Why are hollow tubes stronger than full ones.

[FrenchScience]

Hello,

So my son is working on a school project on why hollow tubes of the same mass are stronger than full tubes.

Can someone please explain this principal to me but without equations,a dumbed down version if you will.He is on 16,so anything college standard will be to difficult,some could you please explain to me how.

Thank you

 

[SteamKing]

Stronger under what type of loading? It makes a difference.

 

[Vanadium 50]

The key is "of the same mass". A hollow tube of the same mass as a rod is bigger.

 

[Malverin]

When the mass is further of inertial axis, it resists bending more. So the tube will be harder to bend.
If the mass is 2 times further (about 2 times bigger diameter), the "bending resistance" will be 4 times greater.

 

[AlephZero]

Be careful about the terminology. A hollow tube is stiffer in bending than a solid rod with the same mass. It is not necessarily stronger.

 

[Malverin]

Be careful about the terminology. A hollow tube is stiffer in bending than a solid rod with the same mass. It is not necessarily stronger.

The stress is smaller too. So it is stronger.

http://www.mdme.info/MEMmods/MEM30006A/Bending_Stress/Bending_Stress.html

http://gauss.vaniercollege.qc.ca/pwiki/index.php/Rotational_Kinetic_Energy_and_Moment_Of_Inertia

 

[SteamKing]

The I in the bending stress formula is not the same I as shown in the diagram attached to Post #6. The bending stress is inversely proportional to I which is the second moment of the area of the cross-section of the beam, whereas the diagram shows I which is the mass moment of inertia of the bodies shown. Two different concepts.

 

[sophiecentaur]

Hello,

So my son is working on a school project on why hollow tubes of the same mass are stronger than full tubes.

Can someone please explain this principal to me but without equations,a dumbed down version if you will.He is on 16,so anything college standard will be to difficult,some could you please explain to me how.

Thank you

You could always give him a sheet of paper and how how easily it folds - then roll it into a tube.

Actually, when you have a well defined direction for your load (e.g. downward), there are sections that work better, weight for weight, than a tube. I and H sections are used for beams in buildings. That must be because they are 'stronger' than tubes under some circus. Otoh, bicycles nearly always used tubes.

 

[Malverin]

The I in the bending stress formula is not the same I as shown in the diagram attached to Post #6. The bending stress is inversely proportional to I which is the second moment of the area of the cross-section of the beam, whereas the diagram shows I which is the mass moment of inertia of the bodies shown. Two different concepts.

Yes it is not the same moment of inertia. My mistake. But that doesn't change the fact, that tube is stronger

http://www.engineeringtoolbox.com/area-moment-inertia-d_1328.html

http://en.wikipedia.org/wiki/Section_modulus

 

[davidm1732]

I'm not sure your request for a "dumbed down" version, without equations was fully met! SophieCentaur had a good illustration with the sheet of paper example. Another classic example is to fold a sheet into a pleated pattern. The sheet can now hold up weight, where the flat sheet was extremely flimsy.

Another similar example... imagine a long board...(IE: a deck board, or 2x6)... if you support it at each end, which way would you lay it so it bends the least when you stand on the mid point... would you lay it flat, or standing up? Intuitively it will bend less if stood on it's end. Similar to the tube vs solid bar example, the board weighs the same...you've only rotated it 90 degrees, but when you stand on it, it bends much less when on end? The math & equations listed above talk about the moment of Inertia (I)... Malverin discussed the distance that the mass is from the neutral axis, and that's the key point here... since the mass of the tube is the same as the mass of the rod, you get a tube with a much larger diameter than the solid rod. Siince the diameter is larger, you have more material further away from the neutral bending axis, so it's stiffer, and bends less (same idea as turning the board on it's end)... same reason why an "I" beam has that shape...the flanges on top and bottom are furthest away from the neutral axis (when in bending... as noted earlier, orientation and load direction are important). The taller you make that "I" beam, the stiffer it will get.
If you look at new home construction, they use what are called "engineered beams"... instead of using 2x10 or 2x12 for floor joists, they create a wooden "I" beam, with a top and bottom flange, and often with OSB (chipboard) as the vertical center web...same idea... the material at the top and bottom of the beam give you your bending strength...the material in the middle does very little.

 

[Baluncore]

A solid round bar has a “neutral axis” that, when the bar is bent, is not in compression or tension and so does not contribute to the resistance to bending. If the material near that neutral axis is removed and relocated to the outside surface of the bar, it becomes a tube and is less flexible than the bar of the same mass. Material is being moved from where it gives little or no advantage to the place where it can give a maximum advantage.

 

[AlephZero]

My mistake. But that doesn't change the fact, that tube is stronger.

You are only considering one factor. There are plenty of other reasons why a hollow tube can be weaker than a solid rod. Distortion of the cross section caused by the loading, local bucking, nonlinear material behavior (plasticity or crack propagation), etc, etc...

 

[AlephZero]

A solid round bar has a “neutral axis” that, when the bar is bent, is not in compression or tension and so does not contribute to the resistance to bending.

That is true for pure bending, but it ignores different effects of shear on a solid and hollow section.

That is one reason why lightweight "hollow" sections (both natural and man-made) are often filled with something other than 100% fresh air. http://www.virginia.edu/ms/research/wadley/celluar-materials.html

 

[Baluncore]

Can someone please explain this principal to me but without equations,a dumbed down version if you will.He is on 16,so anything college standard will be to difficult...

Distortion of the cross section caused by the loading, local bucking, nonlinear material behavior (plasticity or crack propagation), etc, etc...

That is true for pure bending, but it ignores different effects of shear on a solid and hollow section.

Keep It Simple.

 

[sophiecentaur]

Keep It Simple.

Sorry but that is a copout. There is just not a 'simple' explanation. Why do you think Engineers spend years learning about the way materials behave? You are selling them all short if you say that structures are simple to understand. Serious Maths comes into some of the most basic problems in this field. There is no short cut to learning the fundamentals of structural engineering. Rolled up sheets of paper are OK as far as they go but they don't take you any further and it's deluding anyone to tell them otherwise.

 

[FrenchScience]

Thank you all for taking time to reply.

 

[Naty1]

davidm...generally a helpful post...

The taller you make that "I" beam, the stiffer it will get.

yes.

If you look at new home construction, they use what are called "engineered beams"... instead of using 2x10 or 2x12 for floor joists, they create a wooden "I" beam, with a top and bottom flange, and often with OSB (chipboard) as the vertical center web...same idea... the material at the top and bottom of the beam give you your bending strength...the material in the middle does very little.

This seems to contradict the prior quote...in any case, the vertical height of the OSB, or better yet I would think, plywood, determines most of the resistance to bending.

...I and H sections are used for beams in buildings. That must be because they are 'stronger' than tubes under some circus...There is just not a 'simple' explanation.

That's my take.
I found a few insights here which may assist FrenchScience,

http://en.wikipedia.org/wiki/Cylinder_stress

for example,

Note that a hoop experiences the greatest stress at its inside (the outside and inside experience the same total strain which however is distributed over different circumferences), whence cracks in pipes should theoretically start from inside the pipe.

So a larger diameter cylinder seems to exhibit less strain.