huangyhg

euler buckling in hydrostatic pressure
is it possible to get euler buckling of a long slender cylinder at 2000m water depth? we have had some lively discussions, and cannot quite agree.
thanks fo any help.
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interesting question. i think the answer is "no". my reasoning follows.
obviously the lateral hydrostatic pressure can provide no lateral restraint, whilst the axial hydrostatic pressure creates an axial compression. if this axial compression had been created by a tensioned axial cable running down the centre of the cylinder (and not touching the sides), the cylinder could buckle: this is because as the cylinder changes its shape from straight to curved, its ends move together. as its ends move together its end forces get to do some work. very crudely speaking it is this work that, if the axial force is large enough, enables the buckling.
with our cylinder down at the bottom of the marianas trench, the situation is subtly different. here, as the cylinder changes its shape from straight to curved its ends still move together. but this time its end forces change their direction, and they do so in a way that ensures they do no work. no work means no buckling.
sudden thought. there is another way to view this. my initial statement is wrong. (beware the use of that seductive word "obviously".) under large lateral displacements, the lateral hydrostatic pressure can provide lateral restraint. once the cylinder has taken up a curved shape its "tension face" will be longer than its "compression face", and so a restoring lateral force is generated. i haven't attempted any algebra here, but i suspect that this restoring force will exactly counter the inclination of the cylinder's end planes. in fact, archimides probably mandates this.
ok, i'm up for this....i don't know what the catch is at this time, but from my mechanics background long thin shell cylinders can experience an "euler" buckling load subject to lateral pressure similar to that of the hydrostatic condition.
while the long cylinder has a bifurcation point, "euler load" but does exhibit a lower postbuckling behavior. though imperfections in the shell influence an axially loaded cylinder more, imperfections can result in lower postbuckling behavior than the actual "euler" load but not near that of the axially loaded cylinder.
now, the above discussion is based on the uncoupled behavior of each case (hydrostatic and axial). however, given that the postbuckling strength for axially loaded cylinder is about 30% of euler and that of the laterally loaded cylinder to be of 70%, i don't see that the combined behvior will enhance the strength or stability of the cylinder.
thus in my opinion, the cylinder will buckle.
regards,
qshake
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i like this question.
personally i don't think it will buckle. a buckled column has stored energy. where could the energy come from?
not to be argumentative, but ...
i think it will buckle, albeit at a considerably higher load. i think the lateral component of the hydrostatic pressure will stablise the column, but at some stage the compression load will force the column to buckle. this link ...
drop a straight cable into the water. if it euler-buckles, water pressure ought to curl it right up; the tighter the curl the farther down it goes.
but does it need to be a hollow cable?? is there anything inside the cylinder?
i took the original question to be about a solid cylinder, ie a bar. that way potentially distracting side issues like cross-sectional buckling do not arise. perhaps izax1 could clarify.
thank you all for your replies.
the case here is a hollow cylinder with internal athmospheric pressure. it contains electrical equipment to be used at approx 2000 m water depth. we recognise the local buckling (ovalisation) as a real loadcase. but the big question is global axial buckling. (termed euler buckling in some text books) as far as i can see, the axial buckling will be a function of stiffness of the cross section.
from your answers, i can see that there is some differences in opinion. i, myself, am changing from: yes, it will buckle to: no, it will not buckle. there will always be a restoring force to any force direction due to hydrostatic force field. so there will always be a restoring force to the axial force as soon as it start to buckle.
but i am still interested in your input
thank you
think about all those subsea pipelines. they dont buckle laterally due to hydrostatic load. local buckling however is a different issue altogether.
i think that denialfff">fff"> has the good argument, though i prefer a different way of reasoning.
the treatment of euler buckling in columns implicitly assumes that the end forces are coaxial and maintain their initial direction as the buckling starts. this is not true for the underwater cylinder, as the end forces change their directions with buckling, and their effect is even a stabilizing one.
another proof is the also good argument by ussurifff">fff">: for underwater pipelines (or for common piping under vacuum or for pressure vessels and tall columns under vacuum), lateral buckling is not an issue.
local buckling is a different matter, as also noted by ussurifff">fff">: in an unstiffened cylinder under vacuum buckling occurs because of the circumferential stress. however for a circumferentially stiffened cylinder local buckling due to axial stress may be an issue.
prex

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