An syp rafter can span 11.
Ok to use 2 x 4 for for roof rafters.
Structures such as sheds or barns can be frames with rafters every 24 again make sure to consult local codes.
It is always better to have a large rafter rather than be concerned with a sagging roof.
At the pitch range you are looking at the 2x4 is just fine up to 8 6 depending on the lumber grade.
The secret word is truss.
If your project had a rafter length of 8 or less a safe and strong method is to use 2x8 framed 16 on center.
I think you will be fine with 2x4s so long as they are closer than 48 apart.
Rather than having 2 4 purlins every 12 it would make far more sense economically to use 2 6 purlins every 24.
Front and sides will sit on deck on a 2x4 wall with studs 24 oc and screened in.
Somehow i am in a traditionalist camp 16 oc for a 12 foot wall will add only 6 extra 2x4 s or 3 extra if you buy 10 foot lengths for the rafters and 6 extra 2x4 s for studs if you use only a single layer top plate on the bearing walls.
The back of the roof will attach to house with 16 2x4 and lag screws.
Makes construction easier too.
Also if you want to make things cheaper you can do a single slope of the roof and basically cut out the eve cost.
If you live in an area that requires a shed roof rafter to support a heavy load then an spf rafter can only span 7.
You can frame a whole house with nothing but 2x4 but it s easier to do a shed as you won t need engineering probably.
You can use them for roof floor and even wall framing but few sheds will need trusses for walls.
Both of these are for light roof loads.