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Concentric Tubes in Bendine

Concentric Tubes in Bendine

(OP)
Hello all, I am analyzing a design that involves a stainless steel tube in bending. This tube is reinforced with a smaller "doubler tube" snugly fit inside (its OD being equal to the larger tube's ID). The tubes are not bonded, and are free to slide, ignoring friction. I have scoured the internet and my textbooks to no avail - how is the section modulus for this configuration calculated? The area moment of inertia of the cross section is the same regardless of the tubes being bonded or free to slide. I assumed, similar to composite beams, that two sliding tubes would be less stiff than one thick tube... Is this not true?

Many thanks
Mike

RE: Concentric Tubes in Bendine

(OP)
To clarify, I am trying to identify an effective single tube wall thickness to apply in an FEA model, to reduce complexity.

RE: Concentric Tubes in Bendine

If you assume that there is no bond, and no other influence between the two tubes, then the share of the load to each would be simply based on their relative stiffnesses.

Since they are "with" each other in terms of deflection and share the same neutral axis, an equivalent shape would be a shape with the sum of the two moments of inertia...similar to two beams side-by-side but forced to deflect the same amount.

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RE: Concentric Tubes in Bendine

I might add that my qualifier here is important - that there is no influence between the two shapes. There is, however, got to be some influence since the inner tube will want to slide horizontally within the outer tube so some horizontal friction will in fact influence the two to some extent.

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RE: Concentric Tubes in Bendine

(OP)
JAE,

Thanks for your reply. My hangup is this - a shape with an equivalent moment of inertia is just the same two tubes, considered as a solid cross section (unlike a stack of rectangular layers, where the MOI of the composite beam is larger than the sum of the layers). Is it possible that the tubes would not tend to slide under bending, meaning there would be no difference if they were bonded?

RE: Concentric Tubes in Bendine

Assuming the inner tube freely slides inside the outer tube, the MOI is the algebraic sum of the two: I1 + I2. For the combined sections (non-composite) use algebra to calculate the MOI of an equivalent tube with an outside diameter equal to the larger tube. With the same outside diameters, the elastic section modulus of the equivalent tube will be correct.

RE: Concentric Tubes in Bendine

In reality, you've got to have some forces in between the tubes to transfer load from one to the other.
That being said, with the assumptions made in beam bending derivations, if the load is proportioned so that calculated deflection of both tubes is the same, there wouldn't be any sliding or shear between the two tubes.

RE: Concentric Tubes in Bendine

In this scenario, bonding is irrelevant. The neutral axes of both the inner tube and outer tube coincide in space and will share the same curvature. As such:

1) The two sections will behave compositely in flexure in the sense that matters: they will share a common strain diagram.

2) The composite section properties will be identical to the non-composite section properties (I_in + I_out).

So there you have it. You get composite behavior but, in this particular case, it's of no particular benefit.

Quote (OP)

how is the section modulus for this configuration calculated?

Assume that the section behaves compositely (or non-compositely as it's irrelevant here) and calculate S = (I_in + I_out) / c

Quote (OP)

I assumed, similar to composite beams, that two sliding tubes would be less stiff than one thick tube... Is this not true?

No, that assumption is incorrect in this instance.

Quote (OP)

To clarify, I am trying to identify an effective single tube wall thickness to apply in an FEA model, to reduce complexity.

You can simply add the two tube wall thicknesses for equivalent flexural properties.

Quote (OP)

Is it possible that the tubes would not tend to slide under bending, meaning there would be no difference if they were bonded?

That is indeed correct and is probably the key thing to understand about this situation.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

A little proof of what KootK is saying:



The Mc is treating the tube as one, and looks at the stress at extreme fiber of the outer tube and extreme fiber of the inner tube. the results are the same whether you proportion the load by stiffness or treat it as a composite shape.

RE: Concentric Tubes in Bendine

Thanks for the MathCAD confirmation SU10. But for laziness, I would have done that myself.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

but is that the way the inner tube would work ?

you may have a point load on the outer tube, but the inner tube would load up from a non-uniform distributed load (as the outer tube bears against the inner).

my sense says that the two tubes should be less stiff and a single tube, because you have a shear slip boundary between the tubes.

another day in paradise, or is paradise one day closer ?

RE: Concentric Tubes in Bendine

(OP)
Thanks for your replies, you all are fantastic!

RE: Concentric Tubes in Bendine

not so sure about this......effective composite action requires horiz shear capacity between the the 2 tubes...if the assumption is that this capacity does not exist, then , I would check it in the following manner....
1. Check the same two tubes independetly....assume an equal(same) deflection for each and find it's
corresponding applied load. Add the 2 loads to get total load.
2. Check the capacity for the same defection of an equivalent tube with a total I equal to the sum
I1 & I2 and with an OD of the larger tube and wall t equal to t1 + t2...
3. Compare the loads of method 1 with method 2....

RE: Concentric Tubes in Bendine

if the inner tube was an interference fit, then I'd by that the pair of tubes would act like one combined tube (or like the sum of the Is, same diff)

as a sliding fit, there is an obvious difference and the interface of the tubes between the two tubes and a single thick tube. I'd expect the two tubes would deflect more than a single thick tube.

another day in paradise, or is paradise one day closer ?

RE: Concentric Tubes in Bendine

Exactly right. No slip so long as:

1) The vertical positions of the neutral axes for both members are coincident and;

2) The neutral axes of both members are made to have matching curvatures.

1 + 2 = identical strain profiles for both members at all locations. And identical strain profiles, by definition, means no slip.

Quote (rb1957)

I'd expect the two tubes would deflect more than a single thick tube.

I feel that structSU10 pretty convincingly demonstrated that I_composite = I_non-composite. Do you dispute that? If not, why would you think the composite section to be any stiffer?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

"Do you dispute that?" no, the math is straight forward; but will be beam behave that way is a different question.

do you see a different if the inner tube is interference fit ?

in the single thick tube, is there no stress on the parting plane ? (I don't think so, but there is in the two tube case)

in the two tubes, a single point load on the outer tube would not load the inner tube as a point load (IMHO) but the inner tube would be loaded (and the outer tube relieved) by a distributed load (as the outer tube bears against the inner one).

I'd analyze as the outer tube loaded by the point load, reacted by a distributed load and end reactions. At the same time the inner tube is loaded by the distributed load. now calc deflected shapes and tune the distributed load so that deflections of the two are the same.

another day in paradise, or is paradise one day closer ?

RE: Concentric Tubes in Bendine

rb1957 - the loading isn't really relevant here because the physical conditions force both tubes to deflect the same distance, and with the same curvature.
Force follows deflection and visa-versa. Hooke's Law.

No matter how they are loaded, the two tubes are deflecting in the same curve/pattern/degree and so they would indeed (as KootK mentioned) share the same strain diagram.

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RE: Concentric Tubes in Bendine

this is a slip fit to begin with....if the assumption is that there is no effective means of transferring horiz shear between the 2 tubes, it then poses the question why ,in this application, is it necessary at all....one could apply this reasoning to a laminated wood beam and assume that the bonding between layers as being unnecessary...
I have not run the numbers, but my intuition tells me that the stiffeness of the 2 tubes would be approx 75% of that of an equivalent tube as described in the previous posts...then , again, I would not bet my shirt on it....

RE: Concentric Tubes in Bendine

the two tubes would deflect the same, I agree; but would the deflection be the same as one thick tube ... I don't think so.

surely in the thick tube there is some stress where the parting plane is in the two tubes ? surely this affects the results.

surely two tubes with an interference fit would behave differently compared to two tubes with a sliding fit ?

two tubes with an interference fit would behave like a single thick tube.

another day in paradise, or is paradise one day closer ?

RE: Concentric Tubes in Bendine

Quote (rb1975)

do you see a different if the inner tube is interference fit ?

In theory no. Again, because the strain diagrams are identical, there's no need to engage friction whether it's available or not.

In reality, I would expect a tight friction fit to change stresses a bit. Intentionally, I've just been discussing flexural behavior assuming that plane section remain plane. In the wild, the strains at the extreme ends of the two tubes would probably differ a bit due to shear lag up the sides of the tubes. That difference would be, at least partially, ironed out by the action of the friction generated at the interface.

Quote (rb1957)

in the single thick tube, is there no stress on the parting plane ? (I don't think so, but there is in the two tube case)

I would expect there to be some stress at the faux-interface plane in the solid section case. This is conceptually similar to what I mentioned above with respect tot he interference fit. Continuity in the material would tend to enforce strain compatibility more convincingly than shear lag.

Quote (rb1957)

in the two tubes, a single point load on the outer tube would not load the inner tube as a point load (IMHO) but the inner tube would be loaded (and the outer tube relieved) by a distributed load (as the outer tube bears against the inner one).

No doubt, this phenomenon would have an effect on local bearing stresses etc. As JAE described, however, it wouldn't impact theoretical flexural strains.

Quote (SAIL3)

this is a slip fit to begin with....if the assumption is that there is no effective means of transferring horiz shear between the 2 tubes, it then poses the question why ,in this application, is it necessary at all....one could apply this reasoning to a laminated wood beam and assume that the bonding between layers as being unnecessary...

That's precisely the point, it's not necessary in certain cases. Regarding the wood example, consider:

CASE 1: tube and tube as described here.

CASE 2: 4X10 main with with a pair of 2x6 sides for reinforcing. The center lines of all member align.

For both cases, I would submit that the following is true:

1) Both members need some mechanism by which vertical load can be transferred from the directly loaded member to the member not directly loaded. Without this, the curvatures of the various members cannot be made to match.

2) For the tubes, the vertical load transfer mechanism is some complex bearing situation, as intimated by rb1957.

3) For the wood, it's vertical shear transfer in the bolts.

So the bolts in the wood are necessary, just not for horizontal shear transfer. Their role is solely to transfer vertical shear and enforce curvature compatibility among the plies. Fundamentally, this is why we don't have to bother with VQ/It forces when we laminate multi ply wood beams of the same depths. There's just no demand for horizontal shear transfer.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

Quote (KootK)

I_composite = I_non-composite. Do you dispute that? If not, why would you think the composite section to be any stiffer?

Quote (rb1957)

"Do you dispute that?" no, the math is straight forward; but will be beam behave that way is a different question.

rb1957: you confirmed that you agree that I_comp = I_non-comp. With that being the case, how do you justify deflection being different for the two cases? EI is the same for both. How is it that you see the beam behaving differently from our normal Bernoulli assumptions? Is it more than an intuitive feel?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

Koot..the wood beam example should be horiz plies......you are also assuming plane sections remain plane in the 2-tube-example..I can not see any mechanism to accomplish this if there is no horiz shear capacity between the 2 tubes.....

RE: Concentric Tubes in Bendine

Quote (SAIL3)

Koot..the wood beam example should be horiz plies..

It can't be because the horizontal shear transfer would be required. With horizontal plies, the important feature of this thread's example is lost: the neutral axes of the plies, acting independently, are no longer aligned vertically.

Quote (OP)

you are also assuming plane sections remain plane in the 2-tube-example..I can not see any mechanism to accomplish this if there is no horiz shear capacity between the 2 tubes.....

The mechanism is web shear (and potentially lag as I mentioned above). Same as how strain compatibility is enforced between the flanges of a stand alone I-beam. With tube in tube, the two tubes do this job independently but the net effect is the same.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

Quote (KootK)
I_composite = I_non-composite. Do you dispute that? If not, why would you think the composite section to be any stiffer?

Quote (rb1957)
"Do you dispute that?" no, the math is straight forward; but will be beam behave that way is a different question.


I was using "lawyer speak" ... I agree with the math presented, I just don't think the underlying proposition (that deflection of a single thick tube = deflection of two tubes) is correct.

We agree that there is some stress happening on the "faux parting plane" in the single thick tube. I think two tubes with interference fit would exhibit the same behaviour as I think there's something there that'll allow the stress to develop (the interference between the two tubes allows them to talk to one another). If there's a sliding fit then this stress can't develop and so the two tubes are different to the single tube.

How big a difference ? As I've proposed, if the outer tube has a point load, the inner tube will have a distributed load, maybe something like a sine wave. If the outer tube is loaded by a distributed load then I think the difference is very small.

another day in paradise, or is paradise one day closer ?

RE: Concentric Tubes in Bendine

if you say so, Koot.....but, I detect Timoshenko stirring in his grave.....

RE: Concentric Tubes in Bendine

There are several unusual things about tackling this problem, and the best way, of course, isn’t to obscure the real facts of the matter, how the structure really acts. By the nature of makeup of the total shape, there is an unusual math/geometry/section property anomaly in this problem. Since the center is the same for the two pipes, they have individual moments of inertia (MoI), as structSU10 shows above, and adding these two MoI’s gives the same value as a single shape (combined, composite? shape) having the inner min. pipe i.d. and the outer max. pipe o.d. You would never get those two pipes together without some fair sized dia. gap, particularly at 6' long. Thus, there can be considerable slippage btwn. them in action, and some friction action too. You might press two pipes, only 6"-8" long together, and actually have a press fit condition, more like a composite section, but pretty complex to define at the interface.

I maintain that the two pipes do deflect together (in unison), but they share the load in proportion to their relative stiffness’, functions of their MoI’s, E’s and lengths. Since E and L are the same for each, the MoI is the controlling factor. The outer pipe will carry more of the load because of its greater MoI. The section modulus (Sx) must be figured for each pipe, and because of the slip btwn. them there is no single element equivalent for this part of the problem. On the 6 - 12 o’clock axis the stresses might look something like this (no real numbers were run as structSU10 did): near 6 o’clock, at outer o.d. (3"/2) σ = +50ksi; at outer i.d. (2.75"/2) σ = +45ksi; at the inner o.d. (2.68"/2) σ = + approx. 50ksi; at the inner i.d. (2.5"/2) σ = + approx. 45ksi; at the N.A. σ = 0ksi; near 12 o’clock, at the inner i.d. (2.5"/2) σ = approx. -45ksi. Note that at the (2.75"/2) or at (2.5"/2) levels, or any other level the stresses are not the same in the inner and outer pipes, but the deflected shape is.

RE: Concentric Tubes in Bendine

that's another way to look at the problem ...
the stresses in the smaller tube must be higher than the larger one as their deflected shape is the same and the smaller tube has a smaller I/y (proportional to OD^2*t)

another day in paradise, or is paradise one day closer ?

RE: Concentric Tubes in Bendine

Quote (SAIL3)

but, I detect Timoshenko stirring in his grave

Rolling on his side to make room for some clapping? Just foolin'... I know what you meant.

As I see it, the sharing of a common strain diagram is what puts the "composite" in composite behaviour. A cross section could be comprised of interplanetary dust particles seperated by miles for all the difference it makes in Bernoulli flexure. So long as all of the parts follow the same strain diagram, an equivalent section is possible for stress and deflection calcs. And simple as well. All equivalency requires is the ignoring of boundaries / empty space in recognition of strain matching there.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

Quote (rb1957)

the stresses in the smaller tube must be higher than the larger one as their deflected shape is the same and the smaller tube has a smaller I/y (proportional to OD^2*t)

I believe that stresses will be higher in the larger member. Consider:

1) again, that common strain diagram and;

2) the the outer tube attracts more moment which will increase stress.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

Kootk is definitely theoretically correct, there is zero shear demand along the length of the interface of the two pipes, neutral axes coincide so no shear flow between them, and it is also obvious in this case by intuition that the members behave as if they were one solid member for the case of bending. But if there is a non negligible gap between them, some kind of wonky load sharing occurs, where at the mid point the top of outer pipe bears on the inner pipe, and the supported ends the bottom of the inner pipe bears on the upper pipe (assume single span simply supported with a point load at mid span). Based on OPs description though that doesn't apply to his problem.

RE: Concentric Tubes in Bendine

RB:
I haven’t put any real numbers to the real problem yet. I am suggesting (I believe) that the two pipes will be at about yield (50ksi, whatever) at their own extreme fibers at about the same time. This is due to their own/individual M/Sx, and due to their different loading proportion, sharing, which is due to their different stiffness’. I agree with you that there will be some funny localized loadings or stresses; your example, the point load on the outer pipe, being somewhat distributed to the inner pipe at the same general location, some length on the beam. For the slip fit, the two pipes are more or less forced to deflect the same, +/- a few hundredths or thousandths of an inch, by their almost intimate contact. But, these are smaller than the straightness or ovalty tolerance in the pipe, thus some interference in a long length. I also agree with Koot that the interference fit will introduce some new triaxial, very complex, stresses into the picture, that none of us really want to try to define here. The point that I was trying to make is that the two pipes act independently from the normal bending stress standpoint and that except at the N.A. level, where σ = 0ksi in both pipes, the stresses are not the same at any other level in the beam system. Certainly not like someone might be inclined to think if they went too far down the single composite section ‘pipe line,’ er path. I’ll leave the more complex secondary affects to another day.

RE: Concentric Tubes in Bendine

if you have two tubes, a large one and a small one, and deflect them the same; the moment in each is proportional to I (thinking d(x) = M/EI*...) and so the smaller tube has a lower bending stress (because the extreme fiber is less) ... yes, not what I posted before (sigh).

If both tubes are bending along the same deflection curve then stress is proportional to distance from the NA (as M/I is constant) ... not what I posted before ... I still think that losing what is happening on the "faux parting line" should have an effect.

another day in paradise, or is paradise one day closer ?

RE: Concentric Tubes in Bendine

(OP)
KootK:

Quote (KootK)

In reality, I would expect a tight friction fit to change stresses a bit. Intentionally, I've just been discussing flexural behavior assuming that plane section remain plane. In the wild, the strains at the extreme ends of the two tubes would probably differ a bit due to shear lag up the sides of the tubes. That difference would be, at least partially, ironed out by the action of the friction generated at the interface.
What do you mean by "assuming that plane section remains plane". Are you referring to the cross section relative to the NA? Why would it be out-of-plane? Also, where does shear lag come into play? At the released ends of the tubes?

This is now beyond the scope of my analysis, but it is good to know/understand nonetheless.

RE: Concentric Tubes in Bendine

Yeah, it's beyond the scope of all of us that spend our time out in profit-land trying to earn a living. See if the sketch below helpes at all. It applies at all points along the length of a member with the effect being most pronounced at the locations where shear is at its peak values. The effect is usually so minor as to be of no practical consequence.



I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

It seems like they should both be able to develop their individual full plastic moments.

The larger tube just gets there first.

RE: Concentric Tubes in Bendine

Long thread and maybe this has already been discussed, but how exactly do you fit one tube inside the other for the full length? Has this been done before? Seems to me typical construction tolerances would make this extremely difficult to install.

Interesting academic discussion though.

RE: Concentric Tubes in Bendine

i think the first question is why would you (insert a tube in a tube with a sliding fit) ? maybe to reinforce and existing tube ??

practically, since we are talking about a close tolerance fit, i'd probably freeze the inner tube, having verified that it won't be loose in it's final position. maybe scan the ID of the large tube to get a true representation. and, yes, I realise that these ideas are not normally practical.

another day in paradise, or is paradise one day closer ?

RE: Concentric Tubes in Bendine

Quote (jdgengineer)

how exactly do you fit one tube inside the other for the full length?
Just spit on it a few times and ram it home?

RE: Concentric Tubes in Bendine

It occurs to me that we normally neglect shear deflection in beam deflection problems, but if that was considered, it may no longer be possible to get them to deflect identically under the assumptions made. That is in addition to any end effects mentioned above.

RE: Concentric Tubes in Bendine

the two tubes are constrained by geometry to deflect the same.

another day in paradise, or is paradise one day closer ?

RE: Concentric Tubes in Bendine

I finally ran the numbers on this and Koot was correct all along.....as he stated, composite action is not required in this example and the stiffeness is the same for 2-tube setup versus the solid equivalent tube.......learn something new everyday wheather one wants to or not...Timoshenko is again resting in his grave, if not in the same position....

RE: Concentric Tubes in Bendine

Quote (SAIL3)

Koot was correct all along

Hey, even a blind squirrel finds a nut once in a while. Thanks for doing the leg work and for reporting back to share the results.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

The above discussion has been predicated on the two cylinders being of the same material with equivalent elastic moduli. Can I assume that if they were different materials with different elastic moduli that the equivalent EI would be (EI)outer + (EI)inner? I have a real-life reinforcement problem with some wood beams that I would like to reinforce with thick wall steel pipe to counter a termite concern. Thanks!

RE: Concentric Tubes in Bendine

It'll work so long as the respective neutral axes of each piece are at the same location.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

If there is a small gap between the inner and outer pipe in order to achieve a sliding fit, the inner pipe will have a smaller deflection than the outer pipe and will tend to feel a single load at or near midspan.

BA

RE: Concentric Tubes in Bendine

I agree with BAretired. When placing the smaller tube we will have 3 cases.

First one, the smaller tube is a little bigger than specified and then it won't fit without getting a lot of residual stresses.
Secondly, the members perfectly size each one another and then it will behave as described.
Third, probably the most common situation will be to have a gap.


RE: Concentric Tubes in Bendine

I agree, the truthiness of the theory discussed above is sensitive to the ratio gap/deflection. An eighth inch gap in a system deflecting three inches is surely of little consequence. A half inch gap would be a different animal.

Quote (KootK)

It'll work so long as the respective neutral axes of each piece are at the same location.

In the interest of precision, let's revise that to:

It'll work so long as the respective neutral axes of each piece are at the same location and are made to travel in unison.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

@rockitz, I'd prefer to use the "rule of mixtures" and convert both sections to the same material (E)

another day in paradise, or is paradise one day closer ?

RE: Concentric Tubes in Bendine

Fascinating discussion. Among the products my company makes are carbon fiber composite tubes that fit within each other with 0.001" gap between them. The outer tube has an OD of 0.300" and a 0.025" wall thickness and 32" length, to give some perspective. Both the outer and inner tubes are designed to have similar bending stiffness so the inner tube has a greater wall thickness.

rb1957's intuition is correct. Without bonding there is no composite action.

The logic that because the neutral axis is the same for both tubes whether they are bonded or not proves that there must be composite action is flawed. Let's take the case of three point bending. If you take the two tubes separately and bend them the same amount they will each have a certain load in the center of the span. If you place one tube in the other and deflect them the same amount, the measured load will be the sum of the loads measured for each tube. This is non-composite action. So why is this?

The factor that has been overlooked in all of the discussion so far, are the hoop stresses in the tube. When a tube is flexed it wants to ovalize where the tension and compression sides move closer together, which results in a lower "I" in axial bending. In an I-beam the web prevents this. In a tube only the walls can do this and they behave as two "C" shaped springs. So, with a tube in a tube that are not bonded you have four thin springs. When they are bonded they act as two thicker springs, which are stiffer than the four (composite action).

A unique feature of fiber reinforced composite material is that you can tailor material properties by changing the fiber orientations. One way to make a carbon fiber tube is by pultrusion, where fibers and resin are pulled through a shaping die. All the fibers are axial in the tube wall (think fiberglass tent poles). When flexed too far, these tubes fail by splitting axially because they ovalize, and there is no fiber reinforcement in the hoop direction. They have low axial stiffness because of the low hoop stiffness.

Tubes can also be made by table rolling where two sheets of unidirectional preimpregnated fibers (prepreg) are laminated together in a 0/90 orientation and then rolled around a steel mandrel and cured in an oven. Interestingly, a tube that is made from 50% 0 and 50% 90 fiber is stiffer in axial bending than a tube made from the same amount of fiber that is all in the 0 degree direction.

RE: Concentric Tubes in Bendine

Compositepro, you are mixing different matters. All this discussion was about the behavior of two concentric tubes in the frame of the classical elastic beam theory. If you add ovalization to that, then the subject changes.

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RE: Concentric Tubes in Bendine

Quote (compositepro)

If you take the two tubes separately and bend them the same amount they will each have a certain load in the center of the span. If you place one tube in the other and deflect them the same amount, the measured load will be the sum of the loads measured for each tube. This is non-composite action. So why is this?

Actually, in this instance, that is composite behavior. That was one of the interesting findings above. Here, IE_comp = IE_non-comp.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

You are saying that bonded or not bonded the tube in a tube will have the same bending stiffness. That is not true. Bonding the tubes together will increase stiffness.

RE: Concentric Tubes in Bendine

I disagree strongly. That said, I don't have any persuasion arrows in my quiver other than what has already been set out above.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

RE: Concentric Tubes in Bendine

If there is no gap, I agree with KootK. The moment of inertia of any shape is the sum of the moment of inertia of its parts. If there is a gap, the bending stiffness of the solid ring is slightly greater than the sum of the two separate rings. The difference is Eπ(d4-di4)/64 where d = inner diameter of the outer ring and di = outer diameter of the inner ring.



BA

RE: Concentric Tubes in Bendine

It's true and not true. If shear isn't transfer then the members acts individually, but while having concentrics tubes without gap the inertia is not sensitive to shear transfer, just because "y" is continuous in between the members. Acting LIKE a composite action, even when it's not a composite member.



RE: Concentric Tubes in Bendine

I suppose it's a matter of how one defines just what a composite member "is". Is it about the degree of shear transfer available which may vary from zero to infinity? Or is it about achieving certain section properties based on maintaining a common strain profile? For me it's the latter.

I would characterize the two tube setup as "trivially composite". That, implying:

1) Sure, it's composite but then the composite properties are no improvement over the non-composite properties. A bit like concentric sistering in wood construction.

2) Demand for shear flow shear transfer to achieve "composite" is nominally zero unless one introduces a meaningful gap or drills down deep into more granular effects.

I believe that #2 is the important insight from the perspective of OP's original question.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

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