# Calculate shear stress unit conversions [duplicate]

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?

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.

• 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. – user1610950 Sep 20 '17 at 11:28