Hollow Tube vs. Solid Tube: Better Stiffness?

Weight for weight hollow is vastly better.

Hi Del the cat

I don't really get you. What do you mean "weight by weight"

Is there a formula or a calculation for it?

I shall give you a quantitative answer in stead of a qualitative one:

Stiffness is proportional to the inertia moment of the section which is for a circular one J= ∏/32*(D^4-d^4) (for a compression loading in case of a bending 32 becomes 64). Area is A=∏/4*(D^2-d^2). For the same weight the two have same A.

If you note d/D=δ the area is A= ∏/4*D^2*(1-δ^2) from which D^2=4*A/(∏*(1-δ^2)) Now the J= ∏/32*D^4*(1-δ^4) = 0.5*A^2/∏*(1-δ^4)/(1-δ^2).

Because δ<1 the ratio (1-δ^4)/(1-δ^2) > 1 so that the bigger δ the bigger J for the same A i.e. for same linear weight. There is of course a limit set by the wall buckling.

This is the reason why structural tubing has a specific ratio wall/D evn if not under internal pressure.

-not original poster-

Can you break down each of the units you have used? I know D/d = Diameter and ∏=22/7 (Pi) but whats "J" and "δ" ??

Would also depend upon the aimed usage of the material..

A guy over here in Oz got some drive shafts, and they had been "Gun-barreled", he found they were weaker (tearing them apart) possibly due to less Cross sectional area, or the bore wasn't sufficiently clean (deburred/smooth) dunno, still waiting on the manufacturer to get back on that one.

Stiffness from what sense , latteral ,axile , longitudnal , hollow tubing gives better stiffness at angular ,edge stress

Stiffness is the resistance of an elastic body to deflection or deformation by an applied force. It is an extensive material property.

As copied from wiki. Your question is irrelevant as stiffness is always related to bending.

Bending can only be done in two directions and those are torsion, with the circumference of the tube or bar, and axial, this goes perpendicular to the direction of the bar.

Any other deformation process is either compression or stretch and the strength to measure this is tensile strength and shear strenth (not completely but close enough for this purpose)

Your question therefor does not exist as it is a non-question.

sorry

That's bollocks!

elaborate please, always aprreciate your view and specially if mine is wrong.

I just don't see what objection you have to the term stiffness????

Presumably the poster means stiffness in relation to bending. A steel tube certainly is an 'elastic body' that's part of the definition of Young's Modulus.

He may mean torsional stiffness... many cars have torsion springs (usually solid) and I believe torsional stiffness is a perfectly correct term...maybe some of the mech' eng' guys would care to comment?

I agree the Q is a bit wooly as it doesn't specify what is meant by 'better'.

Talking of 'bollocks' presumably you have noticed that the tube residing between these exhibits variable stiffness.

I would think 'resistance to deformation' would be a pretty good definition of stiffness which could be applied to everything from custard skin to steel tubing.

(No offense was intended of course)

Regards

Del

No offense is ever taken as long as terms such as bollocks are explained

I do not have a problem with stiffness, stiffness is a perfectly good way of describing a materials means of dealing with elastic deformation.

Stiffness is therefor alwasy related to some form of bending. As the question was "stiffness in what sense", I feel comfortable with my opposing reply, as the question offered non sensical ways of bending. Longitudinal bending is not bending, it is compression and or stretch which can behave in an elestic way but is never described as bending and also the materials resistance to this, I thought, is not called stiffness.

Torsional stiffness is indeed correct as a spring, hollow or solid, is nothing more than a bar or rod wrapped around a central cylinder. Each segment of the spring is bending torsionally when the spring is compressed or stretched BUT as this is a spring shape, it is not called longitudinal bending either.

Still do not see what was so bollocks about my response , you need to be more specific for me to see that. I never offered a "better" way of putting it even if the q was wooly, I agree on that.

With regards to the resistance to deformation you need to also remember that there are 2 ways to this. One is elastic and the other is non elastic which results in permanent deformation. The resistance against the last one is called hardness, not stiffness.

Over to the cat

Ho hum..I feel we are being pedantic..

The post says 'in stiffness' which is semantically incorrect.

Longitudinal bending is not bending, it is compression and or stretch.

So my longbow doesn't bend eh?

Of course you are right it is stretch one side of the neutral axis and compression t'other but it most assuredly is still bending.

If I put my 25mmx25mm stainless steel tube across a 7foot span to make my computer table..It will bend..no one would say it stretches or compresses.. they'd work out the deflection for the given load... hang on we're talking stiffness here.

Maybe refer to this thread and help me out if you want to do some calc's...you will find the Q less wooly.

I feel maybe we are basically just arguing about semantics.

Now about Kris' bath... I bet the furry git still hasn't smashed it!

Del

Dear Del,

Please tell me you don't mean that you think I posted in reply to the original poster?

I posted in reply to the post directly above me which asked "stiffness in what sense?" By Vikas.

I think we have our wires crossed as I do not understand your argument in relation to my intended reply. Please enlighten me.

Ohh lots of education thank you and Del ..... one more clarification if longitudinal bending is compression , considering a long rod wound as a spring (leaf spring), so we describe spring compression , but than we seperate one spring from other spring on stiffness , torsional stiffness you did describe , due to forces transfered in manner both kind of springs offer ..........bye the way .......bollocks....did put lots of strain and stress together on you ..... sorry for that ...thanks

I have the feeling that some aspects have to be made more transparent.

Bending is the form change under the effect of a force perpendicular to the center line of the bar, tube or whichever slim body is considered. One can find also the bending of a surface under forces perpendicular to it. Torsion is a form change under the effect of torques which are,as vector, on the center line of the bar,...

Coming back to "stiffness" it should be made a difference between the "material" deformation and the "body" deformation. The material's own stiffness is defined by the module of Young. The "body" deformation is a function of the material used to make the "body" and the geometry of the different sections. Of course the way the "body" will deform is a function of the applied loads as well as nature (forces or moments) as directions and intensity.

In fact since everything deforms more or less we deal every moment with "stiffnesses".

The remark made that stiffness should be related to elastic deformations is correct with only one aspect to add: elastic does not mean linear i.e. stiffness is dependent on the deformation magnitude.

Stiffness is NOT always related to bending: a bar under an axial load (compression or tension) will also have a stiffness which gives the relationship between load and deformation. I am sorry but i never heard of a longitudinal bending i only heard about buckling of a bar under excessive axial loads. There is no torsional bending but only torsional deformation.

The term "hardness" describes the capacity of a "material" to resist a penetrator.

The permanent deformation is a consequence of a change in the material behaviour going from its elastic one to an elastoplastic one. This is not related to hardness itself since this change does not depend on harness.

Mechanical limit and hardness are related to each other because the penetration will deform the material over its yield strength. Nevertheless most correlations are made between hardness (Brinell or Rockwell or Vickers) and ultimate strength not yield limit.

Dell the Cat asked for a mechanical comment here it is.

But springs are hollow as well as solid and are tubular , some kind of liquids are filled in hollow springs , may be for damping , and pressure to maintain stiffness . Actually it was not a question at all just countering the original thread , he did mention stiffness , ....... still Thank you.....

I can think of one usage in support of hollow tubing with better stiffness at angular edge stress. Convexed edge of a hair scissor with a slight hollow grind on the inside edge of the blade.

one thing hollow is better as Del put it weight for weight,

But failure to the tube, there will be very little deformation before failure to a tube whereas a solid shaft you'll notice more deformation before failure will occur.

There is shareware called beamboy (google it), Its simple and easy to use. This will give you more info anylasis

Hey. Phoenix... that beamboy is great, no slick user interface but it does the job. I just used it on my beam problem thread in this thread.

Nice steer

Del

glad to assist.

What do you aim to do with the pipe? Application always helps to understanding and getting a well qualified answer?

I sourced some steel, but delivery cost almost the same as the steel!

So I've taken PW's advice and am having a nice top made up in Ash by a local timber company (no delivery cost) .

Cheers one and all

Del

Ignore all of them, they're dodo talking!

Stiffness is the product of the modulus of Elasticity (E) and of the Moment of Inertia (I), period.

A solid tube. deflection related to bending is defined by moment M divided by young's modulus times the area moment of inertia: M/E*Izz

For a constant material and equal moments, the only factor that will change from tube to solid is the area moment of inertia, Izz. essentially, the area moment of inertia decreases as material is taken away from the tube, or rod (essentially the same thing), not matter where the material is taken away from. this serves to increase the denominator in the aforementioned equation, which increases the output: bending. so, a tube will bend more than a rod, which is essentially what you're asking.

consider a very very thin walled tube. bend it. now add some wall thickness without changing the OD of the tube. is it harder to bend or easier? now add wall thickness again, and progress until the wall is so thick you're left with a solid. is it harder or easier to bend?

the bottom line is, if the cross section has more material, it is more resistant to deformation.

strength-to-weight ratio, of course, is a completely different story.

I have a similar question but in regards to a tubular under compressive forces. If I have a 5/15 (.312") tube with a wall thickness of .035" that is 7.240 inches long, and reduce the length to 5.740 inches in length, how much stiffer I (with reference to deflection and/or buckling) will the shorter tube be? THanks Paul

I posted the last item as a guest but have signed on to CR4 since. Thanks Paul

You'd possibly find that more people will take an interest if you started this as a new thread ;o)

Could anyone please let me know if I can substitute for a stainless steel 2 inch diameter tube with .25 inch wall thickness , to be used for the rudder stock in the construction of a rudder for a 40 foot sailboat.

If I use solid 2 inch aluminum tube either Aluminum 6016 T6 or aluminum 6082 T6

would the resistance to deformation and bending be better than the stainless

thanks

Dear Mr. bcp,

Your question is having ambiguity, in the sense, you are mixing two different property.

The STIFFNESS, is applicable for SPRINGS and NOT FOR TUBE and can be explained as " THE DISTANCE THROUGH WHICH, THE SPRING UNDERGOES REDUCTION IN LENGTH, FOR A GIVEN WEIGHT" which means W/ (Length of SPRING BEFORE LOADING - LENGTH OF SPRING AFTER LOADING) expressed in Kgs/cm or Lbs./Inch.

In your case, the tube will undergo either a BENDING resulting in DEFLECTION or VERTICAL COMPRESSION, which may lead to BUCKLE. depending on the SECTION MODULOUS.

Hence, the SECTION MODULOUS is the consideration in both cases, i.e SOLID or HOLOW TUBE.

DHAYANANDHAN.S