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Lat Torsional Buckling

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I have a fairly long beam whose top flange is unbraced, as well as being
subjected to bi-axial bending.  Because of lateral torsional buckling, a
W16x77 is required.  This isn't such a big deal except that the owner is
screaming to cut costs everywhere possible (this building prototype will be
built many times).  I am trying to use a W16x36 with a C12x20.7 channel
combined section.

My question is, how do you calculate Mn for a singly symmetric combined
section in LRFD?  Using ASD it's easy, but I'm using LRFD everywhere else on
this project.

Any help would be greatly appreciated
Jason W. Kilgore
Leigh & O'Kane, L.L.C.
(816) 444-3144