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in my question i have 2 tubes of identical length, the larger placed inside the smaller, both welded to a wall at one end and a rigid plate at the other, a moment of torsion Mt is applied to the outer tube at a distance d from the wall,
in the question i am asked to find the maximum stress in each tube, i know how to do this but have only ever had questions where the torsion was applied at the end. since the inner tube will obviously twist differently to the outer tube i have a problem here, this is statically undefinded, i know that θ1=θ2 (tha angle of twist) due to the rigid plate. but i need some other condition.
what i have tried to do is the following. since the inner tube resists the twistiong, i say that the torsion the outer tube applies to the inner is T1 and the torsion the inner tube applies on the outer tube is T2. as far as directions go T1 is the same as Mt and T2 is opposite.
now what can i say? is T1+T2=Mt? that is what i had done in a case of 2 tubes glued together with torsion applied at their end, but here they twist differently.
i hope this question is clear and someone can help me
in the question i am asked to find the maximum stress in each tube, i know how to do this but have only ever had questions where the torsion was applied at the end. since the inner tube will obviously twist differently to the outer tube i have a problem here, this is statically undefinded, i know that θ1=θ2 (tha angle of twist) due to the rigid plate. but i need some other condition.
what i have tried to do is the following. since the inner tube resists the twistiong, i say that the torsion the outer tube applies to the inner is T1 and the torsion the inner tube applies on the outer tube is T2. as far as directions go T1 is the same as Mt and T2 is opposite.
now what can i say? is T1+T2=Mt? that is what i had done in a case of 2 tubes glued together with torsion applied at their end, but here they twist differently.
i hope this question is clear and someone can help me