Buckling of Tapered Columns with Polygon Cross-Section

Document Type : Original Article


Civil Engineering Dept., Faculty of Engineering, Kafrelsheikh University, Kafelshekh, Egypt


This paper is concerned with the elastic stability of slender tapered columns of regular polygon cross-section with constant volume is presented. Various end conditions of the tapered columns such as pinned ends, clamped -pinned ends and clamped ends are considered in this paper. The analysis is developed using finite element method for linear, parabolic and sinusoidal tapers assuming firstly circular cross-section. The polygon cross-sections other the circular one are studied by investigating a direct relation between the side number of the polygon cross-section and the critical load parameter. The main parameter in this study is the section ratio that defined as the ratio between the section depths at the mid-span of the considered column to that at the column ends. The obtained numerical results are introduced in many curves to describe the relation between the buckling load and the section ratio considering linear, parabolic and sinusoidal tapers and various side number of the polygon cross-section for each end conditions. The obtained results of the buckling factor are simple with satisfactory accuracy compared with results that obtained in other theoretical studies.


Google Scholar


Main Subjects

[1]     Timoshenko, S. P., and Gere, J. M. (1983) “Theory of Elastic Stability”, McGraw-Hill Book Company, London.
[2]     Keller, J. B., (1960) “The shape of the strongest column”, Archive for Rational Mechanics and Analysis, Vol. 5, pp. 275-285.
[3]     Tadjbakhsh, I. and Keller, J. B., (1962) “Strongest columns and isoperimetric inequalities for eigenvalues”, Journal of Applied Mechanics, ASME, Vol. 29, pp. 159-164.
[4]     Barnes, D., C., (1988) The shape of the strongest column is arbitrarily close to the shape of the weakest column”, Quarterly of applied mathematics, Vol. 46, pp. 605-609.
[5]     Cox, S., J. and Overton, M. I., (1992) On the optimal design of columns against buckling”, SIAM Journal of Mathematical analysis, Vol. 23, pp. 287-325.
[6]     Lee, B. K. and Oh, S. J., (2000) Elastica and buckling load of simple tapered column with constant volume”, International Journal of solids and structures, Vol. 37, No. 18, pp. 2507-2518.
[7]     Lee, B. K., Oh, S. J. and Li, G., (2002) Buckling loads of columns of regular polygon cross-section with constant volume and clamped ends”, Electronic Journal of structural engineering, Vol. 2, pp. 76-84.
[8]     Lee, B. K., Carr, A. J. and Li, G., (2006) “Buckling loads of columns with constant volume”, Journal of sound and vibration, Vol. 294, pp. 381-397.