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Homework Help: Maximum shear stress

  1. Jun 18, 2013 #1
    1. The problem statement, all variables and given/known data

    A locked door handle is composed of a solid circular shaft AB with a diameter of b = 108mm and a flat plate BC with a force P = 69N applied at point C as shown. Let c = 532mm , d = 126mm , and e = 153mm .

    2. Relevant equations

    [itex]\tau[/itex]max = [itex]\frac{Tc}{J}[/itex]
    T = internal torque acting at cross section
    c = outer radius
    J = polar moment of inertia → J = [itex]\frac{\pi}{2}[/itex]c4

    3. The attempt at a solution

    I've converted all mm to m.
    I just wanted to see if someone could verify that I am on the right track.
    radius, c = 0.054 m

    1. The torque caused by the P force:
    69 N × 0.532 m = 36.71 N*m → acting along the length of the solid shaft.

    2. Internal torque, T:
    T = 36.71 N*m *0. 126 m = 4.62546 N*m → acting at section m-m

    3. J = [itex]\frac{\pi}{2}[/itex]0.054 m4 = 13.36×10-6m4

    [itex]\tau[/itex]max = [itex]\frac{(4.62546 N*m)*(0.054 m)}{13.36×10^{-6} m^4}[/itex]

    Attached Files:

  2. jcsd
  3. Jun 18, 2013 #2


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    Is the problem asking for max shear stress at the section m-m? You left out the actual question.
    Yes, but I wouldn't say it acts 'along' the length: it is an internal torque that acts about the axis AB
    Why are you multiplying a torque by a distance? Your result is in N*m^2 and incorrect.
    Once you calculate the torsional shear stress, there is the vertical shear stress to consider from the vertical load P.

    Please state the question.
  4. Jun 19, 2013 #3


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    The shear stress due to an applied torque on a circular shaft is T * r / J. You overlooked the units of the polar moment of inertia J, which is m^4.


    tau = T*r/J which has units of N-m * m / m^4 = N/m^2 = Pa, a unit of stress, I believe.

    tau = Tr/J is somewhat analogous to finding the bending stress in a beam, where

    sigma = M * y / I
    Last edited: Jun 19, 2013
  5. Jun 19, 2013 #4


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    The OP incorrectly identified the torque in item 2 of Post 1. The vertical shear in the rod was also neglected, if that is what the problem is asking.
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