Terry Branscombe wrote: If this is correct, hip and jack rafters on a roof with any pitch at all would require a side cut at something less than 22.5 degrees. To my surprise the octagon rafter table value for hip rafter side cuts for a 1/12 pitch roof is 16, producing an angle of over 53 degrees! The jack rafter side cut value for the same roof is given as 6-7/12, which translates into a side cut of 28.75 degrees!
Terry, I don't know anything about the octagon rafter tables. The side cuts on a standard framing square are for the upper shoulders of unbacked Hip rafters, where the common rafter slopes are equal and intersect in plan at 90°. Very limited, in other words.
The angles in any complex roof may be determined by development with as little as a compass and straightedge. For the sake of accuracy I prefer to calculate the angles.
Framing and Joinery Angle Calculator : There are also links to some basic diagrams and tables of formulas.
Here's what I get for the Hip rafter side cut angles using your example, two intersecting 1/12 slopes with an angle in plan between the eaves of 135°:
Side Cut Angle at Hip Rafter Foot = 67.44008°
Side Cut Angle at Hip Rafter Peak = 22.44020°
If you scroll down the page in this link you will find drawings detailing one method of
Developing the Hip Rafter Side Cut Angles . The angles at the Hip rafter feet are designated
R4B, those at the peak are
R4P. The images show an angle in plan between eaves of 90° but this may assume any value.
Another link to some sketches of an
Octagon Gazebo . The common slopes in these examples are 6/12, angle in plan between the eaves is 135°.
Hip Rafter Side Cut Angles:
Side Cut Angle at Hip Rafter Foot = 65.47409°
Side Cut Angle at Hip Rafter Peak = 20.60785°
