Calculating Inside Diam. & Stress of Hollow Steel Shaft

[darkmagic]

Homework Statement

Given:
hollow steel shaft
Torque = 5400 Nm
Torsional Shear = 150 MPa

Required:
Inside diameter
Outside Diameter
Stress on the inside of the shaft

Homework Equations

The Attempt at a Solution

I solved both the diameters which are 64.49 mm and 48.37 mm.
I don't know what formula to use to determine the stress on the inside of the shaft

I used to 16T/[pi d^3) where d is the inside diameter. Am I correct?

 

[rock.freak667]

In general

T/J = (shear stress)/r

so shear stress = Tr/J

at the outer, r = outer radius

at the inner r = inner radius

 

[darkmagic]

The J and r are already substituted in the formula I used. Ok thanks.

 

[darkmagic]

Is J there the J of the smaller circle, with the inside diameter? I got 243 Mpa which is larger than 150 Mpa.

 

[rock.freak667]

Is J there the J of the smaller circle, with the inside diameter? I got 243 Mpa which is larger than 150 Mpa.

Your shaft is a hollow one, so the J = (π/32)(d_outer⁴-d_inner⁴)