At first glance the rafter table stamped into the side of a framing square can be a bit tricky to understand. But it is not so difficult once you get the hang of it. The first thing to understand is that it is based on roof pitches expressed in amount of rise (vertical) over a 12 inch run (horizontal). The table is constructed with values underneath the inch markings on the top of the square. In the picture above I have highlighted in green the rafter length for a 16/12 roof pitch. Because the rafter forms the long side of the the right triangle it needs to be 20 inches for every foot of run, or 20 feet for every 12 feet of run.
The math behind this is pretty simple. Using the pythagorean theorem we know that the square root of the hypotenuse (long side) of a right triangle is equal to the sum of the square of the sides. There a few right triangles where the math works out smoothly. a right triangle with sides of 3 and 4 will have a hypotenuse of 5. (3x3)+(4x4)=5x5. In the case of a 16/12 slope you can see that it follows the same ratio but is just 4 times bigger so the long side will be 5x4or 20.
It gets a bit more complicated when you get to hip or valley rafters. Because they are at a 45 degree angle to regular rafters they have to be longer. You can use the second line of the table to determine their length, or you could also use the pythagorean theorem again, but lengthen the horizontal dimension by 1.414 times since it is now the hypotenuse of a right triangle with even sides (look down at the roof from above to see this).
The next thing the rafter table shows is the difference in length for jack rafters. Jack rafters are those that meet either a hip or a valley rafter. They start out being the same length as regular rafters - so you use the common rafter table to determine this length - but as they work their way along the hip or valley they get shorter and shorter. The "difference in length of jacks" row shows how much shorter each one will be than the previous one based on either a 16 or 20 inch spacing.
The final thing the rafter table shows is how to cut the bevel on the ends of the angled rafters (hip, valley, jack). This is the bevel looking from above. To do this set the square along the top of the rafter with the 12 inch mark on one leg at the end point of the rafter and the "length" given by the rafter table on the other leg the edge of the rafter. Drawing a line from the end point of the rafter will give you the angle you need to cut.
In measuring rafters you need to keep a few things in mind. First is the thickness of the ridge rafter and the top plate. Neither should be included in your calculation of run. In other words, measure run from the inside of the wall and the outside of the ridge rafter. The second thing is that you don't want to have to measure and layout each rafter individually. Make one which fits and then use it as a pattern for all the others. Check the fit first at a few different places as your measurements may be a bit out or you may have a wall which is not quite square to the ridge.
Comments (3)
How do i convert pitch or grade to degrees. Thanks
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Pitch is usually noted as rise over run (5/12 for example). Using a bit of trigonometry we can find the angle. The tangent of an angle of a right triangle = the opposite side over the adjacent side. This is the same as the pitch. To convert the tangent to an angle, we take the arctangent. So for a pitch of 5 in 12 we are looking for the arctangent of 0.41666 which equals 22.6 degrees. Use a computer or calculator to do this. But in case you don't have one available, here are the pitches converted to angles:
Posted by Michael Stannard | June 21, 2007 1:20 AM
Posted on June 21, 2007 01:20
If your laying out your lines on a fountation or floor you want to have a square line to pull all your mearsurements off of. We call it three four five. There a mathmatical way of doing it. I just can't remember. Like if you have one line thats 40 feet 4 inchs and another line thats 25 feet 5 inches. How do you find the number that makes thoughs lines square to eachother?
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The Pythagorean Theorem says that for a right triangle (that is a triangle with one corner which is 90 degrees), the sum of the squares of both sides is equal to the square of the hypotenuse (the longest side). So with a 3-4-5 triangle squaring both sides and adding gives (3x3)+(4x4) = 25. 25 = 5x5 of course. The measurements you give are a bit difficult to do in your head, but a calculator gives (40.333x40.333)+(25.416X25.416) = 2272.784 so the long side will be 47ft 8in. You are better off marking one side at 24 ft, the other at 32 ft and measuring the diagonal. It should be 40ft. 3 yards, 4 yards, 5 yards.... Hope that helps. Simplifying the problem is easier than doing the complicated math. -Jack
Posted by Chris | August 17, 2007 2:12 AM
Posted on August 17, 2007 02:12
In measuring rafters you need to keep a few things in mind. First is the thickness of the ridge rafter and the top plate. Neither should be included in your calculation of run. In other words, measure run from the inside of the wall and the outside of the ridge rafter.
This information is not correct. There will be most often a Difference in the thickness of the ridge board and the wall plate width. The correct way is to measure the run from the outside of the wall to the center of the span, then subtract 1/2 the thickness of the ridge board.
Posted by Ray Trawick | August 28, 2007 3:18 PM
Posted on August 28, 2007 15:18