getting a better picture here originally i thought the beam was going in such that it would hold up the center where the second story was and the load associated with it now i see that the beam (as it is) is to hold up the "top" of the upper floor - or - the roof structure...... if i am correct i think (remember i am no engineer) that a double 2 x 12 would work just fine - put a 4 x 4 under each end - and if not positioned over lower support - ensure support from under the posts