(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A solid circular bar ABCD with fixed supports at ends A and D is acted upon by two equal and oppositely directed torques T_0. The torques are applied at points B and C, each of which is located at a distance x from one end of the bar. (The distance x may vary from zero to L/2).

a) For what distance x will the angle of twist at points B and C be a maximum

b) What is the corresponding angle of twist W_max?

Sorry I cant upload a picture, but basically there is a torque at B which is a distance x from end A of the bar, and another torque at C which is also a distance x to the other end D.

2. Relevant equations

Since it is fixed, then the sum of angles should be zero, correct?

So i would have to sum up the angles as follows: W_ab + W_bc + W_cd = W_ad ?

Also, the sum of torques should be zero.

Do i need to take an integral? If so, how should i approach this?

For each angle, I can make an imaginery cut and use the angle of twist formula, but this is where I am having trouble. Could someone walk me through this?

3. The attempt at a solution

Sum of torques: T_a - T_0 + T_0 - T_d = 0

T_a = T_d

W_ab = [(T_a)x]/GI

W_bc = [(T_a - T_0)]/GI

W_cd = [(T_a - T_0 + T_0)]/GI

where I = (pi/32)(d^4)

I dont believe this is correct

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