You need an engineered glu lam 5 1 4 wide and 24 tall.
How to support 20 foot roof.
If an example roof is 10 feet by 20 feet the total area is 200 square feet.
If smaller beam will sag ugly.
Feet more in presence of snow.
This is where a high pitched roof is necessary.
For larger porches such as wrap around porches you will want to make sure that the support is more than you need.
The distance inside the house from peak to outside wall is 25 7 6m and the beam spans 19 5 6m wall to wall.
Once again a 2 by 4 inch piece of lumber is placed between the trusses and parallel to the ceiling joists.
The other is just used to support the trusses.
I live in the midwest so it need to support snow load too.
A higher pitched roof would be better for extra living space than a lower pitched roof.
A truss joist wood i beam is not enough.
Minimum roof loading is 20 lb sq.
For a 20 foot span wood beam needs to be minimum 18 inches deep.
Multiply the load per square foot by the total area of the roof.
By roof beam i assume you mean the beam will be carrying the load of the roof free span for 20.
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.
Multiplied by 40 pounds per square foot equals 8 000 pounds.
Better design with truss 2 feet deep or more depending on snow load.
A great deal depends on the pitch of the roof.
Almost any wood will do the same geometry of beam or truss is the important thing.