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One story ranch style house with sky lights and cathedral ceiling in North Carolina.

I am in the process of designing a new screen porch. The previous owner had a very low, shallow pitch, shed roof over a deck - that has been removed.

I would like to build up from the existing deck a screen porch, with a roof that is perpendicular to the main roof. The finished product will be 30 feet wide attached to the house and protrude out 14 foot. I have two issues, 1.) the placement of the skylights prevents me from tying in at the same height as the proposed roof line. 2.) There is a fireplace close to centered on the wall where the new roof would tie in.

The only I option that I can think of is a saddle for the width of proposed screen porch. This is where my question is.
For a saddle is there a code requirement for the height/pitch of the saddle? I was on the roof for some rough measurements and it looks like the highest I can make the saddle would be 4 foot high and a total of 30 wide by about 6 feet deep at the ridge. Is this enough pitch for a saddle?

Any other suggestions on how to handle this?
 
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