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The formula for newtons to pascals is below.

$$1\text{ Pa} = 1\text{ N/m}^2 = 9.81\text{ kg/m/s}^2$$

I am trying to solve this problem but the units are a bit confusing. I want to get the shear stress (tau) based on these input variables.

General stress = Force/Area

The force is 1255Nm the area is length 20mm and height 10mm.

$tau = 1.255\ x\ 10^6\ Nmm\ /\ 200\ mm^2$

with straight division,

$1,255,000/200 = 6275$

but I am unsure about the units;

How do I mathematically devise the units?

[Edit 2] I think I've narrowed down the question and would like to see if I am on the right track.

The formula: Tau=Tr/J since I know the Maximum torque, the polar moment of inertia for a solid shaft, I should use the Modulus of rigidity from the material properties sheet for Tau then solve for the radius to get the diameter of the shaft.

Is that correct?

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You might be mixing up units here. You say the applied force is 1255Nm: Is this is a torque application? If so, you might want to look at the Torsion formula, Tau=Tr/J (https://en.wikipedia.org/wiki/Torsion_(mechanics))

If the units of force are (as they should be) Newtons, then the shear stress comes out to be in N/mm^2, as expected.

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  • $\begingroup$ It is a torque application, I think that I am mixing things up. I have 1255Nm and I'm trying to calculate the shear stress that would apply on an area 200mm^2. The reason is I would like to use that shear stress in my formula T/J = Fs/R; The issue is I'd like to solve for radius so that I can figure out the diameter of a solid that will not fail. $\endgroup$ – user1610950 Sep 20 '17 at 11:28

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