Pressure Vessel End Cap Deflection

Spimon

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!

SteamKing

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.

Spimon

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.

Q_Goest

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.

Spimon

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 relevent section of AS1210. Thanks everyone :)