RE: [PSUBS-MAILIST] Pressure Hulls

[Alec Smyth <Asmyth@changepoint.com>]

Ian,

I looked up sphere calculations in Allmendiger and found two similar
equations. Note that both formulas assume Poisson's ration = 0.3, which I
interpret to mean only use them for calculations with steel.

a) The first equation is derived theoretically:

p = 1.21*E*(t/R)^2

where: 

E = modulus of elasticity in compression
t = shell thickness
R = radius to midplane of shell

WARNING: It mentions that in practice, due to variations in sphericity and
shell thickness spheres tend to collapse at much lower pressures than those
calculated... as much as one-fourth the pressure.


b) The second equation is empirical:

p = 0.84*E*(t/R0)^2

where R0 = outside radius


Now for comparing results:

The two equations are very similar, with the second one being more
conservative. But the numbers I get are about an order of magnitude above
what Pat got using your ABS formula. I used 

E = 29,000,000 lbs/in2
t = 1"
R0 = 54"
R = 53.5"

Which gives a result of 12,259 psi for (a) and 8,353 psi for (b), while Pat
got a more reasonable 1,111 psi. I think my results are obviously incorrect,
yet the only obvious way I can see to bring down the values is that I might
be using an incorrect value for E. Yet I checked that in several sources. E
= 2,900,000 would give a nice result, but the units don't jibe.

I'm at a bit of a loss on this discrepancy. Any ideas?



thanks,

Alec



-----Original Message-----
From: Ian Roxborough [mailto:irox@ix.netcom.com]
Sent: Monday, July 01, 2002 1:54 AM
To: personal_submersibles@psubs.org
Subject: Re: [PSUBS-MAILIST] Pressure Hulls


Hi Dewey,

On Sun, 30 Jun 2002 21:20:44 -0700 (PDT)
Dewey Mason <drmason2001@yahoo.com> wrote:

> Hey All,
>    Today I found 3 stainless steel spheres about 9
> feet in diameter+/-. They are about 1" minimum
> thickness with a small increase near the inlet head.
> They are used, having been commercial CO2 tanks for a
> local gas producer. While I do realize the potential
> problems of using used stuff, I think the maintenance
> was good enough to consider it. Does anyone have a
> means to calculate the unreinforced crush depth on
> such a piece?

P = 2Ut/R
Where:
 U = min yield strength
 t = hull thinkness
 R = outside radius

Beware, I could have gotten this wrong...

I copy this out of  The American Bureau of Shipping's
"Rules for Building and classing: Underwater vehicles, systems
and hyberbaric facilities."  But I've seen it many other places
as well (so no worries on copyrights and such).

I'd recomend getting the above book, I've hardly started
it and it's proved very useful.

I'd also recommend check the crush depth several different
ways, such as using different equations and checking them
against a Finite Element Method.  I guess using a real high
safety factor since it's "used" would help too.

>  Hopefully the much smaller diameter will leave enough strength
> difference to put the crush depths very nearly the same. At least to
> where I can P-test the cabins at 75%, and run them at
> 50% of calculated crush, and P-test the mechanical
> compartment at 90%, running it at maybe 80% or so.

Do you have access to a pressure testing facility/chamber?

>    Maybe someone will think I am one of the ones
> needing banishment after this, but I hope to hear the
> thoughts and ideas of those who think I might can
> stay.

Let's save the banishment for people who post multilevel
marketing schemes and adverts not relating to submarines...

Ian.
-- 
The moon ate the sun on Monday and it was an awsome sight to see.