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Timoshenko theory
Wed, 2009-07-22 12:59 - Huma Khalid
Hi all
I developed a Fnnite element code in Maple for Euler Bernoulli Beam Theory. Then I solved a cantilever beam with a vertical load at the free end. On comparing results with comercially available software, my results are good.
Finally I developd the FE formulation for Timoshenko beam theory. for the same cantilever problem, I introduced a small magnitue of shear modulus but the results are highly different from the Euler-Bernoulli beam.
Can any body explain this?
If anyone let me know any link or book having some details of the analysis of Timoshenko beam, it will be highly appreciated.
Huma
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TIMOSHENKO BEAM
You may refer to the following book:
Shame I H & Dym C L
Energy and Finite Element Method in Structural Mechanics,McGraw-Hill
Difference due to the contribution of shear deformation
When we write the equation of equilibrium for Euler Bernoulli beam the part that contributes as the internal energy due to shear deformation becomes zero as a consequence of the assumptions made for Euler Bernoulli beam. Whereas, in case of Timoshenko beam model the internal energy part, due to shear deformation becomes nonzero as a consequence of the relaxation of the Euler Bernoulli beam assumptions. When the shear deformation of the beam becomes significantly larger for large end load and/or less shear modulus value, the contribution of the shear deformation to the internal energy becomes high and shows difference in the results with that of the Euler Bernoulli beam.
You may study "Finite Element Procedures", Bathe K. J., Section:5.4
Thanks for the help
Thanks for the help