I am building a 20'x24' patio roof of treated wood and galvalum 2on12 pitch. Using 6"x6" posts every 12' on the long side Would girders made of 2x12 sandwiched with 1/2 plywood work to span the 20' across with a total of 3 girders then lay crossway 2x8x12 on 24" centers to attach the metal roofing. The roof will be a basic leantoo roof.