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An alternative evaluation of the LTB behavior of mono-symmetric beam-columns

  • Yilmaz, Tolga (Department of Civil Engineering, Eskisehir Osmangazi University) ;
  • Kirac, Nevzat (Department of Civil Engineering, Eskisehir Osmangazi University) ;
  • Anil, O zgur (Department of Civil Engineering, Gazi University)
  • Received : 2018.01.04
  • Accepted : 2019.03.07
  • Published : 2019.03.10

Abstract

Beam-columns are structural members subjected to a combination of axial and bending forces. Lateral-torsional buckling is one of the main failure modes. Beam-columns that are bent about its strong axis may buckle out of the plane by deflecting laterally and twisting as the values of the applied loads reach a limiting state. Lateral-torsional buckling failure occurs suddenly in beam-column elements with a much greater in-plane bending stiffness than torsional or lateral bending stiffness. This study intends to establish a unique convenient closed-form equation that it can be used for calculating critical elastic lateral-torsional buckling load of beam-column in the presence of a known axial load. The presented equation includes first order bending distribution, the position of the loads acting transversely on the beam-column and mono-symmetry property of the section. Effects of axial loads, slenderness and load positions on lateral torsional buckling behavior of beam-columns are investigated. The proposed solutions are compared to finite element simulations where thin-walled shell elements including warping are used. Good agreement between the analytical and the numerical solutions is demonstrated. It is found out that the lateral-torsional buckling load of beam-columns with mono-symmetric sections can be determined by the presented equation and can be safely used in design procedures.

Keywords

References

  1. ABAQUS (2013), ABAQUS Theory Guide; Version 6.13.1.
  2. Adany, S. and Schafer, B.W. (2014), "Generalized Constrained Finite Strip Method for Thin-Walled Members with Arbitrary Cross Section: Primary Modes", Thin-Wall. Struct., 84, 150-159. https://doi.org/10.1016/j.tws.2014.06.001
  3. Andrade, A. and Camotim, D. (2004), "Lateral-torsional buckling of prismatic and tapered thin-walled open beams: Assessing the influence of pre-buckling deflections", Steel Compos. Struct., Int. J., 4(4), 281-301. https://doi.org/10.12989/scs.2004.4.4.281
  4. Andrade, A., Camotim, D. and Providencia e Costa, P. (2007), "On the evaluation of elastic critical moments in doubly and singly symmetric Isection cantilevers", J. Constr. Steel Res., 63, 894-908. https://doi.org/10.1016/j.jcsr.2006.08.015
  5. Asgarian, B., Soltani, M. and Mohri, F. (2013), "Lateral-torsional buckling of tapered thin-walled beams with arbitrary crosssections", Thin-Wall. Struct., 62, 96-108. https://doi.org/10.1016/j.tws.2012.06.007
  6. Assadi, M. and Roeder, C.W. (1985), "Stability of Continuously Restrained Cantilevers", J. Eng. Mech., 111(12), 1440-1456. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:12(1440)
  7. Aydin, R., Ozbasaran, H., Kirac, N. and Gunaydin, A. (2013), "Lateral Torsional Buckling of Double Angle and Tee Cantilevers: A Parametric Study", Proceedings of the Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing, Civil-Comp Press, Stirlingshire, Scotland.
  8. Aydin, R., Gunaydin, A. and Kirac, N. (2015), "On the Evaluation of Critical Lateral Buckling Loads of Prismatic Steel Beams", Steel Compos. Struct., Int. J., 18(3), 603-621. https://doi.org/10.12989/scs.2015.18.3.603
  9. 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. https://doi.org/10.1002/nme.1620020304
  10. Benyamina, A.B, Meftah, S.A., Mohri, F. and Daya, E.M. (2013), "Analytical solutions attempt for lateral torsional buckling of doubly symmetricweb-tapered I-beams", Thin-Wall. Struct., 56, 1207-1219.
  11. Bleich, F. (1952), Buckling Strength of Metal Structures, McGraw Hill, New York, NY, USA.
  12. Bradford, M.A. and Ronagh, H.R. (1997), "Generalized Elastic Buckling of Restrained I-Beams by FEM", ASCE J. Struct. Eng., 123(12), 1631-1637. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:12(1631)
  13. Bui, H.C. (2009), "Buckling Analysis of Thin-Walled Sections Under General Loading Conditions", Thin-Wall. Struct., 47(6), 730-739. https://doi.org/10.1016/j.tws.2008.12.003
  14. Bui, H.C. (2012), "Semi-Analytical Finite Strip Method Based on The Shallow Shell Theory in Buckling Analysis of Cold- Formed Sections", Thin-Wall. Struct., 50(1), 141-146. https://doi.org/10.1016/j.tws.2011.09.005
  15. Chajes, A. (1974), Principles of Structural Stability Theory, Prentice-Hall, Englewood Cliffs, NJ, USA.
  16. Challamel, N., Andrade, A., Camotim, D. and Milisavlevich, B.M. (2010), "Flexural-torsional buckling of cantilever strip beamcolumns with linearly varying depth", J. Eng. Mech., 136, 787-800. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000121
  17. Chen, W.F. and Atsuta, T. (1977), Theory of Beam-Columns: Space Behavior and Design, (Volume 2), McGraw-Hill, New York, NY, USA.
  18. Chen, W.F. and Lui, E.M. (1987), Structural Stability: Theory and Implementation, Elsevier Science Publishing Co. Inc., New York, NY, USA.
  19. Cheng, S., Kim, B. and Li, L. (2013), "Lateral-torsional buckling of cold-formed channel sections subject to combined compression and bending", J. Constr. Steel Res., 80, 174-180. https://doi.org/10.1016/j.jcsr.2012.07.026
  20. Galambos, T.V. and Surovek, A.E. (2008), Structural Stability of Steel: Concepts and Application for Structural Engineers, John Wiley and Sons.
  21. Gu, J.X. and Chan, S.L. (2005), "A Refined Finite Element Formulation for Flexural and Torsional Buckling of Beam-Columns with Finite Rotations", Eng. Struct., 27(5), 749-759. https://doi.org/10.1016/j.engstruct.2004.12.011
  22. Hancock, G.J. and Trahair, N.S. (1978), "Finite Element Analysis of Lateral Buckling of Continuously Restrained Beam-Columns", Civil Eng. Trans. Inst. Eng., Australia, CE20(2), 120-127.
  23. Hill, H.N. and Clark, J.W. (1951), "Lateral buckling of eccentrically loaded I-section columns", Transcations of the ASCE, 116, pp. 1179.
  24. Kim, B., Li, L. and Edmonds, A. (2016), "Analytical Solutions of Lateral-Torsional Buckling of Castellated Beams", Int. J. Struct. Stabil. Dyn., 16, 155044.
  25. Kitipornchai, S. and Richter, N.J. (1978), "Elastic Lateral Buckling of I-Beams with Discrete Intermediate Restraints", Civil Eng. Trans., 20(2), 105-111.
  26. Kitipornchai, S. and Trahair, N.S. (1975), "Buckling of Inelastic IBeams under Moment Gradient", J. Struct. Div., ASCE, 101(5), 991-1004. https://doi.org/10.1061/JSDEAG.0004071
  27. Kitipornchai, S., Dux, P.F. and Richter, N.J. (1984), "Buckling and Bracing of Cantilevers", J. Struct. Div., ASCE, 110(9), 2250-2262. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:9(2250)
  28. Kitipornchai, S., Wang, C.M. and Trhair, N.S. (1986), "Buckling of Monosymmetric I Beams under Moment Gradient", J. Struct. Eng., ASCE, 112(4), 781-799. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:4(781)
  29. Kucukler, M., Gardner, L. and Macorini, L. (2015), "Flexural-torsional buckling assessment of steel beam-columns through a stiffness reduction method", Eng. Struct., 101, 662-676. https://doi.org/10.1016/j.engstruct.2015.07.041
  30. Kus, J. (2015), "Lateral-torsional buckling steel beams with simultaneously tapered flanges and web", Steel Compos. Struct., Int. J., 19(4), 897-916. https://doi.org/10.12989/scs.2015.19.4.897
  31. Lee, H., Jung, D.W., Jeong, J.H. and Im, S. (1994), "Finite Element Analysis of Lateral Buckling for Beam Structures", Comput. Struct., 53(6), 1357-1371. https://doi.org/10.1016/0045-7949(94)90400-6
  32. Lim, N.H., Park, N.H., Kang, Y.J. and Sung, I.H. (2003) "Elastic Buckling of I-Beams under Linear Moment Gradient", Int. J. Solids Struct., 40(21), 5635-5647. https://doi.org/10.1016/S0020-7683(03)00330-5
  33. Magnucka-Blandzi, E. (2009), "Critical State of a Thin-walled beam under combined load", Appl. Math. Model., 33(7), 3093-3098. https://doi.org/10.1016/j.apm.2008.10.014
  34. Mohammadi, E., Hosseini, S.S. and Rohanimanesh, S.M. (2016), "Elastic lateral-torsional buckling strength and torsional bracing stiffness requirement for monosymmetric I-beams", Thin-Wall. Struct., 104, 116-125. https://doi.org/10.1016/j.tws.2016.03.003
  35. Mohri, F., Brouki, A. and Roth, J.C. (2003), "Theoretical and Numerical Stability Analyses of Unrestrained, Mono-Symmetric Thin-Walled Beams", J. Constr. Steel Res., 59(1), 63-90. https://doi.org/10.1016/S0143-974X(02)00007-X
  36. Mohri, F., Eddinari, A., Damil, N. and Potier-Ferry, M. (2008a), "A Beam Finite Element for Non-linear Analyses of Thin-Walled Elements", Thin-Wall. Struct., 46(7), 981-990. https://doi.org/10.1016/j.tws.2008.01.028
  37. Mohri, F., Bouzerira, C. and Potier-Ferry, M. (2008b), "Lateral buckling of thin-walled beam-column elements under combined axial and bending loads", Thin-Wall. Struct., 46(3), 290-302. https://doi.org/10.1016/j.tws.2007.07.017
  38. Mohri, F., Damil, N. and Potier-Ferry, M. (2013), "Buckling and lateral buckling interaction in thin-walled beam-column elements with mono-symmetric cross sections", Appl. Math. Model., 37(5), 3526-3540. https://doi.org/10.1016/j.apm.2012.07.053
  39. Naderian, H.R. and Ronagh, H.R. (2015), "Buckling Analysis of Thin-Walled Cold-Formed Steel Structural Members Using Complex Finite Strip Method", Thin-Wall. Struct., 90, 74-83. https://doi.org/10.1016/j.tws.2015.01.008
  40. Osmani, A. and Meftah, S.A. (2018), "Lateral buckling of tapered thin walled bi-symmetric beams under combined axial and bending loads with shear deformations allowed", Eng. Struct., 165(3), 76-87. https://doi.org/10.1016/j.engstruct.2018.03.009
  41. Ozbasaran, H. (2018), "Optimal design of I-section beam-columns with stress, non-linear deflection and stability constraints", Eng. Struct., 171(February), 385-394. https://doi.org/10.1016/j.engstruct.2018.05.110
  42. Ozbasaran, H. and Yilmaz, T. (2018), "Shape optimization of tapered I-beams with lateral-torsional buckling, deflection and stress constraints", J. Constr. Steel Res., 143, 119-130. https://doi.org/10.1016/j.jcsr.2017.12.022
  43. Ozbasaran, H., Aydin, R. and Dogan, M. (2015), "An Alternative Design Procedure for Lateral-Torsional Buckling of Cantilever I-Beams", Thin-Wall. Struct., 90, 235-242. https://doi.org/10.1016/j.tws.2015.01.021
  44. Papangelis, J.P., Trahair, N.S. and Hancock, G.L. (1998), "Elastic Flexural-Torsional Buckling of Structures by Computer", Comput. Struct., 68(13), 125-137. https://doi.org/10.1016/S0045-7949(98)00037-6
  45. Park, J.S., Stallings, J.M. and Kang, Y.J. (2004), "Lateral-Torsional Buckling of Prismatic Beams with Continuous Top-Flange Bracing", J. Constr. Steel Res., 60(2), 147-160. https://doi.org/10.1016/j.jcsr.2003.08.013
  46. Powell, G and Klingner, R. (1970), "Elastic Lateral Buckling of Steel Beams", ASCE J. Struct. Div., 96(9), 1919-1932. https://doi.org/10.1061/JSDEAG.0002692
  47. Salvadori, M.G. (1956), "Lateral buckling of eccentrically loaded I columns", Transcations of the ASCE, 121, 1163-1178.
  48. Serna, M.A., Lopez, A., Puente, I. and Yong, D.J. (2006), "Equivalent Uniform Moment Factors for Lateral-Torsional Buckling of Steel Members", J. Constr. Steel Res., 62(6), 566-580. https://doi.org/10.1016/j.jcsr.2005.09.001
  49. Soula, A., Meftah, S.A., Mohri, F. and Daya, E.M. (2016), "Lateral buckling of box beam elements under combined axial and bending loads", J. Constr. Steel Res., 116, 141-155. https://doi.org/10.1016/j.jcsr.2015.09.009
  50. Suryoatmono, B. and Ho, D. (2002), "The Moment-Gradient Factor in Lateral-Torsional Buckling on Wide Flange Steel Sections", J. Constr. Steel Res., 58(9), 1247-1264. https://doi.org/10.1016/S0143-974X(01)00061-X
  51. Tankova, T., Marques, L., Andrade, A. and Simoes da Silva, L. (2017), "A consistent methodology for the out-of-plane buckling resistance of prismatic steel beam-columns", J. Constr. Steel Res., 128, 839-852. https://doi.org/10.1016/j.jcsr.2016.10.009
  52. Thai, H.T., Kim, S.E. and Kim, J. (2017), "Improved refined plastic hinge analysis accounting for local buckling and lateraltorsional buckling", Steel Compos. Struct., Int. J., 24(3), 339-349.
  53. Timoshenko, S.P and Gere, J.M. (1961), Theory of Elastic Stability, (2nd Ed.), McGraw-Hill, New York, NY, USA.
  54. Torkamani, M.A.M. and Roberts, E.R. (2009), "Energy Equations for Elastic Flexural-Torsional Buckling Analysis of Plane Structures", Thin-Wall. Struct., 47(4), -463-473. https://doi.org/10.1016/j.tws.2008.06.006
  55. Trahair, N.S. (1993), Flexural-Torsional Buckling of Structures, CRC Press, London, UK.
  56. Wang, C.M. and Kitipornchai S. (1986), "On Stability of Monosymmetric Cantilevers", Eng. Struct., 8, 168-180.
  57. Wang, C.M. and Kitipornchai, S. (1989), "New set of buckling parameters for monosymmetric beam-columns/tie-beams", J. Struct. Eng., 115(6), 1497-1513. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:6(1497)
  58. Yilmaz, T. and Kirac, N. (2017), "Analytical and parametric investigations on lateral torsional buckling of European IPE and IPN beams", Int. J. Steel Struct., 17(2), 695-709. https://doi.org/10.1007/s13296-017-6024-6
  59. Yilmaz, T., Kirac, N. and Kilic, T. (2017), "Lateral-Torsional Buckling of European Wide Flange I-Section Beams", Proceedings of the 2nd World Congress on Civil, Structural and Environmental Engineering (CSEE'17), Barcelona, Spain, April.
  60. Yuan, W., Kim, B. and Chen, C. (2013), "Lateral-torsional buckling of steel web tapered tee-section cantilevers", J. Constr. Steel Res., 87, 31-37. https://doi.org/10.1016/j.jcsr.2013.03.026
  61. Zhang, L. and Tong, G. (2016), "Lateral buckling of simply supported C- and Z-section purlins with top flange horizontally restrained", Thin-Wall. Struct., 99, 155-167. https://doi.org/10.1016/j.tws.2015.11.019