Cb Factor in 13th Edition
Cb Factor in 13th Edition
(OP)
We just came across a unique situation - have asked AISC for a response but thought I'd post it here to see if any of you have any views on it.
Cb in AISC beam design has been calculated using Mmax, and three 1/4 point moments along the unbraced length (MA, MB, and MC). This equation:
Cb = 12.5Mmax
----------------------------------------
2.5Mmax + 3MA + 4MB + 3MC
is given and then AISC states, "Cb is permitted to be conservatively taken as 1.0 for all cases."
This is fine - no problems here.
But now in the 13th Edition, they have introduced a "cross-section monosymmetry parameter, Rm which is based on Iyc and I.
When we use a wide flange with a cap channel for a crane beam we get a value of Rm of about .547.
Using the Rm in the Cb formula we get a Cb value less than 1.0.
So the question is - do we use 1.0 for Cb "conservatively" or should we use the lower value of Cb? Using 1.0 when we calculate Cb = .94 isn't conservative.
But AISC still has the same sentence stating that Cb can be conservatively taken as 1.0 for all cases.
Cb in AISC beam design has been calculated using Mmax, and three 1/4 point moments along the unbraced length (MA, MB, and MC). This equation:
Cb = 12.5Mmax
----------------------------------------
2.5Mmax + 3MA + 4MB + 3MC
is given and then AISC states, "Cb is permitted to be conservatively taken as 1.0 for all cases."
This is fine - no problems here.
But now in the 13th Edition, they have introduced a "cross-section monosymmetry parameter, Rm which is based on Iyc and I.
When we use a wide flange with a cap channel for a crane beam we get a value of Rm of about .547.
Using the Rm in the Cb formula we get a Cb value less than 1.0.
So the question is - do we use 1.0 for Cb "conservatively" or should we use the lower value of Cb? Using 1.0 when we calculate Cb = .94 isn't conservative.
But AISC still has the same sentence stating that Cb can be conservatively taken as 1.0 for all cases.






RE: Cb Factor in 13th Edition
MJ
RE: Cb Factor in 13th Edition
RE: Cb Factor in 13th Edition
The Section F4 LTB Fcr is for the entire compression flange under uniform compression. It can't get any worse than that, so I'd use Cb=1.0 if Cb calculated to be < 1.0.
RE: Cb Factor in 13th Edition
That is what I'm not sure about.
A lower-than-1 Cb is more conservative than Cb=1 obviously.
I did email AISC and got the response that Cb can never calculate BELOW 1.0 by the formula (without Rm). This may be true, but when adding on the Rm factor the Cb can be calculated below 1.0 and the code doesn't really address this...neither does the commentary.
I've re-asked them the question considering the Rm factor along with some data - we'll see what they say.
It is not too often that you get a singly symmetrical beam over two supports -but it does happen -suppose you have a two span continuous beam with an added cover plate?
RE: Cb Factor in 13th Edition
I agree with 271828 that Cb shouldn't ever be less than 1, as that is the constant moment case. I would use Cb=1.
Keep us posted on AISC's response. I have found that anytime you have a question like this, where the code equations aren't clear or give you peculiar results, the guys at the Solutions Center are completely worthless. If it's not in the web site's FAQs, they don't know. I've come across a few questions that had the gurus in the office stumped, and AISC was absolutely no help.
RE: Cb Factor in 13th Edition
I would like to see a graph showing a singly symmetric I shape in double curvature with the bottom flange incrementally reducing to the same width as the web, the instant the bottom flange becomes the same width as the stem, the WT equations are used instead of the Cb with Rm equation of the singly symmetric I shape. I might be able to tell if Cb=1.0 should be the lowest limit. Or better yet, just compare the WT equations against the singly symmetric I shape equations accounting for double curvature with one of the flanges barely larger than the stem. I would think the equations should give closely the same results.
RE: Cb Factor in 13th Edition
In short, there is an applicability limit of
0.1 <= Iyc/Iy <= 0.9
that shouldn't be violated if this equation is to be used. Your combo section might violate this and screw up the equation. The next issue is bigger, however.
They also literally call it Iy-top, not Iyc and show a mono-symm beam on the adjacent page with the bigger flange on top. I'd say this equation probably doesn't work if the smaller flange is in compression, which (I think) is the only way you can get such a small Cb outta this equation.
They also talk about tees a little on that page.
There is actually a much bigger issue with the Cb calc than R -- the load height. This is also included in the SSRC version of the equation. This could drive Cb down, which seems perfectly rational to me.
I think AISC simply accidentally left out some key info:
1. That Rm only applies if Iyc is for the bigger flange.
2. There's an applicability limit.
3. An allowance to calculate Cb using rational analysis. There are lots of Cb equations out there. One of them might fit this problem better than the AISC equation. Folks need to request this so the Spec. Committee will allow it next time.
The bottom line, regardless of what TSC says, is that the base Fcr equation is for a fictitious beam with the bottom flange with the same stress along its entire length. This is the absolute worst case moment diagram. If some of that flange has lesser compression or tension, then Fcr is really bigger than what the equation gives, hence the use of Cb>1.0. Load height is a separate issue and should definitely be considered IMO.
RE: Cb Factor in 13th Edition
Unforunately, there does not appear to be much about Rm and it's source in Comm F-1. The Guide provides the equation for R as e noted above, and states it's "for beams under reverse curvature between brace points". That seems to imply you could add bracing in the right location and have single curvature between brace points and perhaps get out of the reduction, but I don't know if that's stretching too much.
RE: Cb Factor in 13th Edition
RE: Cb Factor in 13th Edition
When you see the equation for Rm, it includes Iyc. Iyc is further defined below that as "moment of inertia about y-axis referred to the compression flange, or if reverse curvature bending, referred to the smaller flange, in4"
So for a span from A to B, with reverse curvature, both flanges experience compression at different points along the unbraced length. Rm is then calculated using the Iyc of the "smaller flange".
I don't see where you can simply neglect Rm (per the direct language of the AISC spec) if you have a small compression flange.
RE: Cb Factor in 13th Edition
RE: Cb Factor in 13th Edition
RE: Cb Factor in 13th Edition
JAE, I hope you'll report back what AISC says.
RE: Cb Factor in 13th Edition
So for the time being, we're using a Cb less than 1.0 for those cases...just to be conservative.
RE: Cb Factor in 13th Edition
Who was the response from in the Solutions Center? Just curious.
MJ
RE: Cb Factor in 13th Edition
RE: Cb Factor in 13th Edition
RE: Cb Factor in 13th Edition