This section is from the book "A Treatise On Architecture And Building Construction Vol2: Masonry. Carpentry. Joinery", by The Colliery Engineer Co. Also available from Amazon: A Treatise On Architecture And Building Construction.
131. A roof may contribute much to the elegance and completeness of any building, as, by its fitness and appropriateness of outline, and its harmony with the structure, it crowns the whole. The angle to which any roof may be built, is variously designated as the pitch, slope, or inclination. There is, in practice, a rule for calculating a roof pitch by the proportion of its span to its height; however, the most simple and practical way of treating this pitch is by calculating the rise, or vertical height, in proportion to the foot of horizontal run.
132. According to the manner of pitching a roof in one or more directions, there is given to it a particular name, which may express the character of the whole roof, or merely name one of its characteristics. A fiat roof is one where there is but a slight pitch, or slant, to its timbers, just sufficient to cause the water to run to its lower edge, which is called the eaves.
The amount of pitch usually given to a flat roof varies from \ inch to 3 inches to a foot, according to circumstances; when the inclination of the roof materially exceeds 3 inches to the foot, the roof comes under the class of single-pitch, or shed, roof, sometimes called a lean-to, as shown in Fig. 44.
This kind of an enclosure is usually built against the side of another structure, already erected - hence its name lean-to - and its roof often has to receive and carry the drip from the main roof above, as well as its own collection of moisture. The single-pitch roof, however, is also frequently used over verandas, and attic dormer-windows, and in other minor positions on the main building.
133. When the pitch falls in both directions from the center of the building, we have what is known as a double-pitch, or gable, roof, as shown in Fig. 45, the plan of which is the rectangle fgh i. This form of roof derives its name from the shape of its ends, the triangle a b c being called a gable, one of which exists at each end of the building. The upper edge of the roof be is called the ridge, and the lower edges, on each side, as at c d, are called the eaves. In the plan fi and gh are the eaves, while jk shows the position of the ridge be.
134. In Fig. 46 (a) is shown in perspective a square structure, with a gable on each of the four sides. The ridges of these gables intersect at o, while the eaves intersect in pairs at a, c and e; the line of intersection o c between the pitches dc and bc, is called a valley. At (b) is shown a plan of this roof, in which the lines d' h' and fb' mark the positions of the ridges, the lines o' a', o' c', o' e', and o'g' show the intersections of the slanting surfaces, called valleys, while the dotted outline g'i' a' is the form of the elevation of the gable over g'h'a.
135. In Fig. 47 (a) is illustrated a rectangular building with a roof pitched back from all four sides, forming a pyramid. The edges o a, ob, and o d, in which these pitches meet, are called hips, and this type of roof is known as hip roof. As the building is not square, in this case, the pitch of the side a ob is different from the pitch of aod, because the point o', as seen in the plan (b), is the intersecting point of all four sides (called the apex) and is farther from /' and h' than from e' and g'; therefore, the proportion of rise to run is different in adjacent sides, and the pitches are necessarily-different.
In the plan of this roof, shown at (b), the lines a' c' and b' d' show the position of the hips intersecting at o'. On the dotted line o' e' is laid off the distance o' k' equal to the height of the roof at the center o' then the lines k' f' and k' h' show the pitch of the rafters, which are parallel to o' f' and o' h'. Likewise when the height of the center point o' is laid off, equal to o' i', the lines i' e' and i' g' give the pitch of the rafters over, and parallel, to o' e' and o' g'.
136. In Fig. 48 we have the framing plan of a hip roof, where all four sides have the same pitch; being a parallelogram in form, its long sides do not meet in an apex, as in Fig. 47, but form a ridge fb. If we lay off on the extended line of this ridge on equal to the height of the ridge above the plate, and connect n c and n a, we have, in the triangle a n c, the outline of a vertical section of the roof through any point on the ridge line fb, and nc or na will be the pitch of the sides of the roof, as well as of the ends, as they are, in this case, both the same. The rafters between the points / and b will be parallel to lf, and their length will be equal to n a, as will also the length of the two rafters fg and b o.
The bevel of the ends of these rafters, where they rest against the ridge fb, called the plumb-cut, is the angle cno, while the bevel on the other end, which foots upon the plate, called the foot-cut, will be the angle ocn. The four hip rafters, fe, be, and ba will have a different length and bevel from those above named. This length and bevel are found as follows: Lay off o k perpendicular to go and equal to be or ba, on plan, make on equal to the height of the ridge over the plate, and connect k n; then k n will be the length of the hip rafters, the angle onk will be the bevel of the plumb-cut, and the angle o k n will be the bevel of the foot-cut.
137. The short timbers, whose lower end rests upon the plate, while the upper end rests against the hip rafter, as shown at im, are called jack-rafters, and though they have the same plumb-cut and foot-cut as the ordinary rafters, they have an additional bevel on their upper ends called the cheek-cut, in order to have them fit nicely against the sides of the hip rafters, ba, be, etc.