Why are the radial and the axial stress in a rotating thin ring null?

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SUMMARY

The discussion centers on the radial and axial stresses in a rotating thin ring, specifically addressing why these stresses are null. It is established that the only stresses present are compressional stresses due to atmospheric pressure, which remain consistent throughout the thickness of the ring due to its thinness. This understanding is crucial for analyzing stress distribution in thin-walled structures under rotation.

PREREQUISITES
  • Understanding of thin-walled structure mechanics
  • Familiarity with stress analysis concepts
  • Knowledge of atmospheric pressure effects on materials
  • Basic principles of rotational dynamics
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  • Study the mechanics of thin-walled structures in detail
  • Explore the effects of atmospheric pressure on material stress
  • Learn about stress distribution in rotating systems
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Mechanical engineers, materials scientists, and students studying structural mechanics or rotational dynamics will benefit from this discussion.

Amaelle
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Homework Statement
look at the image
Relevant Equations
centrifugal forces
Greetings, while studying the stress in the rotating thing ring
1646663324590.png


and find out the last equation that says
1646663393862.png

I would like to understand why?
Thank you!
 
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The radial and axial stresses acting on the surface of the ring are just the compressional stress from atmospheric pressure. Since the ring is very thin, these persist throughout the thickness of the ring.
 
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Chestermiller said:
The radial and axial stresses acting on the surface of the ring are just the compressional stress from atmospheric pressure. Since the ring is very thin, these persist throughout the thickness of the ring.
thanks a million!
 
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