Load Beam Sizing/Calculator Help
You’ve given most of the required information in order to size the beam. I’ll assume some dimensions and you tell me if I’m wrong.
This beam is on the second floor and only supports the roof. The roof load is comprised of Live Loads (snow load and attic storage load) plus Dead Loads (joists plus ceiling finish, plus insulation plus light fixtures, etc.)
You have indicated the snow load is about 20-25 lbs. per square foot (psf). I’ll use 25 psf. You didn’t give the span of the roof joists that rest on this wall, but I’ll estimate 12’ each side. Therefore, if half the span rests on the outside walls, then the remainder rests on the wall. So, 6’ on one side + 6’ on other side of beam = 12’. Then multiply by 25 psf snow load = 300 lbs. per linear foot (plf) snow load on beam.
The required Live Load is 10 psf in attic.  So, 10psf x 12’ = 120 plf live load on beam.
You also indicated that the roof structure rests on this wall and it’s not a truss. The Dead Load of roof framing AND ceiling framing is about 20 psf. Therefore, 20 psf x 12’ = 240 plf on the beam.
So, the Total load is 300 plf + 120 plf + 240 plf = 660 plf on beam (assuming the roof joists and ceiling joists span about 12’ each side on the beam).
So, in order to span about 11’-3”, you’ll need 6-2x8’s or 3-2x10’s or 2-2x12’s. All are pine (per your direction) with a grade of No.1 or better.
If you use Doug. Fir, then you can reduce it to 5-2x8’s with a grade of No.2 and better.
Use two trimmers at each end and make sure there’s a support (something that equals 2 trimmers) under each end all the way down to the footing.
Sizing the footing is another issue. You’ll need to make that a separate question.
If the wall does not have plywood on it to connect the beam to the trimmers, I’d use a metal post cap connector like Simpson ACE series and a metal post base connector.