# Externally pressurized vessel

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How should a thin walled vessel be shaped so that it is stable in compression without buckling intervening upto yield by external pressure?

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In isolation a sphere is the most efficient shape. Unfortunately the vessel is rarely in isolation, so compromises have to be made. What is the particular requirement?

Keith Civil Solutions

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Dear Narasimham:

"Thin walled" constrains the maximum vessel size.

As a comparison, the Trieste had 3.5" thick walls for a sphere of

78" diameter. Applied pressure 16,000 psi (don't know what the factor of safety was).

David A. Smith

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Here's an example of the *wrong* shape ;o) ...

Ned Simmons

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Here's one thought - off the top, not necessarily optimal. It is easy to show that a sphere can handle excess internal pressure until its thin wall yields.

A thin wall sphere with excess external pressure is a whole 'nuther ball game. Recall the rule of thumb for a column not to fail by buckling is a length to diameter of 20 or less (Though 80:1 is usable in certain situations.)

To import this idea into the design of a spherical container: If the effective thickness of the (thin??) walls is 1/20 of the circumference of the sphere, this should be a recipe for buckle resistance. For T = wall thickness, D = diameter of sphere: if T = > pi X D / 20 then T => 0.16 X D

For this idea, 4/3 pi D^3 / 8 - 4/3 pi ( 0.68 X D)^3 / 8 or 4/3 pi (0.32 X D / 2 )^3 or 0.17 X D^3 of low density filling is needed between two thin skins.

Brian Whatcott Altus OK

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Is not sphere for internal pressure? seems corrugations are better, but have no details.

Vacuum bottles.

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A sphere is the most stable shape.

Sure you do. Think accordion. No, corrugations are not better. Any defect from spherical increases the likelihood of failure.

David A. Smith

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Due to buckling as is evident in the railroad car example another poster has given a link to.

Vacuum spheres are used for exhausting hypersonic wind tunnels all the time. The low pressure is needed to simulate high altitude conditions. At work the facility I am responsible for uses a 70 ft diameter sphere which we pump down using a 3 stage condensing steam ejector. Had the opportunity to go inside the sphere last week for the first time since it was constructed in 1990. A unique acoustical environment. The biggest one on the field at NASA LaRC is a 100ft dia one of our other facilities uses as well.

See

70 is on the left, the 100 in the center and several 40s we just took over are on the right.

-- Ed Ruf Lifetime AMA# 344007 ( snipped-for-privacy@EdwardG.Ruf.com)

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Ed,

the \$64 question: how thick are the walls?

Brian whatcott Altus OK

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I don't remember off-hand. However, I don't believe vacuum or pressure loading was the determining factor. I'd imagine wind loads for hurricanes might had been that. However, I can find out next week. Our branch safety head was the TPO in engineering during the minor CoF when it was built.

FWIW, I say pressure loading because we do airbreathing propulsion tests using H2 heated flows so we can dump raw H2 into the sphere in a failure. It was sized to take an H2 detonation starting at something under ~1/7th of an atm. Both these facilities share the sphere. These days, I run the CHSTF.

?field=13&id=2&fac=1-- Ed Ruf Lifetime AMA# 344007 ( snipped-for-privacy@EdwardG.Ruf.com)

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You've probably figured out by now that size matters in this case. So how much volume are you trying to uh...vacuumize?

If the vacuum bottle is "large", the ASME Boiler and Pressure Code Section 8 Div 1 (someone please confirm the section and division), has a whole bunch of design criteria, material/fabrication requirements, table charts and graphs that will enable you to build a workable vacuum bottle. If you do it right and get the right approvals, you can even go into production with it.

Lance

*****
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If the vessel can withstand vacuum then it can probably withstand internal pressure. So among wind,internal/external pressures, is wind load the criterion for deciding wall design thickness ? It is not clear if there is a proper structural theory for stable optimal vacuum vessel design as there is for internal pressure. (So this enquiring post.)

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More a matter of it not designed for that loading than the shape.

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Spheres and cylinders are common shapes that can be easily analyzed.

Really any shape can be made to work with sufficient thickness and proper material selection. Different story if you want the optimal shape.

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Optimal shape is asked for, ...just as the sphere for internal presurization.

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This comment reminds me that supposing that a sphere is optimal as a vacuum tank ain't necessarily so. I define optimal as amount of evacuated volume per weight of container.

This sort of problem is perfectly well suited to a genetic algorithm that can run a stress program on each shape evolved.

But for starters, heres a shape that has a TENSION skin, with compression columns - this might be pretty efficient.

On two hoops of diameter D, place an endcap of radius D

Now with the endcaps facing IN, place a tension skin between the two hoops spaced D apart, this skin is a surface of revolution of a circle, rotated on an axis through the centers of the hoops: a circle centered one diameter away from the axis of rotation. The skins are in tension, and with a maximal excess pressure of 25 psi with a margin, that's a thin skin. The hoops are in compression. There is an unresolved force, that is the force pulling the two hoops towards each other. This "deflating" force is resisted by three, four or five columns placed bewteen both hoops externally.

Brian Whatcott Altus OK

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You asked for a shape that would not buckle. For that an optimal shape is not required.

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Yes, that was what I of course implied. As you say " shape can be made to work with sufficient thickness and proper material selection " .. but when one has to settle for arbitrarily overdesigned vessels, or by single point failure at high stress concenrations etc., the state of art is not showing well.

For an optimally designed pressure vessels performace factor is pressure*volume/ structure weight. By energy considerations this is related to strength/density ratio of the material when a constant stress or simultaneous failure criterion is satisfied.This is way to go for material economy and cost even in case of vacuum.. or so it appears to me.

So my original query may well have been :

How should a thin walled vessel be shaped so that it is stable in compression without buckling intervening upto yield by external pressure for highest/optimum performance (Vacuum pressure* Volume of vessel evacuated/ Vessel weight) ?

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Would a double skin construction be a good idea ?

Yield strength in a buckling situation is almost irrelevant, it's stiffness that counts.

( is weight or cost a critical factor... what is being optimised ? )

Sandwich high modulus carbon fibre would be good,

A ribbed ( internal or external ) shape will out perform a simple shell,

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Thanks. If buckling is altogether avoided it may be relevant.

It is the weight of vessel.

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