Breaking the process of cutting rafters into the four basic characteristics described in this chapter helps to organize the task, but it is still a complicated process. Probably the best way to learn is to work through the steps in figuring individual rafters. The following illustration is an example of a roof that has a number of different rafters and a ridge board identified. Nine additional examples explain how to find the lengths for these rafters and ridge board based on the illustration.
Finding Common Rafter Length — Example 1 on Roof Example Illustration
The roof span at this area is 28′-0", making the run equal to У2 the span of 14′-0" minus half the thickness of the ridge board (3/4"). That makes the adjusted run 13′-111/4". Multiplying that times the diagonal percent for a 6/12 pitch roof (which is 1.118) gives a run diagonal length of 15′-7". If you add that length to the overhang diagonal of 2′-11/s", the rafter length is 17′-81/s". The overhang diagonal
is found by subtracting the fascia (IV2") from the 2’0" overhang, which gives (22У2"), and multiplying by the diagonal percent 1.118.
Finding a Jack Rafter Length — Example 2 on Roof Example Illustration
Most hip rafters are on 90° corners, with the hip runs in the middle of the corner. Because the two sides of a triangle made by a 90° angle and two 45° angles are the same, the run of the jack rafter can be easily found.
The distance of your layout to the center of your rafter is the same distance as your run to the center of your hip. Just subtract one half the thickness of the hip at a 45° angle (11/16") from the run, and multiply that figure by your diagonal percentage. Then add on your overhang diagonal length. This will give you your rafter length. In this example, the rafter is on layout at 8′-0", so we subtract 11/16" (half the thickness of the U/2" hip at 45°), giving 7′-1015/16", which is multiplied by the diagonal percent of 1.118. The result is 8′-101/s". Add this to the overhang diagonal of 2′-11/s" (same as common rafter overhang), and we get a jack rafter length of 10-111/4". Note that because the connection angle is 45° , the measurement should be taken to the center of your cheek cut.
Finding a Ridge End Common Rafter Length—Example 3 on Roof Example Illustration
As long as you use the top cut illustration in “Connection # 1," then this rafter will be cut the same length as the king common rafter adjacent to it.
Finding a Hip Length—Example 4 on Roof Example Illustration
Finding the hip length requires an additional step and uses the hip-val diagonal percent. First find the hip run. It is the diagonal created by a triangle in which the other two sides are the run of the ridge end common and the line from the hip corner to the ridge end common. In this case, the span is 40′, so the run is 20′, and the distance from the corner is also 20′. Using the calculator, enter 20′ for the run, 20′ for the rise, and press the diagonal button.
The result is 28′- 37/16". This distance is the run of your hip.
Subtract half the distance of the ridge at a 45° angle, which for a 11/2" ridge is 11/16", leaving an adjusted hip run of 28′- 23/8". Then find the hip overhang length using a similar procedure. The sides are 2′, which leads to a 2′-915/16" diagonal. Then subtract 11/2" at a 45° angle for the fascia (which is 2V8"), so the hip overhang run is 2′-713/16". Add this figure to the 28′- 23/8" hip run, and you get a hip rafter run of 30′-103/16". Multiplying that number by the hip — val diagonal percent of 1.061 results in a hip rafter length of 32′-83/4". Remember, these lengths are to the middle of the rafter, and each end has two 45° connection angle cuts at a 6/12 hip-val pitch angle.
Finding a Valley Rafter Length— Example 5 on Roof Example Illustration
This valley will be the same length as the hip rafter for the 28′-0" span section, except for the end cuts. On the bottom, the 45° cuts will be concave ( < ) instead of convex ( > ) like the hip. At the top, there will be a full-width 45° cut. The top-end adjustment will require you to subtract one half the thickness of the ridge at 45°, which is 11/16".
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Connection #2 Hip Rafter with Square End Cut |
Finding the valley rafter length is similar to finding the hip length, and requires the following steps:
• Span = 28-0"
• Run = 14′-0"
• Top adjustment = subtract У2 ridge board at 45°
= 11/i6".
• Hip run = 19′-99/i6" = On the calculator enter 14′-0".
Charts provide bird’s mouth plumb line lengths.
— Then press the run button, enter 14′-0".
— Then press the rise button and then the diagonal button.
Overhang hip run = 2′-713/16"
— On calculator enter 1′-10 1/2" run then 1′-10 1/2" rise, then press diagonal.
Add the hip run and the overhang hip run =
19′-99/іб" + 2′-713/іб" = 22′-53/8".
Subtract for the top adjustment %" on a 45° = 11/16" (See “Connection #2“ illustration on previous page.)
Adjust the hip rafter run = 22′-53/s" — 11/16" = 22′-45/16".
Hip rafter length =
22′-45/16" x 1.061 (hip-val diagonal percent) = 23′-811/16".
The top will be a 45° saw cut for the connection angle at a 6/12 hip-val cut for the pitch angle.
The bottom will be concave ( < ), two 45° saw cuts at a 6/12 hip-val cut.
Finding a Valley-to-Ridge Jack Rafter-Example 6 on Roof Example Illustration
There are a couple of ways to find the length of this rafter. The ridge location is easy to establish as half the span of 40′, making it 20′. The valley point can be determined by figuring the distance the valley runs before the rafter starts. In this case, since the rafters all conveniently line up and run at 24"
O. C., the easiest method is to count the rafter spaces from the other side of the roof. In this example, there are seven rafter spaces; therefore the run will be
14′. Subtract half the distance of the 45° bottom cut for the valley rafter (11/16"), and half the thickness of the ridge board (3/4"), and the run will be 13′- 103/16". The rafter length will be 13′-103/16" x 1.118 (diagonal percent) resulting in a 15′-513/16" rafter length. The connection angle at the top will be a 90° saw cut, and the pitch will be at a 6/12 common cut on the speed square. The bottom will be a 45° saw cut at a 6/12 common cut. The measurement will be to the center of the 45° cheek cut.
Finding Valley-to-Hip Jack Rafter Length-Example 7 on Roof Example Illustration
There are different ways to find the run length. Here is a way that has not yet been illustrated. In this example, run length will be figured from the 28′ span length. The run for the 28′ span is 14′.
The top of the rafter is 2′ past the end of the ridge
Jack rafter run lengths equal layout lengths.
board, which will add 2′ to the run going up the hip that it connects to.
The run at the bottom will be shortened by 4′ because it extends up the valley the equivalent of 4′ of run. This leaves 12′ of run. Adjust for top and bottom by subtracting one half of a 45° angle for top and bottom cuts or two times 11/16" (21/8") = 11′-97/8" times 1.118. This makes for a rafter length of 13′-25/8". Both the top and bottom would have a 45° cheek cut for the connection angle and would be marked at a common 6/12 for the pitch angle.
Ridge-to-Ridge Hip Rafter-Example 8 on Roof Example Illustration
In this example, the rafters are so conveniently arranged that we can see the hip rafter goes from the center of one rafter to the center of another rafter with two in between, resulting in a distance of 6′.
Another way to find this length is to calculate the difference in the runs for the ridges that establish the height difference. One has a span of 28′-0" for a run of 14′-0", while the other has a span of 40′-0" for a run of 20′-0".
The difference is 6′-0", the same as we just figured.
Once you have the 6′-0" of run, then you follow the same procedure as with a hip and make the necessary top and bottom adjustments. First establish the hip run. Enter 6′-0" run and 6′-0" rise on the calculator and press diagonal, which gives you the hip run of 8′-5 13/16". The top will be a standard hip connection. Therefore one half the ridge at a 45° angle (11/16") will be subtracted. At the bottom it will be a #2 connection. (Connection #2.) Therefore subtract one half the thickness of the ridge at a 45° angle, or 11/16". The
bottom will also require a square cut 7/16” deep on the end. You can establish the thickness of this square cut by finding the diagonal for the triangle in which the other two sides are the same and created by the balance of the difference between half the distance of the ridge board at 45° and half the distance of the ridge board at 90°.
The 7/16" square cut will not affect your hip run. This means that you can subtract the 11/i6” and 11/i6” to get an adjusted hip run of 8′-311/16". Multiplying 8′-311/16" x 1.061 (hip-val diagonal percent) gives you the ridge to ridge hip rafter length of 8′-93/4 The top cut will be a regular hip cut with convex (>) 45° cuts at a 6/12 hip-val pitch. The bottom will be a 45° cut at a 6/12 hip-val pitch with a 7/16" square cut end.
Finding the Ridge Board Length — Example 9 on Roof Example Illustration
The ridge board runs parallel with the wall at the other end of valley #5 and the hip of the 28′-0" span. That length is 12′-0", so the length of the ridge is 12’0" with adjustments at the ends. The hip connection is a number 1, so one half of the thickness of the common rafter (3/4") is added. At the other end, it is a connection #2, and the ridge will extend to the next rafter, adding 231/4" to the length.
The ridge board length therefore is: 12′-0" + %" + 231/4" = 14′-0". Both ends will be cut at 90° with square ends.
Until you have framed many roofs, cutting rafters is always going to be a challenge. Three ways to make it easier are:
• First, use the diagonal percent to find the rafter length.
• Second, figure lengths to the framing points and then make the adjustments.
• Third, become familiar with and use a construction calculator for the math.
If ever you get stumped, you can always organize your thinking by using the four basic characteristics of cutting rafters:
1. Find the length.
2. Adjust for the top and bottom.
3. Figure the angle cuts for the top, bottom, and bird’s mouth.
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4. Figure the height of the bird’s mouth. |
