Abstract
In this paper, the bending response of box-section beams of finite length is investigated by using energy methods. The basic assumptions used in the present study are that the total strain energy of a box-section beam subjected to uniformly distributed loading can be simplified into a two-stage analysis process. One is the local bending response of the webs and flanges behaving as plates; the other is the overall bending response of the beam with a deformed cross-section. Analytical solutions for both static and dynamic instabilities of box section beams of finite length subjected to transverse uniformly distributed loading are derived by applying the minimum potential energy principle. To validate the analytical solutions developed, geometric nonlinear finite element analyses are also conducted. Good agreement between the present solutions and the FEA results is demonstrated. Finally, the effects of beam length on the limit critical uniformly distributed load are also discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bedair, O. (2015). “Design expression for web shear buckling of box sections by accounting for flange restraints.” Journal of Constructional Steel Research, 110, pp. 163–169.
Brazier, L. G. (1927). “On the flexure of thin cylindrical shells and other thin sections.” Proceedings of the Royal Society, Series A, 116, pp. 104–114.
Hwang, W. S. Kim, Y. P. and Yoon, T. Y. (2009). “Central angle effect on connection behavior of steel box beam-tocircular column.” Structural Engineering and Mechanics, 32(4), pp. 531–547.
Jang, G. W. Choi, S. M. and Kim, Y. Y. (2013). “Analysis of Three Thin-Walled Box Beams Connected at a Joint under Out-of-Plane Bending Loads.” Journal of Engineering Mechanics, 139(10), pp. 1350–1361.
Kim, N. I. (2009). “Dynamic stiffness matrix of composite box beams.” Steel and Composite Structures, 9(5), pp. 473–497.
Kim, Y. and Kim, Y. Y. (2003). “Analysis of thin-walled curved box beam under in-plane flexure.” International Journal of Solids and Structures, 40(22), pp. 6111–6123.
Kotelko, M. Lim, T. H. and Rhodes, J. (2000). “Post-failure behaviour of box section beams under pure bending (an experimental study).” Thin Walled Structures, 38(2), pp. 179–194.
Lanc, D. Vo, T. P. Turkalj, G. and Lee, J. (2015). “Buckling analysis of thin-walled functionally graded sandwich box beams.” Thin Walled Structures, 86, pp. 148–156.
Li, H. F. and Luo, Y. F. (2015). “Experimental and numerical study on cyclic behavior of eccentrically-compressed steel box columns.” Thin Walled Structures, 96, pp. 269–285.
Li, L. Y. and Molyneaux, T. C. K. (1997). “Dynamic instability criteria for structures subjected to sudden step loads.” International Journal of Pressure Vessels and Piping, 70(2), pp. 121–126.
Li, L. Y. (1996). “Approximate estimates of dynamic instability of long circular cylindrical shells under pure bending.” International Journal of Pressure Vessels and Piping, 67(1), pp. 37–40.
Liu, Y. C. and Day, M. L. (2009). “Simplified modelling of thin-walled box section beam.” International Journal of Crashworthiness, 11(3), pp. 263–272.
Liu, Y. C.(2009). “Optimum design of straight thin-walled box section beams for crashworthiness analysis.” Finite Elements in Analysis and Design, 44(3), pp. 139–147.
Shen, H. X. (2015). “Behavior of high-strength steel welded rectangular section beam-columns with slender webs.” Thin Walled Structures, 88, pp. 16–27.
Simitses, G. J. (1987). “Instability of dynamically-loaded structures.” Applied Mechanics Reviews, 40(l0), pp. 1403–1408.
Vanegas, J. D. and Patino, I. D. (2013). “Linear and nonlinear finite element analysis of shear-corrected composites box beams.” Latin American Journal of Solids and Structures, 10(4), pp. 647–673.
Vo, T. P. and Lee, J. (2010). “Interaction curves for vibration and buckling of thin-walled composite box beams under axial loads and end moments.” Applied Mathematical Modelling, 34(10), pp. 3142–3157.
Vo, T. P. and Lee, J. (2009). “Geometrically nonlinear analysis of thin-walled composite box beams.” Computers & Structures, 87(3-4), pp. 236–245.
Wu, Y. P. Liu, S. Z, Zhu, Y. L. and Lai, Y. M. (2003). “Matrix analysis of shear lag and shear deformation in thin-walled box beams.” Journal of Engineering Mechanics, 129(8), pp. 944–950.
Yuan, H. X. Wang, Y. Q. Gardner L, and Shi YJ. (2015). “Local-overall interactive buckling of welded stainless steel box section compression members.” Engineering Structures, 67, pp. 62–76.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yuan, Wb., Bao, Zs., Yu, Nt. et al. Nonlinear bending of box section beams of finite length under uniformly distributed loading. Int J Steel Struct 17, 491–499 (2017). https://doi.org/10.1007/s13296-017-6009-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13296-017-6009-5