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me211solution_8

me211solution_8 - Find each internal torque at the solid...

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Find each internal torque at the solid inner shaft and the outer tube. (FBD) 2 BC BA T T kip i = = n max 4 2(0.5) ( ) 10.2 ksi = (0.5) 2 BC BC T c J τ π = = max 4 4 2(1) ( ) (1 0.75 ) 2 BA BA T c J τ π = = 1.86 ksi = Angle of Twist: 4 4 3 2(12) 0.002032 (1 0.75 )11(10 ) 2 BA BA B T L rad JG φ π = = = / 4 3 2(24) 0.044448 (0.5 )11(10 ) 2 BC BC C B T L rad JG φ π = = = / 0.002032 0.044448 0.04648 2.66 rad C B C B φ φ φ = + = + = = °

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Express the radius as a function of x ( ) r rL r r x r x x L L + = + = Then, the polar moment of inertia is 4 4 4 4 ( ) ( ) 2 2 rL rx r J x L x L L π π + = = + Angle of Twist: 4 4 4 4 4 3 0 0 0 2 2 1 ( ) ( ) 3( ) 12 L L L Tdx TL dx TL TL 4 7 J x G r G L x r G L x r G φ π π = = = = + + π