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Determine angle of twist in shaft

  1. Feb 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Compute the torsional shear stress and angle of twist in degrees in an aluminum tube, 600 mm long, having an inside diameter of 60 mm and outside diameter of 80 mm when subjected to a steady torque of 4500 N*m. Then specify a suitable aluminum alloy for tube.


    2. Relevant equations

    angle = TL/GJ
    J = piD^4/32 (Do^4 - Di^4)

    3. The attempt at a solution

    angle = (4500 N*m)(0.6 m) / (2.8 x 10^-6)(80 x 10^9) = 0.012 rad

    Book answer: 0.0378 rad

    Wrong answer obviously. Why? Thanks
     
  2. jcsd
  3. Feb 16, 2012 #2
    J = piD^4/32 (Do^4 - Di^4)

    This is wrong. Check formula for polar moment of inertia for hollow shaft.
     
  4. Feb 17, 2012 #3
    my book doesn't have it

    two examples for hollow shaft use the same J formula
     
  5. Feb 17, 2012 #4
    The way you have it written, you have the units of length to the 8th power. That is not correct.

    The correct formula is

    J = pi (Do^4 - Di^4)/32
     
  6. Feb 17, 2012 #5
    Thanks for clearing that up
     
  7. Feb 17, 2012 #6
    Re did calculation, same answer
     
  8. Feb 17, 2012 #7
    Did you use Young's Modulus instead of the shear modulus for aluminum?
     
  9. Feb 17, 2012 #8
    Yes I did. Thanks problem solved
     
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