KSCE Journal of Civil and Environmental Engineering Research (대한토목학회논문집)

Korean Society of Civil Engeneers (대한토목학회)
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Strongest Simple Beams with Constant Volume

일정체적 단순지지 최강보

  • 이병구 (원광대학교 토목환경공학과) ;
  • 이태은 (원광대학교 토목환경공학과) ;
  • 김영일 ((주)대정컨설턴트)
  • Received : 2009.01.08
  • Accepted : 2009.02.18
  • Published : 2009.03.31
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Abstract

This paper deals with the strongest beams with the solid regular polygon cross-section, whose volumes are always held constant. The differential equation of the elastic deflection curve of such beam subjected to the concentrated and trapezoidal distributed loads are derived and solved numerically. The Runge-Kutta method and shooting method are used to integrate the differential equation and to determine the unknown initial boundary condition of the given beam. In the numerical examples, the simple beams are considered as the end constraint and also, the linear, parabolic and sinusoidal tapers are considered as the shape function of cross sectional depth. As the numerical results, the configurations, i.e. section ratios, of the strongest beams are determined by reading the section ratios from the numerical data related with the static behaviors, under which static maximum behaviors become to be minimum.

이 논문은 정다각형 중실단면을 갖는 최강보에 관한 연구이다. 이 연구에서 보의 체적은 항상 일정하다. 이러한 보에 집중하중과 만재 사다리꼴 분포하중이 작용하는 경우에 탄성곡선의 미분방정식을 유도하고 이를 수치해석하여 정적 거동을 산정하였다. 미분방정식은 Runge-Kutta법을 이용하여 수치적분을 하였고 미지수인 보의 초기치는 shooting method를 이용하여 산정하였다. 수치해석 예에서는 단순보를 채택하였고, 단면깊이의 형상함수로는 선형, 포물선형 및 정현형의 함수를 채택하였다. 이 연구에서 얻은 수치해석의 결과로부터 보의 정적 최대거동값이 최소가 되는 단면형상 즉 최강단면비를 산정하였다.

Keywords

References

  1. 김영일(2003) 일정체적 변단면보의 정적 최적 단면, 석사학위논문, 원광대학교.
  2. 이병구(2008) 응용수치해석, 원광대학교 구조공학연구실 강의노트.
  3. Atanackovic, T.M. and Simic, S.S. (1999) On the optimal shape of a Pfluger column. European Journal of Mechanics A-Solid, Vol. 18, pp. 903-913. https://doi.org/10.1016/S0997-7538(99)00128-X
  4. Carnahan, B., Luther, H.A., and Wilkes, J.O. (1969) Applied numerical methods. John Wiley & Sons, USA.
  5. Cox, S.J. and Overton, M.I. (1992) On the optimal design of columns against buckling. SIAM Journal on Mathematical Analysis, Vol. 23, pp. 287-325. https://doi.org/10.1137/0523015
  6. Gere, J.M. and Timoshenko, S.P. (1997) Mechanics of materials. PWS Publishing Company, USA.
  7. Haftka, R.T., Grudal, Z., and Kamat, M.P. (1990) Elements of structural optimization. Kluwer Academic Publisher, Dordrecht.
  8. Keller, J.B. (1960) The shape of the strongest column. Archive for Rational Mechanics and Analysis, Vol. 5, pp. 275-285. https://doi.org/10.1007/BF00252909
  9. Keller, J.B. and Niordson, F.I. (1966) The tallest column. Journal of Mathematics and Mechanics, Vol. 16, pp. 433-446.
  10. Lee, B.K., Carr, A.J., Lee, T.E., and Kim, I.J. (2006) Buckling loads of columns with constant volume. Journal of Sound and Vibrations. Vol. 294, Issues. 1-2, pp. 381-387. https://doi.org/10.1016/j.jsv.2005.11.004
  11. Lee, B.K. and Oh, S.J. (2000) Elastica and buckling loads of simple tapered columns with constant volume. International Journal of Solids and Structures, Vol. 37, Issue 18, pp. 2507-2518. https://doi.org/10.1016/S0020-7683(99)00007-4
  12. Taylor, J.E. (1967) The strongest column-energy approach. Journal of Applied Mechanics, ASME, Vol. 34, pp. 486-487. https://doi.org/10.1115/1.3607710
  13. 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. https://doi.org/10.1007/BF02320583