I built a 14' X 14'6" screened porch over my wood deck 5 years ago. The roof rafters are treated 2" X 6" cut to 14'6" lengths. On top of the beams I have 1" X 4" treated slats running perpendicular on top of the rafters. I have installed fiberglass corrugated roofing panels screwed into the 1" X 4" slats. The center of these beams have sagged ½". What can I do to eliminate the sag without installing floor mounted support posts?
Well Bill, there are a two reasons why the roof rafters covering your screened porch may have sagged over time. Either the rafters span too long of a distance for their size, or possibly the rafters are spaced too far apart to properly carry the load of the roof. There are several other factors that also help determine the correct rafter size and spacing when building a roof. Area snow loads, roof pitch, finished roof material and even the grade and species of lumber can increase or decrease the recommended span for a particular size of roof rafter.
If we wanted to know the specific reason your roof rafters are sagging, we would need to know their species and grade, which can sometimes be difficult with treated lumber. Likewise, we would also need to know the rafter spacing, as well as the typical roof loads used in your local area when calculating rafter sizes.
Of course, that information is all water under the bridge, because the rafters are what they are, and they are already nailed in place and sagging. I agree with you that installing some support posts in the middle of your porch area is probably the least desirable solution (although probably the most effective).
Another option could be to double up the existing rafters with an additional 2x6 at each rafter location, essentially converting each 2x6 rafter into a 4x6 rafter. You could even use a floor jack to straighten the sagging rafters prior to sistering the new rafters in place. I like this fix, because it can probably be accomplished without tearing apart the existing roof, and neither the porch's head room or floor area is diminished in any way.
If you are truly worried about the structural integrity of roof rafters, then you should probably have an experienced carpenter or engineer inspect your home and offer you some other potential solutions.