Now that...is what you call an engineering analysis!
"but also of concentric cross-section
>as you travel along its length. Anything outside of that is
>extranneous material, as far as the calculations are concerned"
That is what I find so impressive about engineering, the ability to minimally design for the required stressors, and why amateurs like myself have to overbuild a bit to feel good about it!
Great job Sean!
Joe
From: "Sean T. Stevenson" <cast55@telus.net>
Reply-To: personal_submersibles@psubs.org
To: personal_submersibles@psubs.org
Subject: Re: [PSUBS-MAILIST] TANK / PSI QUESTION
Date: Sun, 12 Feb 2006 17:19:00 -0500
>These are very dissimilar cases. In the case of internal pressure,
>the pressure actually acts to deform the vessel in a manner which
>increases roundness. Imagine looking at a cross section of the
>cylinder in question (i.e. a circle, with a wall thickness). Now
>mentally divide that circle in half. The tensile stress in the
>cylinder wall will need to be the value that holds those halves
>together in the presence of the internal pressure - i.e. the
>pressure multiplied by the projected area. In this case, that
>internal pressure divided by the inner diameter times the length of
>the cylinder (giving an area) gives you the force, which is
>countered by the tensile stress in the area of the cylinder walls -
>i.e. (OD-ID) multiplied by that same length - the length cancels,
>which is why we can examine this as a 2-D problem. Now imagine
>perturbing the geometry of the circle - i.e. making a dent in the
>cylinder wall, either to the inside or the outside - the direction
>doesn't really matter. You will notice that the tensile force in
>the cylinder wall acts to straighten out the dent. As with a
>pressurized can or pop bottle, when you squeeze it, provided you
>don't do it so hard as to cause plastic (non-recoverable)
>deformation, the internal pressure will return it to its former
>shape.
>
>This is not the case with an externally pressurized vessel. A
>vessel subjected to external pressure acts similarly in that the
>compressive stress in the cylinder wall will ideally be equal to the
>external pressure multiplied by the projected area (which is now the
>OD, not the ID of the cylinder), giving the compressive force, and
>we divide this by the area of the cylinder walls to get the
>compressive stress in the cylinder wall. The difference in this
>case is that, if you then dent the cylinder wall in either
>direction, putting it out of round, it is not self-correcting, and
>in fact will cause a stress concentration which tends to cause the
>cylinder to buckle and crush. Any deviation from the perfectly
>round case needs to be accounted for by calculating based on the
>largest perfectly round circle (largest OD, smallest ID) than can be
>inscribed within the circle that actually exists (subject to
>manufacturing and measurement accuracy). This is complicated even
>further when extrapolated to the 3-D case, since our largest circle
>becomes a largest cylinder, which must exist in an actual cylinder
>that needs not only be round, but also of concentric cross-section
>as you travel along its length. Anything outside of that is
>extranneous material, as far as the calculations are concerned. A
>good demonstration of this is standing on an empty pop can. A 200
>lb person can, if careful, balance themselves on an intact aluminum
>soda can. Now, if someone bumps it, even slightly, the resulting
>deformation is unrecoverable and the can crushes. Since it is not
>possible to fabricate perfectly round cylinders which do not deform,
>we must do the next best thing - a combination of thicker than
>theoretically required wall thickness, in conjunction with bracing
>(i.e. ring stiffeners) to prevent any deformation from excessively
>reducing the theoretically perfect cylinder that exists within the
>fabricated one.
>
>Clear as mud?
>
>-Sean
>
>
>Norm Parmley wrote:
>
>>Here's a question to the more mechanical types. If I have a normal
>>rounded metal tank rated for an internal pressure of 200 psi then,
>>I could assume it would be capable of 200 psi external pressure?
>> Norm P.
>>
>
>
>
>
>
>
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