New Beam for cottage

[AzjaST]

Unless there will be heavy load on the attic floor, for this application beam is not necessary. Just sistering floor joists with 2x12 or 2x14 should be enough.

Where do you get 2x14s?

Span tables  [big grin]
But, seriously,  you can sister existing 2x6 or 2x8 with 2x10 or 12 with partial overlap to get 2x14. Or even better, convert each existing set of rafters and joist to truss just by adding king post and two struts. Anything spanning 30' will be monstrous; if 2 posts every 10' are possible than single 9 1/4 LVL will do but make sure these posts have way to transfer loads to the foundation.