Hi TB,
The loads applied to the tie beam would need to include constant dead loads such as the self weight of the various roof and floor members and coverings (tiles, sarking boards, etc.). Then add to this the variable loads like those imposed by the typical items stored in the barn (hay, etc.) and most importantly don't forget the snow, wind & earthquake loads applied to the tie beam by the roof, side wall & foundations.
All of these loads are applied to the tie beam via the various connecting members such as main posts, queen posts, principal rafters, wall plates, sills, braces, intermediate studs, posts, etc.
The effect of all of these loads can be calculated using simple hand cranked approximations but it is much more easily done using a plane frame analysis program where different case study analysis can be made. These case studies will provide you with more than one answer for each of the conditions needing to be checked such as tension, compression, bending, shear & deflection and so you should take the worst values encountered from each of the case studies to size your beam.
Regards
Ken Hume
The short answer is hire an engineer to do this for you. This is what they do.
The guild resource book has a list. Also there is a list on the TFEC site (Timber Framing Engineering Council).
Jim Rogers
