Just use the composite action of the wood members. Since the laminates are symetrical you can transform the section to an equivalent beam made of wood.
NAHB (Nat'l Association of home builders) published span tables for "plywood box beams" and "plywood I beams" in 1981. They do not detail the design procedure used to generate the allowable loads, but the booklets do give some useful data about how plywood can be fabricated into a structural member.
Chapter 16 in "Wood technology in the design of structures" by Hoyle and Woeste has a design method spelled out for plywood/lumber beams. Ditto, chapter 13 of "Structural Design in Wood" by Stalnaker and Harris.
the APA engineered wood handbook also has info on box beams also. Could you just use something like PSL or LVL for the entire section? That would probably be stronger, or are you trying to reinforce something?
