Calculating rafter size with purlin bracing

Question

How do I calculate rafter size with purlin bracing? The total span is ~23' and the purlin bracing is ~9' from one side and ~14' from the other. Is it calculated on total or clear span?

Edit for clarification: It is purlin bracing with a strongback, aka "under-purlin"

I'm trying to obtain a permit to extend my roof line over a room addition and porch. The room already has a roof, but it's a 1/12 slope and prone to leaks. This would bring it up to the ~4/12 pitch of an adjacent addition. I live in the southern part of Zone 2. The only frozen water we see is covered in syrup or in our drinks. The permit office here will accept my sketchup, or even hand drawn, diagrams for a permit. I just have to tell them what size rafter and spacing I plan to use and they will either approve or deny it.

Rough drawing. New rafters in red:

Answer 1

I like your drawing/sketch. Even I understand how you propose to add the "steeper" roof pitch. I even see how you plan to lap the joists at the interior "support" and fasten to the existing roof structure...nice touch.

Unless you plan on using one of those super heavy "concrete" roof tiles that weighs more than 8 lbs. per square foot, 2x8's at 24" oc or 2x6's at 16" oc. (Grade: standard and better) will support a Dead Load of 15 psf plus a Live Load of 15 psf.