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Author Topic: Are hollow tubes stronger than full ones?  (Read 8250 times)

Offline FrenchScientist

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Are hollow tubes stronger than full ones?
« on: 04/12/2013 12:45:50 »
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
« Last Edit: 06/12/2013 17:59:33 by chris »


 

Offline Pmb

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Re: Why are hollow tubes stronger than full ones.
« Reply #1 on: 04/12/2013 17:24:06 »
Quote from: FrenchScientist
So my son is working on a school project on why hollow tubes of the same mass are stronger than full tubes.
That's not true. You're misinterpreting things. Let me clarify the situation for you.

If you have a cylinder of length L and mass M then the one that is a hollow tube is stronger then the one that is a solid rod. The tube has its structure spread out while the rod is concentrated and for this reason the tube is stronger.

However Iím not sure I know how to explain why this is true. I know why intuitively but am unable to express myself as to why. Sorry.
 

Offline evan_au

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Re: Why are hollow tubes stronger than full ones.
« Reply #2 on: 04/12/2013 20:14:26 »
A hollow rod is more rigid than a solid bar of the same mass and composed of the same material because:
  • The material will have a certain elasticity: the relationship between force and length.
  • When the material is concentrated close to the axis (as in a solid rod), the rod can be bent without stretching the material too much. It is not very rigid.
  • Another way of looking at this is that the rod gives a lot of leverage to apply a high force on the material close to the solid rod's axis, causing it to exceed its elastic limit, and the rod fails.
  • However, in a hollow rod, the material is further from the axis, and so will have to stretch further for the hollow rod to deviate a certain distance from a straight line. This makes the hollow rod stiffer.
  • There is a limit to the degree to which you can increase the diameter of a hollow rod - eventually the material is so thin that it tears, or collapses under its own weight.
  • Hollow rods are seen in human and bird bones.
  • In building construction, another shape is more popular: the "I" beam. It has similar properties to a hollow rod in that most of the material is far from the central line, making it stiffer for a given mass. The central web prevents it from collapsing. However, it works best with forces in one direction.

On the other hand, if cost and weight is not a limit, a solid rod of the same diameter as the hollow rod will be stiffer than the hollow rod, and a solid rectangular bar will be stiffer than an "I" beam of the same dimensions. However, they may have problems holding up a building of the same dimensions as it will be much heavier.

A rather mathematical treatment is available here: http://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory
 

Offline alancalverd

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Re: Why are hollow tubes stronger than full ones.
« Reply #3 on: 04/12/2013 20:28:50 »
When you bend a rod, you are stretching the part outside of a line called the "neutral radius", and compressing the part inside.

A tube with the same mass per unit length as a rod of the same material, will have the "outside" and "inside" further from the neutral radius. So in order to achieve the same angle of bend, you have to stretch the outside further and compress the inside more, so you have to do more work to bend the tube than the rod.

The mast of a racing yacht, or a modern fishing pole, are good examples of optimally designed tubes. The problem with both designs, however, is that a small impact can dent or crack a thin tube so there is a practical limit to the life of such structures. 
 

Offline CliffordK

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Re: Why are hollow tubes stronger than full ones.
« Reply #4 on: 04/12/2013 20:30:54 »
"Strength" is all relative to what you're doing.  For merely tensile strength (stretching till breaking), one would have minimal difference between the hollow tube and the solid rod, in fact, the solid rod may do slightly better. 

For bending, however, the hollow tube is usually a bit better, although it may depend somewhat on the ultimate thickness, and the method of applying the force to the tube (point vs distributed vs crushing).

Now, consider an Ideal I-Beam as being an extension of a tube (with no sides).



The I-Beam with the close top and bottom plates has less stretching/compression in the top and  bottom plates, and thus bends easier.

The I-Beam with the widely separated top and bottom plates undergoes two different types of failures.  In the first case, the top and bottom plates collapse, and the beam bends like the case with the two close plates.

In the second case, the separation is maintained, and the top plate goes through much greater stretching than is experienced by the case with the plates close together.

Now...
Back to the tube.
Consider a soda can.
A full soda can is extremely hard to bend, using the liquid to provide additional support.  In many cases tubes are in fact filled.

An empty soda can, however, can be easily bent by forcing a crease, then bending around the crease.  Once bent, it has little remaining strength.

Or, one can force a tear, and then expand the tear. 

A bar, with the equivalent amount of aluminum to the soda can may be easier to bend initially, but it may retain much of its initial strength for repeated bending, while the can that is either torn or creased has little remaining resistance to bending.
 

Offline Phractality

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Re: Why are hollow tubes stronger than full ones.
« Reply #5 on: 04/12/2013 20:39:59 »
Don't confuse strength with modulus (stiffness). Bending strength is the torsion stress needed to break it, bending moment is the ratio of torsion stress to torsion strain. The greater diameter of a hollow tube gives it a higher bending modulus than a solid rod of the same mass per unit of length. This does not affect the bending strength.

Tensile strength is the stretching force required to lengthen the object by a certain fraction. Tensile strength and tensile modulus are independent of the cross section shape.

When you bend an object, you compress the inside of the bend and stretch the outside of the bend. A hollow tube has a greater distance between the compressed part and the stretched part. Greater distance between two forces means greater torque. That's why it takes greater torque to bend a hollow tube.
 

Offline RD

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Offline alancalverd

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Re: Why are hollow tubes stronger than full ones.
« Reply #7 on: 05/12/2013 00:18:26 »
It's interesting that the question was posed by a French scientist. The infamous 1987 hurricane was much more intense in Brittany than in the UK and it was widely reported there that old hollow oak trees had withstood the wind better than young solid ones.   
 

Offline FrenchScientist

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Re: Are hollow tubes stronger than full ones?
« Reply #8 on: 10/12/2013 17:42:52 »
Thank you all for taking time to reply.
 

Offline yor_on

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Re: Are hollow tubes stronger than full ones?
« Reply #9 on: 10/12/2013 19:17:25 »
You might intuitively think of it as when you apply a force to a tube, trying to bend it, the force flows through the mass of its matter. In a hollow tube the only way for this force to flow is around, there is no way to transmit the force trough the empty space inside that hollow tube. In a tube that is solid the force are free to wander all ways through it as its matter transmit that force. A solid tube will bend easier but also, as I think, be able to be stretched much further before breaking, than a hollow. A hollow will hold its rigidity longer, staying 'straight', until meeting the breaking point where it will get ripped apart, if that is the right expression?
 

Offline Bored chemist

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Re: Are hollow tubes stronger than full ones?
« Reply #10 on: 10/12/2013 19:29:02 »
It's interesting that the question was posed by a French scientist. The infamous 1987 hurricane was much more intense in Brittany than in the UK and it was widely reported there that old hollow oak trees had withstood the wind better than young solid ones.   
I can think of at least one other plausible explanation for the difference.
The old trees had survived the last storm (whenever it was) and thus must have had strong foundations.
Quite a lot of teh trees that I have seen blown over are torn out at the roots, rather than snapped off.
 

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Re: Are hollow tubes stronger than full ones?
« Reply #10 on: 10/12/2013 19:29:02 »

 

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