## bending torsion instability of steel pipe

## 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

## RE: bending torsion instability of steel pipe

## RE: bending torsion instability of steel pipe

## RE: bending torsion instability of steel pipe

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

## RE: bending torsion instability of steel pipe

## RE: bending torsion instability of steel pipe

## RE: bending torsion instability of steel pipe

## RE: bending torsion instability of steel pipe

https://www.aisc.org/globalassets/aisc/hss--curved...

## RE: bending torsion instability of steel pipe

## RE: bending torsion instability of steel pipe

... and attached file too

## RE: bending torsion instability of steel pipe

## RE: bending torsion instability of steel pipe

TORSION lateral Buckling and not lateral bucklingof course a pipe can do lateral buckling...but due to high torsional stiffness no torsional lateral buckling

## RE: bending torsion instability of steel pipe

Consider a rectangular beam bent about its MAJOR (strong) axis. As you load the beam, it will reach a point where the beam becomes unstable and wants to return to a lower energy state. In this case, the lower state is bending about the MINOR axis. That is why the instability results in a lateral bend about the minor axis. Now consider the same beam bent about its MINOR axis. In this case, no matter how much you stress the beam, it will never buckle by bending about the MAJOR axis. The reason for this is that the beam is already in its lower energy state (minor axis bending) and will not suddenly jump to its higher energy state (major axis bending). Note that rx and ry (radii of gyration for major and minor axes) are not equal... this is a numerical representative of the higher and lower energy states alluded to.

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

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

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.

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

## RE: bending torsion instability of steel pipe

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

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

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

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

## RE: bending torsion instability of steel pipe

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

https://newtonexcelbach.com/2011/07/06/buckling-of...

The main message is, it's not as simple as often presented.

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/

## RE: bending torsion instability of steel pipe

## RE: bending torsion instability of steel pipe

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

I think the pipe. What's the point?

## RE: bending torsion instability of steel pipe

~~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

## RE: bending torsion instability of steel pipe

In my opinion, you'll not find such a mathematical explanation because it

isin 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

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

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

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

## RE: bending torsion instability of steel pipe

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

## RE: bending torsion instability of steel pipe

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

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.

Think of it more as a force acting through a destabilizing

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

As for

internalforces, 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

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

stabilizingeffect 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

## RE: bending torsion instability of steel pipe

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?

Bifurcation buckling is not about actually moving anything. It's about applied load reaching a point where

resistanceto 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.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

destabilizing forceas 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

againstmy 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

anypotential 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

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

## RE: bending torsion instability of steel pipe

~~(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

That I disagree with though. On balance, a pipe will tend to be

moretorsionally stable than a wide flange. However, stability is notguaranteedby 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

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

You are right. That's probably the reason that explains the OP statement: , meaning not to worry LTB for pipes.

## RE: bending torsion instability of steel pipe

## RE: bending torsion instability of steel pipe

How is that not Lateral Torsional Buckling?

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/

## RE: bending torsion instability of steel pipe

https://archive.org/details/publicsafetycode?and[]=eurocode

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/