Pressure Vessel End Cap Deflection

In summary, the end plate needs to be pressure tested before it can be shipped out to the customer, so the engineer is having a large plate cut to match the flange. The opening is 1500mm in diameter, and the plate is made from a material with low flexural rigidity. The engineer wants to see the calculations to prove that the deflection is next to nothing (AS1210 says it has to be at least 6mm thick). Is there a way to find maximum end cap deflection based on 'normal' information the engineer has or can calculate? Is there something similar to the standard beam deflection formulae for round discs?
  • #1
Spimon
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Hey everyone, hoping someone can point me in the right direction with a deflection question.

A pressure vessel I'm working on needs to be pressure tested before it can be shipped out to the customer, so I'm having a large plate cut to match the flange. The opening is about 1500mm in diameter. It's pretty low internal pressure (less than 1MPa).

I've performed FEA and I know the deflection in my plate is next to nothing (AS1210 says it has to be at least 6mm thick), but the client wants to see the calculations to prove this (you'd think the printed FEA results would be enough).

Is there a way of finding maximum end cap deflection based on 'normal' information I'd have or can calculate?

Is there something similar to the standard beam deflection formulae for round discs?

Thanks very much for any pointers!
 
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  • #2
Assuming that the end plate is bolted effectively to the cylinder so that the outer edge of the plate can be treated as fixed, the deflection at the center is:
w = p * r^4 / (64 * D), where
w is deflection,
r is the radius (either to the inside wall of the pipe or the axis of the bolt circle)
p is the applied pressure on the plate
D is the flexural rigidity of an isotropic plate.
D = E * t^3 / (12 * (1 - nu^2))
E = Young's modulus
nu = Poisson's ratio
t = thickness of the plate

This is the simplest formula. The deflection for simply supported edges is a little more involved.
 
  • #3
Thank you so much! That's the formula I was looking for. The edges will be treated as fixed (with 48 x 22mm bolts, it's not going far!). It's nowhere near in depth enough that the edge deflection is significant. It just has to prove the deflection is 'small'.
Thank you once again.
 
  • #4
Why are you looking at deflection? You should be analyzing the stress in the end cap (also called a blind flange or unstayed head). That stress needs to be below the allowable stress for the material your head is made from. ASME BPV Section VIII, Div 1, para. UG-34 covers calculations for unstayed heads, which would be the right code to design to in the US and other countries where the ASME code governs design.
 
  • #5
I'll be checking stress levels too, but I think deflection will become significant well before the stress is significantly into the elastic region, I'll be checking this.
It may well be quite safe with visible deflection, but customers don't like to see 'static' things move.

It's designed to Australian Standard AS1210. 'Unstayed End' is the term I needed. I've since found the relevant section of AS1210. Thanks everyone :)
 
Last edited:

1. What is the purpose of a pressure vessel end cap?

A pressure vessel end cap is used to seal and close off one end of a pressure vessel, which is a container designed to hold gases or liquids at a high pressure. This end cap helps to maintain the pressure inside the vessel and prevent any leakage or release of the contents.

2. How does deflection of the end cap affect the performance of a pressure vessel?

The deflection of the end cap can significantly impact the performance of a pressure vessel. Excessive deflection can cause stress and strain on the vessel, leading to potential failure and leakage. It can also affect the structural integrity of the vessel, potentially causing it to collapse under high pressure.

3. What factors can cause deflection in pressure vessel end caps?

There are several factors that can contribute to deflection in pressure vessel end caps. These include the pressure and temperature of the contents inside the vessel, the material and thickness of the end cap, and the design and manufacturing process of the vessel.

4. How is deflection of pressure vessel end caps calculated?

Deflection of pressure vessel end caps can be calculated using various methods, including analytical calculations, finite element analysis, and experimental testing. The specific method used will depend on the complexity of the vessel and the accuracy required for the calculation.

5. What steps can be taken to prevent excessive deflection in pressure vessel end caps?

To prevent excessive deflection in pressure vessel end caps, it is essential to carefully design and manufacture the vessel with appropriate materials and thickness. Regular maintenance and inspection can also help to identify any potential issues before they become critical. Additionally, following industry codes and standards can ensure the safe and reliable operation of pressure vessels.

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