Replacing a hollow shaft with a solid shaft

[stainton1]

Homework Statement

" determine the diameter of a replacement solid shaft manufactured from the same material and subjected to the same maximum shear stress and torque"

Ok so I previously calculated the following:

Maximum shear stress= 35.8 x 10⁶
Torque= 450.117 x 10³
Hollow shaft external and internal diameters= 400mm and 200mm

Homework Equations

T/J = shear stress/r

J= Pi x d⁴/32

r= D/2

The Attempt at a Solution

Basically I attemted it in a very long winded way which was found to be wrong when I went through it with my tutor. What happened was I went off an example we done in class which was similar but for replacing a solid shaft with a hollow one whereas I am wanting to replace a hollow shaft with a solid one. I've read the rules on here and I know its not a place to get your assignments done for you but I was hoping someone would be able to give me an explanation and point me in the right direction as my tutor isn't being to helpful. Cheers.

 

[nvn]

stainton1: Hint: Look up or write the formula for polar moment of inertia, J1, of a round tube. Set shear stress tau1 = tau2. Substitute.

 

[DannoXYZ]

Isn't there a difference in the equations for a thin versus thick-walled hollow shaft?

 

[nvn]

DannoXYZ: In the limit, yes, you can obtain a different, approximate formula for a thin tube. But why bother with an approximate formula, when you can instead use the exact formula. Besides, stainton1 does not have a thin tube.