Can a cantilever beam with continuous lateral support develop full plastic resistance? 7

[HanStrulo]

I have a cantilever beam with continuous lateral support at the compression flange. I want to analyze it to develop full plastic resistance moment.

Is that allowed? is the "continuously braced beam against lateral torsional buckling" independent from the support conditions?

Thank you

 

[dik]

It depends of the Class of section it is in Canada. If Class 1 or 2, you can use Zx for the moment resistance. A caution thought, cantilevers don't have a lot of load redistribution when they fail...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[jayrod12]

Where is KootK when we need him? I believe that for cantilevers, the concerning flange isn't necessarily the compression flange due to the mechanism that causes LTB. However I'm not sure if when trying to use the plastic modulus that changes things. I'm a fan of bracing the bottom flange of cantilevers, at a minimum at the tip of the cantilever.

I would argue that it is independent of support conditions. Because technically a cantilever is just half a simple span upside down. So if you had a simple span beam of twice the length of your cantilever with the critical flange fully braced you would use the plastic section modulus for capacity.

 

[271828]

As jayrod12 typed, the compression flange isn't the end of the story for cantilevers and overhangs.

If you can find a copy of the Yura/Helwig Bracing for Stability slides, they talk about this.

The following is useful:

https://www.aisc.org/Lateral-Torsional-Buckling-of-Wide-Flange-Cantilever-Beams-PDF

I don't have the SSRC Guide in front of me, but I recall it having a section on this.

 

[canwesteng]

No, a cantilever needs to have the tension flange braced, or be braced against rotation, but ideally both before I would neglect LTB checks. This should be continuous support though like a deck above, not bracing. For discrete bracing, the type of restraint at support and the restraint at the tip need to be considered. This is handled in Stability Design Criteria for Metal Structures

 

[KootK]

I have a cantilever beam with continuous lateral support at the compression flange. I want to analyze it to develop full plastic resistance moment. Is that allowed? is the "continuously braced beam against lateral torsional buckling" independent from the support conditions?

It really comes down to what exactly you mean by developing the full plastic resistance:

1) If you mean to go 100% plastic and beyond at the cantilever support, as in a plastic hinge, then no, you can't do that. A hinge at a cantilever support means the development of a mechanism and a collapsed structure that is incapable of resisting additional load.

2) I suspect that what you really mean is that you want to use conventional plastic design methods for calculating your bending resistance at the cantilever support. You can do that by recognizing that such methods, by virtue of factors of safety, never actually become fully plastic. Full plastic hinging becomes, rather, one of the limit states that we design to prevent the occurrence of.

If this is your intent, your path forward is simply to keep adding bracing until the LTB capacity that bracing gives you exceeds the moment capacity calculated using conventional, plastic design methods for determining bending resistance.

Where is KootK when we need him?

Gassing up the boatmobile but, clearly, late to the party.

Let the fun, pedantic, contentious proselytizing commence:

3) With regard to the tension flange being the right one to brace, that really stems from consideration of the case where the lowest energy LTB buckling mode is predominantly lateral sway and one is going from no bracing at all to some degree of bracing. In that context, your LTB center of rotation is usually considerably below the bottom flange of the beam. That, in turn, makes the top (tension) flange the most efficient place to go because it's acting over the longest possible lever arm relative to the center of rotation. Check.

However, just because the top flange is the most efficient place for the first brace to go, does that mean that it's the only place for the first brace to go? I don't feel that it does. If your beam is in Jersey and your center of LTB rotation is in Hanoi, it surely does not make a lick of difference which flange you brace because the lever arm is identical for all intents and purposes. So all LTB rotation points in between such extremes (Hanoi vs Shear Center) represent brace locations of varying degrees of effectiveness.

All that said, for routine design, we don't really have great tools available to assess the effect of sub optimal bracing so, generally, the first brace should go on the tension flange.

4) Continuous compression flange bracing creates a situation known as constrained axis buckling. The beam can sway very little laterally and is forced to LTB rotate about the center of the bottom flange (that's the "constrained" axis). This will often improve capacity significantly and there are published equations available to evaluate this although one has to dig a little deeper to find them. AISC's seismic manual touches on this in at least one example I believe.

5) As far as I'm concerned, the best and most practical thing that an engineer can do for a cantilever is:

a) Brace the cantilever tip against sway and;

b) Brace the cantilever tip against rotation.

With that in play, the point of LTB rotation shifts to being above she shear center and the compression flange is once again the most efficient place to add additional bracing.

 

[human909]

Where is KootK when we need him?

That is what is known in the sporting world as an assist. And KootK just came screaming in and scored the winning goal earning himself some pink stars!

 

[KootK]

Thanks for that human909. I feel that this is my best articulation of the cantilever LTB issue to date. The improvements come largely from our fly bracing discussion a while back. As you'll likely recall, I've long used the minimization of potential energy as my stability divining rod for conceptualizing things. Added to that, I now have the very pragmatic bit from the Aussie code perspective that says something like:

1) Brace the critical flange.
2) The critical flange for a particular LTB mode is the one that would move the most.

That's proven to be a very fruitful addition to my kit-o-tools. Knowing which flange moves the most isn't a simple matter for all situations but, for cantilevers, I feel that it mostly is a simple matter. I "see it" which is everything for me.

 

[JLNJ]

If this is a crane beam, you might get some benefit from the loading being applied to the bottom flange.

There are factors out there which show the different buckling values for a cantilevered crane beam (top flange braced just at the support) for bottom flange, centroid, and top flange loading.

 

[human909]

Thanks for that human909. I feel that this is my best articulation of the cantilever LTB issue to date. The improvements come largely from our fly bracing discussion a while back. As you'll likely recall, I've long used the minimization of potential energy as my stability divining rod for conceptualizing things. Added to that, I now have the very pragmatic bit from the Aussie code perspective that says something like:

1) Brace the critical flange.
2) The critical flange for a particular LTB mode is the one that would move the most.

That's proven to be a very fruitful addition to my kit-o-tools. Knowing which flange moves the most isn't a simple matter for all situations but, for cantilevers, I feel that it mostly is a simple matter. I "see it" which is everything for me.

No problems. I agree it was quite a productive discussion. I too learnt plenty. I agree energy analysis is very useful and often not taught as much as it could be as an approach of analysis in structural engineering. I need to improve here, I use it plenty in the science of physics/chemistry/biology in my way of understanding the world but I'm pretty poor with it in structural analysis. I mostly rely on an excellent visual understanding and then onto the codes and computers to do the grunt work. One day I should sit down and crunch more theory.