Fig. 67. Determining Length of Jack Rafters
Second Method: Where jacks are framed so that equal spacings may be laid off, beginning with a full length common rafter, as in [Fig. 67], the simplest method of determining lengths of jacks is to first count the number of spaces between jacks, which must be laid off on ridge or on plate, and divide the length of common rafter by this number. The result will be the common difference between lengths of jacks. The longest jack will be framed first by reducing the length of common rafter by the common difference. The next, by reducing the jack just framed by the common difference, etc. This method is applicable to roofs of any number of sides.
Third Method: If we begin to frame with the shortest jack instead of the longest, we first determine the length of the shortest jack, remembering that its run in the square cornered building will be the same as its spacing from the corner along the plate, or along the ridge in case of a valley jack. In a similar manner the second jack can be framed. The difference in the lengths of these two is the common difference. To the length of this second jack, and to each succeeding jack add the common difference, to get the length of the next.
Fourth Method: As rafters are usually spaced either 16" or 24" apart, a table consisting of the common differences in lengths for the various pitches will be found convenient, [Fig. 49.] The steel square of [Fig. 50] also shows such a table for the square roof.
CHAPTER IV
Roof Frame: any Polygon
Fig. 68. Tangents
30. Tangents; Miter Cuts of the Plate.—Before the principles involved in the laying out of rafters on any type of roof can be understood, a clearer idea of the term tangent as used in roof framing must be had. A tangent of an angle of a right triangle is the ratio or fractional value obtained by dividing the value of the side opposite that angle by the value of the adjacent side. The tangent at the plate, to which reference was made is the tangent of the angle having for its adjacent sides the run of the common rafter and the run of the hip or valley. By making use of a circle with a radius of 12" we may represent the value of this tangent graphically in terms of the constant of common rafter run, [Fig. 68.] By constructing these figures very carefully and measuring the line marked tangent, we may obtain the value of the tangent for the polygon measured in inches to the foot of run of the common rafter. Such measurements, if made to the 1/100 of an inch will serve all practical purposes. A safer way, however, is to make use of values secured thru the trigonometric solutions described in Appendix I, using the graphic solutions as checks. The values of tangents at intervals of one degree are given in the Table of Natural Functions, Appendix II. By interpolation, fractional degree values may be found.
| Fig. 69-a. Table of Tangents | Fig. 69-b. Rafter Table. |