Now I wanted to explain about seated rafters and a ridge beam.

I am aware of the fact that people do it, but I was taught from the standpoint that there are two systems, you do one or the other but not both.

The reason is partially highlighted above: when you have seated rafters, it complicates the whole assembly at the bottom of the roof. When rafter seating is the primary means of support for the roof, then this is all OK because the effort is justified.

BUT, when you have a structural ridge, you are inventing a whole lot of unnecessary work by seating the rafters in the plates or ties beams and, as shown here, complicating hip construction a great deal. You have to cut joints into the ties or plates that weaken them (or require you to use bigger timbers) when you could just as easily lodge the rafter on these timbers and spike them or peg them fast. The rafter seat really adds nothing in this case because of how the rafter is loaded with a structural ridge. You do not need a joint that can resist tension at all, you only need to resist compression which is easily handled by lodging things. In fact, a birdsmouth or other rafter seat is actually less effective under compression than if the rafter were simply lodges. The upward lifting force of the ridge can potentially throw the rafters out of their seats. I always heard, a framed roof will work and for this reason, the old timers never fastened the rafters to anything else if they were hung from a ridge. They seem to have had the right idea, since the pictures below are of a house that has stood strong since about 1710.

To see how simple hip construction can be with a structural ridge, see this image:


Even if you can't use rafters projected past to form the overhang, you can use rafters seated on the outside of a plate or purlin that come just past it, then tack an extension beside them to obtain an overhang, secured up the rafter a good ways with spikes or pegs.

This roof structure, by the way, has steeper hips than the primary roof slopes although maybe it is hard to tel by this picture.
This structure is about 40 feet wide.