# Strength of cylinder as function of internal pressure

1. Aug 12, 2013

### johnschmidt

I understand that a cylinder oriented vertically and bearing a load can be made more resistant to buckling by adding pressure to the (closed) cylinder. For example, an unopened can of soda pop can bear much more load than an opened soda pop can (I found a youtube video showing an unopened can giving way at 6405 N and an opened can giving way at 890 N).

Can this beneficial pressure also be provided by filling the cylinder with a fluid?

For example, if we have an open cylinder 50m tall and 5m in diameter that needs to support a load, can we increase the load bearing capability of the cylinder by filling it with water (which puts pressure on the walls)? It seems counterintuitive to me that a load in one direction on a material would increase its strength in another direction.

What is the relationship between the pressures necessary to strengthen the cylinder and the pressure from a fluid? Is the strengthening pressure much more or much less than the pressure from the fluid?

2. Aug 12, 2013

### SteamKing

Staff Emeritus
When unopened, the soda can is pressurized, which helps prevent the sides from being crushed when the can is handled normally. Once the top is popped, the can can still be easily (and messily) crushed with your hand.

Merely adding fluid to an open cylinder is not going to add much resistance to crushing. For any fluid (or gas) to provide resistance to crushing, the cylinder must be closed to ensure that any internal pressure is not allowed to dissipate if the sides of the cylinder are loaded.

3. Aug 13, 2013

### johnschmidt

So you are saying that the pressure necessary to support the cylinder is much higher than that provided by the weight of the fluid, yes? Hmm, Google suggests the pressure in the unopened can is 117 - 620kPa depending on temperature.

Does anyone know of any equations related to supporting a cylinder bearing a load with internal pressure?

4. Aug 13, 2013

### Baluncore

A few thoughts.

I think you should consider wall segments of the cylinder as a slender column, which it really is. They are, after all, over 60 times as high as they are thick. So the concepts of column stability come into the wall stability. It takes very little internal pressure to keep the wall straight since the force that will buckle the wall needs the wall to be flexible, which is not the case when under even a small amount of pressure.

When a cylinder is under internal pressure the hoop forces preventing the tube splitting along it's length are twice those trying to lengthen the tube. That hoop tension will keep the section circular while the longitudinal forces keep the walls straight. The internal pressure puts the wall under longitudinal tension due to the fluid pressure on the inside of the ends. The column stability question only becomes relevant once the supported load exceeds the internal pressure and moves the wall into compression. The wall however, is still under hoop tension. That hoop tension is not in the ideal direction to support the load. But the internal pressure that creates the hoop tension prevents the buckling of the column by providing horizontal control throughout the full height of the wall. So in the final analysis the wall is no longer a slender unsupported column, so it does not buckle.

5. Aug 13, 2013

### mrspeedybob

Pressure helps support a load because it holds the side walls in vertical tension. In the case of the soda can the area of the top of the can is about 32 cm2 so with a pressure of 500 kpa you have 1600 newtons of support for the load from the pressure alone. Obviously, given the numbers you quoted in your first post, this is not the only effect, but it is a significant one.