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By roof beam i assume you mean the beam will be carrying the load of the roof free span for 20.
How to support 20 foot roof. If smaller beam will sag ugly. If an example roof is 10 feet by 20 feet the total area is 200 square feet. A great deal depends on the pitch of the roof. Multiply the load per square foot by the total area of the roof.
The larger the roof is the more support that you are going to need. This is where a high pitched roof is necessary. Three 2x10 s or 12 s is not enough. From photos i have it looks like single 4x6 not lvl that angles with the roof.
Large 8 x 8 posts are necessary for the use of supporting a porch roof. A higher pitched roof would be better for extra living space than a lower pitched roof. Once again a 2 by 4 inch piece of lumber is placed between the trusses and parallel to the ceiling joists. This number represents the total load that your roof must carry.
Feet more in presence of snow. The distance inside the house from peak to outside wall is 25 7 6m and the beam spans 19 5 6m wall to wall. Minimum roof loading is 20 lb sq. A truss joist wood i beam is not enough.
For a 20 foot span wood beam needs to be minimum 18 inches deep. Better design with truss 2 feet deep or more depending on snow load. I live in the midwest so it need to support snow load too. Multiplied by 40 pounds per square foot equals 8 000 pounds.
Almost any wood will do the same geometry of beam or truss is the important thing.
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