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Constant Stress across a Beam


   My name is Anthony Wittfeldt. I go to Florida Institute of Technology and am currently
enrolled into a Mechanics of Materials coarse. We were going over the formula Tau = VQ/It
and was wondering if there was a beam shape that had Q/t = constant . I originally tried
to use a triangular shape, and after a few equations and plug-in's I canceled that one out.
Then I tried to use a parabolic shape of x^2 and was neck deep in differential functions.
I did go and talk to a couple of my professors and they were not able to give me an ansewer
to my problem. PLEASE HELP!! It's driving me up the wall!!

     Thank You,
      Anthony Wittfeldt


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 could you define what all your variables mean?



Temesgen Markos's picture

Hi Anthony,

I have tried to find out if it is possible to get a shape such that Q/t is a non zero constant. Well I run into mathematical inconsistencies. Anyway that was for fun and I don't think you have to do that to see the impossibility. At the top of the top (or bottom) of the x-section, you always have Q = 0. So the constant Q/t must be zero throughout, which means Q should be zero throughout.

So with the Euler-Bernoulli beam theory you are using, you can't get a constant shear stress across the beam unless the shear force at the x-section is zero in which case you have no shear stress anywhere.

 It would be interesting to see if the Timoshenko beam theory can predict such a scenario though, I am not sure.

I-beam is the best you can get

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