- #1
DevonZA
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Homework Statement
A solid and hollow shaft of the same material must transmit the same maximum torque. The diameter of the solid shaft is 203mm and the outside diameter of the hollow shaft is to be 216mm.
a) Determine the inside diameter of the hollow shaft. (answer = 138.7mm)
b) What percentage saving in mass would be obtained? (answer 33.46%)
Homework Equations
J=π*(D^4)/32
J=π*(D^4-d^4)/32
T/J = G * theta/l = τ/R
The Attempt at a Solution
I figured because I am only given diameters I need to use the polar second moment of area equations
For the solid shaft:
J=π*(D^4)/32
= π*(.203^4)/32
= 1.667x10^-4 m^4
For the hollow shaft (I don't think I can make the value of J the same for both the solid and hollow shaft but I don't know what else to do):
J=π*(D^4-d^4)/32
1.667x10^-4= π*(0.216^4-d^4)/32
d = 214mm
Obviously this is incorrect but I don't know where I have gone wrong