If this calculator from the american wood council is to be believed and if my assumptions about your materials and load are correct the max span is about 10ft for a pine 2x6.
Porch roof rafter spacing.
As a general rule roofs that have a high human occupancy rate should be framed with rafters every 16 structures such as sheds or barns can be frames with rafters every 24 again make sure to consult local codes.
Typical rafter spacing codes will specify a minimum spacing of 16 inches 19 2 inches or 24 inches.
If you move up to 4 by 8 you re usually allowed to span up to 10 feet between posts.
In general the maximum span for a 4 by 6 beam is 6 feet between 4 by 4 posts.
The minimum pitch for a roof is 1 4 12 which translates to 1 4 inch rise to 12 inches of run.
For example in the rafter span table below the highlighted cell in the 40 live load table indicates that 2 x 8 southern yellow pine joists that have a grade of 2 that are spaced 24 apart can have a maximum span of 10 feet 3 inches 10 3 if designing for a live load of 40 lbs ft 2.
A 4 by 10 can usually span up to 12 feet between posts.
Visit the roof framing page for more information on cutting roof rafters and visit the roof pitch calculator for determining rafter lengths based on rise and run.
So the space between rafters can be greater without reducing the maximum span.
If your project had a rafter length of 8 or less a safe and strong method is to use 2x8 framed 16 on center.
The reduced roof rafter span shall be taken as the larger of the distances from the roof rafter support brace to the ridge or to the heel measured horizontally.
Rafters must be strong enough to hold the roof sheathing and the shingles.
However you can only use this pitch with built up roofing or specialized synthetic roofing.
Maximum rafter spans for a patio roof in areas with mild climates patio roofs are generally designed for loads of 30 psf pounds per square foot.
If your local building authority has a rafter spacing code you may not space rafters wider than required by code.
The same concept holds true for roof trusses.
This table agrees that 10 12ft is the max span for typical grade lumber at typical spacings for a 5psf dead load.
The smallest beams for patio covers are typically 4 by 6.
An essential part of planning a patio roof or gazebo project is determining the number size and spacing of rafters beams and posts according to the loads they will carry.
When a reference is made within this rule to a federal statutory provision an industry consensus standard or any other technical publication the specific date and title of the publication as well as the name and address of the promulgating agency are listed in rule 4101 8 44 01 of the administrative code.