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


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


No, that is not correct. The modulus of rigidity is not related to the allowable shear stress in the shaft, so you would not set τ equal to the modulus of rigidity.

What you need is the allowable shear stress. That depends on the material, what type of loading you are using (such as a static load or a repeating load), and what factor of safety is required.

  • $\begingroup$ I updated the question. Keep it simple and forget safety factor for now. Why wouldn't the modulus of rigidity be used in the calculations and if not that, then what or how? $\endgroup$ Sep 27 '17 at 17:01
  • $\begingroup$ this answer is correct. the modulus of rigidity (shear modulus) is an elastic property not directly related to strength. If your data sheet doesn't give any strength data you might say what the material is and maybe someone can help. $\endgroup$
    – agentp
    Sep 27 '17 at 20:25

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