Bending Coefficient, Cb, for Allowable Stress Design 1

[PBJ]

Say I want to really get nit-picky and use true Cb for a beam instead of using the standard conservative Cb=1.0.

When entering the beam curve charts, is it correct to enter using the value M/Cb instead of "Allowable Moment", or should I instead enter using (unbraced length)/Cb for hyperbolic portions of a curve (or Lb/(square root of Cb) for parabolic portions) instead of "Unbraced Length"?

I have always entered with M/Cb (similar to LRFD's Mu/Cb) and the unbraced length. It is only recently where I have seen the Cb applied to the unbraced length itself.

Obviously, this question applies to ASD cases where Lb>Lu.

Thanks for any insight you can offer.

 

[ishvaaag]

The use of the two approaches compared with the closed form formulation of the check should confirm or deny the validity.

 

[JAE]

I don't believe that you can simply adjust your unbraced length or your moment capacity with Cb and enter the charts. If you look at the equations F1-6, F1-7, and F1-8 you will see the following:

The break points for the charts depend upon the square root of Cb.

The allowable stress in F1-6 depends upon Cb used in a denominator added to 2/3 and therefore is not a direct linear relationship.

The applicable allowable stress in some cases is the larger of F1-7 and F1-8, therefore a direct adjustment linearly by Cb is not appropriate.

What you must do is use the equations and skip the charts. They were developed only for Cb = 1.0.

 

[bengineer]

Just as the triple lux may not win you the gold, this method will not necessarily provide you with the correct section.

This method is a good approximation, however the shape should still be checked per the applicable formulas from AISC chapter F.

 

The beam charts you speak of ARE NOT limited to use with Cb=1.0. You CAN enter using Lb/Cb (in place of Cb) for hyperbolic curve portions or Lb/(Cb^(1/2)) for parabolic portions of the curve. Obviously, once your size is selected (preliminarily from the charts), do your final check based on the equations F1-6 through F1-8.

Granted, Cb=1.0 is conservative and 99.9 percent of the time is what is used for expediency in design, but using real Cb is certainly not a prohibitive approach. Using the charts with the "adjusted Cb's" mentioned above is a lot quicker than trial and error checks of beams from the Sx tables with Lb>Lu and real Cb. The charts are the best starting point when Lb>Lu, whether Cb=1.0 or Cb>1.0.

Steel Structures: Design and Behavior", 4th edition, by Salmon and Johnson clearly addresses this topic. (Page 527 for those of you playing along at home.)