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Beam Flex from Torque Force

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You could use type 9 here: Link. You'd use superposition to add the effects of the identical moments at each end. I've no doubt that there's a more direct solution but I was unable to find it online in under 30 seconds.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.
 
Original Poster needs to be more forthcoming about what kind of Torque is being applied. If it is a free moment or free couple being applied to an end or elsewhere along the beam and in the plane of the major axis then some of the offered solutions apply. But if it is a moment applied around the major cross section then the deflection may or may not one of the solutions offered. A.I.S.C. Design Guide #9 has a lot of information about how steel shapes flex or twist when torque is applied.

Jim.
 
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