# Maximum torsion shear stress in cylinder

I am trying to figure out am I doing this calculation correctly.

To get the maximum shear stress for a solid cylindrical pipe I need two formulas:

Moment of inertia = pi/2*r^4

Not sure what this formula is called but its:

max = T*r/ Moment of inertia

I tried to calculate these numbers for a solid shaft that is 20mm in diameter with a torque of 1255nm.

1255*0.02/((pi/2)*0.02^4)

Pascals = 99869726.7902 MegaPascals = 99.87

The material that I have has a yield strength of 490 MPa.

Is the calculation saying that even at 20mm radius the stress will be below the 490MPa that would cause this pipe fail elastically?

Please notice that although you have unwittingly only doubled the diameter, the stresses decreased 8 fold ($$2^3$$), due to the non linearity of the problem. So, you can easily get it wrong.