Determining Tensile Stress on Pressurized Sphere Skin

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Discussion Overview

The discussion focuses on determining the tensile stress on the skin of a pressurized sphere, exploring both thin and thick wall approximations in the context of pressure vessel theory and material strength.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant asks how to determine the tensile stress on a pressurized sphere's skin.
  • Another participant questions whether the thin wall approximation or the thick wall formula is desired.
  • A subsequent reply indicates a preference for any applicable method.
  • A formula for tensile hoop stress is presented: s = (p r)/(2 t), with variables defined as differential pressure, mean wall radius, and membrane thickness.
  • A suggestion is made to derive the thick member stress formula as a foundation for understanding the thin membrane case.
  • A recommendation is given to consult engineering literature on pressure vessels or strength of materials for further information.
  • A specific resource, Schaum's Outline of Theory and Problems of Strength of Materials, is suggested for purchase.

Areas of Agreement / Disagreement

Participants have not reached a consensus on which approximation to use, and multiple approaches are being discussed without resolution.

Contextual Notes

The discussion does not clarify assumptions regarding the applicability of the thin or thick wall formulas, nor does it resolve the mathematical steps involved in deriving the formulas.

linda123
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how to determine the tensile stress placed on the skin of a pressurized sphere
 
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Does one wish the thin wall approximation or the formula for the thick wall?
 
any?
 
s = (p r)/(2 t), where s is the tensile hoop stress, p is the differential pressure across the membrane (assuming internal pressure is much larger than external pressure), r is the mean wall radius, and t is the membrane thickness.

I would recommend one learn to derive the thick member stress formula from which the thin membrane can then be derived.

Of course, one can look in many engineering books on pressure vessels or strength of materials and find the basic formulae.

Consider purchasing - Schaum's Outline of Theory and Problems of Strength of Materials
 
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