Chapter VII: Section 17: , is employed, the end cut and seat cut will be laid out

before the plumb cut. The operator will stand as in Fig. 45-a.

When one rafter has been laid out it is cut and used as a pattern by which to cut similar rafters.

=19. Ridge Piece.=--Roofs may be framed with or without a ridge piece. The use of a ridge piece makes the assembly or raising of a roof somewhat easier, especially a hip roof. Upon an ordinary dwelling a ridge piece is usually a 1" × 6" board. Upon a gabled roof the length of ridge piece will be the same as that of the plate which it is to parallel, and will be laid off by placing the ridge board alongside the plate after the rafter positions have been marked upon the plate. These marks are transcribed upon the ridge board by means of the square and pencil.

On a hip roof, Fig. 54, the length of a ridge piece will be equal to the length of the parallel plate diminished by the length of the plate at right angles to this. This, however, is the theoretic length of ridge as measured from center to center. Enough extra stock must be left on the ridge when framing it to allow full contact of hip cheeks. This additional measurement at each end of the ridge will be equal to ½ the diagonal thickness of the hip plus ½ the thickness of the ridge, Fig. 54, making a total addition equal to the diagonal thickness of the hip plus the thickness of the ridge. Fig. 55 illustrates the placing of the square to determine the diagonal thickness of a hip rafter which strikes the ridge at an angle of 45 degrees.

In reckoning the length of a common rafter which is to rest against a ridge, the total length must be reduced by an amount equal to one-half the thickness of the ridge measured at right angles to the plumb cut, Fig. 56.

=20. Hip and Valley Rafters of Square Cornered Buildings.=--_First Method:_ The line of measurement for length of a hip and valley rafter is along the middle of the back or top edge, as on common and jack rafters. The manner of determining the number to use on the tongue of the square as a constant for the run, in terms of the 12" constant run of the common rafter, when the rise of the hip or valley rafter per foot of common run is taken on the blade; and the manner of constructing a table of unit lengths of hip and valley rafter, per foot of run of common rafter, are illustrated in Figs. 57, 58, 59 and 60. From a study of these illustrations it will be seen that a hip or valley rafter of a square cornered building is in either case the diagonal of a square prism which has for its base dimensions the tangent and run of the roof, and for its height the rise of the roof, Fig. 57. On a square cornered building the run and tangent are always equal.

The length of the diagonal of the base of such a prism, which is the run of the hip or valley rafter, is found by the formula _c′²_ = _a′²_ + _b′²_, Fig. 58. When tangent and run are equal and each taken as 12", the run of the hip or valley equals 16.97", which for practical purposes of carpentry is considered as 17". In laying on the square, then, in framing a hip or valley rafter of a square cornered building, 17" will be taken upon the tongue, the rise of the roof per foot of run of common rafter or per 17" of run of hip or valley rafter, being taken on the blade.

The table of hip and valley lengths per foot of run of common rafter, Fig. 60, will be formed by solving the right triangle _c″²_ = _a″²_ + _b″²_, Fig. 59, for each of the pitches represented.

The positions to be assumed by the worker in framing a hip or valley rafter are similar to those to be assumed in framing the common rafter.

In measuring the length of a hip or valley rafter by the first method, the plumb cut may be laid off first. The upper end of the hip rafter will have to be framed with a side cut as shown in Fig. 61. The measurement for length will be made from a point along the middle of the top arris. Where the second method is employed, the end and seat cuts are laid off first.

=21. Laying off Plumb Cut of Hip or Valley Rafter for Square Cornered Buildings.=--Assuming a position with reference to the rafter similar to that in framing the common rafter, lay off the plumb cut using 17" on the tongue, and on the blade the rise per foot of run of the roof, or common rafter, which is also the rise of a hip or valley on that roof per 17" of hip or valley run. Scribe along the blade.

=22. Side or Cheek Cut of Hip or Valley Rafter.=--_First Method:_ There are a number of ways to lay out a side cut on a square cornered building. The simplest to remember, where no framing tables are at hand, consists in measuring square back from the plumb cut line a distance _A-B_, Fig. 62, equal to the thickness of the rafter being framed. Thru this point lay off another line parallel to the plumb cut line and "carry" this across the top edge of the rafter with the square, as at _D-E_. Now adjust the bevel to pass thru _E_ and _F_, Fig. 62, and the setting is obtained for all side cuts of hip or valley rafters of that pitch of roof. Scribe this line on the top edge of the rafter. Carry it down the remaining side using the same numbers on the square as were used in laying off the plumb cut on the first side.

_Second Method:_ This method of laying off side or cheek cut consists in laying the framing square across the top edge of the rafter, taking 17" on the tongue and the length of hip or valley rafter per foot of run of common rafter for the pitch required on the blade, and scribing along the blade.

=23. Determining Length of Hip or Valley Rafter.=--_First Method:_ If a table of unit lengths of hip or valley per foot of run of common rafter is available, Fig. 60, the total rafter length may be determined by multiplying the unit of hip or valley rafter length per foot of run of common rafter by the total run of common rafter. Do not make the mistake of trying to multiply by the run of the hip or valley rafter. Remember that these tables are all worked out with the 12" run of the common rafter as the base. This is true no matter whether the house is four sided, eight sided, or any other number of sides. The respective tables are based in every case upon 12" run of the common rafter.

Measurements for lengths of hip or valley are to be made along the top edge of the stock beginning at the line for side cut and midway between the point and heel, Fig. 61.

_Second Method:_ This method of determining length of a hip or valley rafter is not unlike the second method described for the common rafter. Here, the numbers are 17 on the tongue, and the rise per foot of run of roof or of common rafter, on the blade. The end and seat cuts are scribed, after which the square is advanced step by step, using these same numbers, as many times as there are feet of run of common rafter. Should there be a fraction of a foot in the run of common rafter an additional and proportional advancement must be made. For example, to frame a hip for a square roof of ¼ pitch, having a run of common rafter of 12' 7". Advance the framing square 12 times, using 17" on the tongue and 6" on the blade. For the fractional advance take 1/12 of 17" or 9-11/12" (the framing square is laid off in twelfths on one side) on the tongue and 7/12 of 6" or 3½" on the blade, and scribe the limit. Fractional foot length of tail will be determined in a similar manner, the run or horizontal extension, or the lookout, of the common rafter determining the number of times the square must be advanced using 17" and 6" for the above given pitch.

=24. Laying off Seat and End Cut of Hip Rafter for Square Cornered Building.=--The seat cut and end cut of a hip rafter will be laid off in a manner quite similar to that used in laying off the seat and end cuts of the common rafter as described in Sec. 18. There will be this difference, of course; the numbers to be used on the square will be 17" on the tongue instead of 12" as in the case of the common rafter. The rise per foot of run will be the same as for the common rafter. The run of the tail of the common rafter determines the length of lookout or the number of times the square will be advanced. The distance 1-3, Fig. 52, must be the same on hip and valley as on common rafter of the same pitch of roof. The end cut of a hip rafter must be mitered to receive the fascia. The amount to be taken off for a square cornered building will be indicated by laying off lines a distance equal to one-half the thickness of the rafter, measured straight back from the lay-out of the end cut, Fig. 63. Since these cuts are identical with the side cut at the upper end of hip or valley, the square may be used as in laying off a side cut, cf. Section 22, second method.

=25. Reduction of Hip or Valley Rafter Length Because of Ridge Piece.=--If a hip rafter of a square cornered building is to be framed against a ridge piece, Fig. 40, its length must be reduced correspondingly. To make such allowance, measure square back from the line of plumb cut a distance equal to ½ the diagonal thickness of the ridge, Fig. 61-A-B.

=26. Backing a Hip Rafter for Square Cornered Building.=--_First Method:_ Since the line of measurement of a hip rafter is along the center of the top edge, if the rafter is framed with the same plumb distance as was given the common rafters, 1-3, Fig. 52, it stands to reason that the roof boards will not fit the top edge of the hip properly until the arrises of the hip have been removed as in the cross-section of Fig. 64. The laying out and removal of these arrises is known as backing the hip.

The amount of backing for a hip rafter will depend upon the rafter thickness, the pitch of the roof, and the number of sides to the plate, and is indicated by gage lines on either side and one on the top edge of the rafter. To determine the location of these gage lines on the sides of the rafter, (1) place the square on the hip as in laying out the seat cut for the hip on which the backing is to be placed, the constant, 17", on the tongue and the rise on the blade, if the house is rectangular, Fig. 64. (2) Measure from the edge of the hip back along the tongue a distance equal to % the thickness of the rafter, and mark. This point gives the setting for the gage. (3) Gage both sides of the rafter and then remove the arrises as shown in the cross-section. Carpenters more frequently frame a hip without backing, allowing the roof boards to rest upon the arrises of the hip, forming a small triangular space between the roof boards and the top edge of the hip. In order to keep these arrises in the same planes as the tops of the common rafters, they must reduce the plumb height 1-3, Fig. 52, of the hip. The amount of reduction, that is, the amount of drop the hip must make is equal to the plumb height of the backing, Fig. 64.

_Second Method:_ Take the rise in inches per foot of run of common rafter on the tongue, and the length of hip or valley per foot of run of common rafter on the blade; scribe along the tongue to get the angle of backing.

=27. Valley Rafters.=--As has been indicated in previous sections of the text, valley rafters have their lengths, plumb cuts, and seat cuts determined like hip rafters.

There is one difference; the valley rafter at its seat must be framed as in Fig. 65 in order that the plumb line may come directly over the corner of the building. The ends of roof boards will rest upon the valley rafter at its center line, which line is in the same plane as that of the common rafters.

Like the hip rafter, the upper end may be laid out first, after which the rafter length is measured from this, the measurement being made along the middle of the back of the rafter, the top edge.

To lay out the cuts shown in Fig. 65-a, proceed as in laying out the end of a hip rafter, as described in Sec. 24, Fig. 63. In the case of an octagon the amount would be 5/12 of that used for the square, Fig. 65-b.

In Figs. 40 and 41 is shown a valley rafter framed thru to the ridge. This is done to give the valley support, for a valley, unlike a hip, is not self supporting when the jacks are attached. Against this valley rafter is framed a second valley rafter. The upper end of this second valley rafter is framed with a plumb cut such as would be given a hip or valley of the same rise and run; the end, however, is cut square across as in the case of a common rafter resting against a ridge.

=28. Framing the Jack Rafter for Square Cornered Buildings; Plumb Cut; Side Cut.=--Jack rafters which have their top ends framed against a hip are known as hip jacks; those having the lower ends framed against a valley are known as valley jacks; those which are framed in between hip and valley are known as cripple jacks.

The jack rafter, being but a portion of a common rafter, is framed in a manner quite like that used in framing the common rafter. The chief difference is in the fact that the jack rafter has a side or cheek cut, and that the lengths of jacks vary with their position along the plate. The order of procedure may be: (1) To lay off the plumb cut, just as for a common rafter having the same rise, that is, using 12" on the tongue, and the rise per foot of run on the blade; scribe along the blade. (2) Lay off the side cut or cheek cut. This is done just as in laying off the side cut of the hip rafter on a square cornered building, first method only, Fig. 62. Where a table of common rafter lengths per foot of run is available, Fig. 49, a second method of laying out the side cut of a jack rafter consists in taking 12" on the tongue of the framing square, and the common rafter length per foot of run for the pitch given, on the blade; laying the square across the edge of the rafter and scribing along the blade. (3) Lay off the length of the jack as determined in the next section. (4) Lay off the seat cut just as in laying off the seat cut of the common rafter for the same pitch of roof, Section 18. Equally common is the practice of beginning with the end and seat cuts.

The framing square of Fig. 50 contains data which makes possible the laying out of side cuts for the square cornered building by means of numbers taken upon tongue and blade.

While the ratios of the numbers used upon the tongue and the blade are always the same for any given pitch, different makers of squares use different numbers for side cuts. The student will have to have special directions for each different make of square. These may be gotten from the manufacturers.

=29. Lengths of Jack Rafters for Square Cornered Roofs.=--_First Method:_ The framing table for common rafters and jack rafters, Fig. 49, may be made use of in determining lengths of jacks. To make use of this table we shall need to know the run of each separate jack. An examination of Fig. 66 shows that in a rectangular house the run of a jack is the same as the length of plate or of ridge which forms the angle. This is true of hip jack, valley jack, or cripple jack. However, such measurements are along the centers of the top edges of the rafters and allowance must be made in the length of the jacks for the thickness of hip or valley rafter. In the case of the cripple jack this amount of reduction will be equal to ½ the diagonal thickness of the hip plus ½ the diagonal thickness of the valley, measured at right angles to the plumb cut, Fig. 61, or measured in the plane of the plate, or a parallel plane.

Top and bottom ends of cripples are alike, but in nailing them in place the lower ends must be held up so that their center lines will strike the center of the valley rafter. Their tops will be kept even with the outer arrises of the hip whether the hip is backed or not.

In determining the true length of hip jack and valley jack we should know that a reduction of ½ the diagonal thickness of hip or valley, measured straight back from the plumb cut, is to be made. In the case of a valley jack resting against a ridge piece, an additional reduction must be made as described in Section 19, Fig. 56. In actual practice carpenters usually measure the length of hip or valley jack from the long point, along the arris, instead of along the center of the top edge, no reduction being made for ½ the diagonal thickness of hip or valley. Cripple jacks are measured from long point to long point, no reduction being made for thickness of hip and valley.

_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.