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# bending torsion instability of steel pipe4

## bending torsion instability of steel pipe

(OP)
Eurocode says that a steel pipe item (part of a structure) is not affected by a bending+torsion instability (i.e. when the torsion stiffness is bigger than the bending stiffness ??). I am looking of literature discussing and explaining such a statement. Thanks

### RE: bending torsion instability of steel pipe

I'm not familiar with the Eurocode, but I believe the question you're asking is can a pipe be subjected to lateral-torsional or flexural-torsional buckling, right? The answer to those is no. Consider that the radius of gyration is the same in all directions.

### RE: bending torsion instability of steel pipe

Bmart is correct. A cruciform (X-Shape) is most susceptible to torsional instability under pure compression because it will twist under compression only. A pipe will not twist under compression, but it may buckle laterally. This concept also applies to lateral-torsional buckling.

### RE: bending torsion instability of steel pipe

I don't understand. Can someone explain me why a section with the same radius of gyration in each direction is not subjected to lateral buckling?

### RE: bending torsion instability of steel pipe

Good question.

A pipe is geometrically stable. For instance, a I-beam under load will deflect downward until reaching a certain point (buckling limit), the tension flange will then rotate sideway and introduce twist, thus instability results. The pipe does not possess this behavior, when stretched to strength limit, it continues deflect downward and simply fail in flexural bending.

### RE: bending torsion instability of steel pipe

retired13 nailed it. That’s the answer

### RE: bending torsion instability of steel pipe

Yes, I know, I agree. But, is it possible to explain it with math? I studied the buckling behavior of thin walled beams with open cross section, but not of beams with closed cross section. Is it possible to prove analitically that lateral buckling doesn't occur in pipe?

### RE: bending torsion instability of steel pipe

I'm not aware there is formulation for this phenomenon. I think it is more or less by observation.

### RE: bending torsion instability of steel pipe

I'm sure you could do it analytically. Add some infestimal rotational displacement, and see if that makes the section any less stable. It wouldn't because the beam is a perfect circle. But you see with a wide flange section, there will be a tendency for the compression flange to want to keep rotating.

### RE: bending torsion instability of steel pipe

Thank you retrograde, but that page report information about rectangular hollow section, not about circolar hollow sections. I'd like to find the formulation for circolar hollow sections

### RE: bending torsion instability of steel pipe

(OP)
... and attached file too

(OP)

### RE: bending torsion instability of steel pipe

#### Quote (Billie93)

I don't understand. Can someone explain me why a section with the same radius of gyration in each direction is not subjected to lateral buckling?
We are talking about TORSION lateral Buckling and not lateral buckling
of course a pipe can do lateral buckling...but due to high torsional stiffness no torsional lateral buckling

### RE: bending torsion instability of steel pipe

4
I'm sure there is some good literature out there, and I recommend you continue to seek it out, but the easiest way to sort through this is to consider the behavior of beams in a general sense. And yes, klaus is correct that it's important to distinquish between LTB and what you learn in undergraduate as Euler (column) buckling. This conversation relates to LTB, not column buckling. Column buckling applies to all unbraced shapes of significant length.

Now consider a circular cross section beam (hollow or solid). There is no strong axis or weak axis because the radius of gyration is the same no matter which way you take it. As you begin to bend the beam, it will not try to tip or buckle about another axis because the moment of inertia is the same in every direction. It is always in the lowest energy state.

Hopefully this helps illustrate why one situation applies while the other doesn't.

### RE: bending torsion instability of steel pipe

robiengIT
Oh, I missed the attached file, I'll read it as soon as I can

Klaus
Yes, of course I know the difference, I've studied the problem of lateral torsional buckling during university (in the case of open cross section). But we called "lateral torsional buckling" as "laterale buckling"

BMart006
Good explanation, thank you! But it is possible to find it out by math?

### RE: bending torsion instability of steel pipe

#### Quote (Billie93)

But it is possible to find it out by math?

We all know that a sphere ball on a dome is at a state of "limited stable", we can prove it becomes unstable mathematically, when it moves a little to the right or left, but is there a mathematics proof when it sits perfectly in the middle? The only expressions I can think of are ΣH = 0 and ΣV = 0, thus there is not possible for the ball to move, and the proof stands.

I think the explanation below is quite simple and straight forward.

#### Quote:

Lateral Torsional Buckling occurs in unrestrained beams. A beam is unrestrained when its compression flange is free to displace laterally and rotate. When I sections are used as beams or beam columns the compression flange is under compressive stress and has a tendency to buckle but it is attached to the tension flange which resists the buckling giving rise to torsion within the beam section. This torsion twists and warps the unrestrained part of beam leading to lateral torsional buckling.

Will a circular shape behave the same - deflected out of shape that given raise to torsion?

### RE: bending torsion instability of steel pipe

Retired13
The ball on a dune is in a point of unstable equilibrium. The equilibrium is stable only in the points where the total potential energy is minimum. Why? If a body (in a minimum point of total potential energy) change his position, the kinetic energy must decrease (because the total energy, in the case of conservative forces, doesn't change): the kinetic energy decrease until the velocity becomes 0, then the velocity becomes negative and the body turn back in his original position. This is stability.
There is always a mathematical explanation.

### RE: bending torsion instability of steel pipe

Billie93,

You explained well. I wonder why you couldn't get over the LTB phenomenon, as BMart006 explained well too, mathematically speaking. You can follow suite to develop theory for circular pipe too, I believe.

### RE: bending torsion instability of steel pipe

This is my point. In literature, I find pretty easily the analytical description of lateral torsional buckling for open cross section subjected to constant flexural moment: the buckling moment (in a section without warping, as a pipe) is proportional to the square root of the moment of inertia in the weak direction mulyiplied by the polar moment of inertia; is this formulation valid even for the buckling moment of a pipe (which is, of course, a closed section and not an open cross section)?

Imagine a pipe subjected to constant moment Mx. The beam will deflect in y direction.
I understand (I hope) that, if you have the same radius of inertia in each direction, when something perturbs equilibrium and makes the section rotate along his longitudinal axis, nothing change, because you don't give any second order moment along a weak direction.
BUT, if something perturbs the equilibrium and makes the section deflect in x direction, it will generate a second order torsional moment. If it is big enough, the beam could buckle. Am I wrong? I know that the torsional rigidity of a pipe is very big, but I would like to understand if in strange structures (with effective length of 60 meters, for example) this phenomena could happen or not.

Thank you for your attention :)

### RE: bending torsion instability of steel pipe

#### Quote (if something perturbs the equilibrium and makes the section deflect in x direction,)

In z-dir, I guess? (x - axial, y - vertical, z - out of xy plane)

### RE: bending torsion instability of steel pipe

Retired13,

I used this:
X orizontal
Y vertical
Z axial

So, I was correct, in that point I talked about x.

Indeed, the moment Mx (which I talked about in my example) is a flexural moment in the x direction, wich generate a deflection in y.

### RE: bending torsion instability of steel pipe

Which one below will be kicked into higher energy state after the additional T = P*e?

### RE: bending torsion instability of steel pipe

#### Quote (IDS)

This might be of interest:

this is a different type of buckling... this is buckling of the wall...like Cylinder buckling
other story

### RE: bending torsion instability of steel pipe

Retired13
I think the pipe. What's the point?

### RE: bending torsion instability of steel pipe

That's the LTB phenomenon graphically (not exact) explained. Yes, the pipe, n Now you can think a mathematical explanation for it. I am running out of bullets, please help yourself.

### RE: bending torsion instability of steel pipe

Omg, I understand that a I section is subjected to LTB and, in general, not a pipe. Thank you for the pictures. I asked for a mathematical analysis, starting from the equations of a beam and searching a condition where the total potential energy is maximum (if it is possible to find that condition, if it is not possible I'd like a mathematical explanation for that). If I asked for it, maybe I can't find it alone.

### RE: bending torsion instability of steel pipe

#### Quote (Billie93)

...if it is not possible I'd like a mathematical explanation for that

In my opinion, you'll not find such a mathematical explanation because it is in fact possible to laterally torsionally buckle an infinitely elastic, shear center loaded circular hollow section. See the mechanism below which is similar to retired13's work. When we say that these members cannot laterally torsionally buckle, what we really mean is that their lateral torsional buckling resistance is so high that it's of no practical interest to us as designers because other failure modes will kick in long before lateral torsional buckling becomes an issue. To numerically assess the lateral torsional buckling strength of a circular hollow section, I believe that one would use the usual equation for elastic lateral torsional buckling as follows:

1) Use the relatively large St. Venant torsional stiffness value associated with your closed section and;

2) Eliminate the term representing the torsional stiffness associated with cross sectional warping.

### RE: bending torsion instability of steel pipe

Thank you for the answer KootK, I agree with every thing you said. Obviously, having big torsional and flexural rigidity, the LTB does not happen for pipe. As I said before, I want to study the problem of particular structures where there are very long pipe (effective length of 50m or more) and I wanted to understand if in these case LTB could happen.
I agree that the right formulation is the "famous" one that we use for open section: to find out that formula I think that the hipotesys of open section is used only to define the warping function, but pipes doesn't warp, so the formula should be' valid.

### RE: bending torsion instability of steel pipe

#### Quote (Billie93)

Thank you for the answer KootK, I agree with every thing you said

Well I like the sound of that. And you're most welcome.

#### Quote (Billie93)

As I said before, I want to study the problem of particular structures where there are very long pipe (effective length of 50m or more) and I wanted to understand if in these case LTB could happen.

It's an interesting problem. I have the following thoughts to offer;

1) As span increases with, say, a point loaded member:

- vertical stiffness decreases with L^4.
- lateral stiffness decreases with L^4
- torsional stiffness decreases with L^1
- bending stress increases with L^2

2) For a member for which deflection is being meaningfully controlled, I don't ever see LTB overtaking deflection.

3) At some rather long length, I suspect that LTB does in fact overtake bending. And I think that Retrograde's interesting table above reflects this fact, even if not for an [ry = rx] member per se.

4) For any real world tube of such great length, it will likely be prudent to consider the destabilizing effect of loading above the shear center rather than at the shear center. There really are not many common ways to load a tube through the shear center and loads located at other locations may well result in:

a) Pure torsional buckling if it is the case that the tube would stay put and the load source would translate laterally or;

b) Something like constrained axis lateral torsional buckling if it is the case that the load would stay put and the tube were free to translate laterally.

### RE: bending torsion instability of steel pipe

Where is the destabilizing force in that diagram though? Effectively, I think all buckling needs to have some kind of force reducing the stability of the member (think secondary moments in euler buckling, or the compression flange of a beam wanting to continue to rotate after an initial rotation, or the top chord of a truss "pushing" through to the tension chord). I just can't rationalize that there is any force there that is causing the buckling. In fact in that sketch I think all the forces are pulling the member back to its centerline.

### RE: bending torsion instability of steel pipe

If you are really into the subject of buckling/bifurcation, this book goes into it to a dizzying extent. I bought the hardback at the last AISC conference. It's quite dry but very informative.

https://www.amazon.com/Guide-Stability-Design-Crit...

### RE: bending torsion instability of steel pipe

Billie93,

I don't know why I keep coming back here. Anyway, here is some math you might be interested in, Link. And here is another one, Link

### RE: bending torsion instability of steel pipe

#### Quote (canwest)

I think all buckling needs to have some kind of force reducing the stability of the member (think secondary moments in euler buckling, or the compression flange of a beam wanting to continue to rotate after an initial rotation, or the top chord of a truss "pushing" through to the tension chord).

In the real world, yes. However, it's usually a geometric imperfection rather than a force per se. And there's no reason to think that our tube wouldn't have such a geometric imperfection. Member sweep would do the trick. In a more abstract way, so might residual weld stresses at the seam welds.

In the world of mathematical, bifurcation bucklin, such a perturbing force / imperfection is not required. Moreover, if the perturbation were a force rather than an imperfection, it would be mathematically incapable of influencing the result. Eigenvalue analyses are largely agnostic to perturbation forces. When we do the classic Euler column derivation in university, that is independent of any perturbation. Rather, you're simply seeking the compression load at which flexural stiffness drops to zero.

#### Quote (canwesteng)

Where is the destabilizing force in that diagram though?

#### Quote (canwesteng)

I just can't rationalize that there is any force there that is causing the buckling.

Think of it more as a force acting through a destabilizing motion rather than a destabilizing force alone. In my sketch, [theta] rotation produces the vertical displacement [Y} which brings the load closer to the ground and, therefore, reduces the potential energy of the system. This is the sense in which LTB is destabilizing.

#### Quote (canwesteng)

In fact in that sketch I think all the forces are pulling the member back to its centerline.

I show one external force in my sketch and, considered in the context of the [theta] motion, it is clearly destabilizing.

As for internal forces, yes, they to tend to pull the member back to it's centerline. That, in effect, is the member's LTB resistance. And it's also true of the strains generated in, say, a wide flange beam when it embarks upon an LTB excursion.

### RE: bending torsion instability of steel pipe

#### Quote (DrZ)

If you are really into the subject of buckling/bifurcation, this book goes into it to a dizzying extent. I bought the hardback at the last AISC conference. It's quite dry but very informative.

Another great option for getting so deep into the weeds that you're staring up at lillipads is shown below. It's lively and engaging in spades, however, as first principle stuff tends to be.

### RE: bending torsion instability of steel pipe

If we ditch the world of mathematics in favor of the real world, there is a significant stabilizing effect to be considered with slender tubes. The applied load acting through the sag present in a slender tube will, itself, create a restoring action serving to inhibit lateral motion. This represents our leaving small deflection theory in the dust however. For this reason, among others, real world LTB truly is the domain of members which are stiff in the loaded direction and relatively soft, in comparison, with respect to lateral motion and twist.

### RE: bending torsion instability of steel pipe

Ok, ignore the my use of the word force, but ultimately there needs to be second order effects that destabilize the member for it to continue to buckle. I don't see how there are any of those in the pipe. Your force brings the pipe closer to ground, but won't move the pipe laterally or torsionally, whereas if it were an open section, the compression flange is going to continue to rotate, just like a column continues to buckle. In your sketch, the external force isn't destabilizing, it only wants to push the member straight down.

### RE: bending torsion instability of steel pipe

#### Quote (canwesteng)

..whereas if it were an open section, the compression flange is going to continue to rotate, just like a column continues to buckle.

It is a subtle but important mistake to think of lateral torsional buckling soley in terms of the compression flange acting like a column. A salient example is the case of unrestrained cantilevers being most effectively braced at the tension flange.

Alternately, simply think of the portion of the tube cross section experiencing compression stress as akin to a compression flange. Such is the case with higher aspect ratio rectangular tube sections which can LTB, right?

#### Quote (canwesteng)

Your force brings the pipe closer to ground, but won't move the pipe laterally or torsionally

Bifurcation buckling is not about actually moving anything. It's about applied load reaching a point where resistance to a hypothetical perturbation would vanish. An Euler column never actually buckles. It simply reaches a level of applied load at which its resistance to buckling drops to zero. Of course, for design purposes, neutral stability is little better than instability.

#### Quote (canwesteng)

In your sketch, the external force isn't destabilizing, it only wants to push the member straight down.

The same is true of the applied load on a wide flange when LTB is derived for that situation.

### RE: bending torsion instability of steel pipe

Here is the destabilizing force, in my opinion. If the pipe deflect, a torsional moment appear. As we do when we talk about stability, we can see that torsional moment as a loss of torsional stiffness. If M0 is big enough, the torsional stiffness of the pipe becomes 0 and we have instability.
Of course, the torsional stiffness of a pipe is very big, so M0 has to be very big to have torsional instability. As we said, we have different kind of collapse before reaching a critical torsional point, and that is sure.
Am I wrong?
Of course, if we increase the span, we reach the critical point with a smaller value of M0.
I started this discussion (in an italian forum, to be honest) beacause I'm a curious man and because I want to understand the behavior of very long pipes subjected to axial compressive force and bending moment: maybe I discover that the resistance of the pipe is a little smaller in the combined M,N buckling verification.

### RE: bending torsion instability of steel pipe

In the strictest sense, there is really no such thing as a destabilizing force as a thing considered separately from a destabilizing perturbation (displacement in our context). The destabilizing effect is that of any combination of:

1) A perturbation displacement and;

2) A force which would do positive work when the perturbation is exacerbated.

In this respect:

3) the axial compression load on an Euler column is the "destabilizing load" when a lateral perturbation is considered (external load moves in direction of load).

4) the applied external load in my sketch is the "destabilizing load" when a lateral torsional perturbation is considered (external load moves in direction of load).

5) an axial tension load on a column is a "stabilizing load" when a lateral perturbation is considered (external load does negative work as the ends draw closer together).

An internal force action really cannot be destabilizing, in the strictest sense, precisely because it does no external work. Rather, it is a manifestation of the member strain required to do the external work.

### RE: bending torsion instability of steel pipe

Interestingly, by extension of the same logic, this too would be mathematically possible, if practically ridonkulous. No doubt many would consider this to a constitute a point against my reasoning. Presently, I do not.

This is somewhat similar to an interesting phenomenon that I noticed when tinkering with buckling analysis using the software package Mastan last fall. If there is any potential for instability, the eigenvalue analysis will find it. It just might be at an applied load ratio (ALR) of 47,000, that's all.

I would play with lateral torsional beam buckling (LTB) and, once all of the expected modes of LTB were restrained, it would start producing "buckling" modes that looked like pure lateral translation (no motion component parallel to the the applied load). They never were pure lateral translation though. Rather, there was always a slight torsional component even if it was imperceptible to the eye.

### RE: bending torsion instability of steel pipe

I think it is worth discussing the difference in behaviour in the diagram posted by retired13 on 14 Jan 20 23:31 and those posted by kootk (16 Jan 20 17:15).

If the point load is applied to the top of the pipe then rotation of the pipe will increase the torque and torsional buckling is a possibility, and there will be a well defined theoretical applied load that will cause torsional buckling. If the load is applied exactly at the shear centre rotation does not increase the torque and the theoretical torsional buckling load is infinite.

This applies to a rectangular closed section as well, but in this case the warping effects will make the theoretical torsional/warping load finite.

For a real pipe the load will not be applied exactly at the centre and the section will not be exactly circular with uniform thickness, so there will be a finite torsional buckling load in this case as well, although it likely to be higher than the buckling load due to local wall buckling.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

### RE: bending torsion instability of steel pipe

Agreed, that's precisely what I was speaking to below. While non-shear center loading is surely more common in the real world, I thought it most instructive to restrict myself to shear center loading because it eliminates some potentially confusing complexity and makes for an apples to apples comparison to the classical wide flange LTB derivation. That said, I'd be thrilled to discuss the finer points of non-shear center loaded LTB with any interested parties.

#### Quote (KootK)

4) For any real world tube of such great length, it will likely be prudent to consider the destabilizing effect of loading above the shear center rather than at the shear center. There really are not many common ways to load a tube through the shear center and loads located at other locations may well result in:

a) Pure torsional buckling if it is the case that the tube would stay put and the load source would translate laterally or;

b) Something like constrained axis lateral torsional buckling if it is the case that the load would stay put and the tube were free to translate laterally.

### RE: bending torsion instability of steel pipe

In my opinion, the load will not always pointing through shear center. As the beam rotates, the load follows but maintain vertical due to gravity (Similar to when floor shakes, we tends to move with it before fall). For the pipe, the additional torsion will produce pure shear in the pipe wall (stable), but for the I beam, due to geometry, it will kick the beam to another state (unstable).

### RE: bending torsion instability of steel pipe

That may well be true in practice but it's not how LTB derivations are developed in the literature. Mathematically, I suspect that accounting for that would add a brutal level of complexity.

Nope, your description is in fact both what probably happens in reality AND how the derivations are developed when the load is positioned above the shear center. Mistakenly, I thought that you were describing a situation in which the load did not remain vertical. My bad.

### RE: bending torsion instability of steel pipe

#### Quote (retired13)

For the pipe, the additional torsion will produce pure shear in the pipe wall (stable), but for the I beam, due to geometry, it will kick the beam to another state (unstable).

That I disagree with though. On balance, a pipe will tend to be more torsionally stable than a wide flange. However, stability is not guaranteed by the mere fact that a pipe section is in play. In fact, it would be quite easy to contrive a situation in which an above shear center vertical load would result in torsional instability in a pipe. In many cases that would actually be pure torsional buckling rather than lateral torsional buckling .

### RE: bending torsion instability of steel pipe

#### Quote (retired13)

For the pipe, the additional torsion will produce pure shear in the pipe wall (stable),

The additional torsion will create additional eccentricity, which for small deflections will be proportional to the torsion.

How is that stable?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

### RE: bending torsion instability of steel pipe

#### Quote:

that would actually be pure torsional buckling rather than lateral torsional buckling

You are right. That's probably the reason that explains the OP statement:

#### Quote:

"Eurocode says that a steel pipe item (part of a structure) is not affected by a bending+torsion instability"
, meaning not to worry LTB for pipes.

### RE: bending torsion instability of steel pipe

I'd actually like to see the exact working of that statement, and the prose immediately surrounding it, if anyone has ready access to the document.

### RE: bending torsion instability of steel pipe

The torsion is due to a lateral offset between the load and the shear centre, which increases as the pipe twists.

How is that not Lateral Torsional Buckling?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

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