Calculate Pressure vessel Collapse Pressure

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Discussion Overview

The discussion revolves around calculating the collapse pressure of a cylindrical pressure vessel with specific dimensions and material properties. Participants explore the implications of wall thickness on stress calculations and the potential for buckling, considering both theoretical and practical aspects of pressure vessel design.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a problem involving a cylindrical pressure vessel with a thickness of 100mm and an inner radius of 254mm, seeking to calculate the pressure that would cause collapse.
  • Another participant questions whether collapse buckling should be considered and asks for the formula used.
  • A participant suggests using the formula for hoop stress, noting that hoop stress is the maximum stress for thick-walled vessels, but expresses confusion about how to incorporate the thickness of the end caps into the calculations.
  • There is a clarification regarding the dimensions, with one participant correcting a typo from meters to millimeters, which significantly affects the applicability of thick-walled pressure vessel equations.
  • One participant recommends researching radial compressive buckling of thin-walled cylinders, drawing an analogy to axial compressive buckling of rods, and provides a practical example of observing buckling in a 2-liter bottle.
  • Another participant agrees that the vessel is classified as thick-walled but raises uncertainty about whether the same mode of instability applies given the specific thickness-to-diameter ratios and pressure differences.

Areas of Agreement / Disagreement

Participants generally agree that the vessel is classified as thick-walled, but there is no consensus on whether collapse buckling should be considered or how it might affect the calculations. Multiple competing views remain regarding the appropriate approach to the problem.

Contextual Notes

Participants express uncertainty about the applicability of thin-walled versus thick-walled equations, particularly in relation to the dimensions provided. There are unresolved questions about the influence of end cap thickness on stress calculations.

Christy001
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Homework Statement


I have a simple cylindrical pressure vessel with thickness 100m and inner radius 254mm,.the cylnder has flat head closed ends but these are thickness 30mm. I need to calculate the pressure that would cause the vessel to collapse given material properties E=207Gpa, poissons 0.3, yield stress = 207Mpa

Homework Equations


I know that there are equations out there for hoop and radial stress which are quite simple but can I just assume I should use only for thickness 30mm

The Attempt at a Solution


I have used the simple equations for hoop and radial stress however I'm not sure if this is correct or not [/B]
 
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Do you consider collapse buckling? If so, what formula did you use?
 
In theory I was thinking of using the formula for hoop stress (as hoop stress is the max stress rather than axial or radial) as this problem is a thick walled rather than thin walled pressure vessel. I do have the equations which are below. So I'm thinking that if I use 207Mpa as the value for hoop stress( which is the yield stress) , a and b though are outer and inner radius therefore I'm confused as this doesn't consider the thickness of the end caps, rather the thickness of the cylinder.
upload_2019-3-17_17-56-42.png
 

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Christy001 said:
thickness 100m and inner radius 254mm,

Are these really the dimensions you want to talk about? 100 thick is a petty thick wall!
 
Sorry typo - 100mm not m !
 
Christy001 said:
Sorry typo - 100mm not m !
That makes quite a bit of difference.
With this mod, the thick walled pressure vessel equations should apply.
 
Google "radial compressive buckling of thin walled cylinders." This is a stability problem analogous to axial compressive buckling of rods. To see the modes of buckling of cylinders, just suck some of the air out of an empty 2 liter bottle. You will see the quadra-lobal buckling pattern.
 
Chestermiller said:
Google "radial compressive buckling of thin walled cylinders." This is a stability problem analogous to axial compressive buckling of rods. To see the modes of buckling of cylinders, just suck some of the air out of an empty 2 liter bottle. You will see the quadra-lobal buckling pattern.
Thanks - but I don't think thin-walled would apply in this case ? Because of the dimensions wouldn't this be classified as a thick walled pressure vessel ?
 
Christy001 said:
Thanks - but I don't think thin-walled would apply in this case ? Because of the dimensions wouldn't this be classified as a thick walled pressure vessel ?
It would be classified as a thick walled vessel. But it is not clear whether this same mode of instability could occur in vessels with thickness-to-diameter ratios and pressure differences characteristic of your system. I wanted to make you aware that such an instability could be possible, and provide some equations for crudely estimating whether it might need to be addressed.
 

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