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Euler buckling in hydrostatic pressure
- Thread starter izax1
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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.
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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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
Eng-Tips Forums:Real Solutions for Real Problems Really Quick.
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 ...
tends to support this thought
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 ...
tends to support this thought
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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
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
I think that Denial 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 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
Online tools for structural design
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
Online tools for structural design
i'd imagine that any cyclinder strong enough to resist the water pressure at a depth of 2km isn't going to globally buckle, unless it's very long (L/D), but then you'd need frames to support the 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
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
We have laid subsea pipelines almost 15km long which were 6" in diameter. By my reckoning that gives a slenderness of 98684. These pipelines do not buckle do to hydrostatic loads.
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.
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.
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