International journal of steel structures (국제강구조저널)

Korean Society of Steel Construction (한국강구조학회)
권호 표지
DOI QR코드

DOI QR Code

Analytical Solutions for the Inelastic Lateral-Torsional Buckling of I-Beams Under Pure Bending via Plate-Beam Theory

  • Zhang, Wenfu (School of Architecture Engineering, Nanjing Institute of Technology) ;
  • Gardner, Leroy (Department of Civil and Environmental Engineering, Imperial College London) ;
  • Wadee, M. Ahmer (Department of Civil and Environmental Engineering, Imperial College London) ;
  • Zhang, Minghao (School of Aeronautics, Northwestern Polytechnical University)
  • Received : 2018.01.07
  • Accepted : 2018.09.12
  • Published : 2018.11.30
⟨ Previous Next ⟩

Abstract

The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China, Scientific Research Foundation of Nanjing Institute of Technology

References

  1. ABAQUS. (2008). Standard user's manual (vols. 1, 2 and 3), Version 6.8-1. USA: Hibbitt, Karlsson and Sorensen, Inc.
  2. Alwis, W. A. M., & Wang, C. M. (1994). Should load remain constant when a thin-walled open profile column buckles? International Journal of Solids and Structures, 31(21), 2945-2950. https://doi.org/10.1016/0020-7683(94)90061-2
  3. Alwis, W. A. M., & Wang, C. M. (1996). Wagner term in flexural-torsional buckling of thin-walled open profile columns. Engineering Structures, 18(2), 125-132. https://doi.org/10.1016/0141-0296(95)00112-3
  4. ANSYS. (2006). Multiphysics, release 12. Canonsburg, PA: Ansys Inc.
  5. Bathe, K. J. (1996). Finite element procedures. NJ: Prentice Hall.
  6. Bleich, F. (1952). Buckling strength of metal structures. New York, NY: McGraw-Hill.
  7. Chen, J. (2011). Stability theory of steel structures and it application (6th ed.). Beijing: Science Press (in Chinese).
  8. Chen, W. F., & Atsuta, T. (1977). Theory of beam-columns. Space behaviour and design (Vol. 2). New York, NY: McGraw-Hill.
  9. EN 1993-1-5:2006. (2006). Eurocode 3: Design of steel structures -Part 1 - 5: Plated structural elements. Brussels: CEN-European committee for Standardization.
  10. Galambos, T. V. (1963). Inelastic lateral buckling of beams. ASCE Journal of the Structural Division, 89(ST5), 217-244.
  11. Gjelsvik, A. (1981). The theory of thin-walled bars. New York: Wiley.
  12. Gotoand, Y., & Chen, W. F. (1989). On the validity of Wagner hypothesis. International Journal of Solids and Structures, 25(6), 621-634. https://doi.org/10.1016/0020-7683(89)90029-2
  13. Hu, H. C. (1982). Variational principle of elasticity and its application. Beijing: Science Press (in Chinese).
  14. Jonsson, J., & Stan, T.-C. (2017). European column buckling curves and finite element modelling. Journal of Constructional Steel Research, 128, 136-151. https://doi.org/10.1016/j.jcsr.2016.08.013
  15. Kala, Z., & Vales, J. (2017). Global sensitivity analysis of lateraltorsional buckling resistance based on finite element simulations. Engineering Structures, 134, 37-47. https://doi.org/10.1016/j.engstruct.2016.12.032
  16. Kitipomchai, S., Wang, C. M., & Trahair, N. S. (1987). Closure of “Buckling of monosymmetric I-beams under moment gradient”. Journal of Structural Engineering ASCE, 113(6), 1391-1395. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:6(1391)
  17. Knag, Y. J., Lee, S. C., & Yoo, C. H. (1992). On the dispute concerning the validity of the Wagner hypothesis. Compurers & Slructures, 43(5), 853-861.
  18. Lu, L. W., Shen, S. Z., et al. (1983). Stability of steel structural members. Beijing: Publishing House of Chinese Construction Industry (in Chinese).
  19. Neal, B. G. (1950). The lateral instability of yielded mild steel beams of rectangular cross section. Philosophical Transactions of the Royal Society London, A242, 197-242.
  20. Ojalvo, M. (1981). Wagner hypothesis in beam and column theory. Engineering Mechanics Division ASCE, 107(4), 669-677.
  21. Ojalvo, M. (1987). Discussion on “Buckling of monosymmetric I-beams under moment gradient. Journal of Structural Engineering ASCE, 113(6), 1387-1391. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:6(1387)
  22. Ojalvo, M. (1989). The buckling of thin-walled open-profile bars. Journal of Applied Mechanics ASME, 56, 633-638. https://doi.org/10.1115/1.3176139
  23. Ojalvo, M. (1990). Thin-walled bars with open profiles. Columbus, OH: The Olive Press.
  24. Reddy, J. N. (1984). Energy principles and variational methods in applied mechanics. New York: Wiley.
  25. Reismann, H., & Pawlik, P. S. (1974). Elasticity: Theory and applications. New York: Pergamon.
  26. Timoshenko, S. P., & Gere, J. (1961). Theory of elastic stability (2nd ed.). New York, NY: McGraw-Hill.
  27. Timoshenko, S., & Woinowsky-Krieger, S. (2010). Theory of plates and shells. New York: Mc-Graw Hill.
  28. Tong, G. S. (2006). Out-plane stability of steel structures. Beijing:Publishing House of Chinese Construction Industry (in Chinese).
  29. Trahair, N. S. (1982). Discussion on “Wagner hypothesis in beam and column theory”. Journal of the Engineering Mechanics Division ASCE, 108(3), 575-578.
  30. Trahair, N. S. (1993). Flexural-torsional buckling of structures (1st ed.). London: Chapman & Hall.
  31. Trahair, N. S. (2012). Inelastic buckling design of monosymmetric I-beams. Engineering Structures, 34, 564-571. https://doi.org/10.1016/j.engstruct.2011.10.021
  32. Valentino, J., Piand, Y. L., & Trahair, N. S. (1997). Inelastic buckling of steel beams with central torsional restraints. Journal of Structural Engineering, 123(9), 1180-1186. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:9(1180)
  33. Vlasov, V. Z. (1961). Thin-walled elastic beams. Jerusalem: Israel Program for Scientific Translations.
  34. Washizu, K. (1968). Variational methods in elasticity and plasticity. Oxford: Pergamon Press.
  35. Zhang, W. F. (2014). Unified theory of free and restricted torsion for narrow rectangular plate, Sciencepaperonline. http://www.paper.edu.cn/html/releasepaper/2014/04/143/ (in Chinese).
  36. Zhang, W. F. (2015a). Plate - beam theory for thin - walled structures , Research Report. Daqing: Northeast Petroleum University (in Chinese).
  37. Zhang, W. F. (2015b). New engineering theory for torsional buckling of steel-concrete composite I-columns. In Proceedings of the 11th international conference on advances in steel and concrete composite structures (Vol. 12, pp. 225-232). Beijing, China.
  38. Zhang, W. F. (2015c). New theory of elastic torsional buckling for axial loaded box-shaped steel columns. In Proceedings of the 15th national symposium on modern structure engineering (pp. 793-804).
  39. Zhang, W. F. (2015d). Energy variational model and its analytical solutions for the elastic flexural-torsional buckling of I-beams with concrete-filled steel tubular flanges. In Proceedings of the 8th international symposium on steel structures (pp. 1100-1108). Jeju, Korea.
  40. Zhang, W. F. (2015e). New engineering theory for mixed torsion of steel-concrete-steel composite walls. In Proceedings of 11th international conference on advances in steel and concrete composite structures (Vol. 12, pp. 705-712). Beijing, China.
  41. Zhang, W. F. (2016). Combined torsion theory for castellated beams with rectangular openings based on continuous model. In Proceedings of the 6th national conference on steel structure engineering technology (Vol. 7, pp. 359-365). Nanjing, China (in Chinese).
  42. Zhang, W. F. (2018). Symmetric and antisymmetric lateral-torsional buckling of prestressed steel I-beams. Thin-Walled Structures, 122, 463-479. https://doi.org/10.1016/j.tws.2017.10.015
  43. Zhang, W. F., Liu, Y. C., Chen, K. S., et al. (2017). Dimensionless analytical solution and new design formula for lateral-torsional buckling of I-beams under linear distributed moment via linear stability theory. Mathematical Problems in Engineering, 2017, 1-23.
  44. Ziemian, R. D. (2010). Guide to stability design criteria for metal structures (6th ed.). NJ: Wiley.

Cited by

  1. Discussion of “Out-Plane Elastic-Plastic Buckling Strength of High-Strength Steel Arches” by Mark Andrew Bradford, Yong-Lin Pi, and Airong Liu vol.146, pp.2, 2018, https://doi.org/10.1061/(asce)st.1943-541x.0002495