In [Fig. 38] is shown the slope of the roof projected into the horizontal plane. By drawing a figure based on a scale of one inch to one foot, all the timbers on the slope of the roof can be measured. Bevel 2, shown in this figure, is to fit the valleys against the ridge. By drawing a line from w square to the seat of the valley to m, making w 2 equal in length to the length of the valley, as shown, and by connecting 2 and m, the bevel at 2 is found, which will fit the valleys against the ridge, as shown at 3 and 3 in [Fig. 36].
Fig. 40. Showing How Cornice Affects Valleys
and Plates in Roof with Unequal Pitches.
In [Fig. 39], is shown how to find the length and cuts of octagon hips intersecting a roof. In [Fig. 36], half the plan of the octagon is shown to be inside of the plate, and the hips o, z, o intersect the slope of the roof. In [Fig. 39], the lines below x y are the plan lines; and those above, the elevation. From z, o, o, in the plan, draw lines to x y, as shown from o to m and from z to m; from m and m, draw the elevation lines to the apex o″, intersecting the line of the roof in d″ and c″. From d″ and c″, draw the lines d″ v″ and c″ a″ parallel to x y; from c″, drop a line to intersect the plan line a o in c. Make a w equal in length to a″ o″ of the elevation, and connect w c; measure from w to n the full height of the octagon as shown from x y to the apex o″; and connect c n. The length from w to c is that of the two hips shown at o o in [Fig. 36], both being equal hips intersecting the roof at an equal distance from the plate. The bevel at w is the top bevel, and the bevel at c will fit the roof.
Again, drop a line from d″ to intersect the plan line a z in d. Make a 2 equal to v″ o″ in the elevation, and connect 2 d. Measure from 2 to b the full height of the tower as shown from x y to the apex o″ in the elevation, and connect d b. The length 2 d represents the length of the hip z shown in [Fig. 36]; the bevel at 2 is that of the top; and the bevel at d, the one that will fit the foot of the hip to the intersecting roof.
When a cornice of any considerable width runs around a roof of this kind, it affects the plates and the angle of the valleys as shown in [Fig. 40]. In this figure are shown the same valleys as in [Fig. 36]; but, owing to the width of the cornice, the foot of each has been moved the distance a b along the plate of the main roof. Why this is done is shown in the drawing to be caused by the necessity for the valleys to intersect the corners c c of the cornice.
The plates are also affected as shown in [Fig. 41], where the plate of the narrow roof is shown to be much higher than the plate of the main roof.
The bevels shown at 3, [Fig. 40], are to fit the valleys against the ridge.