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Homework Help: Statically Indeterminate Torsion Members

  1. Oct 19, 2008 #1
    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
     
  2. jcsd
  3. Oct 25, 2008 #2
    > Since it is fixed, then the sum of angles should be zero, correct?
    Correct, you could deduce that from symmetry (or anti-symmetry)

    > Also, the sum of torques should be zero.
    Correct, you could deduce that from
    > ...two equal and oppositely directed torques T_0....


    If you look further using symmetry, what can you deduce for the angle of rotation at mid-length? Does that simplify your problem?

    What can you deduce for the answer to the question:
    > a) For what distance x will the angle of twist at points B and C be a maximum
     
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