To determine the length of the intercepted hip rafter over c of triangle a b c [Fig. 83-a], the value of b must first be secured.
This value represents common rafter run for hip rafter rising over side c, and run of intercepted common rafter rising over side b.
Length of intercepted hip rising over side c = b x unit length of hip. (Table of lengths of octagon hips in terms of run of common rafter, [Fig. 73.])
Length of intercepted common rafter or jack nearest house = b x unit length of common rafter. (Table of lengths of common rafter in terms of run of common rafter, [Fig. 49.])
It must be remembered that these are theoretic lengths measured down the middle of the top edge of the rafters. In framing, suitable reductions must be made. For example, in framing the intercepted common rafter nearest the building, the rafter must be set over one-half its thickness that it may be nailed against the side of the building. The allowance necessary in order to do this may be secured by measuring the length from the long point instead of the middle of the side or cheek cut. Suitable reduction, too, must be made for the hip thickness in this case one-half the diagonal across the top edge of the hip, laid off at an angle of 22½°, or 5" and 12" on the square. This amount will be laid off straight back from the plumb cut, [Sec. 35], (2) et seq.
Length of hip must be measured along the middle of the top of the rafter.
46. Framing a Roof of One Pitch to Another of Different Pitch.—Occasionally one must frame a roof of one pitch against a roof of another pitch. To determine the cut, if the combination tool is to be used, merely find the difference in degrees of the angles of inclination of the two rafters, and apply the tool as indicated in the tables for making any other plumb cut, Figs. [49], [60] and [73]. The seat cut will be determined by the rise and run of the shed rafter in the usual manner.
Fig. 86. Laying off Cut of Shed Rafter
Where the framing square is to be used, lay the square as in framing a plumb cut on the shed rafter, as at A, [Fig. 86], taking on the tongue, the run, and on the blade the rise of the shed rafter. Next lay a second square as at B, [Fig. 86], taking on the blade the rise and on the tongue the run of the rafter of the main roof, using the blade of A as a reference edge. Blade of B gives the cut.