This is actually more like a built-up member (rather than "composite") and seems very uncommon for use as a wood beam (at least here in S. California). The wood members also seem too small for the 16-ft span and would allow deflections that might be unacceptable (1/2" or greater at mid-span). Also, why not use (2) deeper members such as (2)2x8's with similar combined moment of inertia as the other proposed 2x5's and 2x4 combined. This way, there will be no need to calc shear stresses or provide nailing between members except at the sides. Then again, I still think there might be too much deflection.