Pressure loading on circle shaped plate

[xr4titis]

Hola forum,

We are modifying an existing nozzle (20" I.D. X 8" high X 63" thick hoop) to perform pressure testing on the lid that it mates to. We intend to close off the other end of the nozzle by welding a plate to the bottom of it. We've done this before with the old fabricator "that'll hold" calculations. I'd like to go at this one a little smarter and find the proper thickness required and maybe the stress on the weld.

The information:
P = 165 psi
A = 314 in^2

Assumption:
I can apply a force of P*A at the center of the plate.
I can react that force at the area where the plate meets the nozzle. (O.D. = 21.25 X I.D. = 20)

The question:
How do I calculate moment of inertia across a plate of changing width (a circle).

Any help is appreciated even the proper terminology of what I'm trying to do so I can look it up.

 

[rb1957]

"How do I calculate moment of inertia across a plate of changing width (a circle)." ... you don't, in fact asking raises all sorts of questions about how much structures/stress you know.

uniform pressure on a round plate is a standard problem with a simple handbook solution, but if you're going to apply 52,000 lbs to it you need to be Way more careful.

good luck, and get professional help; or do it the good ol' way.

 

[xr4titis]

Can't say I didn't expect that...I'm a bit rusty. I'm sure we will do it "the good 'ol way" but I'm still want to try and figure this out.

Can't you give me a hint?

 

[GregLocock]

The /hint/ is t^4.

It is covered in Roark. You are looking at a simply supported circular plate, not a beam.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[xr4titis]

Thank you sir. I couldn't find anything in my old textbooks or Machinery's Handbook on this but I did find information on the web leading me to an equation for a distributed load on a circular plate with clamped ends. The resulting displacement is reasonably close to the displacement I get using FEA.

The problem is (I'm embarrassed to ask) is that I cannot successfully relate the displacement to the corresponding stress in the plate.

I'm using Hooke's Law multiplying E (modulus of Elasticity) by the calculated displacement divided by the original thickness. The result does not correlate well with FEA results.

I know this is a dumb question and I would ask the engineer sitting next to me if there was one. Any help is appreciated.

 

[bkal]

As mentioned by Greg, you need to look into Roark. The way you tried to calculate stresses fails as you are not using correct / real strain (to multiply with Young's modulus to get stress value). Deflection of the plate divided by its thickness, while being some measure of strain, is not a real strain, especially as you probably want a stress in the plane of the plate.