Shells Under Pressure

The words you need there are "Myth" and "Curve -Radius" or perhaps Ratio. The discipline you need is called F.E.A. Finite Element Analysis. Basic FEA will depend on 1 the material used 2 the force applied over what area and 3 the time of maximum pressure at a given point 4 temperature along with many other factors.. These are complex calculations so a simple answer is not possible.

Thanks for languages tips:i'd like receive it each time i fail (i am spanishspeaker).I guess for these cases as Nick says must be simpler.-

I can't give a good clear explanation off the top of my head, but an egg is very good at resisting external pressure based on its shape.

If the pressure on the outside of something is equal all around (no differential based on differences of immersion level, for example), a sphere is the best shape for resisting pressure. I think a good way to state it is that for a given volume, a sphere will require the least amount of shell thickness to withstand the pressure.

An egg is very close to that shape, and thus is also very good. In fact (and here I'm uncertain), where there is significant difference in pressure based on something like a difference in immersion level, an egg may be an even better shape than a sphere for resisting that depth varying pressure.

(By a difference in immersion level, I'm really trying to describe a situation where the pressure is coming from a (relatively) dense external liquid (in a gravitational field, or in an accelerated frame of reference, at speeds much less than the speed of light) so there is a significant pressure difference between the top of the egg and the bottom.)

Offhand, I don't know whether it would be best with the wide end up or down. ;-)

O.K.The pressure is same all around a sphere,what equations would you write to know if the shell is going to bear or not the pressure or if it is stable until what pressure value.-

What you are interested in is the shell buckling limit. For fragile materials as the egg shell the limit is related to the ultimate strength, for ductile materials as steel it depends on the yield strength. As long as you only consider a constant curvature radius (a sphere sector) you do not need the FEA to define the limit there are equations for such geometries. An example is q= E(t/R)^2 where E= young modulus; t= thickness and R= radius. This is in the case of an elastic buckling. In the case of an elliptic shape the equation depends on the 2 radius. An egg can be assimilated with 2 ellipsoids with different radius. As one sees the smaller R is the higher the pressure limit. This is the reason why an egg loaded in the direction of the symmetry axis accepts a higher load before collapse.

Hi buddy,when i became to this site some years ago, i came with a "backwards problem" we dicuss it for sometime pressure and stresses inside a torus shell, you remember that? How did you get that formula or where may i read to study more detailed, whats the name of subject? Thanks and regards.-

I remember if you want o copy no problem send me your mail via private channel. I remeber also that you kept to a wrong idea at the time and did not accept the fact that some stresses were not to be computed as you assumed. Or am I wrong ?

Yeah, you are wrong! Anyway i never have hardfeelings to who tries to help and i feel good when i have another to discuss a problem being right or wrong.Any way i remember the sequences of our mailing:First i showed in this forum how i got formulas, kown ones which i think are called Laplace's,i added averages or medium values which you got too with different notation.When i mentioned those were just averages values i already submitted and the way to obtain proper values at any point,you assumed a mistake and search of possible origin for that,then no serious from your side you sent me "the formula" already different from what yourselve calculated before.Should i recognize my mistake and take your last and new formula accepting that just because comes from you? I don't understand why some people would ask a different channel than this to discuss the technical subject and then brings public hardfeelings to the forum.If you have any answer or foundation of your formula show it in this forum thread.Be a man.-

You are completely out to lunch! You are acting in a totally unprofessional way. You have not presented any arguments to show how NickName is wrong. Your way is not the way to resolve this or any other issue. If you are incapable of presenting technical argument in favor of your point of view, perhaps you would be better to keep quiet and listen to others. Possibly, in time, you will learn something, but it is doubtful.

My intention was to send you a copy of the book pages with all formula and the whole logic behing the shell stability computation. Due to your very unpolite and aggressive reaction you can wait till the greek calendas! I shall not any more answer to any question coming from you.

Another consideration is that the egg is not empty, but filled with both a fluid and an embryo. Since the fluids are almost incompressable, the fluid inside the shell resists the crushing force applied to the outside of the shell.

If the shell were emptied, crushing would be fairly easy, and would start at the exit hole where the fluids were removed.

I presume that you never got a look at an egg! There is an air pocket inside which is at least as far as I know a compressible medium. So that the shell is NOT fully filled with INCOMPRESSIBLE fluids!

Egg-zactly, nick name.

The egg could resist bear higher external pressure not mainly because of the curve ratio, but actually it something to do with the filling.

It so happen that the egg is filled with incompressible liquid that is why its tough to bear external pressure.

The submarine is a different thing, the interior pressure are maintained at atmospheric of course for crews to live. You see, the imbalance of the external & the internal pressures made forces along the walls for it to warped at higher pressure than designed.

That an egg can support high external pressure/force is not in doubt, and the standard party trick is to compress an egg length ways between the palms of ones hands. Only a strong person can break a good egg.

One error to put to rest though is the notion that an egg is "filled with incompressible liquid" - IT IS NOT. I can tell you from experience in my childhood as a chicken/poultry egg checker, that they all have an air space in them.

Shell structures are structurally very efficient because they tend to distribute compressive stresses without bending moments, and in some cases without tensile forces. The hemispherical bathysphere for deep-water operation being one common example, and building roof domes being another - though the latter obviously have tensile forces around the base that need to be contained.

In engineering terms the performance of the egg is as it should be, but amazes people because it appears so strong compared with how easily the shell will break from a concentrated side force.

One final point on shell structures, is that once the wall thickness gets quite thin and or the forces get quite high, that like for other structure types, localised elastic buckling can/will take place rather than simple yield/compression failure.

Any good engineering handbook will have some basic thin shell formulae and web searches with terms like "shell structures" or "thin shell formulae" will yield results - though a lot of this material is only available only through subscription.