Given that you have a steep roof, and you're suggesting that the room width might actually be closer to 22', I would count on needing to use 2x10 lumber, or 9 1/2' TJIs for the rafters. IOW, by doing a really steep roof, you're gonna have 30% more snow on it. Conversely, if the roof were only 6:12 pitch (half as steep as your roof) then the surface areas would only be 11% greater than the floor space beneath it. You have to remember that your 12:12 pitch results in a surface area 41.4% larger than the floor space underneath it. But if you can get select lumber, then 2x8s shouldn't be problem for the rafters. I really have to be picky if I want select lumber. If your lumber yards are like mine, you'll be looking at No.2&btr for your lumber. Again, I'll have to check my span tables, but If using dimensional lumber, I think you'll actually need to go with 2x10s for the rafters with a pitch that steep. By size, LVL beams can span the greatest distances and they still call for a 3.5x14' beam. I'll check my span tables later, but I really think that 2 ganged 2X10s isn't enough for this application. The 2x10s will certainly be cheaper, but not strong enough in my estimation. Sounds like you'll have drywall directly on the rafters which means you don't want any more deflection than l/240 or your drywall flexes too much. What really matters is the span between bearing walls and the length of nailing surface where the beam sits on the wall. I'll continue to follow this thread.The 2' extra on each end of the beam doesn't really come into play. The site itself is on a hillside with some slope so foundation will be piers driven 4 to 5 ' topped with 6X6 posts and a strong system of beams and joist. 2 of them are talking prelaminates and the 3rd, lacing together 2 2X10's. Each of the bidders is checking further the local building engineer, inspector and plan to get back to me in a few days (in the country that means a few weeks ). I met with 3 contractors while there to get their plans, estimates to do the foundation, framing, roof, windows, siding, etc.I plan to do all the interior work myself including wiring ,some plumbing, etc. We would use a few cross ties in area not included in the loft. (this permits a small loft on the 2nd floor). The roof pitch would be 1/1 or a 45 degree slant. The ridge beam would be approx: 24' or 26' allowing for a 2' overhang on both ends.

More detail now :The addition would be 19X 20 (possibly 22'). I've been out of town for several days (w/o my laptop) this country property we are discussing.

Lvl ridge beam span tables