47. Framing a Roof of Uneven Pitch.—Not infrequently a roof must be framed in which several pitches are involved. All of the principles necessary for framing such a roof have been developed. It remains for the student to make the applications to uneven pitches. It is advisable to prepare a framing plan as shown in [Fig. 87.] From such a plan it may be seen that the seat and plumb cuts of common and jack rafters are determined in the usual manner, being different upon the different pitches, of course, but determined as for any given pitch. Lengths of common rafters will be determined for any pitch by the tables already made use of, the run being known or determined.
In selecting the numbers to use on the tongue and the blade of the square, in laying out seat and plumb cuts of hip or valley rafters of intersecting roofs of different pitches, any numbers may be used providing they have a ratio equal to that of the run and rise of the rafter being framed. Since the angle of intersection changes with every change of pitch, it is hardly worth while developing a constant to be used on the tongue in framing hip and valley rafters on irregular pitches.
Side or cheek cuts for valley, hip or jacks are determined according to principles developed in [Sec. 35].
Fig. 87. Plan of Uneven Pitches
The backing of hips on roofs of uneven pitches, while the amount to be removed on each side of the hip will vary, is determined by the principles developed in [Sec. 39]. The amount to be removed from each side must be separately determined according to the angle the hip makes with the plate.
Lengths of hip and valley jacks are determined as in [Sec. 42]. Lengths of cripple jacks will not be of uniform length, as in even pitched roofs. The runs for such jacks may be obtained with sufficient accuracy by measurements taken from an accurately made scale drawing.
The following example will make clear the method of attack where it is desired to develop a constant for hip or valley in terms of the common rafter of one of the pitches.
Example:
Given: Main roof, Rise = 8', Run = 12' = ½pitch.
Minor roof, Rise = 5', Run = 6' = 5/12 pitch.
(1) Find the run of valley rafter over c, [Fig. 88-a], in terms of the run of the common rafter over b.