Beam bracing 19

[NewEngineerHere]

Hi everyone:

I am a recent graduate and trying to understand the beam bracing analysis/design.
I read in many texts that the beam flange needs to be braced otherwise it would buckle ( like a wave shape as we see in a column under axial load.)

Now my questions are:

If I have a beam supporting floor slab, (top flange is fully braced- great, no worries) Now, bottom flange needs to braced so it does not rotate (torsional buckling?)
how do I know if I really need to brace or not ? OK, AISC manual gives a Cb equation I can calculate my un-braced length

1) How can I correlate Cb equation with the moment applied to the beam, or stability of the beam ? Cb should tell me how much more moment capacity I am gaining for providing that brace at that distance (correct?).... what does it have to do with stability ?
2) What If I have moment connection (double curvature moment diagram) is it different than simply supported ? ( Do I always need to brace both flanges Tension and compression ?
3) How much load will be brace see? how much should be designed for, is this load coming from the moment or out of plane load ( wind, seismic )?
4) When do I need to brace/add stiffener to the web of the beam ?

My first thoughts are: If the beam works for giving load for moment, shear, and deflect - perfect.....But know I have stability issues I need to understand.

I am just trying to make sense of equations, rules, and develop a sense of what is right and what is wrong (how can I prove by calculation).

Thank you

 

[wannabeSE]

LTB involves the entire beam cross section as evidenced by the fact that code equations and textbook derivations all depend exclusively on whole section parameters.

KootK,
Have you considered AISC 360-10 sections F4 and F5 that rely on Sxc (section modulus referencing the compression flange) to limit the stress in the compression flange for LTB.

 

[KootK]

Have you considered AISC 360-10 sections F4 and F5 that rely on Sxc (section modulus referencing the compression flange) to limit the stress in the compression flange for LTB.

I have now. While calculated with respect to the compression flange, S_xc is still very much a whole section parameter.

Whenever LTB capacity is derived, the derivation is done considering equilibrium of a whole beam section shown rotating about a point in space below the beam and in line with the beam shear centre (below). Given that, is it really so hard to believe that LTB represents a buckling mode involving whole section rotation about a point in space below the beam and in line with the shear centre? Somehow we define LTB as that, calculate it as that, but instead believe that LTB is really just caused by straight buckling of the compression flange?

I've hinted at the inconsistency of the compression flange buckling concept with regard to cantilever LTB several times in this thread but so far nobody's taken up the gauntlet. So I'll be more explicit this time around: if LTB is all about compression flange buckling, why do we brace the tension flange of cantilevers? Surely, if compression flange buckling is the cause of LTB, just bracing that flange would be more effective, right?

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.

 

[canwesteng]

Devil's advocate here, but with cantilevers we aren't bracing the tension or compression flange, as there are no flexural stresses at the end of a cantilever. IMO you should brace the compression flange at the point of support if it's a cantilever running over a column, but for different reasons.

 

[KootK]

I believe that it's irrelevant that there are no flexural stresses at the end of a cantilever. That is still the point where the beam wants to flop over. And tension flange bracing is the most efficient way to prevent that.

You can certainly have an unbraced cantilever tip. You'd just have to contend with a very high effective length factor. As a matter of good practice, I would provide top and bottom flange lateral restraint at the first support in from the cantilever. Although, in theory, you only need one torsional restraint located anywhere along the beam span.

I get the shared feeling that, for the most part, the story of common LTB is the story of compression flange-ish buckling initiated rotation. It's just that that story is incomplete and can lead to poor bracing decisions in the less common cases. Confusion about LTB bracing is rampant on this board which I take to be evidence of that confusion.

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.

 

[canwesteng]

I think of it as a load offset from the shear centre by some infinitesimal amount would tend to cause the beam to buckle torsionally, in the same way some infinitesimal eccentricity or imperfection will cause a column to buckle at some load. Hence the cantilever buckles where there is, in fact, no moment. That's the reasoning I use not to stress too much about LTB in monorails, except in cantilever sections, as you can see by introducing some small eccentricity that the load creates a restorative torsion.

 

[KootK]

Ok, now I see where you're coming from canwesteng. And I agree, load position has a large effect on stability. In fact, it makes me think of an interesting thought experiment. I'll post that when I get to the office and have scanner access.

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.

 

[Jerehmy]

I don't see how the buckled shape of the member justifies that the compression flange doesn't initiate it. One is the result of the other.

High compressive load in flange
Flange wants to buckle out of plane
Member does not have enough rotational resistance --> member buckles. The specific shape is irrelevant to what caused the buckle.

The tension flange is braced in the cantilever because of the shape of the buckle. Just because the origin of rotation for the buckled shape can change doesn't mean the cause of the buckle isn't due to high compressive forces in the flange.

Just because the buckle involves the entire member doesn't mean the cause can't be high compressive forces in the flange.

 

[Jerehmy]

Also, a bottom flange loaded W beam can still have LTB even though the loading is helping to restore the shape.

 

[canwesteng]

But in a cantilever, there are no compressive stresses at the point where LTB occurs

 

[Jerehmy]

Per Salmon "Unlike the flagpole column where the effective pinned-end length is twice the actual length, the lateral-torsional buckling of a cantilever beam is not even as severe as the unbraced segment under uniform moment. If one considers the analogy to a column (compression flange is like a column), such a result is logical. Since the moment at the free end of the cantilever is zero, the compression force in the flange decreases from a maximum at one end to zero at the end; thus, the loading is less severe than if the compression force were constant over the entire length."

 

[Jerehmy]

LTB is like deflection. It involves the entire length of section, not just a specific point. It's an integral over the entire section. That's sort of what the Cb factor takes into account when the moment varies.

 

[canwesteng]

Well, I don't have a copy of Guide to Stability Design Criteria for Metal Structures but I recall there were effective length factors in there for cantilevers, and that text seems to be well backed up with test data, and I'm fairly sure last time I did some cantilever design I took Lu to be greater than L of the cantilever.

 

[Jerehmy]

"Clark and Hill and SSRC Guide, 3rd ed. reported that it is conservative to use the full length as the effective laterally unbraced length for lateral-torsional buckling of cantilever beams. However, the conservativeness of using the actual length for a cantilever depends in large part on having fixed torsional restraint at the supported end as well as having the loading applied at the shear center or at the bottom flange. Since torsional fixity rarely ixist, the authors recommend using the actual cantilever length as the effective laterally unbraced length".

SSRC Guide is Structural Stability Research Council, Guide to Stability Design Criteria for Metal Structures.

 

[KootK]

I submit the beam-column shown below for consideration. It has the following characteristics:

1) The applied axial tension is such that there will never be compression stress anywhere within the beam section.

2) It is self evident that it will eventually laterally torsionally buckle at some value of the parameter y_p, the height of the applied load.

So here we cave a case of LTB where there is no compression flange. Is this a particularly practical example? Clearly not. Does it decouple compression flange buckling from LTB? I think that it does.

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.

 

[Jerehmy]

That wouldn't be LTB. That'd simply be torsion from eccentricity of the load.

Reference something that justifies your point of view. That you can have LTB without compression in the member.

 

[bowlingdanish]

Why does load height affect LTB if it's just compression flange buckling? Wouldn't it only be a destabilising load if the compression flange has already buckled? I'm not suggesting compression in a member isn't a source of instability but surely there's more at play? I just mark it down to magic and move on.

 

[Jerehmy]

Load height affects it because it increases the torsion and thus the buckling. That's why when a beam loaded at the bottom flange at the shear center has a higher LTB moment because the load is helping to stabilize rather than destabilize the beam.

 

[bowlingdanish]

But in your compression flange buckling analogy for there to be any torsion at all, the compression flange needs to have already buckled, at which point the beam has already failed. Why do I care about secondary torsion when my beam has already failed?

If you apply the load at the shear centre, bottom flange or top flange, the compression flange will still take roughly the same load, but they have very different buckling moments.

 

[Jerehmy]

Theoretically, prior to buckling, it doesn't matter where the load is located vertically as long as it is through the shear center.

Realistically, beams aren't perfect, the load will never be exactly through the shear center whether it's buckled yet or not. So it matters.

 

[KootK]

That wouldn't be LTB. That'd simply be torsion from eccentricity of the load.

I beg to differ good sir. The beam moves laterally and rotates torsionally. And those motions reduce the potential energy of the applied load. That, fundamentally, is what LTB is. You yourself pointed out that a load applied below the shear center can still cause LTB. Why would it be any different for load applied above the shear center? One helps, the other hurts -- that's all.

Reference something that justifies your point of view.

I'm trying man! My quiver is gradually running dry however. As I mentioned above, I'm confident in the validity of my tension beam example. Another illustrative example is the tension chord buckling phenomenon in trusses (Link). This is essentially LTB for trusses and can occur regardless of whether or not the compression chord has been properly designed for 100% of the compression load that it will see.


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.