Step 1 determine the load per square foot that the roof must support.
Open beam metal porch roof.
Porch roof ventilation options.
For heavy roofs or in areas with substantial snowfall or winds call your local building department for code requirements.
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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.
For a porch roof the beam needs to be sized according to the maximum snow loads in your area and you must know enough about the porch design to determine how the load will be distributed and over what distance the beam will carry the load.
Proper roof ventilation is an important aspect of home construction.
Of course all of these solutions are a little more expensive than simply nailing 2 x 10s to the sides of your existing posts.
Metal beams could also be used and would eliminate the need for most of the supporting posts across the front of your porch.