Beam bracing
Beam bracing
(OP)
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 :)
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 :)






RE: Beam bracing
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.
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.
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.
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.
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.
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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: Beam bracing
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."
RE: Beam bracing
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RE: Beam bracing
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.
RE: Beam bracing
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.
RE: Beam bracing
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.
RE: Beam bracing
Regardless, Fundamentals of Beam Bracing by Yura 2001 would help NewEngineerHere understand bracing. Link below:
Yura 2001 Bracing
RE: Beam bracing
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: Beam bracing
BA
RE: Beam bracing
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: Beam bracing
BA
RE: Beam bracing
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.
RE: Beam bracing
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.
RE: Beam bracing
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.
RE: Beam bracing
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.
RE: Beam bracing
RE: Beam bracing
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.
RE: Beam bracing
RE: Beam bracing
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: Beam bracing
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.
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SSRC Guide is Structural Stability Research Council, Guide to Stability Design Criteria for Metal Structures.
RE: Beam bracing
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.
RE: Beam bracing
Reference something that justifies your point of view. That you can have LTB without compression in the member.
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RE: Beam bracing
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.
RE: Beam bracing
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.
RE: Beam bracing
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.
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.
RE: Beam bracing
btw that link doesn't work for me, just keeps sending me to my dropbox. If it's what I think it is, where he has the tube column and the cable, the whole system rotates to relieve tension in the cable?
RE: Beam bracing
I disagree. A load applied above the beam will lose potential energy when LTB occurs and therefore exacerbate instability. Load applied below the beam will gain potential energy when LTB occurs and therefore reduce instability. The equilibrium statics of the buckled shape upon which we would formulate bifurcation would be different for the two cases.
Again, I disagree. Other than adding to the perturbation required to get things rolling, accidental torsion and horizontal load eccentricity are not what lateral torsional buckling is about. Mathematical and physical LTB instability can be reached even in an ideal, homogeneous, perfectly straight beam loaded through its shear center. Buckling won't take place without the perturbation but instability certainly will. And it's instability that we check with the code LTB provisions.
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: Beam bracing
Due to basic curvature the top flange of the beam (in compression) reduces in length. The bottom flange extends. As the top flange resists this reduction in length the "less stiff" motion for the top flange that allows it to keep the same length is an out-of-plane curvature (global buckling). This motion causes a global twisting (phi) of the section as the ends are assumed to be restrained against this out of plane buckling. This is LTB as I understand it.
Thus, even a perfect setup with ideal shear center loading and no out-of-plumb elements will rotate due to geometric stiffness constraints.
Maine Professional and Structural Engineer. www.fepc.us
RE: Beam bracing
Argh... I suck. Sorry about that Jerehmy. Try this: Link. I think that you're thinking of the article "discussion" papers that followed this one. Same concepts though.
Hypothetically, as part of the process of formulating equilibrium on the buckled shape and so calculating the bifurcation load. This is conceptually identical to how we derive the Euler buckling load for simple columns.
Precisely. However, in the world of safe structural engineering design, instability (mathematical) and buckling (physical) are both equally dangerous and considered to represent the end of usable capacity.
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: Beam bracing
Suggested, nit picky, technical alteration: for the sake of my wacky example, top chord "compression" is really the location of least tension. But the point that you're making is still spot on as the curvature is a result of the axial stress gradient regardless of whether or not there is actual compression present.
This is also a great segue into an important point that I've so far neglected to make. The elongation in the tension flange contributes to the tendency of the beam to twist. In large measure, that is what makes LTB a whole section phenomenon rather than just compression flange buckling.
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: Beam bracing
I know that's not what LTB is about, but load height still has an effect, which is what we established in your first point. Anything that adds "twisting" would obviously have a negative effect on LTB and anything that resists "twisting" would have a positive effect.
We agree that LTB can occur independent of where the height of the load occurs. So load height can affect LTB, but isn't a cause of it. Therefore, I question if your example would be defined as LTB. If we showed the load hanging at the center of the beam from a cable, would you still say it would buckle? Shouldn't it buckle in either scenario? One at a higher load and one at a lower load because of the bifurcation you talked about in your first point?
RE: Beam bracing
Of course it's a whole section phenomenon, they are all attached and I never meant to insinuate it wasn't. It's just my understand that the LTB is initiated by the flange. There are lots of contributing factors, but the main one, in my opinion, is the out of plane buckling of the compression flange.
Also, in a paper you linked (can't remember which?), it talked about the buckling due to tension flange but that this only happens at much much higher energy states and that fixing the beam against rotation at the supports is usually adequate to prevent this from occurring.
RE: Beam bracing
One of these days I need to have a debate on here about underhung trolley, cantilevered monorail stability with long continuous beams.
Maine Professional and Structural Engineer. www.fepc.us
RE: Beam bracing
RE: Beam bracing
This is not what I said. At least I hope not. Load height matters before LTB occurs because it contributes to mathematical instability, in a big way. Again, with load above the beam, pure rotation causes the potential energy embodied in the load to drop. With load below the beam, pure rotation causes the potential energy to rise. These things are true prior to LTB and go into the derivation of the bifurcation load.
Substantial agreement here.
This "cause" concept is problematic for me. I don't think of it that way. There are bunch of parameters involved in determining LTB stability: load position, beam length, load magnitude, C_w, I_y, E, etc... LTB is "caused" by an excess or deficiency in any or all of these parameters. So I guess that I would say that load position does "cause" LTB as much as an excess or deficiency in any of the other parameters does. I see LTB instability as simply a mathematical state wherein beam sway/rotation reduces potential energy of the system. I don't see it as a failure mode "caused" by one parameter with all others deemed innocent.
Certainly, I would say that it would have the potential to buckle. I couldn't predict actual buckling without knowing the particulars and running the numbers of course.
Yes. Substantial agreement here.
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: Beam bracing
Me too. Need to get you a room with beer and paper. Maybe PowerPoint.
Again, I have trouble with the "cause" concept. I do substantially agree however. For the most common cases, the story of LTB is primarily the story of tje compressed portion of the beam trying to do something akin to buckling about the tension portion of the beam.
This would usually make things worse instead of better. For most beam sections the Iy/Ix ratio decreases as the section depth increases. That means that the elongation and compression in the flanges will produce greater twist, other factors held constant.
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: Beam bracing
Can we just have a national conference for Eng-Tips members to congregate over beer and greasy food, and debate various topics? ;) I know the "Where is Engineering Going In The Next 5 Years" people could probably go on for days on some of their topics. :)
NewEngineer, a good way of (rough) guessing a sections sensitivity to LTB is the ratio of weak axis moment of inertia to strong axis moment of inertia (Iy/Ix in KootK's notation). If bending is being performed about the weak axis, or circular sections such as pipes, then LTB cannot occur. There are other factors to consider as well, hollow shapes such as rectangular tubes are highly resistant to LTB.
Maine Professional and Structural Engineer. www.fepc.us
RE: Beam bracing
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: Beam bracing
BA
RE: Beam bracing
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: Beam bracing
BA
RE: Beam bracing
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: Beam bracing
RE: Beam bracing
@Jerehmy: thanks for the spirited yet gentlemanly debate over the last 48 hours. It was thought provoking and helped to clarify my thinking on LTB. Magic indeed.
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: Beam bracing
Hard to answer that question without seeing some details. A beam must be prevented from rotation about its longitudinal axis at each support in order to be considered stable. This is a code requirement. It may or may not require additional bracing between supports.
BA
RE: Beam bracing
RE: Beam bracing
Here are a few examples I found on google search. Not necessarily shear plate connection, but what gets me thinking is long span beams without bracing against rotation.....
http://dellacooks.com/beautiful-forest-home-of-cas...
http://zainteriora.net/2009/11/25/suppose-design-o...
http://versehead.com/steel-and-concrete-homes/arch...
RE: Beam bracing
Are those steel beams? Hard to see. Looks like glulam beams to me. But in any case, there would have to be fixity between the columns and the beam. Otherwise, the structure is unstable (four hinges in the column).
BA
RE: Beam bracing
Again, they could be glulam beams...not clear.
BA
RE: Beam bracing
Aha! Now we have some steel beams; but the two grey looking beams are not carrying any load. Since they are attached to a column, they may be (probably are) prevented from rotating about their longitudinal axis.
The beams supporting the floor structure are continuously braced on the top flange. So where's the problem?
BA
RE: Beam bracing
As for Picture No.3 : I was under the impression that both flanges must be braced (Am I wrong?) .. If the top is braced continuously by the top flange, shouldn't the bottom flange should have some sort of support against rotation too ? (Logically I think no we don't need since the top flange is assumed to be wide enough to stable the beam..... I may be wrong ....)
What about if the beam loaded with a glass on the top (Picture No.3) was to support a floor slab instead of the glass, would it require a brace for the bottom flange ?
Thank you !
RE: Beam bracing
Buckling occurs when things are in compression. The compression flange of a beam in bending is...well in compression. So it wants to buckle.
In LTB, the compression flange is buckling. That triggers the show. But since the tension flange is not buckling (things in tension don't buckle), it stays put. The compression flange wants to "walk", the tension flange wants to "stay", and the web ties the two flanges together.
Like a dog tied to a tree, the compression flange is trying to run off but it is getting tugged by the web and pivoting around that tension-flange of a tree.
That's LTB. The rest are details.
Koot -- I dig your swagger and energy in this post. But I don't understand why you think that explanation of LTB isn't the start of the LTB story.
"We shape our buildings, thereafter they shape us." -WSC
RE: Beam bracing
These statements are incorrect or, at the very least, misleadingly imprecise. And it is exactly this misunderstanding of instability that leads to all of the confusion regarding LTB.
Compression is not required for buckling. All that is required for buckling is a load and resisting stiffness that drops to zero. Here are some examples:
1) When a tension brace is a in a wall fails due to P-Delta effects, that's buckling.
2) Bottom chord bracing is often required on trusses to prevent the tension chords from buckling (Link).
3) The example that I posted above with a beam loaded from above but with every fiber in tension (2 Jun 15 14:46). That's compression free buckling.
So riddle me this:
You can brace the bottom, compression flange of a cantilever continuously but, if the top flange isn't restrained, it will still LTB under enough load. The top, tension flange will roll over the bottom flange like a dog tied to a tree (love that).
If compression flange buckling initiates LTB, and the compression flange is continuously restrained in this example, how is it that LTB is still a viable failure mode? My theory of LTB explains this. The compression flange buckling theory clearly does not.
To some extent I agree with you. To quote 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: Beam bracing
No. 1 is described thus: "Warm Corridor With Timber Deck And Wooden Exposed Beam Ceiling Also Glass Wall Panels And Overlooks The Beautiful Zen Garden Design Ideas". Doesn't sound like steel beams.
No. 2 is too dark to discern much of anything. If the beams are steel, the top of the upper beam is braced by roof joists. The lower beam, if steel, would need to be prevented from torsional rotation at each end. The beam would need to be capable of carrying the design moment with an unbraced length equivalent to the span.
The beams in No. 3 appear to be simple spans. The bottom flange is in tension and does not require bottom flange bracing whether it supports a floor or not.
Continuous beams may require bottom flange bracing in the vicinity of inflection points but not necessarily. If the beam section is stocky enough to carry the load without bracing, then bracing is not required but torsional rotation must be prevented at the supports.
BA
RE: Beam bracing
With all my prosthelytizing, I almost forgot to send you this NewEngineerHere: Link. Despite being old as dirt, this is still my goto document for practical beam bracing guidance. Spend an hour with it and all will be revealed... Well, lots anyway.
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: Beam bracing
From AS4100:
5.5 CRITICAL FLANGE
5.5.1 General
The critical flange at any cross-section is the flange which in the absence of any restraint at that section would deflect the farther during buckling. The critical flange may be determined by an elastic buckling analysis (see Clause 5.6.4) or as specified in Clauses 5.5.2 and 5.5.3.
5.5.2 Segments with both ends restrained
The critical flange at any section of a segment restrained at both ends shall be the compression flange.
5.5.3 Segments with one end unrestrained
When gravity loads are dominant, the critical flange of a segment with one end unrestrained shall be the top flange.
When wind loads are dominant, the critical flange shall be the exterior flange in the case of external pressure or internal suction, and shall be the interior flange in the case of internal pressure or external suction.
Once you have determined the critical flange you can then calculate the effective length of the critical flange based off factors in the code. These factors simply depend on whether the critical flange is unrestrained, partially restrained, laterally restrained, or fully restrained. For example, the first picture in your previous post where the beam above the sliding doors is supporting the roof is fully restrained at each end by the perpendicular steel beam. You can see the beam outside and they are probably welded at the intersection. The other beams you show are also fully restrained at each end by intersecting beams or columns.
RE: Beam bracing
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: Beam bracing
This link actually refers to restraining buckling of the diagonal compression member in the truss. It states that the bottom chord of a truss may not provide adequate restraint against lateral movement of the diagonal compression member, thus you cannot use the diagonal member length as the effective compression length in all cases. Nothing to do with LTB.
This type of failure is similar to a tension cable moving to the side when a tight rope walker falls off. Although this, by simple definition, may be LTB since the beam deflects laterally and exhibits torsion, I don't think it is the same LTB definition that is broadly used by the engineering community. If you use this same example but with the load applied below the centre of gravity then it will not fail in LTB but will fail by tension in the bottom flange.
RE: Beam bracing
I disagree. Firstly, your only two choices for the diagonal compression member are a) K=1 and b) K=infinity. So the tension chord has to brace the compression web. The compression web leans on the tension chord for its stability which, in turn, makes the tension chord itself the next stability issue. One way to tell is by the equations proposed to evaluate the tension chord. They're all about the lateral stiffness of that chord. For the most part, stiffness only comes into play in capacity calculations when stability is an issue.
This is entirely analogous to the situation where you use a diagonal kicker to brace a beam that might LTB buckle. Once you've dealt with the beam, the next problem is to design the kicker itself to ensure that it won't buckle.
So, the tension chord issue is definitely a buckling issue. But is it a lateral torsional buckling issue? More on that later. For now, I'll point out that a) tension chord buckling represents a global rotation of a truss, just like LTB and b) what is a truss, really, other than a solid section beam with some extraneous web material removed? Tension field theory anyone?
Not true. With the load applied below the centre of gravity, the beam is less likely not to buckle but not guaranteed not to buckle. Just look at picture "B" in the document that you posted.
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: Beam bracing
The lack of a precise definition of LTB really is a problem in this debate. My two analogies make perfect sense to me because I hold a certain model of LTB in my head that makes the comparison obvious to me. You, and others, have different models in your heads that lead you to question the validity of my analogies. Bridging that gap is difficult.
To address this, I propose an unconventional definition of LTB to be our gold standard here. Usually, we deal in bifurcation theory when discussing LTB, similar to Euler buckling. Trouble is, that's the result of 4th order DiffEQ manipulation and doesn't really speak to anyone's intuition other than perhaps Galambos, Yura, Timoshenko, and Bazant. They'll probably be drinking buddies in non-denominational heaven.
A much simpler definition of LTB is the energy definition in my opinion. Here's how I see LTB when viewed from the energy perspective:
1) As a consequence of entropy, all systems tend to minimize embodied energy. When physical movement of a structure would result in a lower embodied energy, you get that physical movement and we call it buckling.
2) When LTB occurs, a beam flops to the side and starts to resist load about its weak bending axis rather than its strong bending axis. This increases deflection and moves the load closer to mother earth. This reduces the potential energy.
3) When LTB occurs, additional strain energy accumulates in the beam in the form of beam twist (J/Cw) and beam lateral sway (Iy). These represent the "lateral" and "torsional" in lateral torsional buckling.
3) If the loss of potential energy mentioned in #2 exceeds the gain in strain energy mentioned in #3, you get LTB. The end. And nowhere has compression been mentioned as requisite.
In my mind, this definition means that only two criterion need to be satisfied for a buckling mode to be considered LTB.
1) Whole section flopping over needs to result in the applied load moving closer to the earth.
2) Whole section flopping over would generate additional stain energy by way of some combination of beam rotation and/or beam lateral sway.
Both of my analogies, the truss and the top loaded beam, satisfy both of these requirements.
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: Beam bracing
I believe I am way too late in the game, but I do not understand what all the fuss is. You can easily prevent a beam from failing in LTB by bracing the web only (a sufficient depth that is). The compression flange will be left to do whatever is next in line in the limit states (local buckling, yielding). All you need is a couple of forces with an adequate lever arm to resist the LTB instability. The compression flange may or may not be involved.
"It is imperative Cunth doesn't get his hands on those codes."
RE: Beam bracing
Don't cry for me Argentina! Seriously, it's exactly this kind of rare debate that I come here for. And, obviously, I played a rather active role in dragging a simple question out into near triple digit posting.
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: Beam bracing
Maybe this will open your mind about structural instability - Link
"It is imperative Cunth doesn't get his hands on those codes."
RE: Beam bracing
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: Beam bracing
"It is imperative Cunth doesn't get his hands on those codes."
RE: Beam bracing
EIT
www.HowToEngineer.com
RE: Beam bracing
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: Beam bracing
"It is imperative Cunth doesn't get his hands on those codes."
RE: Beam bracing
RE: Beam bracing
Yes. Yes Yes. Structural engineering fees are not high enough to spend all sorts of time proving that bracing (among other things) is not required. And besides, the money it costs to fight tooth and nail over bracing for typical structural elements is often handily greater than the money to install the disputed item(s).
Ultimately, I see these discussions as a passionate attempt to understand the behavior, if only for our enjoyment...and maybe for that unique project which requires pulling a sophisticated engineering rabbit out of our hat.
That said, I believe the KootK is much closer explaining the general LTB behavior than others, even with some of the digression. It is clear that the phenomenon is a coupling of numerous components (torsional stiffness, minor axis flexural stiffness, and others).
"It is imperative Cunth doesn't get his hands on those codes."
RE: Beam bracing
RE: Beam bracing
"It is imperative Cunth doesn't get his hands on those codes."
RE: Beam bracing
I've have also thought about LTB being mostly a torsional problem, so I'm a bit surprised with all the buckling talk. If the bottom flange can't move relative to the top flange than you don't have LTB (or atleast that's my understanding). So I see why simply attaching the top flange to the deck (i.e. only bracing the compression flange) may not be sufficient as the bottom flange can still move relative to the top flange. I suppose this is where that tension buckling demonstration would help one visualize why.
EIT
www.HowToEngineer.com
RE: Beam bracing
Also, kootk, if the beam in your model was loaded on it's weak axis, would it still want to dlop over? It's already in its most stable orientation so where's it going to go? It seems in your model it would still twist. But you wouldn't call this twist LTB would you? If it's loaded on its strong axis you would call it LTB. What about the weak axis?
Does you interpretation of LTB allow for weak axis LTB? I've still been mulling this over.
RE: Beam bracing
1. LTB cannot be generated for weak axis oriented I-shapes, unless I am misreading your post.
2. How is it already in it's most stable orientation? What does that mean? His sketch shows a post rigidly connected to the beam - that is it; the post is free to rotate above. And, besides, if the post was not very flexurally stiff, it could be restrained out of plane to the sketch at the top and still allow the eccentric instability in the beam to occur.
"It is imperative Cunth doesn't get his hands on those codes."
RE: Beam bracing
The sentence before, I said what if it's loaded on its weak axis. The weak axis is more stable than the strong axis for transverse loading. I said nothing about the post so I'm not sure why you brought it up. And I was specifcally asking kootk about his interprtstion of LTB with his diagram and how weak axis bending is incorporated into his interpretation.
If the beam in the diagram is unstable whether the beam is loaded on its weak or strong axis, is it still LTB? Thats what I'm getting at.
RE: Beam bracing
I obviously misunderstood what you said. My apologies - I will leave the rest of the thread to you and KootK.
"It is imperative Cunth doesn't get his hands on those codes."
RE: Beam bracing
RE: Beam bracing
Anyways - I think I am losing interest in the thread, as I am still confused about the initial argument regarding the compression flange buckling dominating the onset of LTB. Maybe I will check back in to this thread in a few years to see what has happened.
"It is imperative Cunth doesn't get his hands on those codes."
RE: Beam bracing
@Macgruber22: don't leave! I don't really have a "camp" without you.
@Jerehmy: I think that I see your point regarding weak axis LTB. The two point litmus test that I proposed above requires a third point, making it:
3) Lost potential energy from #1 >= strain energy stored from #2.
With this addition, the weak axis example would not meet my proposed LTB definition. It would fail test #3 and would just be combined flexure and torsion. And I think that's what both of us, and MacGrubber, believe should be the case.
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: Beam bracing
1) A system may buckle due to insufficient stiffness of a member in tension if, and only if, the systems also contains a member in compression.
2) Unlike a compression member, a tension member cannot buckle internally in non-system fashion.
I'd like very much to hear any arguments or examples that may contradict these statements. Here is my analysis of the tension example that we've discussed so far:
1) Tension chord buckling. Here a lack of tension chord flexural stiffness leads to a system buckling mode that I contend is analogous to beam LTB. The compression chord and webs are in compression.
2) MacGruber's videos. Again, a lack of flexural stiffness in the tension members leads to system buckling. Compression would be present within the sliding mechanism that connects the tension members.
3) A tension only brace failing under P-Delta effects. Here, insufficient axial stiffness of a tension member leads to system failure. The compression members are the braced frame columns.
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: Beam bracing
RE: Beam bracing
RE: Beam bracing
I don't think that the videos were posted to suggest tension buckling as a common, practical design consideration. Rather, they were posted to support the claim that stiffness deficiencies in compression free members can dominate the response of systems prone to instability. And, certainly, the videos accomplish that.
Are there forms of buckling/instability for which this is not true?
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: Beam bracing
@kootk - what about the square tension ring example deforming into a parallelogram? I suppose whatever is loading the the tension ring would probably be in compression.
Although maybe not. What if you had a pool. To support the pool you had a ring of beams. This could be a tension ring. If square then you have may have LTB problems as well as bracing at the corner problems. hmm....
EIT
www.HowToEngineer.com
RE: Beam bracing
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: Beam bracing
This doesn't apply to KootK's beam diagram since the beam is loaded above the shear centre. "Flexural-torsional buckling does not occur in beams bent about their minor axis... except where the load is applied at a point higher than 1.0bf above the centre of gravity (where bf = flange width of the I- or channel section)." - Steel Designers Handbook 7th Ed. Therefore, if KootK says that the beam in pure tension should fail in LTB then it should also fail if the beam was rotated 90 degrees and loaded in the weak axis.
RE: Beam bracing
RE: Beam bracing
This would apply if the beam were oriented weak axis with the post vertical. I thought that we were discussing a case where the beam were oriented weak axis and the post was horizontal. Literally my original sketch tuned on its side. I'll leave it to Jerehmy and Mac to indicate if their understanding is the same as mine.
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: Beam bracing
1) the beam flipping to strong axis an deflecting less vertically,
2) the post rotating and shifting the load closer to the earth.
3) strain energy accumulating due to twist/sway.
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: Beam bracing
Fallout from this would be that a horizontally oriented and loaded beam (talking about strong-axis bending here) would have a higher LTB capacity since buckling does not bring the load closer to earth.
Also, this point only matters for loads that have mass. For massless loads, such as wind, this does not apply (because we're talking about potential energy here correct? P = mgh?)
This seems like a fairly easy thing to test. Is there any evidence that this plays a major role? My gut feels as though it would be a minor factor.
RE: Beam bracing
RE: Beam bracing
And the point still stands that for a horizontally loaded beam, the load doesn't move closer to earth whether the beam is buckled or not, so there is no change in potential energy regardless where the force comes from.
RE: Beam bracing
I vote for lower LTB capacity in this scenario so long as the load is applied on the compression side of the beam shear center. For the same beam rotation, the horizontal setup will move the load towards the ground faster than the vertical setup. At least, that's how it will work in the early stages of rotation. As rotation advances, the vertical setup will shed potential energy more quickly and the horizontal setup will shed it more slowly.
Like canwesteng, I believe that any load has potential energy associated with it. Even when dealing with mass, it's really the weight multiplied by distance that represents the energy. I was hoping to explain the equivalency here in a manner that my high school physics teacher would approve of. Sadly, I'm not up to the task...
I don't know of any specific testing. Certainly, if one were feeling ambitious, the impact could be studied simply through analytical investigation. I'm not volunteering for that though. When it comes to theory, I'm more of a talker than a doer.
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: Beam bracing
Ah, I see. Time for more edits. Let's change:
To the more general, if a bit clumsy sounding:
2) The post rotating and moving the applied load in the direction of the applied load and, in the process, expending work in the energetic sense.
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: Beam bracing
Don't consider me a "challenger." I've been a member of this forum for years and I've followed you a long time (no need to remind me of your tag line, it's memorable). You clearly are proficient and enthusiastic - and someone needs to grab the baton and run. That's the purpose of this site.
And, to channel another member's memorable tag line (rowingengineer),
So, two engineers sharing their beliefs. I'm not trying to talk past you, I'm just sharing my viewpoint.
----
I'll be honest - I'm torn on this thread. If it's purpose is to have a spirited debate on the mathematical underpinnings of a structural theory and be very,very right - then it succeeds. If it's purpose is to understand LTB in a manner that will keep structures standing - in other words, be right enough - I think it misses a bit far.
Muddy thinking causes muddy designs. Muddy designs cause failures. So we guard against failures by keeping our minds simple and clear. Complexity and being too right shouldn't be the goal.
Over time, even he simplified that down to, "All models are wrong, but some are useful."
This is a central tenant of structural engineering - at least the kind I practice and believe in. Be clear, be simple.
I'll give you an example:
This is the fork in the road - because my statement is not that incorrect.
I'm not talking about a hypothetical structural system that is unstable when a tension load is applied (although I enjoyed the video and thinking into it!), a system that is clearly unbraced so it kicks when there is 0.001lbs of lateral load applied to it (clearly unstable and bad), or other unique cases.
Whenever I find myself wading into too many "yeah, but" examples, I think of Phil Mickelson's (pro golfer) famous backwards chip shot. It's a hypothetical where you convince yourself that it makes most sense to strike the ball away from the hole. Sure, it makes sense in theory, it's possible that you'll use it and it's neat to think of...but the average golfer shouldn't build their golf game around it. It's too hard to execute and there just aren't many practical situations where it's useful. It's pretty cool, though.
It's those types of examples and getting too far into the weeds on theory that "leads to all the confusion regarding LTB." Not my (and other's) simplifications.
I'll share another thought. Robert Maillart was one of the fathers of reinforced concrete design. Master bridge builder. An engineer's engineer. He introduced the concept of a shear center (discussed earlier), so mathematically - he was no slouch.
But he didn't let imprecision get in the way of creation. Take the Schwandbach Bridge. No mathematical theory existed that could precisely analyze it. Sure, FEM could take a good swing at it now - but before FEM, engineers had to imagine. Maillart knew that the guard rails were stiff so they probably stiffened his very slender arch. How much? He wasn't sure. But over a long career and work on several smaller structures, he had a pretty good idea.
His mind was clear. He simplified the problem down, designed it, built it and it's beautiful... imprecise as it is.
Stiffened arch. Propped cantilever. Bundled tube. From simple ideas spring creative, beautiful and generally safe structures. Complex structures that put too much emphasis on accuracy can end up like the Hartford Civic Center.
I know my theory, my differential equations and my energy methods. But when I start a design (or teach design), I stay far, far, far away from them. Because they can muddy the mind. Too right may be too much. Clear and simple never fails.
So to me, "Buckling occurs when things are in compression...things in tension don't buckle" is a model may sometimes be wrong, but it's very useful. And that's good enough for me - especially as a starting point for understanding the behaviors of structural systems.
"We shape our buildings, thereafter they shape us." -WSC
RE: Beam bracing
I will take the liberty of distilling your position to this:
While more or less agreeing with the theory discussed here, you feel that it is too complicated to be of practical use. Moreover, you feel that a "too right" understanding of the theory will lead to reduced safety as it will "muddy" the understanding of simpler, occasionally incorrect algorithms.
As rebuttal, I submit the following:
1) At least quarterly, on this very forum, we participate in threads by folks who don't know how to brace beams for lateral torsional buckling. Usually it's cantilever bracing; occasionally it's inflection point bracing. I won't provide links to examples as I feel that would be indecorous. Why don't they know what to do? They don't know because they're fixated on the simplified "compression flange bracing" algorigthm.
2) Also at least quarterly, someone here will post a link to a news story about a building collapse that cost oodles of money and, from time to time, the lives of some humans. Here's yesterday's: Link. What kind of buildings are these? They're steel. What kind of failures are they? They're buckling / bracing failures, often during construction and occasionally during service.
3) For over fifty years, and even the first few years of my career, it was accepted dogma that beam inflection points could be considered as points of bracing. And you can bet your bonnet that there were plenty of practical engineers out there that saw no value in pushing the envelope any further on the theory side. I'm glad that some folks saw value in it, however, as it turns out that there's no theoretical basis for inflection point bracing whatsoever. It's 100% wrong and unsafe.
In summary, while you feel that this discussion pushes us into "too right" territory, I contend that our profession is generally spending too much time in the "too wrong" territory. And that's costing money and lives.
For shame! To willfully deny your junior engineers a complete understanding that you yourself posses is to risk turning them into algorithmic technicians instead of creative engineers.
Those brilliant, clear minded engineers that you cited above? It's a safe bet that most of those guys are theoretical rock stars that knew when they could set the theory aside precisely because they understood the fundamentals so well. It's that kind of understanding that we should cultivate in our rookies.
When I'm teaching LTB theory to a junior engineer at his or her desk, instead of debating it with equals on line, the whole shebang doesn't take more than 15 minutes. And that's fifteen minutes well spent in my opinion.
On a lighter note, I believe that pursuit of truth and beauty are the only reasons to get up in the morning other than the satisfaction of our base urges. That's why I participate in theoretical discussions and that's why I push on when the practical minded folk cry foul.
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: Beam bracing
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: Beam bracing
I'm right with you there. It's important to know the theory and research -- because simplifications work right up until they don't. I certainly don't want the next generation to be a flock of B- engineers and I'm not advocating for mediocrity.
I have just found that the road to expertise starts simple. That's why I tend to defend simple analogies that are easy to communicate, conceptualize and remember. It's hard to remember things, and harder without a firm grasp of the simple. I just come across too many engineers with analysis print-out in their hands telling me their wacky structure works because they "did calculations on it." *Shutters*
Braced by "inspection point" is a perfect example. If you can't hold it, you shouldn't really count on it. It may work mathematically again, but math is just another model which may or may not describe the world. It's up to the curious engineer, with a firm grasp of the simple, to decide upon which tools they depend. (Actually, I'm interested to hear that there's no actual basis for it. How the heck did it become a thing?)
And I agree with you-- our profession does spend too much time in the "too wrong" category. I wish it was because they had a Kootk-like expertise but chose to selectively simplify to quickly and creativity design wonderful structures... but it's not. It's often because they don't keep it simple and they get lost in their own design.
I do have a question about your cantilevered beam bracing example. You may have already fielded this above somewhere: Where does LTB end and rotational instability begin? Isn't a cantilever with an unbraced tension flange just incredibly susceptible to rotational movement? Is it really getting kicked over due to LTB?
"We shape our buildings, thereafter they shape us." -WSC
RE: Beam bracing
nonplussed tossed out a little pearl that went under the radar:
If I may be so bold as to suggest it, you may want to add that to your list 'o straight forward concepts. It addresses all of the practical cases that I can think of where bracing would be anywhere other than the compression flange.
I have no idea. In hindsight, it's completely obvious. For me to explain, however, some will have to suspend their disbelief and take some of my theory as given.
Imagine an interior span of of a continuous, uniformly loaded beam. One inflection point either side, rotational restraints at the supports. As always, the load wants the beam to flop over and deflect more so that it can shed potential energy. On the other side of the energy balance equation, you've got the strain energy accumulated in the beam via torsion and lateral sway. It is self evident that the strain energy of interest is that integrated between points of physical rotational restraint, not between points of inflection.
For a more intuitive interpretation, consider that it is torsional and weak axis beam stiffness that prevents LTB and therefore, conversely, torsional and weak axis flexibility that facilitates LTB. And the torsional and lateral flexibility is clearly a function of the physical, rotationally unbraced length rather than the distance between strong axis inflection points. It's really quite strange that strong axis bending moment inflection points were thought to affect lateral torsional buckling when all of the parameters that go into the LTB checks relate to torsional and weak axis properties.
This will unavoidably sound like the blatant self promotion of my own ideas but I'm going to go for it anyhow. The only reason that can think of for the rise of the inflection point bracing concept is the misconception that LTB is exclusively about flange compression buckling. Since there's no flange compression at the inflection points, then there must be no tendency to LTB, right?
I got started when inflection point bracing was just being phased out. I worked in a very young office and I remember standing around with a bunch of my colleagues staring at a RAM S-Beam input screen that had "Consider Inflection Point Bracing" as a check box. We debated, got nowhere, and my boss made the call. So long as IP bracing yielded more economical results, and was generally accepted by the engineering community, that's what we would do. I designed a number of Gerber systems that way.
LTB is, generically, rotation about a point in space vertically aligned with the shear center. That makes it part rotation and part lateral sidesway. How much of each depends on where that point of rotation is. If it's at the centroid, then it's 100% rotation. If the point of rotation is miles below the bottom flange, then it's mostly lateral sway. While much depends on the conditions of the back span, I think that cantilever LTB tends to be more about sway than non-cantilever LTB. At least, the crazy high effective length factors for cantilevers would seem to suggest that. Torsionally, a cantilever isn't all that much different from a simple span beam of twice the cantilever length.
An example that you may find interesting is that of constrained axis lateral torsionl buckling. Above, I mentioned that it appears in the Seismic Design Manual, 2nd ed. It turns out that it also show up in the much more economically priced AISC design guide 25. It considers buckling about the center of the top flange and will produce much improved capacities for drag strut and chords in composite floor systems.
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.