang, Y.B. and Yau, J.D. (1987),"Stability of beams with tapered I-sections", J. Eng. Mech., (ASCE), 113(9), 1337-1357. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:9(1337)

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