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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, |