To Find The Length Of A Common Rafter. First Method: The theoretic length of a rafter is indicated by the center lines in Figs. 45-a and 48. In estimating the total length of stock for a rafter having a tail, the run of tail or length of lookout must be considered.
The pitches most commonly used are the half, third, and quarter. From an examination of Fig. 43 it will be seen that the length of a common rafter is the hypotenuse of a right triangle whose legs are the rise and the run of the roof. The problem, then, of finding the length of a common rafter when the rise and run are known is merely that of solving the equation c2 = a2 +b2.
Practical carpenters would not consider it economy to take time to solve for rafter lengths in this manner, for every variation in rise or run would necessitate a rather long solution. Instead, they have discovered that for every foot of run of a rafter the length of the rafter increases proportionately, the ratio of rise to run remaining the same, Fig. 44. With a table, therefore, in which the length of rafter for each foot of run, for each of the common pitches is given, the length of rafter for any given pitch can be found by merely multiplying the constant given by the amount of run for that particular rafter.
Fig. 48. Rafter Length.
Fig. 49 shows such a table worked out for a rather extended number of pitches. From this table it will be seen that the number to take as a constant for the run is 12", and that the rise in inches per foot of run is taken upon the other member of the framing square. A jack rafter as will be illustrated later is but a shortened common rafter, therefore, what is said of the common rafter is also true of the jack rafter. The jack, however, has an additional cut which will be discussed in another section.
Determine the length of a common rafter of a house with a 25' span and a quarter pitch, without tail.
Fig. 49. Framing Table for Common Rafter.
Run = 12½'
Length per foot of run for quarter pitch = 13.42"
12.5 X 13.42" = 167.75" = 13.98'
(Looking for the nearest fractional value of .98 in the Table of Decimal
Equivalents in Appendix III, 63/64 or practically 1') The rafter would be framed 14' in length.
When a tail is a part of the rafter, proceed in the manner described adding the run of the tail, or length of lookout, to the run of the rafter.
Fig. 50 shows a framing square, containing among other data, the rafter lengths per foot of run. To use the data pertaining to common or jack rafter lengths, (1) consider the run as 12" taken on the tongue; (2) select upon the blade along its outer edge the inch mark which represents the rise of the roof per foot of run required to give the pitch specified; (3) the number directly below this mark, reading across the blade in the space marked "Length of Common Rafter Per Foot of Run" gives the length per foot for that particular rise or pitch.
Fig. 50. Framing Square Detail.
As a check for rafter length computations, the following procedure is suggested: Selecting the run as 12" on the tongue and the rise in inches per foot of run on the blade, place one square upon another as shown in Fig. 51, using that side of the square divided into inches and twelfths. Do not use the end of the blade, the rounded corner makes it impossible to secure the accuracy demanded. Extreme accuracy is required if the constant is to be used for rafters of considerable length of run. Read the diagonal length between the numbers representing the run and rise. Read the whole number of inches as feet, and the fractions as inches, and take off any fractional remainder upon a very sharp pointed pair of dividers. Read this divider spacing by means of the hundredths scale on the framing square. The result should, if the work is very accurately done, be the same as that obtained by computation from the tables, even to the hundredths place decimal. Upon ordinary work where great accuracy is not required carpenters sometimes determine this constant for a given pitch by placing the framing square as in Fig. 4o or 47, taking upon the tongue the run and on the blade the rise, marking along both tongue and blade. The distance between these marks is then read on a square placed along the edge.
Second Method: In determining rafter length, an equally common practice is to lay the framing square as is shown in Fig. 45-a.
While in this position the seat cut is scribed, cf. Section 18, and also a short sharp line scribed along the other member of the square at the top edge of the rafter. The square is moved along, using the same numbers, and another advance mark scribed. This operation is repeated just as many times as there are feet in the run of the common rafter. With a span of 24' the operation would be repeated 12 times.
Should the run not happen to be in even feet, the square would be placed as many times as there were full feet in the run. In addition it would be advanced that fractional part which the fraction of the run was of 12". For example, in a run of 12' 7", with a roof of ¼ pitch, the square would be advanced 12 times using the number 12 on the tongue and 6 on the blade. In addition to this the square would be advanced using 7/12 of 12" or 7" on the tongue and 7/12 of 6" or 3½' on the blade. As these numbers do not allow enough of the square to rest on the rafter to give a full line, as soon as the advance limit of rafter length is indicated the square may be moved up, using the set of numbers first used, that is 12" and 6". On common rafters, this last operation is simplified by noting that the fractional run, divided by 12, times 12, always equals itself. The final position of the square, therefore, may be obtained by simply sliding the member, used in laying out the last full foot line which parallels the seat cut, an additional distance equal to the fractional foot of total run, Fig. 44. The tail length is obtained similarly, Fig. 44.
Fig. 51. Finding Rafter Length by Scaling.
Fig. 52. Laying out Rafter.