Chapter III: Roof Frame: Square Cornered Buildings

=15. Roof Framing.=--The problem of framing the various members of a roof is not a difficult one provided the underlying principles are understood, and dependence placed upon this understanding rather than upon mere knowledge of what figures to use upon the square to get the cuts, without knowing why those figures are used. An effort will be made in this treatment to indicate the "why."

Fig. 39. Roof Types]

In Fig. 39 are illustrated four types of roof. Figs. 40, 41, and 42 illustrate the rafter forms and the names of the various cuts to be made in framing the members to place. The common rafter, it will be seen, has three cuts--plumb or ridge cut, seat or heel or plate cut, and end cut. The hip, valley, and jack have four cuts each; a side cut or cheek cut is possessed by each in addition to the three cuts belonging to the common rafter.

Before any rafter can be framed, the rise and run of the common rafter, in other words, the pitch of the roof, must be known.

In roof framing, the "run" of a rafter when in place is the horizontal distance measured from the extreme end of the seat to a point directly below the ridge end of the rafter, Fig. 43. The "rise" is the vertical distance from the ridge end of the rafter to the level of the seat. The "pitch" of a roof or rafter is the ratio of the rise of the rafter to the span or whole width of the building.

The terms rise, run, and rafter length have still another set of meanings--they may be used to designate "unit" lengths. In all such cases 12" of run of the common rafter is assumed as the base, and the other unit lengths or constants are computed from this constant. The numerical values of these constants will be computed as the development of the subject of roof framing makes their use necessary.

It will be noted in Fig. 44 that the constant of run, or 12", is taken along the tongue and the rise per foot of run along the blade of the square. It is not essential that this order be followed; the beginner will generally find it easier to visualize his work, however, if he keeps the tongue for either rise or run, and the blade for the opposite. There are occasions when the reverse order is necessary no matter which form is followed, so that it is unwise to insist upon only one way.

The variation in terminology in roof framing is so general that the beginner will do well to familiarize himself with the most common. Hereafter an effort will be made to confine the text to the following: plumb cut, seat cut, end cut, side cut.

The value to a beginner of a carefully made plan of a roof to be framed with necessary data such as rafter lengths and positions indicated thereon, cannot be too strongly emphasized. Architects not infrequently prepare elaborate and complete framing plans for the use of the carpenter. Upon intricate plans, experienced men prepare plans before attempting to frame the same. Fig. 43 illustrates a framing plan ready for the placing thereon of the necessary data, such as measurements along the plate for spacing the rafters, lengths of rafters, ridge pieces, etc.

=16. Framing the Common Rafter; Laying out the Plumb Cut.=--While in this discussion the plumb cut is first described, it should be understood that it is equally as convenient and more common among carpenters to begin the framing of the members of a square cornered roof frame with the end and seat cuts. In framing other than a square cornered roof it is somewhat more convenient to begin with the plumb cut.

The method of framing of the common rafter is the same for all buildings, whether the buildings have four sides or more or less. (1) Place the framing square as in Fig. 45-b, taking 12" on the tongue as the run, and upon the blade the rise in inches per foot of run. Keep these numbers against the crowning, or what is to become the top edge of the rafter, and scribe along the blade. This gives the plumb cut. Occasionally a carpenter will be found who frames to a center line rather than the top edge of a rafter.

Figs. 45, 46 and 47 illustrate the proper position of the worker relative to his work. Such a position will seem awkward to the beginner but he should learn to visualize his work while in this position that the efficiency of framing may not be reduced thru the awkward position first likely to be assumed.

=17. 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. 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.

_Example:_

Determine the length of a common rafter of a house with a 25' span
and a quarter pitch, without tail.

_Solution:_

Run = 12#'
Length per foot of run for quarter pitch = 13.42"
12.5 × 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.

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. 46 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.

=18. Laying off Common Rafter Seat Cut and End Cut.=--_First Method:_ Having determined the rafter length as directed in Sec. 17, first method, (1) lay off this length along the upper edge beginning at the plumb cut. The whole number of feet is more safely "taken off" by means of a pole marked in feet, and of good length. The rule or square may be used to transmit fractional parts of a foot. (2) Place square as at "b," Fig. 52, standing as in Fig. 45-b, and scribe a plumb line as indicated at 1-2, Fig. 52. (3) From the point 1, Fig. 52, measure along the line marked 1-2 a distance equal to one-half that of 1-2. The distance 1-3 may be increased or decreased somewhat when an extreme pitch makes it advisable. As a rule this should be 2½" to 3". (4) Place the square as at _c_, Fig. 52, with the edge of the tongue resting on 3 and scribe a line for the seat cut, as 3-4. These last marks give the bird's mouth joint which is to fit over the plate.

While many carpenters allow end cutting of the rafter tails to wait until the rafters are set in place so that they may be lined and cut while in position, certain kinds of work permit the ends to be cut at the same time the remainder of the rafter is framed. In this latter method the square is placed as in Fig. 44 and (5) the end cut scribed. The point of cutoff on the tail is determined in the same manner as that used in determining rafter length, the run of the tail being considered and the tail length being measured from the point 1, Fig. 52.

Where a cornice is of unusual width, tails are usually framed independent of the rafters and are then spiked to the ends of the rafters either above or below the plate, Fig. 53.

_Second Method:_ Where the second method of finding length,