Fig. 7
Fig. 8
Fig. 9
66. In [Fig. 7] is shown the plan and elevation of a hip roof, having a deck z. The pitch of the roof being the same on each side, the line c d shows the true length of the common rafter l m.
In [Fig. 8] is shown the method of developing the true lengths of the hips and the true size of one side of the roof. Let a b c d represent the same lines as the corresponding ones in [Fig. 7]. From the line a d, [Fig. 8], through b and c, draw perpendiculars, as g h and e f; lay off from g and e on these lines, the length of the common rafter c d, [Fig. 7], and draw the lines a h and d f, [Fig. 8]; then the figure a h f d will represent the true shape and size of the side of the roof shown in the elevation in [Fig. 7]. The area of the triangle d e f is equal to the area of the triangle a g h or a similar triangle a i h. Hence, the portion of the roof a h f d is equal in area to the rectangle a i f e, the length of which is half the sum of the eave and deck lengths, while its breadth is the length of a common rafter.
67. A method of obtaining the lengths of valley rafters, applicable also to hip rafters, is shown in [Fig. 9], which is the plan of a hip-and-gable roof. To ascertain the length of the valley rafter a b, draw the line a c perpendicular to a b and equal in length to the altitude of the gable; then draw the line c b, which will represent the true length of the valley rafter a b.
68. As an example of roof mensuration, the number of square feet of surface on the roof shown in [Fig. 10] will be calculated.
