Skip to main content
Log in

Elasticas and buckling loads of shear deformable tapered columns with both hinged ends

  • Sturctural Engineering
  • Published:
KSCE Journal of Civil Engineering Aims and scope

Abstract

This paper deals with the geometrical non-linear analyses of the buckled columns. Differential equations governing elasticas of the buckled columns are derived, in which both effects of taper type and shear deformation are included. Three kinds of tape types such as breadth, depth and square tapers are considered. Differential equations are solved numerically to obtain the elasticas and buckling loads of such columns. End constraint of both hinged ends is considered. The effects of shear deformation on the elastica of the buckled column and buckling load of column are extensively investigated. Experimental studies are presented that complement theoretical results of non-linear responses of the elasticas.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Al-Khagaji, A.W. and Tooley, J.R. (1986).Numerical Methods in Engineering Practice, Holt, Reinhart and Winston, New York, NY.

    Google Scholar 

  • Chucheepsakul, S., Bunchareon, S., and Huang, T. (1995). “Elastica of simple-variable-arc-length beam subjected to end moment.”Journal of Engineering Mechanics, ASCE, Vol. 121, pp. 762–767.

    Article  Google Scholar 

  • Euler, L. (1774). Methodus inveniendi lineas curvas maxima minimive proprietate gaudentes, Additamentum I,De Curvis Elasticis, Lausanne and Geneva.

  • Gere, J.M. and Timoshenko, S.P. (1984).Mechanics of materials, Books/Cole Engineering Division, Monterey, CA.

    Google Scholar 

  • Goto, Y., Yoshimitsu, T., and Obata, M. (1990). “Elliptic integral solutions of plane elastica with axial and shear deformations.”International Journal of Solids and Structures, Vol. 26, No. 4, pp. 375–390.

    MATH  MathSciNet  Google Scholar 

  • Gupta, A.K. (1985). “Vibration of tapered beams.”Journal of the Structural Division, ASCE, Vol. 121, pp. 762–767.

    Google Scholar 

  • Haftka, R.T., Gurdal, Z. and Kamat, M.P. (1990).Elements of structural optimization, Kluwer Academic Publishers, Dardrecht.

    MATH  Google Scholar 

  • Huddleston, J.V. (1972). “Effect of shear deformation on the elastica with axial strain,”International Journal for Numerical Methods in Engineering, Vol. 4, pp. 433–444.

    Article  Google Scholar 

  • Lee, B.K. (1990). “Numerical analysis of large deflections of cantilever beams.”Journal of Korean Society of Civil Engineers, Vol. 10, pp. 1–7.

    Google Scholar 

  • Lee, B.K. and Oh, S.J. (2000). “Elastica and buckling load of simple tapered columns with constant volume.”International Journal of Solids and Structures, Vol. 37, pp. 2507–2518.

    Article  MATH  Google Scholar 

  • 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.

    Google Scholar 

  • Lee, B.K. and Wilson, J.F. (1993). “Elastica of cantilevered beam with variable cross-section.”International Journal of Non-Linear Mechanics, Vol. 28, No. 5, pp. 579–589.

    Article  Google Scholar 

  • Rojahn, C. (1968).Large deflections of elastic beams, Thesis for Engineers, Stanford University, USA.

    Google Scholar 

  • Schmidt, R and Da Deppo, D.A. (1971). “A survey of literature on large deflection of non-shallow arches, bibliography of finite deflections of straight and curved beams, rings and shallow arches.”Journal of the Industrial Mathematics Society, Vol. 21, pp. 91–114.

    Google Scholar 

  • Sheinman, I and Adam, M. (1987). “The effect of shear deformation on the post-buckling behavior of laminated beams.”Journal of Applied Mechanics, ASME, Vol. 54, pp. 558–562.

    Article  MATH  Google Scholar 

  • Sotiropoulou, A.B. and Panayotounakos, D.E. (2004). “Exact parametric analytic solutions of the elastica ODEs for bars including effects of the transverse deformation.”International Journal of Non-Linear Mechanics, Vol. 39, pp. 1555–1570.

    Article  MATH  MathSciNet  Google Scholar 

  • Theocaris, P.S. and Panayotounakos, D.E. (1982). “Exact solutions of non-linear differential equations concerning the elastic line of a straight rod due to terminal loading.”International Journal of Non-Linear Mechanics, Vol. 17, No. 5/6, pp. 395–402.

    Article  MATH  MathSciNet  Google Scholar 

  • Wang, C.Y. (1981). “Large deflections of an inclined cantilever with an end load.”International Journal of Non-Linear Mechanics, Vol. 16, pp. 155–164.

    Article  MATH  Google Scholar 

  • Wilson, J.F. (1993).Experiments on the strength of solids, McGraw-Hill, Inc., New York, NY.

    Google Scholar 

  • Wilson, J.F., Holloway, D.M. and Biggers, S.B. (1971). “Stability experiments on the strongest columns and circular arches.”Experimental Mechanics, Vol. 11, pp. 303–308.

    Article  Google Scholar 

  • Wilson, J.F. and Snyder, J.M. (1988). “The elastica with end-load flip-over,”Journal of Applied Mechanics, ASME, Vol. 55, pp. 845–848.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Byoung Koo Lee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, B.K., Km, S.K. Elasticas and buckling loads of shear deformable tapered columns with both hinged ends. KSCE J Civ Eng 10, 275–281 (2006). https://doi.org/10.1007/BF02830781

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02830781

Keywords

Navigation