Minimum roof loading is 20 lb sq.
How to support 20 foot roof.
This number represents the total load that your roof must carry.
Three 2x10 s or 12 s is not enough.
Feet more in presence of snow.
If smaller beam will sag ugly.
This is where a high pitched roof is necessary.
A great deal depends on the pitch of the roof.
I live in the midwest so it need to support snow load too.
Multiplied by 40 pounds per square foot equals 8 000 pounds.
From photos i have it looks like single 4x6 not lvl that angles with the roof.
Multiply the load per square foot by the total area of the roof.
If an example roof is 10 feet by 20 feet the total area is 200 square feet.
By roof beam i assume you mean the beam will be carrying the load of the roof free span for 20.
Better design with truss 2 feet deep or more depending on snow load.
Almost any wood will do the same geometry of beam or truss is the important thing.
The distance inside the house from peak to outside wall is 25 7 6m and the beam spans 19 5 6m wall to wall.
Large 8 x 8 posts are necessary for the use of supporting a porch roof.
Once again a 2 by 4 inch piece of lumber is placed between the trusses and parallel to the ceiling joists.
A higher pitched roof would be better for extra living space than a lower pitched roof.
You need an engineered glu lam 5 1 4 wide and 24 tall.
The larger the roof is the more support that you are going to need.
For a 20 foot span wood beam needs to be minimum 18 inches deep.