Why 17 represents the run for all the hips and valleys, will be understood by examining Fig. 19, in which 17 is shown to be the diag onal of a foot square.
In equal-pitch roofs the corners are square, and the plan of the hip or valley will always be a diagonal of a square corner as shown at 1, 2, 3, and 5 in Fig. 14.
In Fig. 1S are shown -k pitch, pitch and 1 pitch over a square corner.
The figures to be used on the square for the hip, will be 17 for run in each case. For the k pitch, the figures to be used would be 17 inches run and 4 inches rise, to correspond with the 12 inches run and 4 inches rise of the common rafter. For the s pitch, the figures to be used for hip.would be 17 inches run and 9 inches rise, to corre spond with the 12 inches run and 9 inches rise of the common rafter; and for the 1- pitch, the figures to be used on the square will be 17 inches run and 12 inches rise, to correspond with the 12 inches run and 12 inches rise of the common rafter.
It will be observed from above, that in all cases where the plan of the hip or valley is a diagonal of a square, the figures to be used on the square for run will be 17 inches; and for the rise, whatever the roof rises to the foot of run. It should also be remembered that this is the condition in all roofs of equal pitch, where the angle of the hip or valley is a 45-degree angle, or, in other words, where we have the diagonal of a square.
It has been shown in Fig. 12 how other figures for other plan angles may be found ; and that in each case the figures for run vary according to the plan angle of the hip or valley, while the figure for the height in each case is similar.
In Fig. 14 are shown a variety of runs for common rafters, but all have the same pitch; they rise 9 inches to the foot of run. The main roof is shown to have a span of 27 feet, which makes the run of the common rafter 13 feet 6 inches. The run of the front wing is shown to be 10 feet 4 inches; and the run of the small gable at the left corner of the front, is shown to be 8 feet.
The diversity exhibited in the runs, and especially the fractional part of a foot shown in two of them, will afford an opportunity to treat of the main difficulties in laying out roof timbers in roofs of equal pitch. Let it be determined to have a rise of 9 inches to the foot of run; and in this tion it may be well to member that the tional rise to the foot run for roofs of equal pitch makes not the least ference in the method of treatment.
To lay out the common rafters for the main roof, which has a run of 13 feet 6 inches,proceed as shown in Fig. 16.
Take 12 on the blade and 9 on the tongue, and step 13 times along the rafter timber. This will give the length of rafter for 13 feet of run. In this example, however, there is another 6 inches of run to cover. For this additional length, take 6 inches on the blade (it being a foot run) for run, and take of 9 on the tongue (which is inches), and step one time. This, in addition to what has already been found by stepping 13 times with 12 and 9, will give the full length of the rafter.
The square with 12 on blade and 9 on tongue will give the heel and plumb cuts.
Another method of finding the length of rafter for the 6 inches is shown in Fig. 16, where the square is shown applied to the rafter timber for the plumb cut. Square No. 1 is shown applied with 12 on blade and 9 on tongue for the length of the 13 feet. Square from this cut, measure 6 inches, the additional inches in the run; and to this point move the square, holding it on the side of the rafter timber with 12 on blade and 9 on tongue, as for a full foot run.
It will be observed that this method is easily adapted to find any fractional part of a foot in the length of rafters.
In the front gable, Fig. 14, the fractional part of a foot is 4 inches to be added to 10 feet of run; therefore, in that case, the line shown measured to 6 inches in Fig. 16 would measure only 4 inches for the front gable.
Heel Cut of Common Rafter. In Fig. 16 is also shown a method to lay out the heel cut of a common rafter. The square is shown applied with 12 on blade and 9 on tongue; and from where the 12 on the square intersects the edge of the rafter timber, a line is drawn square to the blade as shown by the clotted line from 12 to a. Then the thickness of the part of the rafter that is to project beyond the plate to hold the cornice, is gauged to intersect the dotted line at a; and from a, the heel cut is drawn with the square having 12 cn blade and 9 on tongue, marking along the blade for the cut.