HELP: Supporting Vaulted Ceiling Mid-Beam
I suspect the loading on the new “flush beam” is more than the 2700 lbs. outlined in the question. I calculated 2800 lbs. and that’s without the weight of the upper wall resting on the new beam. (However, I think that would be about 250 lbs. per linear foot on the new beam.)
Depending on the species and grade, a new 4x10 beam 20’ long can support about 2800 lbs. mounted in the middle of the span AND a 4x12 beam 20’ long can support about 3100 lbs. mounted in the middle of the span. (I used a SPF species with a higher than normal grade... like “select structural”.
In addition to holding everything up, you’ll need to hold everything down too, if you live in a high wind area. I’d use Simpson steel connectors between the existing beam and new beam.
Remember, the support posts (and footing) at each end will need to support about 1400 lbs. minimum.
If you’re located in a seismically active area or high wind area, you’ll need to check for shear walls, etc. too.