Diggler306,
I have been a registered Architect for 35 years and am very comfortable with structural design. Your triple 14" LVL over a 23.6' span will carry a total load of 6,227 lb. assuming you plan on adding a 1/2" gypsum board ceiling. The 2x6 joists at 24" o.c. spanning 11.5' will carry 16...