Maximum axial load is proportional to the second moment of area? 5

[DukeGlacia]

Maximum axial load is proportional to the second moment of area. Thus can we reason that aluminium cans are cylindrical because they have a high second moment of area(mr^2) compared to other shapes(Which gives it a higher max axial load.)?

 

[BAretired]

Cylindrical cans are capable of withstanding internal pressure better than other shapes too. Maybe that is why aluminum cans are cylindrical. But are they always cylindrical? Some cans are rectangular, but they may not be aluminum. Is your question limited to aluminum cans or could we consider tin cans as well?

On the other hand, circular cans waste a lot of storage space due to the large gaps between them. Square cans would be more efficient for storage.

BA

 

[JStephen]

For aluminum cans, axial load would be proportional to the area times an adjustment factor for the thickness ratio.
I'm not aware that the shape of aluminum cans was selected based on axial compressive strength.

 

[DukeGlacia]

Thanks for the reply !When you use Euler's column Formulae to calculate the maximum vertical stress it can carry, the max stress tends to be larger for cylinders than for cuboid(cicumscribed). So is it possible to reason that cylinders are stronger to vertical loads when compared to cuboids(circumscribed)?(not limited to any material)

 

[SlideRuleEra]

Economics may be at work, too. For a fixed volume, a cylinder makes the most efficient use of material than any other common shape, except a sphere. More cans per pound of aluminum. No doubt the product producers don't want to spend any more on containers that necessary.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[TLHS]

Yeah, while vertical load capacity for stacking is good, I'm guessing can wall thickness is primarily governed by internal pressure and durability concerns.

Also, I suspect that axial failure in cans isn't governed by full section buckling. They're too squat. Your failure mechanism is likely local wall buckling.

 

[DukeGlacia]

So leave alone cans. If we have a two object pretty long in height(same height). One is a hollow cylinder(uncovered on both ends) and the other is a hollow cuboid.If we look from the top the cuboid(top view:square) circumscribes the cylinder. Now which one has a higher critical buckling load?

 

[IDS]

The animation here:

https://newtonexcelbach.wordpress.com/2011/07/06/buckling-of-tubes-2/

might be of interest.

Long cylindrical tubes do have a higher buckling load than the circumscribed square tube (all other things being equal), but it isn't just a matter of Euler buckling load (see link for more details).

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[TLHS]

Assuming full section buckling, the square will have a higher critical buckling load. The material is all further away or at the same distance from the neutral axis than the same material in the circular section.

The cylinder will do better in wall buckling, though, so it may turn out to be stronger depending on the loading situation.

 

[DukeGlacia]

Thanks alot to everyone! This is my first day on eng-tips but its beyond awesome !!! Found my answer

 

[IDS]

On the question of aluminium cans, I suspect the current shape is governed by a combination of ease of manufacture (avoiding a seam between the walls and the base), and minimising wall thickness with stacking loads probably being the critical load case. But that's just a guess, I'm no aluminium can scientist.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[BAretired]

I once asked a farmer what he did with all his produce. He replied "Well, we eat what we can and what we can't, we can".

BA

 

[RPMG]

No, pop cans are not cylindrical for axial load (compression), but what is the perfect shape for a pop can?

The number 1 failure mode is due to dropping or impact. The ideal shape for this is a sphere. Spheres, on impact, deform which reduces the volume. Thus creating an internal pressure. Internal pressures create hoop stress. While a sphere might be great in terms of hoop stress, it is not practical from a shipping, stacking, and storage standpoint.

A cylinder is the compromise. Circles have hoop stress, which is tensile. Squares have bending and flexure. It just so happens that aluminum, which is terrific in tensile strength, is terrible with bending because it deforms so easily.

So, cans are aluminum because of a high tensile material strength, not axial (compression), and cylindrical to take advantage of its tensile strength.

 

[Jerehmy]

can't believe no one posted this video yet. It's about the history of aluminum cans and why they chose the shape.

http://youtu.be/hUhisi2FBuw

 

[dhengr]

BA:
That’s can-didly uncanny.