Numerical analysis of steel columns subject to eccentric loadings

Keywords: Compressive actions, Critical buckling load, Eccentric loadings, Finite element, Modelling, Steel columns


Buckling of framed and plated structures has been a great concern that researchers try to handle over the past decades. In most developing nations such as ours, fewer or no experimental trials are available to obtain requisite information for the proper understanding of this phenomenon. It is on this premise that an attempt is made to conduct a preliminary study to numerically evaluate the buckling of steel columns under eccentric loadings. To achieve this, a static, linear perturbation analysis was initially performed on a pin-ended steel column using the subspace Eigen solver for the different buckled mode shapes to illustrate the likely behaviour of the column when subjected to compressive actions. Then, the static, general analysis was conducted with the column subjected to varying magnitudes of eccentric loadings. It was required to determine the load level at which the column would fail when subjected to these eccentric loadings. Consequently, a base load value equivalent to 10 % of Euler's critical buckling load was used. This load value was thereafter increased by 20 % in sequence. It was discovered that 10 % of the Euler's critical buckling load can alter the stiffness of the column when loaded eccentrically. It was further observed that the steel column finally failed at a load greater than 20 % of the Euler's critical buckling load and 40.1% of Rankine's critical buckling load. This is because the permissible deflection for unbraced columns may be taken as the quotient of effective length of column to 250, which translates to 13.8 mm. Therefore, the maximum deflection of 14.72 mm reached by applying an eccentric load of 514 kN exceeds the allowable limit of 13.8 mm.


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P. K. Paik, and A. K. Thayamballi, Ultimate limit State Design of Steel-Plated Structures, West Sussex: John Wiley & Sons, 2002, pp. 13-15.

E. Ufuah, and C. G. Bailey, "Performance of offshore platform deck under running pool fire," 6th European Conference on Steel and Composite Structures, European Convention for Constructional Steelwork, August 31 - September 2, Budapest, Hungary, 2011, pp. 1635-1640.

C. G. Bailey, I. W. Burgess, and R. J. Plank, "The lateral-torsional buckling of unrestrained steel beams in fire," J. Constr. Steel Res., vol. 36, no. 2, pp. 101-119, 1996.

S. M. Fadi, and A. Farid, “Nonlinear finite element modelling of dynamic localizations in high strength steel columns under impact,” Int. J. Impact Eng., vol. 52, pp. 47-61, 2013.

M. T. Pagoulatou, X. H. Dai, and D. Lam, “Finite element analysis on the capacity of circular concrete-filled double-skin steel tubular (CFDST) stub columns,” Eng. Struct. J., vol. 72, pp. 102–112, 2014.

Y. Kruti, and V. Vandynskyi, “Exact solutions of buckling problem of columns loaded by self-weight,” Conf. Ser.: Mater. Sci. Eng., 708012062, 2019.

Y. Zhang, C. Wang, and Z. Zhang, “Tests and finite element analysis of pin-ended channel columns with inclined simple edge stiffeners”, J. Constr. Steel Res., vol. 63, pp. 383-395, 2007.

B. K. Hadi, “Wrinkling of sand wish column: comparison between finite element analysis and analytical solution”, Composite Structure, vol. 53, pp. 477- 482, 2001.

M. K. James, "Shear deformation and buckling of columns revisited," Civ. Eng. Res. J., vol. 2, no. 1, pp. 14-18, 2017.

S. K. Kashyap, S. Kumar, M. Mallick, R. P. Singh, and M. Verma, "A comparative study between experimental and theoretical buckling load for hollow steel columns," Int. J. Eng. Sci. Tech., vol. 10, no. 3, pp. 27-33, 2018.

R. K. Gupta, “Comparative study of thermal post-buckling analysis of uniform slender and shear flexible columns using rigorous finite element and intuitive formulations,” Int. J. Mech. Sci., vol. 51, pp. 204–212, 2009.

A. Sastranegara, T. Adachi, and A. Yamaji, “Improving energy absorption of impacted column due to transverse impact: a finite element analysis,” Int. J. Impact Eng., vol. 32, pp. 444–460, 2005.

L-H. Hana, W-D. Wang, and X-L. Zhao, “Behaviour of steel beam to concrete-filled SHS column frames: finite element model and verifications,” Eng. Struct., vol. 30, pp. 1647-1658, 2008.

R. B. Ali, and M. M. Islam, "Concentric vs. eccentric loadings on different shapes of CFST columns: a theoretical investigation on axial compressive strength according to AISC guidelines," World Sci. News, vol. 99, pp. 119-132, 2018.

ABAQUS Standard/explicit user’s manual, Version 6.8-2, vol. 1,2,3 and 4. USA: Dassault Systèmes Simulia Corp., Providence, RI.

P. M. M. Vila Real, N. Lopes, L. Simões da Silva, P. Piloto, and J. M. Franssen, “Numerical modelling of steel beam-columns in case of fire-comparison with Eurocode 3,” Fire Saf. J., vol. 39, pp. 23-39, 2004.

S. P. Timoshenko, and J. M. Gere, Theory of Elastic Stability, New York: McGraw Hill, 1961.

C. M. Wang, C. Y. Wang, and J. N. Reddy, Exact Solutions for Buckling of Structural Members, Florida: CRC Press LLC, 2005.

E. Ufuah, and H. T. Tashok, "Behaviour of stiffened plates subjected to accidental loadings," Eng. Lett., vol. 21, no. 2, pp. 95-100, 2013.

BS 5950: Part 1, Structural use of steelwork in buildings; Code of practice for design- rolled and welded sections, 2000.

How to Cite
Ufuah, E. (2021). Numerical analysis of steel columns subject to eccentric loadings. Journal of Advances in Science and Engineering, 4(1), 1-12.
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