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As we noted earlier, the four most common roof designs you will encounter as a Builder are gable, hip, intersecting, and shed. In this section, we will examine various calculations, layouts, cutting procedures, and assembly requirements required for efficient construction. GABLE Next to the shed roof, which has only one slope, the gable roof is the simplest type of sloping roof to build because it slopes in only two directions. The basic structural members of the gable roof are the ridgeboard, the common rafters, and the gableend studs. The framework is shown in figure 213. Figure 213.—Framework of a gable roof. The ridgeboard is placed at the peak of the roof. It provides a nailing surface for the top ends of the common rafters. The common rafters extend from the top wall plates to the ridge. The gableend studs are upright framing members that provide a nailing surface for siding and sheathing at the gable ends of the roof. Common Rafters All common rafters for a gable roof are the same length. They can be precut before the roof is assembled. Today, most common rafters include an overhang. The overhang (an example is shown in fig. 214) is the part of the rafter that extends past the building line. The run of the overhang, called the projection, is the horizontal distance from the building line to the tail cut on the rafter. In figure 214, note the plumb cuts at the ridge, heel, and tail of the rafter. A level seat cut is placed where the rafter rests on the top plate. The notch formed by the seat and heel cut line (fig. 215) is often called the bird’smouth.
The width of the seat cut is determined by the slope of the roof: the lower the slope, the wider the cut. At least 2 inches of stock should remain above the seat cut. The procedure for marking these cuts is explained later in this chapter. Layout is usually done after the length of the rafter is calculated. CALCULATING LENGTHS OF COMMON RAFTERS.— The length of a common rafter is based on the unit of rise and total run of the roof. The unit of rise and total run are obtained from the blueprints. Three different procedures can be used to calculate common rafter length: use a framing square printed with a rafter table; use a book of rafter tables; or, use the stepoff method where rafter layout is combined with calculating length. Framing squares are available with a rafter table printed on the face side (fig. 216). The rafter table makes it possible to find the lengths of all types of rafters for pitched roofs, with unit of rises ranging from 2 inches to 18 inches. Let’s look at two examples: Figure 216.—Rafter table on face of a steel square. Example 1. The roof has a 7inch unit of rise and a 16foot span. Look at the first line of the rafter table on a framing square to find LENGTH COMMON RAFTERS PER FOOT RUN (also known as the bridge measure). Since the roof in this example has a 7inch unit of rise, locate the number 7 at the top of the square. Directly beneath the number 7 is the number 13.89. This means that a common rafter with a 7inch unit of rise will be 13.89 inches long for every unit of run. To find the length of the rafter, multiply 13.89 inches by the number of feet in the total run. (The total run is always onehalf the span.) The total run for a roof with a 16foot span is 8 feet; therefore, multiply 13.89 inches by 8 to find the rafter length. Figure 217 is a schematic of this procedure. If a framing square is not available, the bridge measure can be found by using the Pythgorean theorem using the same cut of 7/12: 7^{2} + 12^{2} = 193^{2}; the square root of 193 is 13.89. Two steps remain to complete the procedure.
Example 2. A roof has a 6inch unit of rise and a 25foot span. The total run of the roof is 12 feet 6 inches. You can find the rafter length in four steps.
SHORTENING.— Rafter length found by any of the methods discussed here is the measurement from the heel plumb line to the center of the ridge. This is known as the theoretical length of the rafter. Since a ridgeboard, usually 1 1/2 inches thick, is placed between the rafters, onehalf of the ridgeboard (3/4 inch) must be deducted from each rafter. This calculation is known as shortening the rafter. It is done at the time the rafters are laid out. The actual length (as opposed to the theoretical length) of a ratler is the distance from the heel plumb line to the shortened ridge plumb line (fig. 218). Figure 218.—The actual (versus theoretical) length of a common rafter. LAYING OUT.— Before the rafters can be cut, the angles of the cuts must be marked. Layout consists of marking the plumb cuts at the ridge, heel, and tail of the rafter, and the seat cut where the rafter will rest on the wall. The angles are laid out with a framing square, as shown in figure 219. A pair of square gauges is useful in the procedure. One square gauge is secured to the tongue of the square next to the number that is the same as the unit of rise. The other gauge is secured to the blade of the square next to the number that is the same as the unit of run (always 12 inches). When the square is placed on the rafter stock, the plumb cut can be marked along the tongue (unit of rise) side of the square. The seat cut can be marked along the blade (unit of run) side of the square. Figure 219.Steel square used to lay out plumb and seat cuts. Rafter layout also includes marking off the required overhang, or tail line length, and making the shortening calculation explained earlier. Overhang, or tail line length, is rarely given and must be calculated before laying out rafters. Projection, the horizontal distance from the building line to the rafter tail, must be located from drawings or specifications. To determine tail line length, use the following formula: bridge measure (in inches) times projection (in feet) equals tail line length (in inches). Determine the bridge measure by using the rafter table on the framing square or calculate it by using the Pythagorean theorem. Using figure 220 as a guide, you can see there are four basic steps remaining. Figure 220.—Laying out a common rafter for a gable roof. Step 1. Lay out the rafter line length. Hold the framing square with the tongue in your right hand, the blade in the left, and the heel away from your body. Place the square as near the right end of the rafter as possible with the unit of rise on the tongue and the unit of run on the blade along the edge of the rafter stock. Strike a plumb mark along the tongue on the wide part of the material. This mark represents the center line of the roof. From either end of this mark, measure the line length of the rafter and mark the edge of the rafter stock. Hold the framing square in the same manner with the 6 on the tongue on the mark just made and the 12 on the blade along the edge. Strike a line along the tongue, his mark represents the plumb cut of the heel. Step 2. Lay out the bird’smouth. Measure 1 1/2 inches along the heel plumb line up from the bottom of the rafter. Set the blade of the square along the plumb line with the heel at the mark just made and strike a line along the tongue. This line represents the seat of the bird’smouth. Step 3. Lay out the tail line length. Measure the tail line length from the bird’ smouth heel plumb line. Strike a plumb line at this point in the same manner as the heel plumb line of the common rafter. Step 4. Lay out the plumb cut at the ridgeboard. Measure and mark the point along the line length half the thickness of the ridgeboard. (This is the ridgeboard shortening allowance.) Strike a plumb line at this point. This line represents the plumb cut of the ridgeboard. StepOff Calculations and Layout The stepoff method for rafter layout is old but still practiced. It combines procedures for laying out the rafters with a procedure of stepping off the length of the rafter (see fig. 221). In this example, the roof has an 8inch unit of rise, a total run of 5 feet 9 inches, and a 10inch projection. Figure 221.Stepoff method for calculating common rafter length. First, set gauges at 8 inches on the tongue and 12 inches on the blade. With the tongue in the right hand, the blade in the left hand, and the heel away from the body, place the square on the right end of the rafter stock. Mark the ridge plumb line along the tongue. Put a pencil line at the 12inch point of the blade. Second, with the gauges pressed lightly against the rafter, slide the square to the left. Line the tongue up with the last 12inch mark and make a second 12inch mark along the bottom of the blade. Third, to add the 9inch remainder of the total run, place the tongue on the last 12inch mark. Draw another mark at 9 inches on the blade. This will be the total length of the rafter. Finally, lay out and cut the plumb cut line and the seat cut line. Roof Assembly The major part of gableroof construction is setting the common rafters in place. The most efficient method is to precut all common rafters, then fasten them to the ridgeboard and the wall plates in one continuous operation. The rafter locations should be marked on the top wall plates when the positions of the ceiling joists are laid out. Proper roof layout ensures the rafters and joists tie into each other wherever possible. The ridgeboard like the common rafters, should be precut. The rafter locations are then copied on the ridgeboard from the markings on the wall plates (fig. 222). The ridgeboard should be the length of the building plus the overhang at the gable ends. Figure 222.—Ridgeboard layout. The material used for the ridgeboard is usually wider than the rafter stock. For example, a ridgeboard of 2 by 8inch stock would be used with rafters of 2by 6inch stock. Some buildings are long enough to require more than one piece of ridge material. The breaks between these ridge pieces should occur at the center of a rafter. One pair of rafters should be cut and checked for accuracy before the other rafters are cut. To check the first pair for accuracy, set them in position with a 1 1/2inch piece of wood fitted between them. If the rafters are the correct length, they should fit the building. If, however, the building walls are out of line, adjustments will have to be made on the rafters. After the first pair of rafters is checked for accuracy (and adjusted if necessary), one of the pair can be used as a pattern for marking all the other rafters. Cutting is usually done with a circular or radialarm saw. COLLAR TIE.— Gable or doublepitch roof rafters are often reinforced by horizontal members called collar ties (fig. 223). In a finished attic, the ties may also function as ceiling joists. Figure 223.—Calculation for a collar tie. To find the line length of a collar tie, divide the amount of drop of the tie in inches by the unit of rise of the common rafter. This will equal onehalf the length of the tie in feet. Double the result for the actual length. The formula is as follows: Drop in inches times 2, divided by unit or rise, equals the length in feet. The length of the collar tie depends on whether the drop is measured to the top or bottom edge of the collar tie (fig. 223). The tie must fit the slope of the roof. To obtain this angle, use the framing square. Hold the unit of run and the unit of rise of the common rafter. Mark and cut on the unit of run side (fig. 224). Figure 224.—Laying out end cut on a collar tie. METHODS OF RIDGE BOARD ASSEMBLY.— Several different methods exist for setting up the ridgeboard and attaching the rafters to it. When only a few Builders are present, the most convenient procedure is to set the ridgeboard to its required height (total rise) and hold it in place with temporary vertical props (fig. 225). The rafters can then be nailed to the ridgeboard and the top wall plates. Figure 225.Setting up and bracing a ridgeboard when only a few workers are available. Plywood panels should be laid on top of the ceiling joists where the framing will take place. The panels provide safe and comfortable footing. They also provide a place to put tools and materials. Common rafter overhang can be laid out and cut before the rafters are set in place. However, many Builders prefer to cut the overhang after the rafters are fastened to the ridgeboard and wall plates. A line is snapped from one end of the building to the other, and the tail plumb line is marked with a sliding Tbevel, also called a bevel square. These procedures are shown in figure 226. The rafters are then cut with a circular saw. Figure 226.Snapping a line and marking plumb cuts for a gableend overhang. This method guarantees that the line of the overhang will be perfectly straight, even if the building is not. Over each gable end of the building, another overhang can be framed. The main framing members of the gableend overhang are the fascia, also referred to as "fly" (or "barge") rafters. They are tied to the ridgeboard at the upper end and to the fascia board at the lower end. Fascia boards are often nailed to the tail ends of the common rafters to serve as a finish piece at the edge of the roof. By extending past the gable ends of the house, common rafters also help to support the basic rafters. Figures 227 and 228 show different methods used to frame the gableend overhang. In figure 227, a fascia rafter is nailed to the ridgeboard and to the fascia board. Blocking (not shown in the figures) rests on the end wall and is nailed between the fascia rafter and the rafter next to it. This section of the roof is further strengthened when the roof sheathing is nailed to it. In figure 228, two common rafters arc placed directly over the gable ends of the building. The fascia rafters (fly rafters) are placed between the ridgeboard and the fascia boards. The gable studs should be cut to fit against the rafter above. Figure 227.Gableend overhang with the end wall framed under the overhang. Figure 228.Gableend overhang with the end wall framed directly beneath the rafters. End Framing Gableend studs rest on the top plate and extend to the rafter line in the ends of a gable roof. They may be placed with the edge of the stud even with the outside wall and the top notched to fit the rafter (as shown in fig. 228), or they maybe installed flatwise with a cut on the top of the stud to fit the slope of the rafter. The position of the gableend stud is located by squaring a line across the plate directly below the center of the gable. If a window or vent is to be installed in the gable, measure onehalf of the opening size on each side of the center line and make a mark for the first stud. Starting at this mark layout the stud spacing (that is, 16 or 24 inches on center [OC]) to the outside of the building. Plumb the gableend stud on the first mark and mark it where it contacts the bottom of the rafter, as shown in figure 229, view A. Measure and mark 3 inches above this mark and notch the stud to the depth equal to the thickness of the rafter, as shown in view B. Figure 229.—Calculating common difference of gableend studs. The lengths of the other gable studs depend on the spacing. The common difference in the length of the gable studs may be figured by the following method:
and, 2 x 6 inches (unit of rise) or 12 inches (common difference). The common difference in the length of the gable studs may also be laid out directly with the framing square (fig. 229, view C). Place the framing square on the stud to the cut of the roof (6 and 12 inches for this example). Draw a line along the blade at A. Slide the square along this line in the direction of the arrow at B until the desired spacing between the studs (16 inches for this example) is at the intersection of the line drawn at A and the edge of the stud. Read the dimension on the tongue aligned with the same edge of the stud (indicated by C). This is the common difference (8 inches for this example) between the gable studs. Toenail the studs to the plate with two 8d nails in each side. As the studs are nailed in place, care must be taken not to force a crown into the top of the rafter. HIP Most hip roofs are equal pitch. This means the angle of slope on the roof end or ends is the same as the angle of slope on the sides. Unequalpitch hip roofs do exist, but they are quite rare. They also require special layout methods. The unit length rafter table on the framing square applies only to equalpitch hip roofs. The next paragraphs discuss an equalpitch hip roof. The length of a hip rafter, like the length of a common rafter, is calculated on the basis of bridge measure multiplied by the total run (half span). Any of the methods previously described for a common rafter may be used, although some of the dimensions for a hip rafter are different. Figure 230 shows part of a roof framing diagram for an equalpitch hip roof. A roof framing diagram may be included among the working drawings; if not, you should lay one out for yourself. Determine what scale will be used, and lay out all framing members to scale. Lay the building lines out first. You can find the span and the length of the building on the working drawings. Then, draw a horizontal line along the center of the span. Figure 230.—Equalpitch hip roof framing diagram. In an equalpitch hip roof framing diagram, the lines indicating the hip rafters (AF, AG, BI, and BK in figure 230) form 45° angles with the building lines. Draw these lines at 45°, as shown. The points where they meet the center line are the theoretical ends of the ridge piece. The ridgeend common rafters AC, AD, AE, BH, BJ, and BL join the ridge at the same points. A line indicating a rafter in the roof framing diagram is equal in length to the total run of the rafter it represents. You can see from the diagram that the total run of a hip rafter (represented by lines AFAGBIBK) is the hypotenuse of a right triangle with the altitude and base equal to the total run of a common rafter. You know the total run of a common rafter: It is onehalf the span, or onehalf the width of the building. Knowing this, you can find the total run of a hip rafter by applying the Pythagorean theorem. Let’s suppose, for example, that the span of the building is 30 feet. Then, onehalf the span, which is the same as the total run of a common rafter, is 15 feet. Applying the Pythagorean theorem, the total run of a hip rafter is:
What is the total rise? Since a hip rafter joins the ridge at the same height as a common rafter, the total rise for a hip rafter is the same as the total rise for a common rafter. You know how to figure the total rise of a common rafter. Assume that this roof has a unit of run of 12 and a unit of rise of 8. Since the total run of a common rafter in the roof is 15 feet, the total rise of common rafter is the value of x in the proportional equation 12:8::15:x, or 10 feet. Knowing the total run of the hip rafter (21.21 feet) and the total rise (10 feet), you can figure the line length by applying the Pythagorean theorem. The line length is:
To find the length of a hip rafter on the basis of bridge measure, you must first determine the bridge measure. As with a common rafter, the bridge measure of a hip rafter is the length of the hypotenuse of a triangle with its altitude and base equal to the unit of run and unit of rise of the rafter. The unit of rise of a hip rafter is always the same as that of a common rafter, but the unit of run of a hip rafter is a fixed unit of measure, always 16.97. The unit of run of a hip rafter in an equalpitch roof is the hypotenuse of a right triangle with its altitude and base equal to the unit of run of a common rafter, 12. Therefore, the unit of run of a hip rafter is:
If the unit of run of a hip rafter is 16.97 and the unit of rise (in this particular case) is 8, the bridge measure of the hip rafter must be:
This means that for every unit of run (16.97) the rafter has a line length of 18.76 inches. Since the total run of the rafter is 21.21 feet, the length of the rafter must be the value of x in the proportional equation 16.97:18. 76::21.21:x, or 23.45 feet. Like the unit length of a common rafter, the bridge measure of a hip rafter can be obtained from the unit length rafter table on the framing square. If you turn back to figure 216, you will see that the second line in the table is headed LENGTH HIP OR VALLEY PER FT RUN. This means "per foot run of a common rafter in the same roof." Actually, the unit length given in the tables is the unit length for every 16.97 units of run of the hip rafter itself. If you go across to the unit length given under 8, you will find the same figure, 18.76 units, that you calculated above. An easy way to calculate the length of an equalpitch hip roof is to multiply the bridge measure by the number of feet in the total run of a common rafter, which is the same as the number of feet in onehalf of the building span. Onehalf of the building span, in this case, is 15 feet. The length of the hip rafter is therefore 18.76 x 15, or 281.40 inches—23.45 feet once converted. Step off the length of an equalpitch hip roof just as you do the length of a common rafter, except that you set the square to a unit of run of 16.97 inches instead of to a unit of run of 12 inches. Since 16.97 inches is the same as 16 and 15.52 sixteenths of an inch, setting the square to a unit of run of 17 inches is close enough for most practical purposes. Bear in mind that for any plumb cut line on an equalpitch hip roof rafter, you set the square to the unit of rise of a common rafter and to a unit of run of 17. Sstep off the same number of times as there are feet in the total run of a common rafter in the same roof; only the size of each step is different. For every 12inch step in a common rafter, a hip rafter has a 17inch step. For the roof on which you are working, the total run of common rafter is exactly 15 feet; this means that you would step off the hiprafter cut (17 inches and 8 inches) exactly 15 times. Suppose, however, that there was an odd unit in the common rafter total run. Assume, for example, that the total run of a common rafter is 15 feet 10 1/2 inches. How would you make the odd fraction of a step on the hip rafter? Remember that the unit of run of a hip rafter is the hypotenuse of a right triangle with the other side each equal to the unit of run of a common rafter. In this case, the run of the odd unit on the hip rafter must be the hypotenuse of a right triangle with the altitude and base equal to the odd unit of run of the common rafter (in this case, 10 1/2 inches). You can figure this using the Pythagorean theorem
or you can set the square on a true edge to 10 1/2 inches on the blade and measure the distance between the marks. It comes to 14.84 inches. Rounded off to the nearest 1/16 inch, this equals 14 13/16 inches. To layoff the odd unit, set the tongue of the framing square to the plumb line for the last full step made and measure off 14 13/16 inches along the blade. Place the tongue of the square at the mark, set the square to the hip rafter plumb cut of 8 inches on the tongue and 17 inches on the blade, and draw the line length cut. Rafter Shortening Allowance As in the case with a common rafter, the line length of a hip rafter does not take into account the thickness of the ridge piece. The size of the ridgeend shortening allowance for a hip rafter depends upon the way the ridge end of the hip rafter is joined to the other structural members. As shown in figure 231, the ridge end of the hip rafter can be framed against the ridgeboard (view A) or against the ridgeend common rafters (view B). To calculate the actual length, deduct onehalf the 45° thickness of the ridge piece that fits between the rafters from the theoretical length. Figure 231.Shortening a hip rafter. When no common rafters are placed at the ends of the ridgeboard the hip rafters are placed directly against the ridgeboard. They must be shortened onehalf the length of the 45° line (that is, onehalf the thickness of the ridgeboard When common rafters are placed at the ends of the ridgeboard (view B), the hip rafter will fit between the common rafters. The hip rafter must be shortened onehalf the length of the 45° line (that is, onehalf the thickness of the common rafter). If the hip rafter is framed against the ridge piece, the shortening allowance is onehalf of the 45° thickness of the ridge piece (fig. 231, view C). The 45° thickness of stock is the length of a line laid at 45° across the thickness dimension of the stock. If the hip rafter is framed against the common rafter, the shortening allowance is onehalf of the 45° thickness of a common rafter. To lay off the shortening allowance, first set the tongue of the framing square to the line length ridge cut line. Then, measure off the shortening allowance along the blade, set the square at the mark to the cut of the rafter (8 inches and 17 inches), draw the actual ridge plumb cut line. (To find the 45° thickness of a piece of lumber, draw a 450 line across the edge, and measure the length of the line and divide by 2.) Rafter Projection A hip or valley rafter overhang, like a common rafter overhang, is figured as a separate rafter. The projection, however, is not the same as the projection of a common rafter overhang in the same roof. The projection of the hip or valley rafter overhang is the hypotenuse of a right triangle whose shorter sides are each equal to the run of a common rafter overhang (fig. 232). If the run of the common rafter overhang is Figure 232.—Run of hip rafter projection. 18 inches for a roof with an 8inch unit of rise, the length of the hip or valley rafter tail is figured as follows:
The overhang may also be stepped off as described earlier for a common rafter. When stepping off the length of the overhang, set the 17inch mark on the blade of the square even with the edge of the rafter. Set the unit of rise, whatever it might be, on the tongue even with the same rafter edge. Rafter Side Cuts Since a common rafter runs at 90° to the ridge, the ridge end of a common rafter is cut square, or at 90° to the lengthwise line of the rafter. A hip rafter, however, joins the ridge, or the ridge ends of the common rafter, at other than a 90° angle, and the ridge end of a hip rafter must therefore be cut to a corresponding angle, called a side cut. The angle of the side cut is more acute for a high rise than it is for a low one. The angle of the side cut is laid out as shown in figure 233. Place the tongue of the framing square along the ridge cut line, as shown, and measure off onehalf the thickness of the hip rafter along the blade. Shift the tongue to the mark, set the square to the cut of the rafter (17 inches and 8 inches), and draw the plumb line marked "A" in the figure. Then, turn the rafter edgeup, draw an edge centerline, and draw in the angle of the side cut, as indicated in the lower view of figure 233. For a hip rafter to be framed against the ridge, there will be only a single side cut, as indicated by the dotted line in the figure. For one to be framed against the ridge ends of the common rafters, there will be a double side cut, as shown in the figure. The tail of the rafter must have a double side cut at the same angle, but in the reverse direction. Figure 233.—Laying out hip rafter side cut. The angle of the side cut on a hip rafter may also be laid out by referring to the unit length rafter table on the framing square. (Look ahead to figure 241.) You will see that the bottom line in the table is headed SIDE CUT HIP OR VALLEY USE. If you follow this line over to the column headed by the figure 8 (for a unit of rise of 8), you will find the figure 10 7/8. If you place the framing square faceup on the rafter edge with the tongue on the ridgeend cut line, and set the square to a cut of 10 7/8 inches on the blade and 12 inches on the tongue, you can draw the correct sidecut angle along the tongue. Bird’sMouth Laying out the bird’ smouth for a hip rafter is much the same as for a common rafter. However, there are a couple of things to remember. When the plumb (heel) cut and level (seat) cut lines are laid out for a bird’smouth on a hip rafter, set the body of the square at 17 inches and the tongue to the unit of rise (for example, 8 inchesdepending on the roof pitch) (fig. 234, view A). When laying out the depth of the heel for the bird’smouth, measure along the heel plumb line down from the top edge of the rafter a distance equal to the same dimension on the common rafter. This must be done so that the hip rafter, which is usually wider than a common rafter, will be level with the common rafters. Figure 234.Backing or dropping a hip rafter: If the bird’smouth on a hip rafter has the same depth as the bird’smouth on a common rafter, the edge of the hip rafter will extend above the upper ends of the jack rafters. You can correct this by either backing or dropping the hip rafter. Backing means to bevel the top edges of the hip rafter (see fig. 235). The amount of backing is taken at a right angle to the roof surface on the top edge of the hip rafters. Dropping means to deepen the bird’smouth so as to bring the top edge of the hip rafter down to the upper ends of the jacks. The amount of drop is taken on the heel plumb line (fig. 234, view D). Figure 235.Backing or dropping a hip rafter. The backing or drop required is calculated, as shown in figure 234, view B. Set the framing square to the cut of the rafter (8 inches and 17 inches) on the upper edge, and measure off onehalf the thickness of the rafter from the edge along the blade. A line drawn through this mark and parallel to the edge (view C) indicates the bevel angle if the rafter is to be backed. The perpendicular distance between the line and the edge of the rafter is the amount of the drop. This represents the amount the depth of the hip rafter bird’smouth should exceed the depth of the common rafter bird’smouth (view D). INTERSECTING An intersecting roof, also known as a combination roof, consists of two or more sections sloping in different directions. A valley is formed where the different sections come together. The two sections of an intersecting roof mayor may not be the same width. If they are the same width, the roof is said to have equal spans. If they are not the same width, the roof is said to have unequal spans. Spans In a roof with equal spans, the height (total rise) is the same for both ridges (fig. 236). That is, both sections are the same width, and the ridgeboards are the same height. A pair of valley rafters is placed where the slopes of the roof meet to form a valley between the two sections. These rafters go from the inside corners formed by the two sections of the building to the corners formed by the intersecting ridges. Valley jack rafters run from the valley rafters to both ridges. Hipvalley cripple jack rafters are placed between the valley and hip rafters. Figure 236.Intersecting roof with equal spans. An intersecting roof with unequal spans requires a supporting valley rafter to run from the inside corner formed by the two sections of the building to the main ridge (fig. 237). A shortened valley rafter runs from the other inside comer of the building to the supporting valley rafter. Like an intersecting roof with equal spans, one with unequal spans also requires valley jack rafters and hipvalley cripple jack rafters. In addition, a valley cripple jack rafter is placed between the supporting and shortened valley rafters. Note that the ridgeboard is lower on the section with the shorter span. Figure 237.—Intersecting roof with unequal spans. Valley Rafters Valley rafters run at a 45° angle to the outside walls of the building. This places them parallel 10 the hip rafters. Consequently, they are the same length as the hip rafters. A valley rafter follows the line of intersection between a mainroof surface and a gableroof addition or a gableroof dormer surface. Most roofs having valley rafters are equalpitch roofs, in which the pitch of the addition or dormer roof is the same as the pitch of the main roof. There are unequalpitch valleyrafter roofs, but they are quite rare and require special framing methods. In the discussion of valley rafter layout, it is assumed that the roof is equal pitch. Also, the unit of run and unit of rise of an addition or dormer common rafter are assumed to be the same as the unit of run and rise of a mainroof common rafter. In an equalpitch roof, the valley rafters always run at 45° to the building lines and the ridge pieces. Figure 238 shows an equalspan framing situation, in which the span of the addition is the same as the span of the main roof. Since the pitch of the addition roof is the same as the pitch of the main roof, equal spans bring the ridge pieces to equal heights. Figure 238.Equalspan intersecting roof. Looking at the roof framing diagram in the figure, you can see the total run of a valley rafter (indicated by AB and AC in the diagram) is the hypotenuse of a right triangle with the altitude and base equal to the total run of a common rafter in the main roof. The unit of run of a valley rafter is therefore 16.97, the same as the unit of run for a hip rafter. It follows that figuring the length of an equalspan valley rafter is the same as figuring the length of an equalpitch hip roof hip rafter. A valley rafter, however, does not require backing or dropping. The projection, if any, is figured just as it is for a hip rafter. Side cuts are laid out as they are for a intersecting valley rafter.hip rafter. The valleyrafter tail has a double side cut (like the hiprafter tail) but in the reverse direction. This is because the tail cut on a valley rafter must form an inside, rather than an outside, corner. As indicated in figure 239, the ridgeend shortening allowance in this framing situation amounts to onehalf of the 45° thickness of the ridge. Figure 239.Ridgeend shortening allowance for equalspan Figure 240 shows a framing situation in which the span of the addition is shorter than the span of the main roof. Since the pitch of the addition roof is the same as the pitch of the main roof, the shorter span of the addition brings the addition ridge down to a lower level than that of the mainroof ridge. Figure 240.Equal pitch but unequal span framing. There are two ways of framing an intersection of this type. In the method shown in figure 240, a fulllength valley rafter (AD in the figure) is framed between the top plate and the mainroof ridgeboard. A shorter valley rafter (BC in the figure) is then framed to the longer one. If you study the framing diagram, you can see that the total run of the longer valley rafter is the hypotenuse of a right triangle with the altitude and base equal to the total run of a common rafter in the main roof. The total run of the shorter valley rafter, on the other hand, is the hypotenuse of a right triangle with the altitude and base equal to the total run of a common rafter in the addition. The total run of a common rafter in the main roof is equal to onehalf the span of the main roof. The total run of a common rafter in the addition is equal to onehalf the span of the addition. Knowing the total run of a valley rafter, or of any rafter for that matter, you can always find the line length by applying the bridge measure times the total run. Suppose, for example, that the span of the addition in figure 240 is 30 feet and that the unit of rise of a common rafter in the addition is 9. The total run of the shorter valley rafter is: Referring to the unit length rafter table in figure 241, you can see the bridge measure for a valley rafter in a roof with a common rafter unit of rise of 9 is 19.21. Since the unit of run of a valley rafter is 16.97, and the total run of this rafter is 21.21 feet, the line length must be the value of x in the proportional equation 16.97:19.21::21.21:x, or 24.01 feet. Figure 241.Rafter table method. An easier way to find the length of a valley rafter is to multiply the bridge measure by the number of feet in onehalf the span of the roof. The length of the longer valley rafter in figure 240, for example, would be 19.21 times onehalf the span of the main roof. The length of the shorter valley rafter is 19.21 times onehalf the span of the addition. Since onehalf the span of the addition is 15 feet, the length of the shorter valley rafter is 15 x 9.21 = 288.15 inches, or approximately 24.01 feet. Figure 242 shows the long and short valley rafter shortening allowances. Note that the long valley rafter has a single side cut for framing to the mainroof ridge piece, whereas the short valley rafter is cut square for framing to the long valley rafter. Figure 242.Long and short valley rafter shortening allowance. Figure 243 shows another method of framing an equalpitch unequalspan addition. In this method, the inboard end of the addition ridge is nailed to a piece that hangs from the mainroof ridge. As shown in the framing diagram, this method calls for two short valley rafters (AB and AC), each of which extends from the top plate to the addition ridge. Figure 243.Another method of framing equalpitch unequalspan intersection. As indicated in figure 244, the shortening allowance of each of the short valley rafters is onehalf the 45° thickness of the addition ridge. Each rafter is framed to the addition ridge with a single side cut. Figure 244.Shortening allowance of valley rafters suspended ridge method of intersecting roof framing. Figure 245 shows a method of framing a gable dormer without sidewalls. The dormer ridge is framed to a header set between a pair of doubled mainroof common rafters. The valley rafters (AB and AC) are framed between this header and a lower header. As indicated in the framing diagram, the total run of a valley rafter is the hypotenuse of a right triangle with the shorter sides equal to the total run of a common rafter in the dormer. Figure 246 shows the arrangement and names of framing members in this type of dormer framing.
The upper edges of the header must be beveled to the cut of the main roof. Figure 247 shows that in this method of framing, the shortening allowance for the upper end of a valley rafter is onehalf the 45° thickness of the inside member in the upper doubled header. There is also a shortening allowance for the lower end, consisting of onehalf the 45° thickness of the inside member of the doubled common rafter. The figure also shows that each valley rafter has a double side cut at the upper and lower ends. Figure 247.—Valley rafter shortening allowance for dormer without sidewalls. Figure 248 shows a method of framing a gable dormer with sidewalls. As indicated in the framing diagram, the total run of a valley rafter is again the hypotenuse of a right triangle with the shorter sides each equal to the run of a common rafter in the dormer. You figure the lengths of the dormer corner posts and side studs just as you do the lengths of gableend studs, and you lay off the lower end cutoff angle by setting the square to the cut of the main roof. Figure 249 shows the valley rafter shortening allowance for this method of framing a dormer with sidewalls. Figure 248.—Method of framing gable dormer with sidewalls.
Figure 249.Valley rafter shortening allowance for dormers with sidewalls. Jack Rafters A jack rafter is a part of a common rafter, shortened for framing a hip rafter, a valley rafter, or both. This means that, in an equalpitch framing situation, the unit of rise of a jack rafter is always the same as the unit of rise of a common rafter. Figure 250 shows various types of jack rafters. Figure 250.Types of jack rafters. A hip jack rafter extends from the top plate to a hip rafter. A vane y jack rafter extends from a valley rafter to a ridge. (Both are shown in fig. 251.) A cripple jack rafter does not contact either a top plate or a ridge. A valley cripple jack extends between two valley rafters in the long and short valley rafter method of framing. A hipvalley cripple jack extends from a hip rafter to a valley rafter. Figure 251.—Valley cripple Jack and hipvalley cripple jack. LENGTHS.— Figure 252 shows a roof framing diagram for a series of hip jack rafters. The jacks are always on the same OC spacing as the common rafters. Figure 252.—Hip jack framing diagram. Now, suppose the spacing, in this instance, is 16 inches OC. You can see that the total run of the shortest jack is the hypotenuse of a right triangle with the shorter sides each 16 inches long. The total run of the shortest jack is therefore: Suppose that a common rafter in this roof has a unit of rise of 8. The jacks have the same unit of rise as a common rafter. The unit length of a jack in this roof is: This means that a jack is 14.42 units long for every 12 units of run. The length of the shortest hip jack in this roof is therefore the value of x in the proportional equation 12:14.42::16:x, or 19.23 inches. This is always the length of the shortest hip jack when the jacks are spaced 16 inches OC and the common rafter in the roof has a unit of rise of 8. It is also the common difference of jacks, meaning that the next hip jack will be 2 times 19.23 inches. The common difference for hip jacks spaced 16 inches OC, or 24 inches OC, is given in the unit length rafter table on the framing square for unit of rise ranging from 2 to 18, inclusive. Turn back to figure 241, which shows a segment of the unit length rafter table. Note the third line in the table, which reads DIFF IN LENGTH OF JACKS 16 INCHES CENTERS. If you follow this line over to the figure under 8 (for a unit of rise of 8), you’ll find the same unit length (19.23) that you worked out above. The best way to determine the length of a valley jack or a cripple jack is to apply the bridge measure to the total run. The bridge measure of any jack is the same as the bridge measure of a common rafter having the same unit of rise as the jack. Suppose the jack has a unit of rise of 8. In figure 241, look along the line on the unit length rafter tables headed LENGTH COMMON RAFTER PER FOOT RUN for the figure in the column under 8; you’ll find a unit length of 14.42. You should know by this time how to apply this to the total run of a jack to get the line length. The best way to figure the total runs of valley jacks and cripple jacks is to lay out a framing diagram and study it to determine what these runs must be. Figure 253 shows part of a framing diagram for a main hip roof with a long and short valley rafter gable addition. By studying the diagram, you can figure the total runs of the valley jacks and cripple jacks as follows: Figure 253.—Jack rafter framing diagram.
SHORTENING ALLOWANCES.— A hip jack has a shortening allowance at the upper end, consisting of onehalf the 45° thickness of the hip rafter. A valley jack rafter has a shortening allowance at the upper end, consisting of onehalf the 45° thickness of the ridge, and another at the lower end, consisting of onehalf the 45° thickness of the valley rafter. A hipvalley cripple has a shortening allowance at the upper end, consisting of onehalf the 45° thickness of the hip rafter, and another at the lower end, consisting of onehalf the 45° thickness of the valley rafter. A valley cripple has a shortening allowance at the upper end, consisting of onehalf the 45° thickness of the long valley rafter, and another at the lower end, consisting of onehalf the 45° thickness of the short valley rafter. SIDE CUTS.— The side cut on a jack rafter can be laid out using the same method as for laying out the side cut on a hip rafter. Another method is to use the fifth line of the unit length rafter table, which is headed SIDE CUT OF JACKS USE (fig. 241). If you follow that line over to the figure under 8 (for a unit of rise of 8), you will see that the figure given is 10. To lay out the side cut on a jack set the square faceup on the edge of the rafter to 12 inches on the tongue and 10 inches on the blade, and draw the sidecut line along the tongue. BIRD’SMOUTH AND PROJECTION.— A jack rafter is a shortened common rafter; consequently, the bird’smouth and projection on a jack rafter are laid out just as they are on a common rafter. Ridge Layout Laying out the ridge for a gable roof presents no particular problem since the line length of the ridge is equal to the length of the building. The actual length includes any overhang. For a hip main roof, however, the ridge layout requires a certain amount of calculation. As previously mentioned, in an equalpitch hip roof, the line length of the ridge amounts to the length of the building minus the span. The actual length depends upon the way the hip rafters are framed to the ridge. As indicated in figure 254, the line length ends of the ridge are at the points where the ridge centerline and the hip rafter center line cross. In the figure, the hip rafter is framed against the ridge. In this method of framing, the actual length of the ridge exceeds the line length, at each end, by onehalf the thickness of the ridge, plus onehalf the 45° thickness of the hip rafter. In the figure, the hip rafter is also framed between the common rafters. In this method of framing, the actual length of the ridge exceeds the line length at each end by onehalf the thickness of a common rafter. Figure 254.Line and actual lengths of hip roof ridgeboard. Figure 255, view A, shows that the length of the ridge for an equalspan addition is equal to the length of the addition top plate, plus onehalf the span of the building, minus the shortening allowance at the mainroof ridge. The shortening allowance amounts to onehalf the thickness of the mainroof ridge. Figure 255.—Lengths of addition ridge. View B shows that the length of the ridge for an unequalspan addition varies with the method of framing the ridge. If the addition ridge is suspended from the mainroof ridge, the length is equal to the length of the addition top plate, plus onehalf the span of the building. If the addition ridge is framed by the long and short valley rafter method, the length is equal to the length of the addition top plate, plus onehalf the span of the addition, minus a shortening allowance onehalf the 45° thickness of the long valley rafter. If the addition ridge is framed to a double header set between a couple of double mainroof common rafters, the length of the ridge is equal to the length of the addition sidewall rafter plate, plus onehalf the span of the addition, minus a shortening allowance onehalf the thickness of the inside member of the double header. Figure 256, view A, shows that the length of the ridge on a dormer without sidewalls is equal to onehalf the span of the dormer, less a shortening allowance onehalf the thickness of the inside member of the upper double header. View B shows that the length of the ridge on a dormer with sidewalls is the length of the dormer rafter plate, plus onehalf the span of the dormer, minus a shortening allowance onehalf the thickness of the inside member of the upper double header. Figure 256.Lengths of dormer ridge. SHED A shed roof is essentially onehalf of a gable roof. Like the fulllength rafters in a gable roof, the fulllength rafters in a shed roof are common rafters. However, the total run of a shed roof common rafter is equal to the span of the building minus the width of the top plate on the higher rafterend wall (fig. 257). Also, the run of the overhang on the higher wall is measured from the inner edge of the top plate. With these exceptions, shed roof common rafters are laid out like gable roof common rafters. A shed roof common rafter has two bird’smouths, but they are laid out just like the bird’smouth on a gable roof common rafter. Figure 257.Shed roof framing. For a shed roof, the height of the higher rafterend wall must exceed the height of the lower by an amount equal to the total rise of a common rafter. Figure 258 shows a method of framing a shed dormer. This type of dormer can be installed on almost any type of roof. There are three layout problems to be solved here: determining the total run of a dormer rafter; determining the angle of cut on the inboard ends of the dormer rafters; and determining the lengths of the dormer sidewall studs. Figure 258.Method of framing a shed dormer. To determine the total run of a dormer rafter, divide the height of the dormer end wall, in inches, by the difference between the unit of rise of the dormer roof and the unit of rise of the main roof. Take the dormer shown in figure 259, for example. The height of the dormer end wall is 9 feet, or 108 inches. The unit of rise of the main roof is 8; the unit of rise of the dormer roof is 2 1/2; the difference is 5 1/2. The total run of a dormer rafter is therefore 108 divided by 5 1/2, or 19.63 feet. Knowing the total run and the unit of rise, you can figure the length of a dormer rafter by any of the methods already described. As indicated in figure 259, the inboard ends of the dormer rafters must be cut to fit the slope of the main roof. To get the angle of this cut, set the square on the rafter to the cut of the main roof, as shown in the bottom view of figure 259. Measure off the unit of rise of the dormer roof from the heel of the square along the tongue as indicated and make a mark at this point. Draw the cutoff line through this mark from the 12inch mark. Figure 259.Shed dormer framing calculation. You figure the lengths of the sidewall studs on a shed dormer as follows: In the roof shown in figure 259, a dormer rafter raises 2 1/2 units for every 12 units of run. A mainroof common rafter rises 8 units for every 12 units of run. If the studs were spaced 12 inches OC, the length of the shortest stud (which is also the common difference of studs) would be the difference between 8 and 2 1/2 inches, or 5 1/2 inches. If the stud spacing is 16 inches, the length of the shortest stud is the value of x in the proportional equation 12:5 1/2::16:x, or 7 5/16 inches. The shortest stud, then, will be 7 5/16 inches long. To get the lower end cutoff angle for studs, set the square on the stud to the cut of the main roof. To get the upper end cutoff angle, set the square to the cut of the dormer roof. INSTALLATION Rafter locations are laid out on wall plates and ridgeboards with matching lines and marked with X’s, as used to lay out stud and joist locations. For a gable roof, the rafter locations are laid out on the rafter plates first. The locations are then transferred to the ridge by matching the ridge against a rafter plate. Rafter Locations The rafter plate locations of the ridgeend common rafters in an equalpitch hip roof measure onehalf of the span (or the run of a mainroof common rafter) away from the building comers. These locations, plus the rafter plate locations of the rafters lying between the ridgeend common rafters, can be transferred to the ridge by matching the ridgeboads against the rafter plates. The locations of additional ridge and valley rafters can be determined as indicated in figure 260. In an equalspan situation (views A and B), the valley rafter locations on the mainroof ridge lie alongside the addition ridge location. In view A, the distance between the end of the mainroof ridge and the addition ridge location is equal to A plus distance B, distance B being onehalf the span of the addition. In view B, the distance between the line length end of the mainroof ridge and the addition ridge location is the same as distance A. In both cases, the line length of the addition ridge is equal to onehalf the span of the addition, plus the length of the addition sidewall rafter plate. Figure 260, view C, shows an unequalspan situation. If framing is by the long and short valley rafter method, the distance from the end of the mainroof ridge to the upper end of the longer valley rafter is equal to distance A plus distance B, distance B being onehalf the span of the main roof. To determine the location of the inboard valley rafter, first calculate the unit length of the longer valley rafter, or obtain it from the unit length rafter tables. Let’s suppose that the common rafter unit of rise is 8. In that case, the unit length of a valley rafter is 18.76. Figure 260.Intersection ridge and valley rafter location layout. The total run of the longer valley rafter between the shorter rafter tiein and the rafter plate is the hypotenuse of a right triangle with the altitude and base equal to onehalf of the span of the addition. Suppose the addition is 20 feet wide. Then, the total run is: You know that the valley rafter is 18.76 units long for every 16.97 units of run. The length of rafter for 14.14 feet of run must therefore be the value of in the proportional equation 16.97:18.76::14.14:x, or 15.63 feet. The location mark for the inboard end of the shorter valley rafter on the longer valley rafter, then, will be 15.63 feet, or 15 feet 7 9/16 inches, from the heel plumb cut line on the longer valley rafter. The length of the additional ridge will be equal to onehalf the span of the addition, plus the length of the additional sidewall top plate, minus a shortening allowance onehalf the 45° thickness of the longer valley rafter. If framing is by the suspended ridge method, the distance between the suspension point on the mainroof and the end of the mainroof ridge is equal to distance A plus distance C. Distance C is onehalf the span of the addition. The distance between the point where the inboard ends of the valley rafters (both short in this method of framing) tie into the addition ridge and the outboard end of the ridge is equal to onehalf the span of the addition, plus the length of the additional ridge (which is equal to onehalf of the span of the main roof), plus the length of the addition sidewall rafter plate. Roof Frame Erection Roof framing should be done from a scaffold with planking not less than 4 feet below the level of the mainroof ridge. The usual type of roof scaffold consists of diagonally braced twolegged horses, spaced about 10 feet apart and extending the full length of the ridge. If the building has an addition, as much as possible of the main roof is framed before the addition framing is started. Cripples and jack rafters are usually left out until after the headers, hip rafters, valley rafters, and ridges to which they will be framed have been installed. For a gable roof, the two pairs of gableend rafters and the ridge are usually erected first. Two crewmembers, one at each end of the scaffold, hold the ridge in position. Another crewmember sets the gableend rafters in place and toenails them at the rafter plate with 8d nails, one on each side of a rafter. Before we proceed any further, see table 21 as to the type and size nails used in roof framing erection. Each crewmember on the scaffold then endnails the ridge to the end of the rafter. They then toenail the other rafter to the ridge and to the first rafter with two 10d nails, one on each side of the rafter.
Table 21.—Recommended Schedule for Nailing the Framing and Sheathing of a WoodFrame Structure Temporary braces, like those for a wall, should be set up at the ridge ends to hold the rafter approximately plumb, after which the rafters between the end rafters should be erected. The braces should then be released, and the pair of rafters at one end should be plumbed with a plumb line, fastened to a stick extended from the end of the ridge. The braces should then be reset, and they should be left in place until enough sheathing has been installed to hold the rafters plumb. Collar ties, if any, are nailed to common rafters with 8d nails, three to each end of a tie. Ceilingjoist ends are nailed to adjacent rafters with 10d nails. On a hip roof, the ridgeend common rafters and ridges are erected first, in about the same manner as for a gable roof. The intermediate common rafters are then filled in. After that, the ridgeend common rafters extending from the ridge ends to the midpoints on the end walls are erected. The hip rafters and hip jacks are installed next. The common rafters in a hip roof do not require plumbing. When correctly cut and installed, hip rafters will bring the common rafters to plumb. Hip rafters are toe nailed to plate comers with 10d nails. Hip jacks are toe nailed to hip rafters with 10d nails. For an addition or dormer, the valley rafters are usually erected first. Valley rafters are toe nailed with 10d nails. Ridges and ridgeend common rafters are erected next, other addition common rafters next, and valley and cripple jacks last. A valley jack should be held in position for nailing, as shown in figure 261. When properly nailed, the end of a straightedge laid along the top edge of the jack should contact the centerline of the valley rafter, as shown. Figure 261.Correct position for nailing a valley jack rafter.


David L. Heiserman, Editor  Copyright © SweetHaven
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Revised: May 18, 2013