This section is from the book "Carpentry", by Ira Samuel Griffith. Also available from Amazon: Carpentry.

**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 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.

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"

Fig. 83-a..

Fig. 83-b..

Framing Rafters of Octagon Bay 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.

To frame the remaining hips of Fig. 83-a proceed in a manner similar to that just described. In this case the angle made by the hip when it lies in the plane of the plate and the side of the house will be 67½ degrees. Why? Fig. 84-a. The framing tool or protractor and T-bevel provide the simplest means of framing. If one wishes to use the framing square he will find that by using the tangent value of 67½° he gets 28.97" to take on the blade when 12" is taken on the tongue. This he cannot find, of course. He may either take other smaller numbers having the same ratio, or he might'better take the cotangent value of 67½°. Cot of an angle of a right triangle is the ratio of the adjacent side to the opposite side.

Angle A' = 67½°, Fig. 84-a. Cot 67½° - .414 when V = 1. When b' = 12" cot A' = 4.97" or 5".

(1) Place the square as in Fig. 84-b and scribe along the blade. By this time the student should have observed that the tangent value of any angle increases as the cotangent value of the angle decreases and vice versa. Note that when a cotangent value is used, 12" is still taken on the tongue and the same number as for the tangent value of that number of degrees is taken on the blade, but that the scribing is done along the blade and not along the tongue as is the case when tangent values are used. (2) Proceed from this point as in Sec. 35, (2) et seq.

To frame the jack intercepted by the side of the house. Fig. 85-a; (1) Proceed to find the miter for the intercepted jack when it

Fig. 84-a..

Fig. 84-b..

Framing Octagon Hip Intercepted at 67½° lies in the plane of the plate. It is 45 degrees. Tan 45 degrees = 1 when b " = 1. Tan 45 degrees = 12" when b " = 12 ". (2) Place the square as in Fig. 85-b and scribe along the tongue. (3) From this on, continue as in Sec. 35, (2) et seq.

From these solutions the student should be able to generalize sufficiently to care for rafters of any angle of intersection with the side of a building, and of any pitch. The use of the framing tool or protractor and T-square is strongly recommended upon

Fig. 85-a..

Fig. 85-b..

Framing an Intercepted Jack such work as this. Nothing but tradition prevents its more general use in carpentry. Having determined the lay-out for the side cut of these rafters, the length of each must next be determined. To determine the length of hip or jack intercepted by the side of the house and the plate: (1) Determine the run of the intercepted part of the common or jack rafter, as b, Fig. 83-a. (2) By means of the table of rafter lengths per foot of run compute the length of rafter under consideration.

In determining the run of an intercepted part it is necessary to have data concerning the size of the octagon and the amount cut off by the building. The lines E-D and F-D, Fig. 83-a, when dimensioned, give this data. The actual lengths of the various hips, jacks, etc., in practical carpentry, upon small bays, are usually determined by actual measurement from the plate or sill to the proper point of intersection on the building as indicated by a stick or extension rule held at the proper angle. Sometimes a large scale drawing is made and the runs taken from this. Upon large work where accuracy is necessary and measurements impossible, trigonometric solutions should be used.

To determine the length of the intercepted hip rafter over c of triangle ab c Fig. 83-a, the value of b must first be secured.

This value represents common rafter run for hip rafter rising over side c, and run of intercepted common rafter rising over side b.

Length of intercepted hip rising over side c = bxunit length of hip. (Table of lengths of octagon hips in terms of run of common rafter, Fig. 73.)

Length of intercepted common rafter or jack nearest house = b x unit length of common rafter. (Table of lengths of common rafter in terms of run of common rafter, Fig. 49.)

It must be remembered that these are theoretic lengths measured down the middle of the top edge of the rafters. In framing, suitable reductions must be made. For example, in framing the intercepted common rafter nearest the building, the rafter must be set over one-half its thickness that it may be nailed against the side of the building. The allowance necessary in order to do this may be secured by measuring the length from the long point instead of the middle of the side or cheek cut. Suitable reduction, too, must be made for the hip thickness - in this case one-half the diagonal across the top edge of the hip, laid off at an angle of 22½°, or 5" and 12" on the square. This amount will be laid off straight back from the plumb cut, Sec. 35, (2) et seq.

Length of hip must be measured along the middle of the top of the rafter.

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