This section is from the book "Constructive Carpentry", by Charles A. King. Also available from Amazon: .
Irregular Roofs. In laying out the rafters of an irregularly shaped house or one with unequal pitches, a plan should be drawn showing every rafter in the roof, and the angles of their intersections with the plate, hip, and valley rafters.
The lengths of. all kinds of rafters and their plumb and seat cuts may be found by using the actual figures of their rise and run, unless they are of the ordinary pitches; then the constants for the cuts should be used, as previously described. Thus the bridge measure of the run on Bl. and the rise on To. will give the length, and the plumb and seat cuts of any rafter in any roof.
Each side of a roof of unequal pitches should be laid off with little attention to the intersection of the rafters and those of the adjoining sides. The run of each rafter may be taken from the plan, the rise of the jack and cripple rafters from the bevel board. Slide the square along the base line of the roof, as described in Topic 55, the rise of the common, hip, and valley rafters being found by the usual methods, the bridge measure giving the lengths.
The side or cheek cuts are usually confusing to the young workman who frames his first irregular roof, but if the principle illustrated by b, Fig. 79, is fully understood and accurately applied, there need be no trouble, as the distance ab will give the cheek cut of any angle of intersection, if measured square with the plumb cut. The same method may be used in cutting the rafters against a circle or any irregular shape.
It will be seen that the eaves of an uneven pitched house will not have the same projection upon all sides if the plates for both pitches are of the same height; therefore this defect may be corrected by raising or lowering the plate upon one or the other of the sides, or by making the bird's mouth joint so that it will give the same projection upon all sides, and so that the eaves will be upon the same line all around the house. If there is not too much difference in the pitches, this is the usual method.
66. Curb roofs is a term applied to mansard, French, and gambrel roofs, which have an angle in their contour above the plate of the house. This angle is formed by a curb plate which is supported by the rafters of the lower section of the roof, and which supports the rafters of the upper section. A curb plate is used also where a deck or flat section of the roof is necessary, for instance, where the hip and valley rafters meet in an awkward manner, or where other members of the roof do not intersect as they should, though a deck is often desired and planned.
 
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