Fig. 57. Hip or Valley Rafter is Diagonal of Square Prism
In reckoning the length of a common rafter which is to rest against a ridge, the total length must be reduced by an amount equal to one-half the thickness of the ridge measured at right angles to the plumb cut, [Fig. 56.]
Fig. 58-a. Hip Rafter.
Fig. 58-b. Valley Rafter
20. Hip and Valley Rafters of Square Cornered Buildings.—First Method: The line of measurement for length of a hip and valley rafter is along the middle of the back or top edge, as on common and jack rafters. The manner of determining the number to use on the tongue of the square as a constant for the run, in terms of the 12" constant run of the common rafter, when the rise of the hip or valley rafter per foot of common run is taken on the blade; and the manner of constructing a table of unit lengths of hip and valley rafter, per foot of run of common rafter, are illustrated in Figs. [57], [58], [59] and [60]. From a study of these illustrations it will be seen that a hip or valley rafter of a square cornered building is in either case the diagonal of a square prism which has for its base dimensions the tangent and run of the roof, and for its height the rise of the roof, [Fig. 57.] On a square cornered building the run and tangent are always equal.
Fig. 59. Determining Unit Length of Hip or Valley Rafter.