Hi all
According to Timoshenko beam theory shear stress is distributed uniformly across the cross-section depth which is contrary to real distribution of shear stress i.e parabolic distribution. I know there is a shear adjusment factor (5/6 for rectangular cross-section) can solve this problem. But I don't know how can I utilize this adjustment factor in the beam formulation to get parabolic distribution.
Could anybody please help me?
Regards
Huma
Huma, Timoshenko beam
Huma,
Timoshenko beam theory DOES NOT predict a uniform shear stress distribution. In fact, if you look in his book on the Theory of Elasticity you will see that he derives a result that indicates a parabolic distribution of shear stress across the cross-section of a cantilever. You need to look in his book to see how the prabolic distribution arises. Many other elasticity books will show the result also.
For a rectangular cross-section if you take average shear stress divided by maximum shear stress on the cross-section you will get 2/3.
However, a higher value of 5/6 has been proposed by others. You may look at the following article for more on this topic and references.
http://www.afs-journal.org/index.php?option=article&access=standard&Ite…
regards,
Louie