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Homework Help: Replacing a hollow shaft with a solid shaft

  1. Jan 14, 2010 #1
    1. The problem statement, all variables and given/known data

    " determine the diameter of a replacement solid shaft manufactured from the same material and subjected to the same maximum shear stress and torque"

    Ok so I previously calculated the following:

    Maximum shear stress= 35.8 x 106
    Torque= 450.117 x 103
    Hollow shaft external and internal diameters= 400mm and 200mm

    2. Relevant equations

    T/J = shear stress/r

    J= Pi x d4/32

    r= D/2

    3. The attempt at a solution

    Basically I attemted it in a very long winded way which was found to be wrong when I went through it with my tutor. What happened was I went off an example we done in class which was similar but for replacing a solid shaft with a hollow one whereas I am wanting to replace a hollow shaft with a solid one. I've read the rules on here and I know its not a place to get your assignments done for you but I was hoping someone would be able to give me an explanation and point me in the right direction as my tutor isn't being to helpful. Cheers.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 14, 2010 #2

    nvn

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    stainton1: Hint: Look up or write the formula for polar moment of inertia, J1, of a round tube. Set shear stress tau1 = tau2. Substitute.
     
    Last edited: Jan 15, 2010
  4. Jan 14, 2010 #3
    Isn't there a difference in the equations for a thin versus thick-walled hollow shaft?
     
  5. Jan 15, 2010 #4

    nvn

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    DannoXYZ: In the limit, yes, you can obtain a different, approximate formula for a thin tube. But why bother with an approximate formula, when you can instead use the exact formula. Besides, stainton1 does not have a thin tube.
     
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