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Analytical study of elastic lateral-torsional buckling of castellated steel beams under combined axial and bending loads

  • Saoula Abdelkader (Department of Civil Engineering, University of Ibn Khaldoun) ;
  • Abdelrahmane B. Benyamina (Department of Civil Engineering, University of Ibn Khaldoun) ;
  • Meftah Sid Ahmed (Laboratoire des Structures et Matériaux Avances dans le Genie Civil et Travaux Publics, Universite Djillali Liabes)
  • Received : 2023.10.13
  • Accepted : 2024.07.24
  • Published : 2024.08.10
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Abstract

This paper presents an analytical solution for correctly predicting the Lateral-Torsional Buckling critical moment of simply supported castellated beams, the solution covers uniformly distributed loads combined with compressive loads. For this purpose, the castellated beam section with hexagonal-type perforation is treated as an arrangement of double "T" sections, composed of an upper T section and a lower T section. The castellated beam with regular openings is considered as a periodic repeating structure of unit cells. According to the kinematic model, the energy principle is applied in the context of geometric nonlinearity and the linear elastic behavior of materials. The differential equilibrium equations are established using Galerkin's method and the tangential stiffness matrix is calculated to determine the critical lateral torsional buckling loads. A Finite Element simulation using ABAQUS software is performed to verify the accuracy of the suggested analytical solution, each castellated beam is modelled with appropriate sizes meshes by thin shell elements S8R, the chosen element has 8 nodes and six degrees of freedom per node, including five integration points through the thickness, the Lanczos eigen-solver of ABAQUS was used to conduct elastic buckling analysis. It has been demonstrated that the proposed analytical solution results are in good agreement with those of the finite element method. A parametric study involving geometric and mechanical parameters is carried out, the intensity of the compressive load is also included. In comparison with the linear solution, it has been found that the linear stability underestimates the lateral buckling resistance. It has been confirmed that when high axial loads are applied, an impressive reduction in critical loads has been observed. It can be concluded that the obtained analytical solution is efficient and simple, and offers a rapid and direct method for estimating the lateral torsional buckling critical moment of simply supported castellated beams.

Keywords

References

  1. ABAQUS ver. 6.13 (2013), ABAQUS Standard User's Manual, Hibbit, Karlsson and Sorensen Inc. Pawtucket, RI, USA.
  2. Aydin, R., Gunaydin, A. and Kirac, N. (2015), "On the evaluation of critical lateral buckling loads of prismatic steel beams", Steel Compos. Struct., 18(3), 603-621. https://doi.org/10.12989/scs.2015.18.3.603.
  3. Benyamina, A.B., Meftah S.A., Mohri F. and Daya E.M. (2013), "Analytical solutions attempt for lateral torsional buckling of doubly symmetric web-tapered I-beams", Eng. Struct., 56, 1207-1219. https://doi.org/10.1016/j.engstruct.2013.06.036.
  4. Blodgett, O. (1996), Design of Welded Structures, Lincoln Arc Welding Foundation, Cleveland, OH.
  5. Braga, J.J.V., Linhares, D.A., Cardoso, D.C.T. and Sotelino, E.D. (2021), "Failure mode and strength prediction of laterally braced Litzka-type castellated beams", J. Construct. Steel Res., 184, 106796. https://doi.org/10.1016/j.jcsr.2021.106796.
  6. Carvalho, A.S., Rossi, A. and Martins, C.H. (2022), "Assessment of lateral-torsional buckling in steel I-beams with sinusoidal web openings", Thin-Wall. Struct., 175. https://doi.org/10.1016/j.tws.2022.109242.
  7. Ellobody, E. (2011), "Interaction of buckling modes in castellated steel beams", J. Construct. Steel Res., 67(5), 814-825. https://doi.org/10.1016/j.jcsr.2010.12.012.
  8. Kerdal, D. and Nethercot, D.A. (1984), "Failure modes for castellated beams", J. Construct. Steel Res., 4(4), 295-315. https://doi.org/10.1016/0143-974X(84)90004-X.
  9. Kim, B., Li, L.-Y. and Edmonds, A. (2016), "Analytical solutions of lateral-torsional buckling of castellated beams", Int, J. Struct. Stab. Dyn., 16(08), 1550044. https://doi.org/10.1142/S0219455415500443.
  10. Luo, C., Wang, F., Chen, H., Chen, L., Fu, C., Chen, Y. and Liao, Q. (2022), "Castellated steel beams under impact load", J. Construct. Steel Res., 196, 107394. https://doi.org/10.1016/j.jcsr.2022.107394.
  11. Mohebkhah, A. and Azandariani, M.G. (2020), "Shear resistance of retrofitted castellated link beams: Numerical and limit analysis approaches", Eng. Struct., 203. https://doi.org/10.1016/j.engstruct.2019.109864.
  12. 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. Mathem. Modelling, 37(5), 3526-3540. https://doi.org/10.1016/j.apm.2012.07.053.
  13. Morkhade, S. (2017), "Experimental investigation for failure analysis of steel beams with web openings", Steel Compos. Struct., 23, 647-656. https://doi.org/10.12989/scs.2017.23.6.647.
  14. Saoula, A., Meftah, S.A., Mohri, F. and Daya, E.M. (2016), "Lateral buckling of box beam elements under combined axial and bending loads", J. Construct. Steel Res., 116. https://doi.org/10.1016/j.jcsr.2015.09.009.
  15. Saoula, A., Selim, M.M., Meftah, S.A., Benyamina, A.B. and Tounsi, A. (2021), "Simplified analytical method for lateral torsional buckling assessment of RHS beams with web openings", J. Struct., 34, 2848-2860. https://doi.org/10.1016/j.istruc.2021.09.034.
  16. Soltani, M., Asgarian, B. and Mohri, F. (2014), "Elastic instability and free vibration analyses of tapered thin-walled beams by the power series method", J. Construct. Steel Res., 96. https://doi.org/10.1016/j.jcsr.2013.11.001.
  17. Soltani, M.R., Bouchair, A. and Mimoune, M. (2012), "Nonlinear FE analysis of the ultimate behavior of steel castellated beams", J. Construct. Steel Res., 70. https://doi.org/10.1016/j.jcsr.2011.10.016.
  18. Sonck, D. and Belis, J. (2017), "Lateral-torsional buckling resistance of castellated beams", J. Struct. Eng., 143(3). https://doi.org/10.1061/(asce)st.1943-541x.0001690.
  19. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability, McGraw-Hill Book Company, New York, 1961.
  20. Vlasov, V.Z. (1959), Thin-Walled Elastic Beams, Moscow, (French translation: Pieces Longues en Voiles Minces), Eyrolles, Paris,
  21. Wang, P., Wang, X. and Ma, N. (2014), "Vertical shear buckling capacity of web-posts in castellated steel beams with fillet corner hexagonal web openings", Eng. Struct., 75. https://doi.org/10.1016/j.engstruct.2014.06.019.
  22. Yoo, C.H. and Lee, S. (2011), Stability of Structures: Principles and Applications, Elsevier.
  23. Yost, J.R., Dinehart, D.W., Hoffman, R.M., Gross, S.P. and Callow, M. (2012), "Experimental and analytical investigation of service-load stresses in cellular beams", J. Eng. Mech., 138(8), 953-962. https://doi.org/10.1061/(asce)em.1943-7889.0000405.
  24. Zhou, X., Li, J., He, Y., He, Z. and Li, Z. (2018), "Finite element analysis of thermal residual stresses in castellated beams", J. Construct. Steel Res., 148, 741-755. https://doi.org/10.1016/j.jcsr.2018.06.026.
  25. Ziane, N., Meftah, S.A., Ruta, G., Tounsi, A. and Adda Bedia, E.A. (2015), "Investigation of the instability of FGM box beams", Struct. Eng. Mech., 54(3), 579-595. https://doi.org/10.12989/sem.2015.54.3.579.
  26. Zirakian, T. and Showkati, H. (2006), "Distortional buckling of castellated beams", J. Construct. Steel Res., 62(9). https://doi.org/10.1016/j.jcsr.2006.01.004.
  27. Zirakian, T. and Showkati, H. (2007), "Experiments on distortional buckling of I-beams", J. Struct. Eng., 133(7). https://doi.org/10.1061/(asce)0733-9445(2007)133:7(1009).