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]

@RFreund: like any real world structure, the ring beam system that you've referenced has a bunch of possible modes of instability. You'd have to narrow it down for me before I could offer up anything meaningful. With a low slope roof and relatively compressible connections, snap through buckling might be an interesting topic of study.

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.

 

[nonplussed]

Maybe this will open your mind about structural instability - Link

I think I have to respectfully disagree with everyone's opinion on this 'tension buckling' problem. To me this video perfectly represents Mohr's circle with respect to shear stresses. Even when a body is loaded in pure axial force there will always be shear stresses within the body. The pin connection in the video has zero shear strength and therefore it fails even with minor shear stress.

1. LTB cannot be generated for weak axis oriented I-shapes, unless I am misreading your post.

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.

 

[canwesteng]

nonplussed - Don't confuse internal stresses with end reactions. The rollers are not within the body, and shear stress in the member must decrease from a maximum somewhere on the member to zero at that point. If instead of two tension members with a roller at the middle we had one tension member with a roller at the end it is obvious the member doesn't start sliding.

 

[KootK]

"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).

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.

 

[KootK]

Actually nonplussed, whether the post were vertical or horizontal, I would say that there could be potential for LTB. It would be the energetic interplay between:

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.

 

[Jerehmy]

Kootk, with respect to your 2nd point about "load moving closer to earth".

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.

 

[canwesteng]

The horizontal load, and wind load, all have associated potential energy.

 

[Jerehmy]

Wind does not have potential energy wrt to gravity, which is what kootk's second point was talking about.

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.

 

[KootK]

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.

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.

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?)

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...

Is there any evidence that this plays a major role?

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.

 

[KootK]

Wind does not have potential energy wrt to gravity, which is what kootk's second point was talking about.

Ah, I see. Time for more edits. Let's change:

2) the post rotating and shifting the load closer to the earth.

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.

 

[MJB315]

Kootk,

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),

Arguing with an engineer is like wrestling with a pig in mud. After a while, you realize that they like it.

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.

Since all models are wrong the scientist cannot obtain a "correct" one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena.

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:

Buckling occurs when things are in compression...things in tension don't buckle

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.

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

 

[KootK]

You take an odd tack for someone not wanting to be seen as a challenger MBJ315. For first you challenge my theoretical ideas, and now you challenge my very philosophy!

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.

I know my theory...but when I...teach design I stay far, far, far away from them[it]. Because they[it] can muddy the mind. Too right may be too much. Clear and simple never fails.

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.

 

[KootK]

@MBJ315: because of your willingness to throw down and wax philosophical, I've decided to promote you from challenger to friendly combatant. Pay is the same.

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.

 

[MJB315]

Ha, ok - I'll take friendly combatant.

Learn the rules like a pro, so you can break them like an artist.

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

 

[KootK]

Killer quote MJB315. That may make my top five. And cudos on your KootK handling skills. You and my wife should have a chat about how to diffuse "difficult" individuals. We are now in substantial agreement.

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.

nonplussed tossed out a little pearl that went under the radar:

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.

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.

Actually, I'm interested to hear that there's no actual basis for it. How the heck did it become a thing?

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.

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?

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.