Determine angle of twist in shaft

[togo]

Homework Statement

Compute the torsional shear stress and angle of twist in degrees in an aluminum tube, 600 mm long, having an inside diameter of 60 mm and outside diameter of 80 mm when subjected to a steady torque of 4500 N*m. Then specify a suitable aluminum alloy for tube.

Homework Equations

angle = TL/GJ
J = piD^4/32 (Do^4 - Di^4)

The Attempt at a Solution

angle = (4500 N*m)(0.6 m) / (2.8 x 10^-6)(80 x 10^9) = 0.012 rad

Book answer: 0.0378 rad

Wrong answer obviously. Why? Thanks

 

[LawrenceC]

J = piD^4/32 (Do^4 - Di^4)

This is wrong. Check formula for polar moment of inertia for hollow shaft.

 

[togo]

my book doesn't have it

two examples for hollow shaft use the same J formula

 

[LawrenceC]

The way you have it written, you have the units of length to the 8th power. That is not correct.

The correct formula is

J = pi (Do^4 - Di^4)/32

 

[togo]

Thanks for clearing that up

 

[togo]

Re did calculation, same answer

 

[LawrenceC]

Did you use Young's Modulus instead of the shear modulus for aluminum?

 

[togo]

Yes I did. Thanks problem solved