Steel Beam Bracing for Stability (Uplift)

[MattJM]

Using notes from the AISC Bracing for Stability Seminar, I have tried using Yura's equations for Cb for uplift conditions (tension flange continuously braced) and cannot get the same results.

This occurs for cases where I have a simple span.
For example: a simple span girder in uplift with bracing at midpoint, I get Cb = 1.78, while the notes say Cb = 1.3.

Has anyone tried this and found this as well?

 

[JAE]

I get 1.3.

Are you using

12.5(Mmax)
--------------------------------------------
2.5(Mmax) + 3(M1) + 4(M2) + 3(M3)

For an uplift condition, with a brace at midspan on the compression flange, your M(max) occurs at the brace (for a simple span as you say). The three moments (M1, M2, and M3) are at 1/8, 1/4, and 3/8 along the span (i.e. the quarter points of the unbraced length which is half the span).

For a 16' span with 1 k/ft on it, I get the following numbers:

M(max) = 32 ft-k
M1 = 14 ft-k
M2 = 24 ft-k
M3 = 30 ft-k

 

[MattJM]

Thanks a bunch. I will try this. I was using the three formulae outlined in the seminar material, which are based only on the end moments and CL moments at each section between braced points.

Three cases
Case A - Both end moments are positive or zero:
Cb = 2.0 - (Mo+0.6M1)/MCL

Case B - M0 is negative, m1 is positive or zero:
Cb = (2M1-2MCL=0.165Mo)/(0.5M1-MCL)

Case C - Both end moments are negative:
Cb = 2.0 - (Mo+M1)/MCL *(.165+M1/3Mo)

Thanks again

 

[271828]

Just using the basic AISC Chapter F Cb equation, if you have no bracing on the tension side and a compression flange brace at midspan, you should get 1.3. See the 13th Ed. Manual Table 3-1, 4th moment diagram from the bottom. It's obvious that this is the form that was used in the example you saw.

I see the equations you typed on Page 1-17 of the 2006 notes. I would expect to get a Cb>1.30 using these equations. Cb=1.78 seems low. When I've used those in the past, I seem to remember getting numbers that looked more like 3 or 4.

 

[MattJM]

Thanks again.

The main reason I am looking into this is that I have a blast uplift condition for my floor beams. Yura's equations suggest that with only the tension flange braced, I could reasonably use a Cb of 2.0, presumably due to twisting resistance provided by the ten flange brace (whether the code actually allows this is a different matter which was previously discussed here).

However, before I make that decision, I am (unsuccessfully)trying to validate some of the Cb values presented in the seminar material (I found again in the notes for the AISC Steel Design After College course), namely

Uplift with no bracing Cb=2.0 Lb=L
Uplift with bottom flange braced at midpoint Cb=1.3, Lb=.5L
Uplift with bot flange braced at 1/3 pts Cb=1.0, Lb=.33L

The equations and the reported values do not seem to match. I will continue to look into this unless anyone has discovered something I have not.

Thanks again for your help.