CHAPTER IIIRoof 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."

GABLE HIP SHED GAMBRELFig. 39. Roof Types

InFig. 39are illustrated four types of roof. Figs.40,41, and42illustrate 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.

Fig. 40. Roof Details

Fig. 41. Plan of Roof Rafters

The terms rise, run, and rafter length have still another set ofmeanings—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.

Fig. 42. Raising the Rafters

It will be noted inFig. 44that 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.

Fig. 43. Run, Rise and Length

Fig. 44. Unit Length of Common Rafter

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 menprepare plans before attempting to frame the same.Fig. 43illustrates 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.

Fig. 45-a-b. Laying off Common Rafter

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 inFig. 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 givesthe plumb cut. Occasionally a carpenter will be found who frames to a center line rather than the top edge of a rafter.

Fig. 46. Position in Laying off Plumb Cut when Laid off before Seat Cut

Figs.45,46and47illustrate 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.

Fig. 47. Laying off Plumb Cut when Seat Cut is First Laid off

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-aand48. 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 ofFig. 43it 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 equationc²=a²+b².

Fig. 48. Rafter Length

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. 49shows 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' spanand a quarter pitch, without tail.

Fig. 49. Framing Table for Common Rafter

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 DecimalEquivalents 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. Framing Square Detail

Fig. 50shows a framing square, containing among other data, the rafter lengths per foot of run. To use the data pertaining tocommon 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 inFig. 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 inFig. 46or 47, taking upon the tongue the run and on theblade the rise, marking along both tongue and blade. The distance between these marks is then read on a square placed along the edge.

Fig. 51. Finding Rafter Length by Scaling

Second Method:In determining rafter length, an equally common practice is to lay the framing square as is shown inFig. 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. 52. Laying out Rafter

18. Laying off Common Rafter Seat Cut and End Cut.—First Method:Having determined the rafter length as directed inSec. 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 afoot. (2) Place square as at "b,"Fig. 52, standing as inFig. 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 atc,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.

Fig. 53. Independent Rafter Tail

Fig. 54. Length of Ridge Piece

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 inFig. 44and (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, Section 17, is employed, the end cut and seat cut will be laid out before the plumb cut. The operator will stand as inFig. 45-a.

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

Fig. 55. Determining Diagonal Thickness of Hip of Square Corner.

Fig. 56. Reduction of Common Rafter for Ridge Piece.

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 thediagonal thickness of the hip plus the thickness of the ridge.Fig. 55illustrates the placing of the square to determine the diagonal thickness of a hip rafter which strikes the ridge at an angle of 45 degrees.

Fig. 57. Hip or Valley Rafter is Diagonal of Square Prism

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.

Fig. 58-a. Hip Rafter.

Fig. 58-b. Valley Rafter

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 hipand valley rafter, per foot of run of common rafter, are illustrated in Figs.57,58,59and60. 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.

Fig. 59. Determining Unit Length of Hip or Valley Rafter.

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 formulac'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 trianglec²=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 thehip rafter will have to be framed with a side cut as shown inFig. 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.

Fig. 60. Framing Table for Hip or Valley Rafters

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 distanceA-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 edgeof the rafter with the square, as atD-E. Now adjust the bevel to pass thruEandF,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.

Fig. 61. Side Cut

Fig. 62. Laying off Side Cut

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 alongthe 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.

Fig. 63. Miter Cut of Hip Rafter End

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 inSec. 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 asfor 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.

Fig. 64. Backing the Hip Rafter

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 ofFig. 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 tothe 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 footof 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 inFig. 65in 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 inFig. 65-a, proceed as in laying out the end of a hip rafter, as described inSec. 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.40and41is 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, isframed 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 ofFig. 50contains 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 ofFig. 66shows that in a rectangular house the run of a jack is the same as the length of plateor 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.

Fig. 66. Lengths of Jack Rafters.

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.

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 inFig. 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 ofFig. 50also shows such a table for the square roof.

Back to Index Next