Fig. 81. Side Cut Fig. 82. End Cut

44. Translating Framing Problems from Protractor to Framing Square and Vice Versa.—Frequently it is desirable to translate framing problems from degrees to numbers to be used upon the steel square, and vice versa. To change from degree framing to steel square framing it is only necessary to remember that the numbers to use on the square must be numbers such that their ratio one to the other shall give a tangent value equal to that given in the Table of Natural Functions, Appendix II, for the angle under consideration.

Example:
Given: Angle of inclination of common rafter or of roof = 30 degrees.
Find the numbers to take on the square to frame seat and plumb cuts.
Solution:
Tan 30° = .577 (by Table, Appendix II).
By agreement, run of common rafter takes 12" on one member of the
square for constant of run.
Therefore, rise must be 6.93", or 611/12", must be taken on the other
member of the square. (The base of the table is 1 so that for
12" run we must have 12" x .5774.)

In a similar manner the number to be taken on the blade, when the inclination of any other common or jack rafter is given, may be determined. In the case of the hip or valley inclination, however, it must be remembered that 17" is to be taken on the tongue for the run in the square cornered house, with 13" in the octagon, which will necessitate multiplying the tangent value of the angle of inclination by 17 and 13 respectively to find the number to take on the blade when one or the other of these is taken on the tongue.

Example:
Given: Side cut of jack rafter, or hip or valley = 38 degrees.
Find the numbers to use on the framing square to lay off this
same angle.
Solution:
Tan 38° = .7813
By agreement, we shall take 12" on the tongue.
The number to be taken on the blade must be, therefore,
12" x .7813 = 9⅜
(In the case of the side cut, any number other than 12" might have
been assumed on the tongue.)
Example:
Given: A hip rafter on a square roof which is framed with 17" on the
tongue and 8" on the blade.
To find the angle of inclination of the hip.
Solution:
8/17 = .4706
The angle whose tan = .4706 is 25° 19′

45. Framing an Octagon Bay.—Whatever may be one's opinion as to the propriety of the octagon bay architecturally, its very common use makes it obligatory upon the builder to know how to properly frame it.

Referring to Figs. [72] and [a]83-a] it will be seen that the octagon bay is but a portion of a full octagon set up against the side of a house. From this it follows that the framing of the plate, sills, the laying out of plumb and seat cuts, and side or cheek cuts of jacks that rest against hips, etc., will be according to principles discussed in previous sections of the text. The chief thing which needs explanation is the matter of laying out side cuts for hips and jacks which are to rest against the side of the building.

Fig. 83-a.Fig. 83-b.
Framing Rafters of Octagon Bay

Consider the bay as cut along the line I-J, [Fig. 83-a]. To frame the hip nearest the building: (1) Determine the angle which would give the side or cheek cut of the rafter involved when the rafter has no pitch, that is, when it lies in the plane of the plate. [Fig. 83-a] indicates the manner of determining this angle, which will be found to be 22½°. If we wish to use a framing square instead of a framing tool we may readily translate the 22½°. We shall find that 12" taken on the tongue of the square will require 4.97" or 5" on the blade. (2) Place the square as in [Fig. 83-b] and scribe along the tongue. Remember that this gives the miter when the rafter lies in the plane of the plate. This would give the cut to be used where ceiling joist or floor joist of octagon bay are run parallel with the rafters. On small bays, joists are seldom run thus but are run parallel with other joists of the house. No special directions are needed for setting the protractor, or the combination tool, the manner of setting and placing is so obvious. (3) Once having this miter when the rafter lies in the plane of the plate, proceed as directed in [Sec. 35], (2) et seq. With one such rafter framed the mates may be laid out by transposition.