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

 

[KootK]

To begin with, it's important to recognize that lateral torsional buckling (LTB) has nothing to do with flange buckling. Rather, it is the tendency of the section as a whole to rotate about a point in space that is on the same vertical axis as your beam shear center. Therefore, it's most useful to think of bracing the entire section against rotation rather that bracing individual flanges against buckling.

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

For a gravity loaded, simple span beam, the point of LTB rotation is at a distance below the bottom flange of the beam. Even with the bottom flange unbraced, top flange bracing alone is enough to prevent LTB rotation about this point. With the top flange braced, it's actually still possible for the beam to LTB rotate about a point in space at the elevation of the deck restraint. This LTB buckling mode is analogous to tension chord buckling in trusses (Link). The good news is that this second mode of LTB buckling requires a good deal more energy to initiate and is therefore fairly easy to prevent. It normal circumstances, it is prevented by the bottom flange acting as a horizontally spanning girt between supports. This is part of the reason that our codes insist on torsional restraint at the ends of simple span beams that engages a majority of the beam cross section.

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 ?

The LTB equations are derived assuming uniform moment along the length of the beam which is the worst case from a stability standpoint. Most beams do not have uniform moment diagrams which is an improvement. Cb is simply way to approximate that improvement. Note that Cb has nothing to do with unbraced length and will not alter it in any way.

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 ?

With negative moments in play, there will likely be unbraced lengths of the beam over which bottom flange (compression flange) bracing will be required. The main exception is cantilever beams which are most effectively braced at the tension flange. For the most part, double curvature within a single unbraced length affects Cb and is accounted for there.

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 )?

The load is coming from the moment. The AISC manual has an entire section dedicated to require brace strength and stiffness which addresses this issue quite thoroughly. In the past bracing for 2% of the compression force in the flange was common. I think that, still, AISC's seismic manual require bracing for 5% is some situations where the flange is expected to make excursions into the plastic range.

4) When do I need to brace/add stiffener to the web of the beam ?

There are several reasons to do this including web shear buckling, web crippling, web yielding, and overall section rotational restraint at supports. All are addressed in the AISC manual and only the last really impacts LTB.

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.

 

[CURVEB]

Great explanation.

 

[Ron]

Nice job, KootK...

 

[NewEngineerHere]

Thank you very much Kootk. This is the kind of explanation I was looking for. It's more clear to me.

 

[Jerehmy]

Kootk, the section rotates because the compression flange buckles (globally not locally). So that first sentence doesn't make sense to me.

 

[KootK]

I did my darnedest to explain that concept in this recent post Jerehmy: Link.

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 agree that rotational restraint prevents LTB. I disagree that it has nothing to do with compression buckling. It has everything to do with compression buckling. The compression flange is restrained in it's weak axis by the web and can only buckle by it's strong axis, laterally. That's what causes the rotation. It's a long column that has continuous lateral support on one side and none on the other.

To say it has nothing to do with buckling is the exact opposite of what a steel textbook says. Here's an excerpt from Salmon, Johnson, and Malhas:

"At higher compressive loads the rectangular flange will tend to buckling by bending about axis 2-2 of Fig. 9.1.1b. It is this sudden buckling of the flange about its strong axis in a lateral direction that is commonly referred to as lateral buckling."

 

[Leftwow]

What does buckling laterally have to do with torsion?

 

[Jerehmy]

The flange and web are a fixed connection. If the flange displaces laterally, the whole section has to rotate, i.e torsion.

 

[KootK]

@Jerehmy:

I would say that compression flange buckling is to lateral torsional buckling as the bi-moment concept is to torsion. The bi-moment concept is a useful analog that aids physical understanding and captures many of the features of the torsion phenomenon. However, the bi-moment concept is not torsion. Rather, it is an incomplete representation of beam torsion and must be set aside when the simplification is inappropriate.

Likewise, compression flange buckling is not LTB. 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. While LTB and compression flange buckling may present nearly identically in the majority of practical cases, they are two distinctly different phenomena and treating them as universally interchangeable will lead to misunderstandings in some cases. One such case is beam cantilevers, where it is most appropriate to brace the tension flange rather than the compression flange.

At the risk of offending Mr. Salmon et all, I consider the statement that you quoted to represent a green belt level understanding of LTB. While it will lead students and practitioners in the right direction 90% of the time, it will leave them without the tools required to evaluate more complex scenarios where the answer is not merely "brace the compression flange".



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 never said compression flange buckling is LTB. I said that lateral torsional buckling is caused by out of plane buckling of the compression flange.

I understand the equations involve the entire section. We all agree that adequate rotational restraint prevents LTB. The more rotational resistance of the section the less likely for LTB to occur.

I don't disagree with anything you said about how to brace it. Just that it has nothing to do with buckling of the compression flange.

 

[KootK]

I said that lateral torsional buckling is caused by out of plane buckling of the compression flange.

I get that this is the point that you're making. And it is precisely this point that I dispute. Compression flange strong axis buckling does not cause LTB. A lack of whole section torsional / lateral resistance to a combined sway / rotation buckling mode is what causes LTB. Is compression flange buckling a close approximation in a number of common scenarios? You bet. Will the concept lead one to brace unwisely in non-standard situations such as cantilevers? Definitely.

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 guess I'll just have to disagree with you on this one.

Regardless, Fundamentals of Beam Bracing by Yura 2001 would help NewEngineerHere understand bracing. Link below:

Yura 2001 Bracing

 

[KootK]

AISC's seismic design manual also contains an interesting example that I've not seen elsewhere: an axially loaded beam column forced to LTB about the compression flange connection to the deck above. Tricky calc but much improved capacity. Neat stuff.

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.

 

[BAretired]

This is an area of structural analysis which is difficult to fully comprehend, so some conservatism is recommended, particularly when analyzing cantilevers and overhangs. The following article by Trahair is worth a bit of study.

BA

 

[KootK]

Agreed. One layer of complexity that we haven't even touched upon is that the LTB stability of one braced segment is significantly affected by the warping stiffness of the adjacent segments, especially for cantilevers. Factor that in and things get intractable in a hurry. Darn differential equations.

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.

 

[BAretired]

When designing a new structure, it is easier to put in bracing than to perform the calculation showing it is not necessary; when analyzing an existing condition where bracing can no longer be added economically, it gets a little trickier.

BA

 

[NewEngineerHere]

Thank you a lot Kootk and Jerehmy.

BAretired brings up the question that is running in the back of my head; If I had to design a new structure, how to locate these bracings, when will they be needed, when not needed (and why not.?).....

This is has been a good learning start point for me. Thanks everyone.

 

[KootK]

The only mandatory bracing that I can think of is:

1) That required at beams supports.
2) That mandated by the AISC seismic code in regions of plastic hinging etc.

Other than that, it's up to you. It winds up being an interplay between amount of bracing and weight of the beam section. Often, you will additionally see,

1) At least one bottom flange brace on either side of the support for continuous multi-span beams and Gerber beams.
2) A brace at the splice locations for Gerber beams.
3) A brace at the end of a cantilever.
4) A brace where vertical bracing ties into a beam midspan.

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.