Euler buckling in hydrostatic pressure
Euler buckling in hydrostatic pressure
(OP)
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.
Thanks fo any help.






RE: Euler buckling in hydrostatic pressure
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.
RE: Euler buckling in hydrostatic pressure
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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RE: Euler buckling in hydrostatic pressure
Personally I don't think it will buckle. A buckled column has stored energy. Where could the energy come from?
RE: Euler buckling in hydrostatic pressure
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 ...
http://www.pathwayb.com/Squirm.htm
tends to support this thought
RE: Euler buckling in hydrostatic pressure
RE: Euler buckling in hydrostatic pressure
RE: Euler buckling in hydrostatic pressure
RE: Euler buckling in hydrostatic pressure
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
RE: Euler buckling in hydrostatic pressure
RE: Euler buckling in hydrostatic pressure
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 Ussuri: 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 Ussuri: 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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RE: Euler buckling in hydrostatic pressure
the axial stress in the cyclinder from pressure is only 1/2 the hoop stress (pR/t) ...
a sense of the geometry would be nice ... L, D, t
RE: Euler buckling in hydrostatic pressure
They can buckle laterally in a process known as upheaval buckling.
Upheaval buckling occurs when trenched pipelines are subjected to an axial compression force as a result of high temperature and pressure within the pipeline. The pipeline experiences a large vertical displacement as a result and pushes up through the soil cover, leaving the pipeline exposes to impact from anchors or trawlboards. But the forces which cause this to happen are applied loads over and above the environmental loads.