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

 

[Jerehmy]

In your example you show phi as the rotation. How does it rotate? If it's a perfect column and beam, and the load is perfectly through the shear center, and you have no compressive force because of T, I'd argue it would not buckle and not rotate. But it would definitely be unstable. Kind of like a perfect slender column that has P=Fy*Ag applied to it.

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?

 

[KootK]

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

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.

Load height affects it because it increases the torsion and thus the buckling.

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.

 

[TehMightyEngineer]

Jerehmy, I believe it would rotate because it has to.

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.

http://www.fepc.us

 

[KootK]

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?

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.

In your example you show phi as the rotation. How does it rotate?

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.

If it's a perfect column and beam, and the load is perfectly through the shear center, and you have no compressive force because of T, I'd argue it would not buckle and not rotate. But it would definitely be unstable. Kind of like a perfect slender column that has P=Fy*Ag applied to it.

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.

 

[KootK]

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.

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.

 

[Jerehmy]

To your first point. It doesn't matter UNTIL LTB occurs, which is what we both said. So the load height does not matter until LTB occurs.

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?

 

[Jerehmy]

I'm having trouble keep up with the posts haha.

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.

 

[TehMightyEngineer]

Yes, least tension is obviously more accurate term as neither of the flange are under compressive stress. Glad to see my understanding of LTB roughly matches yours.

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.

http://www.fepc.us

 

[NewEngineerHere]

[/Due to basic curvature the top flange of the beam (in compression) reduces in length. The bottom flange extends].. What about if we have a deep W-shape (I-shape) beam with a neutral axis far away from the most farther fiber, would it help to prevent the situation you described ?

 

[KootK]

To your first point. It doesn't matter UNTIL LTB occurs, which is what we both said. So the load height does not matter until LTB occurs.

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.

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.

Substantial agreement here.

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.

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.

If we showed the load hanging at the center of the beam from a cable, would you still say it would buckle?

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.

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?

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.

 

[KootK]

I'm having trouble keep up with the posts haha.

Me too. Need to get you a room with beer and paper. Maybe PowerPoint.

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.

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.

What about if we have a deep W-shape (I-shape) beam with a neutral axis far away from the most farther fiber, would it help to prevent the situation you described ?

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.

 

[TehMightyEngineer]

Me too. Need to get you a room with beer and paper. Maybe PowerPoint.

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.

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.

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.

http://www.fepc.us

 

[KootK]

I've actually given some thought to setting a meet and greet with Albertan structural guys. We seem to be very well represented M by some very capable folks here. I just don't know how to set that up without violating site anonymity policy.

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]

There was a group called ESSE (Edmonton Society of Structural Engineers) which met several times a year. It seemed to attract a reasonable number of members for two or three years but eventually, interest waned and we haven't met in the last decade.

BA

 

[KootK]

Maybe what we need is a Structural Engineers Association of Alberta. BC and just about every US state have one.

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]

I still have a couple of ESSE beer mugs.

BA

 

[KootK]

Sweet! Can you leave that to me in your will should you meet an untimely demise?

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.

 

[NewEngineerHere]

I know we went through a lot of details here about beam bracing. But........ I have seen some steel beams drawings spanning without any brace and their end condition is a simple welded/bolted plate (Not moment connection)....and they are supporting a floor slab,,,, how is this beam stable ? no brace in middle, no brace at end

 

[KootK]

The beams that you mentioned are likely braced continuously along their top flanges via attachment to the slab. And the simple shear connections at the ends are generally considered adequate rotational restraints. This is all that is required for simple span beams without axial loads.

@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.

 

[BAretired]

@NewEngineerHere(OP),

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