bending coefficient, cb, for allowable stress design

huangyhg

bending coefficient, cb, for allowable stress design
the use of the two approaches compared with the closed form formulation of the check should confirm or deny the validity.
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.
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.
n-gin-ear (visitor)20 jan 02 10:48
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.)