# Tau max value in torsion calculation [duplicate]

I am going to try and ask this question again.

In this formula to calculate shear stress in a solid shaft: τ = T r / J

If I want to solve for the radius; I should use the modulus of rigidity from the material sheet in the formula for τ ?

example, knowing T = 1000Nm J = pi * R^2 / 2 τ = modulus of rigidity from material sheet

If I want to design for a solid shaft with a known material and known torque then I can use the formula: τ = T r / J
replacing

[EDIT]

Density     2.6989 g/cc 0.097504 lb/in³
Mechanical Properties   Metric  English Comments
Hardness, Vickers   15  15  Annealed
Modulus of Elasticity   68.0 GPa    9860 ksi
Poissons Ratio  0.36    0.36    calculated
Shear Modulus


I added the above material property. Let's say that I am making a solid shaft that will be under torsional stress, the shaft will be spinning but at a low RPM so there's no shocks to them.

To keep things simple forget about about factor of safety.

τ = modulus of rigidity from the material property sheet, is that correct? If it's not correct; how would I calculate the diameter of the shaft based on the info that I have which are; maximum torque the polar moment of inertia the mechanical property sheet