Thick walled Pressure vessel -Principle stresses

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Discussion Overview

The discussion revolves around calculating principal stresses in a thick-walled pressure vessel that is pressurized from the inside. Participants explore the relationships between radial, hoop, and axial stresses, and seek clarification on the appropriate formulas for determining principal stresses.

Discussion Character

  • Homework-related, Technical explanation

Main Points Raised

  • One participant asks for the formulae to calculate principal stresses after determining radial, hoop, and axial stresses.
  • Another participant suggests assuming the pressure vessel is cylindrical and notes that the stresses must be added, emphasizing their independence due to being perpendicular.
  • It is mentioned that the hoop stress is typically twice the axial stress, indicating it may be the limiting factor in a cylindrical vessel.
  • One participant asserts that the radial, hoop, and axial stresses are the principal stresses in the system.
  • Another participant confirms that there are no shear stresses involved, only the three normal stresses (radial, hoop, and axial).

Areas of Agreement / Disagreement

Participants generally agree on the identification of radial, hoop, and axial stresses as the principal stresses. However, there is no consensus on the specific formulas to use for calculating these stresses or on the implications of their relationships.

Contextual Notes

Some assumptions about the geometry of the pressure vessel and the nature of the stresses may not be explicitly stated, and the discussion does not resolve the mathematical steps necessary for calculating principal stresses.

har_rai
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Homework Statement



Hi, I trying to calculate principle stresses for pressure vessel (thick walled) which is pressurized from inside. I calculated all 3 stresses radial, hoop and axial and looking for what formulae to use to get to principle stresses.
thanks

Homework Equations

The Attempt at a Solution

 
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Can we assume your thick walled pressure vessel is a cylinder?
The stresses must be added. But they are perpendicular and so are independent.

The radial stress is compressive, the other two tension. Hoop stress is usually twice the axial and so hoop stress is probably the limiting factor in a cylindrical vessel.
 
har_rai said:

Homework Statement



Hi, I trying to calculate principle stresses for pressure vessel (thick walled) which is pressurized from inside. I calculated all 3 stresses radial, hoop and axial and looking for what formulae to use to get to principle stresses.
thanks

Homework Equations

The Attempt at a Solution

The radial, hoop, and axial stresses are the principal stresses in this system.
 
Chestermiller said:
The radial, hoop, and axial stresses are the principal stresses in this system.
Thanks for the reply. So there is no shear stress in this, only 3 normal stresses (radial, hoop and axial).
 
har_rai said:
Thanks for the reply. So there is no shear stress in this, only 3 normal stresses (radial, hoop and axial).
Correct.
 

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