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Are the 2x8's spanning the 10' direction or the 20' direction?
Are these joists supporting the attic only?
Is this 2x8 supporting perpendicular roof framing?
Something isn't quite making sense.
If the 2x8 is running left/right and the rafters are running left/right, what is the 2x8 supporting?
Is the beam supporting the rafters or just the ceiling joists?
What is the city and state so I can look at snow loading?
What is the joist length on each side of the beam?
You will need a double 2x12 doug-fir no. 2.
You would need three 1.75" x 7.25" LVL 2.0E
Either. You need*****
No problem. I'm happy to help. Good luck with your project.