Vol. 20 No. 5 (2017) Cover Image
Vol. 20 No. 5 (2017)

Published: November 30, 2017

Pages: 1154-1159

Articles

Estimating Elastic Buckling Load for an Axially Loaded Column Bolted to a Simply Supported Plate using Energy Method

Mustafa Kamal Al-Kamal 1
1 Civil Engineering Department, Al-Nahrain University, Baghdad, Iraq
History
  • Received: August 10, 2017
  • Available Online: November 3, 2017

Abstract

This paper deals with the elastic stability of a column bolted at its mid-height to a simply supported square plate and subjected to a concentrated load, using energy method. A uniform homogeneous column is assumed to be pinned at both ends. From symmetry considerations, half of the column is modeled by making the plate acting as a torsion spring on the column at its mid-height. The column length and cross-section, plate dimensions and thickness, and the material properties for the column and the plate catch the interest of the author. The problem is solved by using energy method and ultimately, the elastic buckling load is found. The analytical elastic buckling load is compared with a numerical solution obtained from finite element method using SAP2000. The numerical results agree with the analytical solution.  The finite element model is refined to catch the actual effect of the bolted plate on the elastic buckling load. It has been found that the elastic buckling load is increased due to the increase in the rotational stiffness provided from the plate.

Keywords

References

  1. C.M. Wang, C.Y. Wang, J.N. Reddy (2005), “Exact Solutions for Buckling of Structural Members”, CRC Press LLC, Florida.
  2. I.H. Shames, C.L. Dym (1985), “Energy and Finite Element Methods in Structural Mechanics”, Hemisphere Publishing Corporation, New York.
  3. Reddy, J. N. (2002), “Energy Principles and Variational Methods in Applied Mechanics”, 2nd edition, John Wiley, New York.
  4. S.P. Timoshenko, J.M. Gere, “Theory of Elastic Stability”, McGraw Hill, New York, 1961.
  5. I. Elishakoff, F. Pellegrini (1987), “Exact and Effective Approximate Solutions of Some Divergent Type Non-Conservative Problems”, Journal of Sound and Vibration, 114 (1) 143-147.
  6. I. Elishakoff, F. Pellegrini (1988), “Exact Solutions for Buckling of Some Divergence Type Non-Conservative Systems in Terms of Bessel and Lomel Functions”, Computer Methods in Applied Mechanics and Engineering, 66 (1) 107-119.
  7. M. T. Atay, S. B. Coskun (2009), “Elastic Stability of Euler Columns with a Continuous Elastic Restraint Using Variational Iteration Method”, Computers and Mathematics with Applications, 58 (11-12) 2528-2543.
  8. M. Basbuk, A. Erylmaz, S.B. Coskun, M. T. Atay (2016), “On Critical Buckling Loads of Euler Columns With Elastic End Restraints”, Hittite Journal of Science and Engineering, 3 (1) 09-13.
  9. A. Erylmaz, M. T. Atay, S.B. Coskun, M. Basbuk (2013), “Buckling of Euler Columns with a Continuous Elastic Restraint via Homotopy Analysis Method”, Journal of Applied Mathematics, Volume 2013, Article ID 341063, 8 pages.
  10. J.H.P. Sampaio, J. R. Hundhausen (1998), “A Mathematical Model and Analytical Solution for Buckling of Inclined Beam-Columns”, Applied Mathematical Modelling, 22 (6) 405-451.
  11. N. Zdravkovic, M. Gasic, M. Savkovic (2013), “Energy Method in Efficient Estimation of Elastic Buckling Critical Load of Axially Loaded Three-Segment Stepped Column”, FME Transactions, 41 (3) 222-229.
  12. J. Rychlewska (2015), “A New Approach for Buckling Analysis of Axially Functionally Graded Beams”, Journal of Applied Mathematics and Computational Mechanics, 14 (2) 95-102.
  13. MATLAB and Statistics Toolbox Release 2013a ®, The MathWorks, Inc., Natick, Massachusetts, United States.
  14. SAP2000 ® Version 18 (2015), Computers & Structures, Inc., Berkeley, California, USA.
  15. American Concrete Institute (2014), “Building Code Requirements for Structural Concrete and Commentary (ACI 318-14 / ACI 318R-14)”, Farmington Hills, Michigan.