# torsional reaction in prismatic beam

I have an (isotropic, nothing fancy about it) beam of length L, fixed at ends A and B. At distance a from A, there is a torsional moment Mt.
is the reacting torsional moment a A MtA = -Mt x (L-a) / L and the reacting moment at B MtB = -Mt x a/L ?
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No
Brian W
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Reacting moment MtA = MtB = -1/2Mt
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On Fri, 7 Dec 2007 10:43:06 -0800 (PST), the_mesar

I will fess up that I initially gave a comparable answer from 'gut-feelings' alone. The Wolfram folks have a good on line text with a torsionally stressed equilateral prism cross section beam. I didn't take the time to peruse it. But i started to think about a rubber prismatic c/s beam. If I torsionally stress the beam near one end, it's THAT end that takes most of the reaction, I fancy.....
Brian Whatcott Altus OK
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So where are we now with the "answer"?
I did a quick "reality" check on the OP's proposed solution.....at the limit cases & the "mindless" one & it looked ok.
I approached it based on the concept of torsional (or any type) springs in parallel.
Limit cases; limit cases x=0 & x=L 1) infinitlely stiff & flexible
x=L/2 2) equally flexible.
but just because the solution works at the ends & the middle doesn't mean it's good everywhere. :)
cheers Bob
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wrote:

...
I guess my aversion to ch..-li... anonymous posters just kicks in at times and I don't give a s...
I know - I am a very, very grouchy person, but just sometimes.
Brian W
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On Fri, 07 Dec 2007 18:17:52 -0800, BobK207 wrote:

torsional deformation is proportional to the length of the beam and to the moment... So where the deformation is half, the reaction must be half....?
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On Sat, 08 Dec 2007 01:13:01 +0000, Brian Whatcott wrote:

that was my gut-feeling too...If you hold it near where the moment acts, you feel the total load....