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 ?
No
Brian W
Reacting moment MtA = MtB = -1/2Mt
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
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
...
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
that was my gut-feeling too...If you hold it near where the moment acts, you feel the total load....
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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