1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Statically Indeterminate Torsion Members
Loading...