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yep, circ saw. sawzall for trimming to eliminate over cutting is sweet idea darsunt. If you're decent with the circ saw you'll be fine, miter saw would take forever to setup each cut.
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The building code is a minimum standard, and merely meeting it instead of exceeding it equates to building your project to the worst standard that the law will allow.
Actually, I doubt there is any posibility of cutting a Bird's Mouth in a rafter with a Miter Saw because the term Bird's Mouth, usually but not always, implies a length of tail on the rafter.
Yes, you might possibly manage to cut just a seat on a short, cut-off rafter end. But it would take a HUGE Miter Saw blade (bigger than you or I have), and it would also take a friend or two to help man-handle the hanging end of the rafter while you made the cuts for a Bird's Mouth with a tail. Although I seriously doubt it, you might be able to do it with a sliding Miter Saw, but I suspect you may not have one of those.
Lay it out with a framing square.
Cut it almost all the way (don't over-cut the line on either side) with a skill (circular) saw.
Finish both cuts with either a Sabre Saw (Jig Saw) or a Sawzall, or as I do, simply a good hand saw. Takes about a minute or less with a hand saw.
There are three basic cuts used in creating the rafter; the plumb cut at the top of the rafter where it fits against the ridge plate; the tail cut that creates the outside edge of the building eaves; and the bird's mouth, which positions the rafter on the top of the wall plate.
Hold the framing square with the manufacturer's name up; this is called the “face” of the square, and the opposite side is the “back.” The long arm of the square is the “blade,” and the short arm is the “tongue.”
In this example we'll use a 1/3 pitch as shown in the drawing below, this means a rise of 8 inches for each 12 inches of run (an 8/12 pitch roof).
The first step is to lay the square on the edge of the rafter board and locate 8 inches on the tongue (the rise), and 12 inches on the blade (the unit of run). All on the same side (EDGE) of the framing square. Measure from the point on the blade to the point on the tongue—it should be 14-7/16 inches. Multiply this by the run of the building. We're using 10 feet in this example, excluding the overhang. The resulting figure is 144-3/8 inches. (14.4375 x 10=144.375 or 14 3/8") We add 12 inches for the overhang to get a final figure of 156-3/8 inches.
Now, what this means in simple terms is this. You know that it takes a longer piece of wood to run up the slope of a roof than it does to simply lay flat across the floor. Shucks you can look up and plainly see that. But how much longer? That's where (in this case) you use the 14-7/16" you figured out with the distance between the two framing square measurements.
For every 12 inches a board stretches across the floor, (in this case 10 of those 12" increments since it's 10' feet across) it would take 14-7/16" running up a slope to cover the same level distance.
Of course, the steeper the roof, the longer the slanted (rake) length of wood would be required to cover that same 12" across the floor. Conversely, the lower the rake (closer to level and flat) the shorter the measurement would be till it eventually returned to 12" again when the wood was again lying parallel to the floor.
Here's a tip that may help your visualization while laying out rafters: The only cuts used on a common rafter are the plumb and level... and maybe on a cheap job, a square cut on the end.
The larger drawing of a 2x12 rafter may help visualize the relationship between measurements. Be sure to check with your local building department because sometimes they limit the depth of a bird's mouth they will allow you to cut out of a rafter.
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Willie T
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