The length of the diagonal of the base of such a prism, which is the run of the hip or valley rafter, is found by the formula c'² = a'² + b'², [Fig. 58.] When tangent and run are equal and each taken as 12", the run of the hip or valley equals 16.97", which for practical purposes of carpentry is considered as 17". In laying on the square, then, in framing a hip or valley rafter of a square cornered building, 17" will be taken upon the tongue, the rise of the roof per foot of run of common rafter or per 17" of run of hip or valley rafter, being taken on the blade.
The table of hip and valley lengths per foot of run of common rafter, [Fig. 60], will be formed by solving the right triangle c² = a′² + b′², [Fig. 59], for each of the pitches represented.
The positions to be assumed by the worker in framing a hip or valley rafter are similar to those to be assumed in framing the common rafter.
In measuring the length of a hip or valley rafter by the first method, the plumb cut may be laid off first. The upper end of the hip rafter will have to be framed with a side cut as shown in [Fig. 61.] The measurement for length will be made from a point along the middle of the top arris. Where the second method is employed, the end and seat cuts are laid off first.
21. Laying off Plumb Cut of Hip or Valley Rafter for Square Cornered Buildings.—Assuming a position with reference to the rafter similar to that in framing the common rafter, lay off the plumb cut using 17" on the tongue, and on the blade the rise per foot of run of the roof, or common rafter, which is also the rise of a hip or valley on that roof per 17" of hip or valley run. Scribe along the blade.
Fig. 60. Framing Table for Hip or Valley Rafters
22. Side or Cheek Cut of Hip or Valley Rafter.—First Method: There are a number of ways to lay out a side cut on a square cornered building. The simplest to remember, where no framing tables are at hand, consists in measuring square back from the plumb cut line a distance A-B, [Fig. 62], equal to the thickness of the rafter being framed. Thru this point lay off another line parallel to the plumb cut line and "carry" this across the top edge of the rafter with the square, as at D-E. Now adjust the bevel to pass thru E and F, [Fig. 62], and the setting is obtained for all side cuts of hip or valley rafters of that pitch of roof. Scribe this line on the top edge of the rafter. Carry it down the remaining side using the same numbers on the square as were used in laying off the plumb cut on the first side.
Second Method: This method of laying off side or cheek cut consists in laying the framing square across the top edge of the rafter, taking 17" on the tongue and the length of hip or valley rafter per foot of run of common rafter for the pitch required on the blade, and scribing along the blade.
