Fig. 76. King-Post
Lengths of hip or valley tails will be determined in a similar manner from the same table.
Second Method: This consists in successive placings of the square, using the same numbers on tongue and blade as will be used in laying out the plumb cut for this particular roof. The successive advances will be determined, as in the hip or valley of a square cornered building, by the number of feet in the run of the common rafter of this roof. A fractional part of a foot in run will be treated in a manner similar to that described for the square cornered building. Suitable allowance must be made for the fact that the length of rafter is along the middle of the top edge of the rafter, when this latter method is used.
Example:
An octagonal roof of ¼ pitch has a span of 25′.
The run of common rafter = 12' 6".
Taking 13" on the tongue and 6" on the blade lay off
successively 12 measurements. Take 6/12 or ½ of 13" or 6½"
on the tongue and 6/12 or ½ of 6" or 3" on the blade for
the fractional footof run.
37. Reductions in Lengths for King-Post.—Suitable reduction must be made for king-post, should there be one, [Fig. 76], or for rafter thicknesses should no king-post be used, [Fig. 75-b]. Where a king-post is used the reduction will be ½ the width of the square out of which the king-post is formed, the measurement being made square back from the line of the plumb cut, as in reducing common rafter lengths for ridge piece, [Fig. 56.]
Where an apex is formed as in [Fig. 75-b], one pair of hips is framed each with a run equal to ½ the octagon's diagonal, with cuts at the top the same as those of common rafters. The second pair will be similarly framed but the lengths will each be reduced an amount equal to ½ the thickness of the first pair, measuring straight back from the plumb cut. The third and fourth pairs will be reduced an amount equal to ½ the diagonal thickness of the rafters already framed, measured straight back from the plumb cut, Figs. [74-a] and [75-b]. These rafters will have to have double side cuts as indicated in [Fig. 75-b]. It will be noted that these latter rafters meet the others at an angle of 45 degrees, making the framing of the side cut similar to that of a square cornered building except that these are given double cheeks.
38. Seat and End Cut of Octagonal and other Polygonal Hips and Valleys.—The method of procedure in laying out the seat and end cuts of octagonal and other polygonal hips and valleys is similar to that described for the square hip, except of course, the numbers to use on the square will differ. These numbers will be determined by the run of the hip for that particular roof, and by the rise in inches per foot of run of common rafter. In the case of the octagon the numbers will be 13" on the tongue, and the rise on the blade. The length of tail may be figured by the tables, if such are available, or the framing square may be advanced successively as many times as there are feet in the run of the tail or the lookout of the common rafter of that roof, as heretofore described.
The miter cut on the end of a hip rafter and in the crotch of a valley rafter will vary with the tangent value of the plate. For the octagon, whose tangent is 5" the measurement from the end cut and at right angles to it will be 5/12 that used on the square cornered building. This same ratio will hold for the measurement at the crotch of the valley, [Fig. 65-b].
39. Backing Octagonal and other Hips.—The principle involved in determining the amount of backing on hip rafters for the octagon, as well as that of other polygons, is similar to that for backing hips for the square cornered building.
