Where I refer to Section 6.21.15 --> that is actually the
buckling equation for conical sections. The corresponding one for
cylindrical shells is actually in 6.19.13, but the concept is the
same.
-Sean
On 16/12/2010 9:39 PM, Sean T. Stevenson wrote:
In response to a number of questions that have arisen recently on
the list with regard to pressure hull design, I have begun
composing a primer on this topic which will attempt to address all
of these common questions. I will post it to the list when it is
complete. It is taking a while to do, but I want to make sure
that it is sufficiently thorough. I also have the optimization
software on the back burner - my real-world work has limited the
amount of time I have been able to spend on this, but I have not
abandoned it completely. There is still much to be done before I
will be comfortable with a general release.
To briefly address failure lobes - it has been determined
experimentally that the number of lobes present in a cylindrical
shell failed by buckling is predictable within a probability
distribution, and is dependent on the diameter, wall thickness and
overall length (or length between heavy stiffeners) of the shell,
as well as the Poisson's ratio (directional strain relationship)
of the shell material. For visualization, the video you linked to
shows a good example of a six lobe buckling failure. The way this
is implemented in the ABS calculations is a bit counterintuitive -
rather than calculate n explicitly, the designer is expected to
repeat the calculation for the limit pressure for the overall
buckling mode for multiple values of n, and take the lowest result
as the actual limit pressure. I note that the value of Poisson's
ratio is not actually included in the ABS calculation, so I must
assume that ABS has made conservative assumptions in order to
simplify what would otherwise be a lengthy derivation for the
benefit of the designer. In this case, you simply start with n=2,
and repeat the calculation for n=3, n=4, etc. If you look at the
first equation presented in section 21.15, this _expression_ for
limit pressure contains two terms. For some, but not all, sets of
shell geometry values, at n=2, the first of these terms is
dominant, and as you increase n, the second will become dominant.
The corresponding graph, Section 6, Figure 4, shows curves from
n=2 to n=6: The implication is that increasing n beyond a
reasonable number of values will just end up increasing the limit
pressure, and while you could do this ad infinitum, this is
irrelevant because what we are looking for is the minimum limit
pressure - the point is to make sure that if your particular
geometry allows for either of the two terms to be the dominant one
as n is varied, that this situation is identified and the lowest
possible limit pressure used. Ergo, you want to repeat this
calculation for a few values of n, and if your result is steadily
increasing, you can stop calculating and go back to your lowest
calculated value.
The overall buckling mode of failure has the lowest usage factor
(eta) specified by ABS: 0.50, which corresponds to a factor of
safety of 2.0 for this failure mode. This highest eta value
specified by ABS is 0.8 for inter-stiffener strength (1.25 safety
factor), so if you design your pressure hull such that all of the
maximum allowable working pressures for each mode of failure are
identical, your hull will fail by inter-stiffener strength failure
- a deterministic, predictable mode of failure in comparison to
buckling.
-Sean
On 16/12/2010 7:25 PM, Jon Wallace wrote:
Hi Les,
I'm afraid I cannot adequately explain failure lobes and so I
won't even try. In layman terms they refer to the number of
"dents" created when a cylinder fails by general instability (I
think). However I do not understand why a particular cylinder
of specific dimensions would fail with two lobes instead of
three, four, five, or six lobes.
The following video link shows a good series of illustrations of
failure lobes. At 3:01 they show what appears to be a one lobe
failure. At 3:06 it shows what they describe as "A near
perfect 6 lobe failure". So these will at least show you what
a failure lobe looks like. http://www.dailymotion.com/video/x86dsc_collapse-of-model-submarine-pressur_tech
The following link also does a good job of illustrating local
buckling and general instability. Scroll down about two-thirds
and look for Figures 11.1, 11.2, 11.3, etc. In Figure 11.2 you
can see that the cylinder appears to have failed with two
lobes. Be careful with this link...you might need to piece it
together carefully if it gets split into separate lines by the
mailing list mailer.
http://books.google.com/books?id=rv0QXKI0HvMC&pg=PA289&lpg=PA289&dq=buckling+vs+general+instability&source=bl&ots=WYPwdqGZU6&sig=mtT5QVjTCj8_sLX4o9CZakPsUL8&hl=en&ei=zc8KTc3TKYGBlAea5J2tDA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CCEQ6AEwAQ#v=onepage&q&f=false
The multiple references to "maximum allowable working pressure"
are specific to the kind of failure being calculated. Cylinder
failure can be by general instability, buckling, inter-stiffener
strength, etc. From previous discussion about this, the goal is
to adjust your cylinder specifications so that all the "maximum
allowable working pressure" results are as close as possible to
each other. You won't ever get any of them exactly the same,
but extreme differences are not preferable.
The usage factor is essentially a safety margin. Use the
defaults and you will end up with the ABS recommended "Design
Depth" or maximum operating depth. Ok, Alan, Jim, and Sean, did
I get that right this time??? :)
Jon
On 12/16/2010 9:27 PM, Les & Anna wrote:
Hi Jon
You referred to the psubs
spread sheet for ribbed calculations,
I have been playing with this
spread sheet and perhaps you or someone else can, excuse
my ignorance, tell me to what the following changeable
colums refer to'
1. n - "no of circumferential
lobes for failure calculation" ?
2. n - "maximum allowable
working pressure?".........(several times under several
headings with different values applied.) also what units?
3. n - "usage factor?"
Also not sure if it is me or
the site, but the activation to the acrobat document site
for the "mettalic pressure boundary components" does not
appear to work.
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