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Homework Help: Equivalent torque of hollow shaft

  1. Jul 1, 2010 #1
    1. The problem statement, all variables and given/known data

    A solid circular shaft has a diameter of 200mm. What would be the dimension of a hollow
    shaft which could replace it (i.e. transmit the same torque for the same maximum shear
    stress), and what would be the percentage reduction in the material required? The internal
    and external diameters of the hollow shaft are to be in the ratio of 4:5. (Ans: 23.84 cm,
    19.07 cm; 48.9%)

    2. Relevant equations

    T/J = G(theta)/L = tao/R
    J = pi(d)^4/32


    3. The attempt at a solution

    J = pi(0.2)^4/32 = 0.000157

    pi(5d)^4/32 - pi(4d)^4/32 = 0.000157

    d = 0.2m

    5d = 1m (wrong)
     
  2. jcsd
  3. Jul 1, 2010 #2

    rock.freak667

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    Homework Helper

    You are right in that you want Jsolid = Jhollow

    But this statement means that d/D = 4/5 or d = 0.8D (d = internal, D= external)

    And Jhollow = π/32 (D4-d4)
     
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