Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Effect of shear deformation on the critical buckling of multi-step bars

  • Li, Q.S. (Department of Building and Construction, City University of Hong Kong)
  • Received : 2002.02.25
  • Accepted : 2002.12.03
  • Published : 2003.01.25
⟨ Previous Next ⟩

Abstract

The governing differential equation for buckling of a one-step bar with the effect of shear deformation is established and its exact solution is obtained. Then, the exact solution is used to derive the eigenvalue equation of a multi-step bar. The new exact approach combining the transfer matrix method and the closed form solution of one step bar is presented. The proposed methods is convenient for solving the entire and partial buckling of one-step and multi-step bars with various end conditions, with or without shear deformation effect, subjected to concentrated axial loads. A numerical example is given explaining the proposed procedure and investigating the effect of shear deformation on the critical buckling force of a multi-step bar.

Keywords

References

  1. Ari-Gur, J. and Elishakoff, I. (1990), "On the effect of shear deformation on buckling of columns withoverhang", J. Sound Vib., 139, 165-169. https://doi.org/10.1016/0022-460X(90)90782-U
  2. Banerjee, J.R. and Williams, F.W. (1994), "The effect of shear deformation on the critical buchling of columns",J. Sound Vib., 174(5), 607-616. https://doi.org/10.1006/jsvi.1994.1297
  3. Dinnik, A.N. (1950), "Scientific paper of A.N. Dinnik", Academy of USSR Publishing, Moscow.
  4. Iyengar, N.G.R. (1988), Structural Stability of Columns and Plates, John Wiley & Sons, New York.
  5. Karman, T.V. and Biot, M.A. (1940), Mathematical Methods in Engineering, McGraw-Hill, New York.
  6. Li, Q.S., Cao, H. and Li, G.Q. (1994), "Stability analysis of a bar with multi-segments of varying cross-section",Comput. Struct., 53(5), 1085-1089. https://doi.org/10.1016/0045-7949(94)90154-6
  7. Li, Q.S., Cao, H. and Li, G.Q. (1995), "Stability analysis of bars with varying cross-section", Int. J. SolidsStruct., 32(21), 3217-3228. https://doi.org/10.1016/0020-7683(94)00272-X
  8. Li, Q.S. (2000), "Exact solutions for buckling of non-uniform columns under axial concentrated and distributedloading", European Journal of Mechanics, A/Solids, 20, 485-500. https://doi.org/10.1016/S0997-7538(01)01143-3
  9. Li, Q.S. (2001), "Buckling of multi-step non-uniform beams with elastically restrained boundary conditions",Journal of Constructional Steel Research, 57(7), 753-777. https://doi.org/10.1016/S0143-974X(01)00010-4
  10. Li, Q.S. (2002), "Non-conservative stability of multi-step non-uniform columns", Int. J. Solids Struct., 39(9),2387-2399. https://doi.org/10.1016/S0020-7683(02)00130-0
  11. Timoshenko, S.P. (1936), Theory of Elastic Stability, McGraw-Hill, New York
  12. Vaziri, H.H. and Xie, J. (1992), "Buckling of columns under variably distributed axial loads", Comput. Struct.,45(3), 505-509. https://doi.org/10.1016/0045-7949(92)90435-3

Cited by

  1. Stability of Nonuniform Cracked Bars Under Arbitrarily Distributed Axial Loading vol.42, pp.1, 2004, https://doi.org/10.2514/1.9040
  2. Optimum buckling design of axially layered graded uniform columns vol.57, pp.5, 2015, https://doi.org/10.3139/120.110734
  3. Analytical solution for buckling of asymmetrically delaminated Reissner’s elastic columns including transverse shear vol.45, pp.3-4, 2008, https://doi.org/10.1016/j.ijsolstr.2007.09.027
  4. Critical buckling load optimization of the axially graded layered uniform columns vol.54, pp.4, 2015, https://doi.org/10.12989/sem.2015.54.4.725
  5. Exact buckling analysis of composite elastic columns including multiple delamination and transverse shear vol.30, pp.6, 2008, https://doi.org/10.1016/j.engstruct.2007.10.003
  6. Shear deformation effect in flexural-torsional buckling analysis of beams of arbitrary cross section by BEM vol.35, pp.2, 2010, https://doi.org/10.12989/sem.2010.35.2.141
  7. Optimal design of the transversely vibrating Euler-Bernoulli beams segmented in the longitudinal direction vol.44, pp.5, 2019, https://doi.org/10.1007/s12046-019-1084-2