This section is from the book "Carpentry", by Ira Samuel Griffith. Also available from Amazon: Carpentry.

**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.

Fig. 86. Laying off Cut of Shed Rafter.

Side or cheek cuts for valley, hip or jacks are determined according to principles developed in Sec. 35.

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' = ⅛ pitch. 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.

Fig. 87. Plan of Uneven Pitches.

Solution: c2 = a2+b2=(7½)2+62, (a : 12 :: 5 :8, whence a = 7½) c=9.60'

Expressing this run of valley in terms of 12" of run of common rafter over b.

9.60': 6'::x: 12".

x = 19.20". (Check this value by scale drawing.)

Length of valley rafter, then, is found by taking 19.20" on the tongue with 10" (5/6 of 12") on the blade, advancing the setting as many times as there are feet in the run of the common rafter over b.

The numbers just given will give the plumb cut and the seat cut of this valley rafter.

(2) Find the side cut of the valley rafter when it rests against the ridge of the minor roof.

Fig. 8S-a. Uneven Pitches.

Solution: The side cut of the valley when allowed to rest in the plane of the b 6 / 12 plate = angle B, Fig. 88-a, whose tangent=b/a = 6/7½ ( = 12/15 =.800=38° 40')

Therefore, take 7½" on the blade (always the run of intercepted common rafter of major roof), and 6" on the tongue (always the run of the common rafter of the minor roof); scribe on the blade.

For side cut of valley rafter when it is to be fitted to a ridge of the major roof, the lay-out when in the plane of the plate is obtained by means of these same numbers, but the scribing is done on the tongue. This lay-out in either case is for the rafter when lying in the plane of the plate. Having secured this, proceed as in Sec. 35, (2).

Side cuts of jacks for the minor roof are determined by the length of the ridge over a, Fig. 88-a, and the length of the rafter over b. But the length of the ridge over a= the run of the intercepted common rafter of the major roof, 7½' here. A general rule may be derived, therefore: For the side cut of a jack on a minor roof take on the blade of the square the run of the intercepted common rafter of the major roof (inches for feet), and on the tongue

Fig. 88-b..

Fig. 88-c..

Side Cuts of Jacks for Uneven Pitches take the length of rafter of the minor roof; scribe on the tongue, Fig. 88-b. For the side cut of jacks on a major roof, take on the tongue of the square the run of the common rafter of the minor roof, and on the blade the length of the intercepted common rafter of the major roof; scribe on the blade, Fig. 88-c.

A new problem arises in connection with uneven or irregular pitches, the problem of making the projecting cornice member one with another. Manifestly, if one part of a roof is steeper than another and the plate the same height all around the building, the cornice cannot be made to meet in the same plane. This difficulty is overcome by raising the plate of the steeper roof an amount equal to the difference in the rises of the two pitches for a run equal to that of the projecting cornice. For example, in a half-pitch the rise would be 24" for a run of 24" in the cornice. In a quarter-pitch rise for a 24" run of cornice would be 12", a difference in rises of 12". The plate of the steeper roof must be raised that much higher than that for the lower pitch.

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