mr. sea,
my bad, I guess I took your last question "or know of a quick solution of all W sections" to mean a quick solution to solve for all W sections.
Try this... transform the slab into an equivalent steel area (make sure the beam and concrete is considered composite). Next, determine the neutral axis. Calculate the moment of inertia. Determine the allowable stress and then find the resisting moment!
Many structural steel books have this design example, including the AISC. "You know", the kind you buy in stores! Maybe someone can provide you with more tables, however, I would recommend calculating all the "I" values for self gratification.