This section is from the book "Constructive Carpentry", by Charles A. King. Also available from Amazon: .
Valley Rafters. The lengths and cuts of valley rafters (gh, Fig. 80) may be found by the same methods as those used in finding the lengths and cuts of hip rafters : if the valley is to fit against the ridge, as at k, the top cut is the same. The plumb side of the seat cut should be made as shown in Fig. 81, so that the center of the rafter may be fitted to the plate, as the center, a, is upon the line of the plumb cut. There is no difference in the plumb height of the valley and the common rafters at the plate, as the roof sheeting of both sides of the valley meets at the center of the top edge of the valley rafter, which is in line with the common rafters.
If the top of a valley rafter is cut against a hip, as at g, Fig. 80, the plumb cut is the same as that of a hip rafter, but the end cut is square across. This applies only to roofs of rectangular shape, and of even pitches.
 
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