Elastic Bifurcation, Postbuckling Behavior, and Collapse of Thin-Walled Regular Polygonal Columns
Publication: Journal of Engineering Mechanics
Volume 149, Issue 1
Abstract
This paper summarizes recent findings concerning the elastic bifurcation and postbuckling behaviors of thin-walled regular convex polygonal tubes subjected to uniform compression. Such cross sections exhibit rotational symmetry, a feature that is at the root of several behavioral peculiarities, which are demonstrated using a specialization of Generalized Beam Theory (GBT). In particular, it is shown that (1) duplicate bifurcation loads can occur both in linear stability analyses and postbuckling analyses; (2) local or distortional buckling can be critical, depending on the cross-section geometry; (3) the pure local postbuckling behavior is very similar to that of simply supported plates under uniaxial compression; (4) the pure distortional postbuckling behavior has no postcritical strength and is imperfection-sensitive; and (5) the unstable nature of distortional buckling generates an unstable local-distortional interaction even if the distortional critical load is well above the local one. For comparison and validation purposes, results obtained with finite strips and shell finite-element models are reported.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. In particular, all the buckling and postbuckling results displayed in the paper figures can be provided.
Acknowledgments
The first and third authors are grateful for the FCT (Portugal Foundation for Science and Technology) support through funding UIDB/ 627 to the research unit CERIS.
References
Avent, R., and J. Robinson. 1976. “Elastic stability of polygon folded plate columns.” J. Struct. Div. 102 (5): 1015–1029. https://doi.org/10.1061/JSDEAG.0004326.
Bebiano, R., D. Camotim, and R. Gonçalves. 2018. “GBTul 2.0—A second-generation code for the GBT-based buckling and vibration analysis of thin-walled members.” Thin-Walled Struct. 124 (Dec): 235–257. https://doi.org/10.1016/j.tws.2017.12.002.
Bebiano, R., R. Gonçalves, and D. Camotim. 2015. “A cross-section analysis procedure to rationalise and automate the performance of GBT-based structural analyses.” Thin-Walled Struct. 92 (5): 29–47. https://doi.org/10.1016/j.tws.2015.02.017.
Bulson, P. 1969. “The strength of thin-walled tubes formed from flat elements.” Int. J. Mech. Sci. 11 (7): 613–620. https://doi.org/10.1016/0020-7403(69)90060-5.
Chen, J., H. Fang, and T. Chan. 2021. “Design of fixed-ended octagonal shaped steel hollow sections in compression.” Eng. Struct. 228 (12): 111520. https://doi.org/10.1016/j.engstruct.2020.111520.
Davis, P. 1979. Circulant matrices. New York: Wiley.
GBTUL (Generalized Bean Theory at the University of Lisbon). 2022. “About GBTUL.” Accessed September 21, 2022. http://www.civil.ist.utl.pt/gbt/.
Godat, A., F. Legeron, and D. Bazonga. 2012. “Stability investigation of local buckling behavior of tubular polygon columns under concentric compression.” Thin-Walled Struct. 53 (Mar): 131–140. https://doi.org/10.1016/j.tws.2011.12.013.
Gonçalves, R., and D. Camotim. 2011. “Generalised beam theory-based finite elements for elastoplastic thin-walled metal members.” Thin-Walled Struct. 49 (10): 1237–1245. https://doi.org/10.1016/j.tws.2011.05.011.
Gonçalves, R., and D. Camotim. 2013a. “Buckling behaviour of thin-walled regular polygonal tubes subjected to bending or torsion.” Thin-Walled Struct. 73 (Aug): 185–197. https://doi.org/10.1016/j.tws.2013.08.006.
Gonçalves, R., and D. Camotim. 2013b. “Elastic buckling of uniformly compressed thin-walled regular polygonal tubes.” Thin-Walled Struct. 71 (Oct): 35–45. https://doi.org/10.1016/j.tws.2013.04.016.
Gonçalves, R., and D. Camotim. 2013c. “On the behaviour of thin-walled steel regular polygonal tubular members.” Thin-Walled Struct. 62 (10): 191–205. https://doi.org/10.1016/j.tws.2012.08.006.
Gonçalves, R., and D. Camotim. 2014. “The vibration behaviour of thin-walled regular polygonal tubes.” Thin-Walled Struct. 84 (Nov): 177–188. https://doi.org/10.1016/j.tws.2014.06.011.
Gonçalves, R., P. Le Grognec, and D. Camotim. 2010a. “GBT-based semi-analytical solutions for the plastic bifurcation of thin-walled members.” Int. J. Solids Struct. 47 (1): 34–50. https://doi.org/10.1016/j.ijsolstr.2009.09.013.
Gonçalves, R., M. Ritto-Corrêa, and D. Camotim. 2010b. “A new approach to the calculation of cross-section deformation modes in the framework of generalized beam theory.” Comput. Mech. 46 (5): 759–781. https://doi.org/10.1007/s00466-010-0512-2.
Liu, H.-X., H. Fang, J.-Y. Zhu, and T.-M. Chan. 2021. “Numerical investigation on the structural performance of octagonal hollow section columns.” Structures 34 (Dec): 3257–3267. https://doi.org/10.1016/j.istruc.2021.09.056.
Martins, A. D., D. Camotim, R. Gonçalves, and P. B. Dinis. 2018. “Enhanced geometrically nonlinear generalized beam theory formulation: Derivation, numerical implementation, and illustration.” J. Eng. Mech. 144 (6): 04018036. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001457.
Martins, A. D., R. Gonçalves, and D. Camotim. 2019a. “On the local and distortional post-buckling behaviour of thin-walled regular polygonal tubular columns.” Thin-Walled Struct. 138 (Jan): 46–63. https://doi.org/10.1016/j.tws.2019.01.033.
Martins, A. D., R. Gonçalves, and D. Camotim. 2019b. “Post-buckling behaviour of thin-walled regular polygonal tubular columns undergoing local-distortional interaction.” Thin-Walled Struct. 138 (2): 373–391. https://doi.org/10.1016/j.tws.2019.02.020.
Martins, A. D., R. Gonçalves, and D. Camotim. 2021. “Post-buckling behaviour of thin-walled regular polygonal tubes subjected to bending.” Thin-Walled Struct. 166 (21): 108106. https://doi.org/10.1016/j.tws.2021.108106.
Montaldi, J. 2012. Notes on circulant matrices. Manchester, UK: Manchester Institute for Mathematical Sciences School of Mathematics, The Univ. of Manchester.
Schafer, B. 2008. “CUFSM version 3.12—Elastic buckling analysis of thin-walled members.” Accessed March 19, 2020. http://www.ce.jhu.edu/bschafer/cufsm.
Schardt, R. 1989. Verallgemeinerte technische biegetheorie. Berlin: Springer.
Schardt, R. 1994. “Generalized beam theory—An adequate method for coupled stability problems.” Thin-Walled Struct. 19 (94): 161–180. https://doi.org/10.1016/0263-8231(94)90027-2.
Silvestre, N. 2007. “Generalised beam theory to analyse the buckling behaviour of circular cylindrical shells and tubes.” Thin-Walled Struct. 45 (Feb): 185–198. https://doi.org/10.1016/j.tws.2007.02.001.
Simulia Inc. 2008. ABAQUS standard. Vélizy-Villacoublay, France: Dassault Systèmes.
Teng, J., S. Smith, and L. Ngok. 1999. “Local buckling of thin-walled polygonal columns subjected to axial compression or bending.” In Vol. 1 of Proc., 2nd Int. Conf. on Advances in Steel Structures (ICASS 99), 109–115. Hong Kong: Elsevier.
Wittrick, W., and P. Curzon. 1968. “Local buckling of long polygonal tubes in combined compression and torsion.” Int. J. Mech. Sci. 10 (10): 849–857. https://doi.org/10.1016/0020-7403(68)90024-6.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jun 5, 2022
Accepted: Aug 13, 2022
Published online: Nov 7, 2022
Published in print: Jan 1, 2023
Discussion open until: Apr 7, 2023
ASCE Technical Topics:
- Bifurcations
- Buckling
- Compressive strength
- Continuum mechanics
- Cross sections
- Distortion (structural)
- Dynamics (solid mechanics)
- Elastic analysis
- Engineering fundamentals
- Engineering mechanics
- Linear analysis
- Material mechanics
- Material properties
- Materials engineering
- Mathematics
- Post buckling
- Solid mechanics
- Strength of materials
- Structural analysis
- Structural behavior
- Structural dynamics
- Structural engineering
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