You need an engineered glu lam 5 1 4 wide and 24 tall.
How to support 20 foot roof.
For larger porches such as wrap around porches you will want to make sure that the support is more than you need.
Three 2x10 s or 12 s is not enough.
This number represents the total load that your roof must carry.
A great deal depends on the pitch of the roof.
Multiplied by 40 pounds per square foot equals 8 000 pounds.
I live in the midwest so it need to support snow load too.
A truss joist wood i beam is not enough.
The larger the roof is the more support that you are going to need.
Better design with truss 2 feet deep or more depending on snow load.
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.
Feet more in presence of snow.
If an example roof is 10 feet by 20 feet the total area is 200 square feet.
A higher pitched roof would be better for extra living space than a lower pitched roof.
From photos i have it looks like single 4x6 not lvl that angles with the roof.
By roof beam i assume you mean the beam will be carrying the load of the roof free span for 20.
The other is just used to support the trusses.
Multiply the load per square foot by the total area of the roof.
Almost any wood will do the same geometry of beam or truss is the important thing.
Large 8 x 8 posts are necessary for the use of supporting a porch roof.
This is where a high pitched roof is necessary.