Determine angle of twist in shaft

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SUMMARY

The discussion focuses on calculating the angle of twist and torsional shear stress in a hollow aluminum tube subjected to a torque of 4500 N*m. The correct formula for the polar moment of inertia (J) for a hollow shaft is J = π(Do^4 - Di^4)/32, where Do is the outer diameter and Di is the inner diameter. The initial calculation used the wrong units, leading to an incorrect angle of twist. The final resolution confirmed the use of the shear modulus instead of Young's modulus for aluminum, correcting the calculation.

PREREQUISITES
  • Understanding of torsional mechanics
  • Familiarity with shear modulus and Young's modulus
  • Knowledge of polar moment of inertia calculations
  • Basic proficiency in algebra and unit conversion
NEXT STEPS
  • Study the derivation and application of the polar moment of inertia for hollow shafts
  • Learn about the differences between shear modulus and Young's modulus in material science
  • Explore advanced torsion analysis techniques for different materials
  • Investigate the properties and applications of various aluminum alloys
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Mechanical engineers, materials scientists, and students studying torsional mechanics or structural analysis will benefit from this discussion.

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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
 
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J = piD^4/32 (Do^4 - Di^4)

This is wrong. Check formula for polar moment of inertia for hollow shaft.
 
my book doesn't have it

two examples for hollow shaft use the same J formula
 
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
 
Thanks for clearing that up
 
Re did calculation, same answer
 
Did you use Young's Modulus instead of the shear modulus for aluminum?
 
Yes I did. Thanks problem solved
 

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