Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
권호 표지

Elastica of Cantilever Column with Constant Volume Subjected to Combined Loads

조합하중을 받는 일정체적 캔틸레버 기둥의 정확탄성곡선

  • Published : 2007.10.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with the elastica of deflected cantilever column with the constant volume. The columns are subjected to combined loads consisted of an axial compressive load and a couple moment at the free end. Differential equations governing the elastica of such column are derived, in which both the effects of taper type and shear deformation are included. Three kinds of taper types are considered: linear, parabolic and sinusoidal tapers. Differential equations are solved numerically to obtain the elastica of objective columns. The effects of various system parameters on the elastica are investigated extensively. Experimental studies were carried out in order to verify the theoretical results of non-linear behavior of the elasticas.

이 논문은 일정체적 캔틸레버 기둥의 정확탄성곡선(elastica)에 관한 연구이다. 기둥의 자유단에 압축하중과 모멘트 하중으로 구성되는 조합하중이 작용하는 캔틸레버 기둥의 정확탄성곡선을 지배하는 비선형 미분방정식과 경계조건을 유도하였다. 미분방정식에는 전단변형효과를 고려하였다. 기둥의 변단면으로는 정다각형 단면을 갖는 선형, 포물선형 및 정현의 변단면을 채택하였다. 기둥의 정확탄성곡선을 해석하기 위하여 유도된 미분방정식을 수치해석하였다. 수치해석의 결과를 이용하여 기둥의 무차원 변수들이 정확탄성곡선에 미치는 영향을 분석하였다. 실험실 규모의 실험을 실시하여 이 연구에서 얻어진 수치해석의 결과를 검증하였다.

Keywords

References

  1. Arbabi, F. (1991) Structural Analysis and Behavior. McGraw-Hill, Inc
  2. Euler, L. (1774) Methodus inveniendi lineas curvas maxima minimive proprietate gaudentes, Additamentum I. De Curvis Elasticis. Lausanne and Geneva
  3. Gere, J.M., Timoshenko, S.P. (1997) Mechanics of Materials, PWS Publishing Company
  4. Haftka, R.T., Gurdal, Z., Kamat, M.P. (1990) Element of Structural Optimization, Kluwer Academic Publisher
  5. Lee, B.K, Carr, A.J., Lee, T.E., Ahn, D.S. (2005) Elasticas and buckling loads of shear deformable tapered columns. International Journal of Structural Stability and Dynamics. 5(3), pp.317-335 https://doi.org/10.1142/S0219455405001684
  6. Lee, B.K., Carr, A.J., Lee, T.E., Kim, I.J. (2006) Buckling loads of columns with constant volume. Journal of Sound and Vibration, 294, pp.381-387 https://doi.org/10.1016/j.jsv.2005.11.004
  7. Lee, B.K., Kim, S.K., Lee, S.W. (2007) Geometrical non-linear analysis of cantilever column with constant volume. Journal of Korean Society of Civil Engineers, 27(1A) , pp.59-67(in Korean)
  8. Lee, B.K., Kim, S.K., Park, K.K. (2006) Critical loads of tapered Beck's columns with clamped and spring supports. Journal of the Computational Structural Engineering Institute of Korea, 19(1), pp.85-92(in Korean)
  9. Lee, B.K., Oh, S.J. (2000) Elastica and buckling loads of simple tapered columns with constant volume. International Journal of Solids and Structures, 37, pp.2507-2518 https://doi.org/10.1016/S0020-7683(99)00007-4
  10. Sakiyama, T. (1986) A method of analyzing the elastic buckling of tapered columns. Computers & Structures, 23(1), pp.119-120 https://doi.org/10.1016/0045-7949(86)90112-4
  11. Takagi R., Maeda M., S. J. Duan, S.J., Nakagawa, K. (1997) A proposal for optimum structural design with the largest buckling load. Computer & Structures, 63(5), pp.1033-1036 https://doi.org/10.1016/S0045-7949(96)00400-2
  12. Wilson, J.F. (1993) Experiments of the Strength of Solids, McGraw-Hill, Inc
  13. Wilson, J.F., Holloway, D.M. (1971) Stability experiments on the strongest columns and circular arches. Experimental Mechanics, 11, pp.303-308 https://doi.org/10.1007/BF02320583