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Thin Cylinder Theory

  1. May 4, 2005 #1

    brd

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    Can anyone tell me what equation I need to use to determine the torsional shear stress using the thin cylinder theory to a copper cylinder which is under pressure and a twisting force (torque).
     
    Last edited: May 4, 2005
  2. jcsd
  3. May 4, 2005 #2

    FredGarvin

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    You have a combined loading scenario.

    The pressure will create a normal stress. However, when you do a Mohr's circle on the pressure alone, you will develop a shear stress on your location rotated 45° in plane. From the pressure alone, Mohr's theory will show you that the max shear is [tex]\tau_{max} = \frac{pr}{4t}[/tex] where:
    p = pressure in psi
    r = outer radius in in.
    t = wall thickness in in.

    The normal stress resulting from the pressure is [tex]\sigma = \frac{pr}{t}[/tex].

    The shear stress due solely to the torque applied will be
    [tex]\tau = \frac{T*c}{J}[/tex] where:
    T = applied torque in in*lbf
    c = outer radius in in.
    J = polar moment of inertia in in^4

    You'll have to combine the stresses in the same directions and do a Mohr's Circle on the total load to determine the principle stresses.
     
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