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I have a question about how to figure the correct angles for a wall in a home we’re building. We have scissor trusses with a 4/12 ceiling pitch. We built an 8′ high interior wall that goes perpendicular to the trusses, and we want to build a knee wall from the top of the 8′ wall up to the pitched ceiling. That’s not our problem though. This is…the interior wall goes perpendicular to the trusses for 12′ then turns a 45-degree angle for 4′ then another 45-degree angle (which makes it parallel with the scissor trusses above). The problem is – since the ceiling is sloping at a 4/12 pitch, when we go to cut the top plates that fasten to the ceiling, the angles at the 45 degree turns can’t be cut at 22.5 degrees the way the top of the level wall is. How would we go about figuring that angle? Also the knee wall studs that go up to the ceiling directly above the 4′ angled part of the wall will have to have compound angles at the top. How would we figure those angles? We could get it figured out the old trial & error way, but it would sure be nice to know how to accurately figure the angles and only have to cut them once! Thanks for any help. RayT
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I have used a couple of methods for this, however most times calculations are slower than trial and error. The problem with calculating the angles is that all plates must have bevel ripped edges making them plumb. If you want to make this effort, you can calculate all your angles the same way you calculate irregular hips and valleys. Hopefully you don't use the trial and error method there.
*Hi Ray, Love that big sky country. I can't solve all your math here but I'll provide some clues. Presuming 16" o.c. stud layout, what I think you want to know is the difference in length for studs (ie on layout the difference will be the same from 1 stud to the next etc.). A 45 deg. angle to the roof would be the C squared side of the old A squared + B squared = C squared. A and B are equal because the 45 degrees creates an equilateral triangle. So if A=16" (your stud spacing) then the run is the square root of 1/2 of 16 squared (11.31"). Your rise for this run distance is 3.77" (3-3/4"). That is, as 4" is to 12" so also 3.77" is to 11.31". Now install your plates, scribe your first stud, and add 3-3/4" to each succussive stud. If the wall was long you would find the studs get short because 3-3/4" is 21 thousandths shorter than the theoretical difference. In the real world your roof pitch is probably off, the floor is not level, and your plates won't be at a 45 degree angle either. In other words after you do your math, you better check your fit as you go and make the necessary adjustments. In fact we call this act carpentering. The tin bangers and mud sloppers call it wood butchering. Can you tell its been a long day? I just got in 21.5 billable hours today (time and a half after 8).JoeP.S I could be wrong the difference might be 2.6666". Either way after all the math they still must simply fit.
*Ray,4/12 pitch = 18 1/2 degrees5/12 pitch = 22 1/2 degreesSo if your trusses are creating a 4/12 ceiling, you may want to reconsider the bevel that you are putting on the studs for the wall that runs perpendicular to the trusses.If the slope is 4/12, then to cut the studs on the 45 degree wall, the correct ANGLE for the compound cut is 13 1/4 degrees, and the BEVEL is 13 degrees.Also, if you want the edges of the top plates to be plumb, rip a 13 degree bevel on them also.If the studs are 16" on center, each stud will be 3 3/4" longer than the preceeding one.Sorry, don't have enough time this morning to go into details and formulas, but what it boils down to is this: If you were cutting a hip roof with a 4/12 pitch, the hips would be cut at 4/17, or 13 1/4 degrees. That's the ANGLE for the compound cut on the studs.If you wished to cut "backing bevels" on the tops of the hip rafters so that they would plane in with the common and jack rafters, the correct backing bevel would be 13 degrees. That's the BEVEL cut on the studs, as well as the bevel rip on the top plates.