# Thin Cylinder Theory

#### brd

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).

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#### FredGarvin

Science Advisor
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 $$\tau_{max} = \frac{pr}{4t}$$ where:
p = pressure in psi
r = outer radius in in.
t = wall thickness in in.

The normal stress resulting from the pressure is $$\sigma = \frac{pr}{t}$$.

The shear stress due solely to the torque applied will be
$$\tau = \frac{T*c}{J}$$ 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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