Calculate Pressure vessel Collapse Pressure

[Christy001]

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]

 

[Chestermiller]

Do you consider collapse buckling? If so, what formula did you use?

 

[Christy001]

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.

 

[Dr.D]

thickness 100m and inner radius 254mm,

Are these really the dimensions you want to talk about? 100 thick is a petty thick wall!

 

[Christy001]

Sorry typo - 100mm not m !

 

[Dr.D]

Sorry typo - 100mm not m !

That makes quite a bit of difference.
With this mod, the thick walled pressure vessel equations should apply.

 

[Chestermiller]

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.

 

[Christy001]

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 ?

 

[Chestermiller]

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.