Beam Lateral Torsional Buckling - Cb (Yura Equation) Limits - Existing Steel Beams 1

[r-struct]

When using Yura's Cb Equation below (with continuous top flange lateral support), do you limit Cb to some maximum value?
I am checking some existing beams continuous over columns whose moment gradients results in Cb with values ranging from 3 to 4.
As a side note, in CSA S16, the omega sub 2 factor (Canadian counterpart of Cb factor),it is limited to 2.5 - but I understand that the expression given in there assumes top and bottom flange of the beam are both laterally unsupported throughout the unbraced length of the beam.

Looking forward to hear what the more experienced folks in here think.
Thanks in advance.

 

[KootK]

When using Yura's Cb Equation below (with continuous top flange lateral support), do you limit Cb to some maximum value?

I don't limit it to a maximum value and see no need to. Looked at in detail, it's pretty damn hard to buckle a beam with continuous lateral restraint.

 

[r-struct]

Thanks KootK! This is authoritative enough for me!

That's what I think too, but cannot find any literature that can justify it other than Yura's 1995 "Bracing for Stability" paper. I might need to dig further to satisfy my curiosity.

This expression has been there for quite a while and I am surprised it still has to make it in the codes.

 

[KootK]

That's kind of you to say.

If you're interested in a deep dive on this, this thread is that: Link. It's a monster but you probably only need to read the first 20 posts or so to get what you need. I also posted a Yura paper earlier on which I believe may be more relevant than the one that you referenced.

For what it's worth, I'm a Canadian practitioner as well. As far as I'm concerned, we should just disband CISC and roll with AISC as a north american standard like we do with light gauge. The AISC document is more advanced and more cohesively written that ours. We're just reinventing the wheel needlessly and unnecessarily. I've even called CISC on some discrepancies between the two standards and they flat out told me that they consider anything in AISC satisfactory for Canadian practice.

I'm all for national solidarity but this just isn't the right place for that. Let's stick to Stanley cups and dominating North American timber design. Know your strengths...

 

[r13]

If we are talking the same bending coefficient, C[sub]b[/sub], then:

In the 9th Ed. of AISC Manual, C[sub]b[/sub] + 1.75(M[sub]1[/sub]/M[sub]2[/sub])+0.3(M[sub]1[/sub]/M[sub]2[/sub])[sup]2[/sup] <=2.3.
In which M[sub]1[/sub] is the smaller and M[sub]2[/sub] the larger bending moment at the ends of the unbraced length.... When the bending moment at any point within an unbraced length is larger than that at both ends of this length, the value of C[sub]b[/sub] shall be taken as unity (as for simply supported beams)......C[sub]b[/sub] may conservatively be taken as unity for cantilever beams.

This coefficient is to account for the effect of brace to allow for a permissible increase of bending stress, for compact or noncompact members with unbraced length greater than L[sub]c[/sub] (maximum unbraced length, for which the bending stress F[sub]b [/sub] = 0.66F[sub]y[/sub] is allowed. I think the expression was the same on older manuals.

 

[Settingsun]

The number should become large as the degree of hogging becomes small. At the limit, the beam is sagging (or zero moment) over the full length so is fully restrained.

 

[Guest090822]

As "retired13" mentioned, AISC used to limit Cb to 2.3 and AASHTO currently limits Cb to 2.3 as well using similar equations.

My 2001 AISC LRFD manual uses the EQN Cb = 12.5 Mmax / (2.5 Mmax + 3Ma + 4Mb + 3Mc) but there is no limit stated. I don't have the book I need in front of me right now, but I know that they plotted the curve against the AISC 9th edition EQN and it gave similar results but was easier to figure out. I don't recall why they dropped the limit on it though.

 

[KootK]

With respect to the Yura recommendations specifically, it's worth nothing that he has fundamentally changed the nature of the "bucket" that is Cb:

1) Originally, the bucket contained only the effect of moment gradient between points of full rotational restraint.

2) In Yura's recent work, the bucket now contains #1 AND the effect of intermediate lateral restraints that do not fully restrain the cross section rotationally.

 

[r-struct]

Hi KootK, your prompt and helpful responses yesterday are appreciated.
The thread you linked is informative and kind of entertaining as well. The Yura paper you posted is a great addition to my stability library and could see it to be of practical help with future projects.

 

[r-struct]

Retired13, TheRick109, steveh49 thank you all for your input.
I believe KootK’s last note summarizes the options that we now have at our disposal, depending on our design’s restraint conditions, in calculating the Cb value based on Yura’s research.

 

[r13]

This is my gut impression that, before reading Yura's paper and knowing LRFD equation, so might not be correct. The original, I guess, is pointing to the old ASD equation. IMO, it utilize the Cb factor (effected by unbraced length) AND l/ϒ[sub]T[/sub] (stiffness of member braced against twist, in which l is the brace length) in determine the allowable stress of beam members either braced or not braced, and if braced, the stiffness in between the braced points. The LRFD equation is a modification of the original to fit the ultimate stage design rather than a change. I do need to read the paper though.