The length 5 is found as shown in Fig. 20, by meas uring 4 inches from a to m along the run of common rafter for one foot. Upon in erect a line to cut the seat of the valley at c; from c to a will be the run of the valley to correspond with 4 inches run of the common rafter, and it will measure 5x inches.
How to Treat the Heel Cut of Hips and Valleys. Having found the lengths of the hips and valleys to correspond to the common rafters, it will be necessary to find also the thickness of each above the plate to correspond to the thickness the common rafter will be above the plate.
In Fig. 21 is shown a corner of a square building, showing the plates and the plan lines of a hip. The length of the hip, as already found, will cover the span from the ridge to the corner 2; but the sides of the hip intersect the plates at 3 and 3 respectively; therefore the distance from 2 to 1, as shown in this diagram, is measured backwards from a to 1 in the manner shown in Fig. 17; then a plumb line is drawn through 1 to m, parallel to the plumb cut a-17. From m to o on this line, measure the same thickness as that of the common rafter; and through o draw the heel cut to a as shown. • In like manner the thickness of the valley above the plate is found; but as the valley as shown in the plan figure, Fig. 22, projects beyond point 2 before it intersects the outside of the plates, the distance from 2 to 1 in the case of the valley will have to be measured outwards from 2, as shown from 2 to 1 in Fig. 23; and at the point thus found the thickness of the valley is to Le measured to cor respond with that of the com mon rafter as shown at m n.
The 19} taken on the blade represents the actual length of a hip or valley that will span over a run of 17 inches. The bevel is marked along the blade.
The cut across the back of the short valley to fit it against the side of the long valley, will be a square cut owing to the two plan lines being at right angles to each other.
In Fig. 25 is shown the steel square applied to a jack rafter to cut the back bevel, to fit it against the side of a hip or valley. The figures on the square are 12 on tongue and 15 on blade, the 12 repre senting a foot run of a common rafter, and the 15 the length of a rafter that will span over a foot run; marking along the blade will give the bevel.
The rule in every case to find the back bevel for jacks in roofs of equal pitch, is to take 12 on the tongue to represent the foot run, and the length of the rafter for a foot of run on the blade, marking along the blade in each case for the bevel.
In a 1-pitch roof, which is the most common in all parts of the country, the length of rafter for a foot of run will be 17 inches; hence it will be well to remember that 12 on tongue and 17 on blade, marking along the blade, will give the bevel to fit a jack against a hip or a valley in a i-pitch roof.
In a roof having a rise of 9 inches to the foot of run, such as the one under consideration, the length of rafter for one foot of run will be 15 inches. The square as shown in Fig. 25, with 12 on tongue and 15 on blade, will give the bevel by marking along the blade.
To find the length of a rafter for a foot of run for any other pitch, place the two-foot rule diagonally from 12 on the blade of the square to the figure on tongue representing the rise of the roof to the foot of run; the rule will give the length of the rafter that will span over one foot of run.
The length of rafter for a foot of run will also determine the difference in lengths of jacks. For example, if a roof rises 12 inches to one foot of run, the rafter over this span has been found to be 17 inches; this, therefore, is the number of inches each jack is shortened in one foot of run. If the rise of the roof is 8 inches to the foot of run, the length of the rafter is found for one foot of run, by placing the rule diagonally from 12 on tongue to 8 on blade, which gives 141 inches, as shown in Fig. 26. This, therefore, will be the number of inches the jacks are to be shortened in a roof rising 8 inches to the foot of run. If the jacks are placed 24 inches from center to center, then multiply 14'4 by 2 = 29 inches.