Stability Criteria of an Euler Column with a Continuous Elastic Restraint and Classical End Conditions
Main Article Content
Abstract
The objective of this research work is aiming at the determination of the stability criteria and corresponding buckling shape function for a continuous elastically restrained Euler column in which the elastic restraint can be viewed and modeled as Winkler-type foundation. The column with 10 combinations of classical end condition is considered. The method of problem analysis starts with formulating the dimensionless governing equation for the column buckling and then analytical solving. It is founded that most of the obtained stability criteria are highly nonlinear transcendental equations represented in terms of the required implicit stability parameters.
Article Details

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright @2021 Engineering Transactions: A Research Publication of Mahanakorn University of Technology
Faculty of Engineering and Technology
Mahanakorn University of Technology
References
J.M. Gere and S.P. Timoshenko, Mechanics of Materials, 3rd Edition, PWS-KENT Publishing Company, Boston, 1990.
F. Bleich, Buckling Strength of Metal Structures, McGraw-Hill Book Company, Singapore, 1952.
S.P. Timoshenko and J.M. Gere, Theory of Elastic Stability, 2nd Edition, McGraw-Hill Book Company, Inc., Singapore, 1961.
D.O. Brush and B.O. Almroth, Buckling of Bars, Plates, and Shells, McGraw-Hill Book Company, New York, 1975.
G.J. Simitses, An Introduction to the Elastic Stability of Structures, Prentice-Hall, Inc., New Jersey, 1976.
https://www.structuralguide.com/types-of-column-failures/
M. Hetenyi, Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor, 1946.
V.Z. Vlasov and U.N. Leont’ev, Beams, Plates and Shells on Elastic Foundations, Israel Program for Scientific Translations Ltd, Jerusalem, 1966.
https://mardiansyahpipeline.wordpress.com/2015/02/05/pipeline-buckling/
https://civil-engg-world.blogspot.com/2013/01/What-Long-Column-Behavior-Pile-Foundation.html
https://www.mdpi.com/2412-3811/9/8/123
T.M. Atanackovic and B.N. Novakovic, “Optimal shape of an elastic column on elastic foundation,” Eur. J. Mech. A/Solids, vol. 25, pp. 154-165, 2006.
T.M. Atanackovic, B.B. Jakovljevic and M.R. Pethovic, “On the optimal shape of a column with partial elastic foundation,” Eur. J. Mech. A/Solids, vol. 29, pp. 283-289, 2010.
M.T. Atay and S.B. Coskun, “Elastic stability of Euler columns with a continuous elastic restraint using variational iteration method,” Comput. Math. Appl., vol. 58, pp. 2528-2534, 2009.
A. Eryilmaz, M.T. Atay, S.B. Coskun and M. Basbuk, “Buckling of Euler columns with a continuous elastic restraint via homotopy analysis method,” J. Appl. Math., vol. 2013, 341063 (8 pages), 2013.
V.E. Melissianos and C.J. Gantes, “Buckling and post-buckling behavior of beams with internal flexible joints resting on elastic foundation modeling buried pipelines,” Struct., vol. 7, pp. 138-152, 2016.
A.A. Ghadban, A.H. Al-Rahmani, H.A. Rasheed and M.T. Albahttiti, “Buckling of nonprismatic column on varying elastic foundation with arbitrary boundary conditions,” Math. Probl. Eng., vol. 2017, 5976098 (14 pages), 2017.
B.G. Johnston, “Column buckling theory: Historic hightlights,” J. Struct. Eng., vol. 109, no. 9, pp. 2086-2096, 1983.
B. Thurlimann, “Column buckling – Historical and actual notes,” J. Constr. Steel Res., vol. 17, pp. 95-111, 1990.
C.M. Wang, S. Kitipornchai and K.M. Liew, “Research on elastic buckling of columns, beams and plates: Focusing on formulas and design charts,” J. Constr. Steel Res., vol. 26, pp. 211-230, 1993.
P. Posayanant, W. Wongwanishwatana, P. Premthamkorn and Y. Sompornjaroensuk, “Buckling criteria of an Euler column with both ends elastically restrained: Analytical solution and verification,” Eng. Trans. MUT, 2025, paper submitted for publication. (in Thai)
E. Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, Inc., Singapore, 2006.
J.J. Tuma, Engineering Mathematics Handbook, 2nd, Enlarged and Revised Edition, McGraw-Hill Book Company, New York, 1979.
G.H. Golub and C.F. Van Loan, Matrix Computations, 2nd Edition, The Johns Hopkins University Press, Baltimore, 1990.