I recently cut studs for a wall that intersects a 7/12 pitch at a 45º angle so that the top plate maintains the slope of the roof. Does anyone know how to calculate these complex cuts? What if the wall was at 30º? For me, it was trial and error.
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yes, get a squangle by mayes(company that makes the tool). i believe it is a logarythim(spellcheck) formula in triganometry that will allow you to mathamaticaly calculate the lengths and angles for that application but i don't remember the formula so i always calculate them in the field like this: a wall at a 45 degree angle to a 7 in 12 pitch top cut of stud is a compound angle. the stud is marked at 22 1/2 degree angle and the saw foot is set also at 22 1/2 degrees to make the cut on the mark. this gives you "two" angles or a compound angle. i arrive at this by using the squangle, a 7 in 12 pitch on the common side is 30 degrees but on the hip and valley side it is 22 1/2 degrees. a hip or valley rafter is at a 45 to the commons so this works for a wall at a 45 for the top cut. this does not work for other than 45 degree angles, but it will get you in the ballpark for a quicker period of trial and error. the advantage of a squangle over a speed square is that when you set it at a pitch you can read the angle for both commons and hips. this is helpfull when setting saw foot angle. to determine an angle other than 45, 30 degrees frinstance, i would start at about 20 or 19 degrees and check on a piece of scrap for plumb, remember both mark on stud and saw foot have to be at the same angle for a 45, not so on more or less than 45 so if mark on stud is 20 try setting saw foot at 25 degrees. see what i'm gettin at, - 2 1/2 then + 2 1/2, there is a relationship there. depends which way wall is going in relation to roof. after you have determined top cut compound angles you determine lengths by measuring long point and short point. layout as if you were framing wall with studs squared and on layout and snap a line from LP to SP. use scrap piece so you don't get twisted around (hold it up the way it goes and lay it down the way wall is framed) and use squangle to transfer from top of stud at chalk line to side of stud for cut and there you go. also there will be a corresponding compound angle on top and double plates depending on which way yer goin. try it with a scrap first and check for fit, LP is reverse of SP. remember to record the angles on one of the studs in the wall for backing blocks for drywall at lid later.
What's wrong with trial and error? Cut the first and last studs then scribe the rest to the plates. I say this cause I never have the calculator when I need it.
Goodwood,
I had exactly the same question at JLC in September. I had a wall at 30° to a 6-12 roof. I'm on my way out right now, I'll try and find all my notes. The suggestion everyone gave me was to visualize the wall as a hip and then figure accordingly.
I'll post later on. Try posting this question on Joe Fusco's website. The guys that frequent that forum are the same guys that answered my question. http://www.josephfusco.org/phpbb/index.php
I think it is a good idea to learn how do figure these cuts using math. Trial and error shouldn't be a first choice. There is nothing wrong with using a calculator on the jobsite. We used to use trial and error to find the radius of an arch. In the time it takes to do that, I can figure the radius using math, the Construction Master, or using geometry and have the arch cut out. Trial and error is a waste of time and should only be used if there is no other quick and accurate method available.
I'll post later. The formulas aren't difficult, but I don't want to post and give you inaccurate info. I've learned the hard not to post without checking myself :-)
i agree with you that its a good idea to have the formulas, but disagree about trial and error wasting time determining radius point for an arch. to scribe the arch so you can cut it out you still need to determine the percentage of the circle that will serve as the arch, and the centerline perpendicular to the bottom of the arch that you will use to drive the nail and hang the tape on to scribe the line. once you have done that, and you need to anyway, the calculator won't, it is easy to measure from top of arch at centerline and bottom of arch on either right or left end. frinstance you make a pencil mark at 6' from both locations, 7', then 8' and that and about 2 seconds of thinking about it will tell you which direction to go in. even if you get the exact measurement with the calculator and don't have to fine tune i will be done before you.
I think that my understanding of trial and error is a little different than yours. I'll explain how we used to do arches. Let's say the opening is 6'. At 3' we might measure up 4". Now we have to figure the radius. If we use trial and error, we have to pull a radius from either of the bottom points and the top point (any 2 will get close enough). I would have to keep testing it until I find the right radius.
How many attempts will it take until I find the radius? Too many. I asked our finish carpenter one day about arches. He told me to just connect each bottom point with the top point and draw a line or snap the line. The find the mid point of those 2 diagonal lines and square off of that. Where they cross is the center point of the arch.
Now, I use a Constrution Master ProTrigPlusIII for a many different tasks. One of them is finding the radius of a circle or arch. It takes 3 seconds. I can also use it to find the complex cuts on studs in about 10 seconds. In the time it takes to climb a ladder and figure the cuts, I can have the numbers for the cuts and they will be exact. I wouldn't have to climb the ladder. I hate climing ladders because I bang my shins around too much :-)
I'm sure your method works well for you and you are proficient at it. I have a big desire to learn the math behind the things I build. That doesn't mean I'm faster or cleaner than others, but it works for me.
Edited 6/8/2003 12:18:09 PM ET by TIMUHLER
For those who care, here is helpful formula.
If you are given the width and height of the arch (usually the case):
H=height
W=width
radius of circle=[(H*H)+(.25{W*W})]/2H
BTW, if anybody could remind how to get the square notation appear. I could simplify the equation a good bit.
Jon Blakemore
I make arches with a spline.
two nails on the ends push the middle up as far as you need and trace your arch.
KISS :)Mr T
Do not try this at home!
I am an Experienced Professional!
DITTO!
2²
try alt3069
That is hold alt key down, type in the number 3069 on the number key pad next release the alt key. NOT the numbers at the top of the key board.
Thanks
Fred and Joe,
Thank-you for the "²" notation help.
r=(H²+1/4W²)/2H
Jon Blakemore
Jon,
X²
I use Alt 509.
Joe Carola
tim i also like to know the math, and actually did look it up once and the calculator remembers it so if you have it on hand that is great but.......ok opening is 6',at 3' we measure up 4". we have to determine, or layout on the floor a piece of plywood to cut right. we are both at the same step here. now we mark the ends and the centerline and measure up the 4" at the centerline, still at same point right. now you get the calculator and start entering the numbers and in 3 seconds, you will measure down from the centerline mark that is 4" up from the bottom and drive a nail on the centerline you have extended down to hook your tape and scribe the arc right. if your calculation was exact your scribe mark hits top at center and both sides at end. but you check with the tape first before you make the mark, to make sure you are not marking the scribe incorrectly right? what i do at that point is measure down from top mark at 6, 7, and then 8'. then i measure from the right end (cause i'm a right kinda guy, it could be the left as well) and mark on the centerline at 6, 7, and 8'. now my two 6' marks are 6" apart. my two 7' marks are 4" apart, and my 8' mark is 2 1/2 inches apart. just by looking at that i can (and anyone will be able to do this as well after doing it just a few times) guestimate about how far i need to go in the same 3 seconds, and i have to admit that if you are quick with the calculator you might be ahead at this point, but i won't be far behind and if you are not exact with the calculator you have to go through the steps i have already accomplished to arrive at the same point. now this is assuming that we are both working and thinking at the same pace, no advantage of one person over another, save the method they are using to calculate. either way we use we are both going to double check with the tape before we make the mark right, norm always says measure twice cut once. after you have used this method a few times i bet you won't even reach for the calculator unless you are just curious. i had a math teacher in high school that would allow use of a calculator in class because he said if you don't know what and how to enter you will still get the answer wrong, it just saves time on the calculations. but when i am going to frame a rake wall at angle or scribe a cut line for an arch i am going to physically double check my calculations, so you should have an efficient method of doing this anyway, by measuring before i do this work and if you have an efficient method in my opinion you are wasting time with the calculator. you have to climb the ladder and bang your shins to double check anyway, and i like to do that before i cut the first stud on a scrap block held plumb and eyeballed for fit for a rake wall at angle before i end up with a bigger truckload of firewood than i already have.
Skids,
First off, great name :-) I like it.
Second, I'm glad you are questioning me. I can't tell you how many times I've been questioned and then realized the other person is/was right.
Now, I followed your last post, but I still disagree. I think that is because you and I have different methods for those times we trial and errored it (sp?). My method is this,
Cut the plywood blank and tack it to the ground. I think you and I are on the same page here. Now I don't snap a line on the ground. I use the line that follows the seam of the subfloor (lengthwise). Now what I would do if I was using trial and error is to make sure that the plywood blank is square to that line on the ground. Then I would measure from the top mark and the the bottom mark until they matched numbers and then mark it and tack a nail. Voila! got the radius.
Now, if I was using the CM and already had the blank tacked but not squared: I would do this: 6'run, 4" rise Conv Diag = 164" radius (about 3 seconds :-))
Now I would've already tacked the blank to the ground with one nail at the 4" mark. I would pull from that nail 164" and swing a short arc and tack a nail where that arc crossed the line of the subfloor. I would pull my tape from that nail like I was going to draw the arch, but I would start from either bottom point. I could adjust the blank that small amount to make the 164 work. I eyeball the blank pretty square to begin with so it hardly has to move.
Now I know that sounds wordy, but I'm telling you, when I do it on the job, it is very quick and accurate. I really do believe that I would have the arch drawn and be on my way to cut it in the same time it would have taken me to trial and error the radius.
Now as far as the sequence to figure the cuts on the studs, Try this for a 6-12 roof with the wall at 30°
Face Cut:
30 pitch
12"run
Diag=13 7/8"
Tan-1(6"/13 7-8")=23.40°rounded
Bevel=Tan-1((21.65tan)*(30tang))=12.90°
21.65=sine of the hip at 30° for a 6-12roof
(Thanks to everyone that helped with with this problem in September)
I might be wrong, but I think those are the correct number. It might seem slow to figure the sine of the hip angle and some of the other math, but assume that the person who is using the calc is just as proficient at that as the person climbing the ladder. If each is equally proficient at their preferred method, the calc is faster every time. I firmly believe this. Whenever you can eliminate climbing a ladder, you save time.
By the way, which part of the country do you work in? I'm in the PacNW. Are you busy right now? We are swamped with work. I'm always curious as to how other parts of the country are doing. What kind of work do you do?
Edited 6/8/2003 8:04:42 PM ET by TIMUHLER
i live in northern california but also work in los angeles on occasion, grew up and went to high school in southern santa barbara county, thats where i got the nickname, been using it ever since. ya i see your point at the arch, i also use the seam whenever i can but good point about the tack nail at the top/centerline thanks. but still with your method pulling a tape and making 3 quick marks at 6,8,&10' from both top and bottom edge and look at it just a few seconds and you will be able to guess the radius point within inches i bet! most of us who spend a lifetime measuring can. i will admit your calculator will beat the squangle method on the rake wall at 30 degrees but with a standard 45 the common for the pitch and the hip and valley for the pitch give you both the angles. i still reccomend making the cut you describe on a block and holding it up at 30 or 60 degrees depending on the wall your at and eyeballing to see if it planes in, and measuring LP and SP for length of studs after your happy with angle, taking into account that plates are more than 3" when installed at the angle of a rake wall at any degree. then framing that wall (bottom plate nailed) and marking studs tacked on layout with a chalk line, & transfered with a squangle. i agree about eliminating unneccasary trips on the ladder but i do go up to to eyeball unless i have done several of these recently and know they look right from memory. also i haven't done production framing in 15 years, i'm trying to be a design/build guy these days. i also very much enjoy the discusion/debate and have learned from it. thank you........chris
Skids,
I enjoy this forum for the same reason. I have learned more from the guys that post here and other forums, than I would've learned in the next 5 years. Most of that has been from guys disagreeing with me or others.
I hope you stay busy and that the design build works for you.
Tim
With the CMP Calculator, you just need to know the run and the rise or (width and height).
If you had a width of 6' and a height of 11" and you needed to find the radius of that arched opening or window, you can do this on the CMP Calculator.
6' [Run]
11" [Rise]
[Conv] [Diag] = 64-7/16" = Radius
That's the measurment you tack your nail at and hook your tape and scribe the arc.
The CMP gives you the answer. It dosen't teach you how to figure it.
Without the CMP.
(W² ÷ 8xH) + (H ÷ 2) = Radius
Joe Carola
ya but joe you still need to snap a centerline on the plywood you are cutting extended out to drive the nail in to hook the tape and make the mark. you still need to measure the ends and the height of of the radius at the centerline, if for nothing else just to eliminate extra cutting and or waste of material right? if we both do that at exactly the same speed and you reach for the calc while i go for the tape by the time you are done with the calc and double check with tape i am right there with you and didn't need the calc. i still say a good framer needs to physically double check calculations before he cuts and assembles and raises a wall, it sucks to take it down and take it apart. if you use the most efficient way to double check, recreating the numbers the calculator has given you, ya don't need the calc. remember the pyramids are proof that men have been clever for a very long time. i think they knew before they erected anything that it would fit.
I still double check myself all the time. I didn't start using a Cmp until about a year ago. Even after 19 years of framing, I'll still cut two commons and check first. I can't tell you how many times when I'm laying out a rafter and get asked a million questions. It takes two minutes to check.
I worked with a framer one time that figured his commons to half the span of the house, mark his plumbcut and then deduct 1/2 the thickness of the ridge, which is fine, I don't do it that way, I deduct the ridge first and then layout the common, but that's me. Any way he never checked the rafters and when we went to nail them up they didn't fit right. We figured out that he never deducted for 1/2 the thickness of the micro ridge. About 80 rafters.
Even when I started using a calculator I didn't trust them. I always did the math by hand. These CMP are great once you know what to putr in them.
For me I spend alot of time plumbing and straightening walls with mason lines because when I get to the rafters I don't want any problems, especially 90' in the air on a scaffold. ;-)
Joe Carola
Joe,
A few messages back you posted:
Without the CMP.
(W² ÷ 8xH) + (H ÷ 2) = Radius
I figured it out to be:
(WxW ÷ 8xH) + (H ÷ 2) = Radius
Did you forget the xtra W or did I mess something up.
Thanx,
M2akita
A few messages back you posted:
Without the CMP.
(W² ÷ 8xH) + (H ÷ 2) = Radius
I figured it out to be:
(WxW ÷ 8xH) + (H ÷ 2) = Radius
Did you forget the xtra W or did I mess something up.
W² or X² Just means, squaring the number. The number is squared when it is multiplied by itself.
On a calculater you have a X² button. I used 6' as the width above, so if you just press 72 and then press X², it returns 5184. It automatically multiplies 72x72 = 5184.
By pressing X² button on the calculator, it will Square any number for you.
What you wrote, WxW is right. It's the same as W².
Here's a couple other ones.
(W ÷ 2)X² ÷ (H) + (H) ÷ 2 = Radius
(W² + 4 x H²) ÷ (8 x H) = Radius
Joe Carola
It is much easier to just cut a single bevel cut on the studs.
Yours will be a 7/17.
this will leave the "high" side of the wall away from the ceiling and you can just rip a bevel strip to fill it up.
Actually angles on each side of your stud will be 7/17 from level.
Think about it.... the cut edge on each side will follow the same line as a hip/valley rafter would.
4 or 5 years ago ihad to frame in similar walls and the math eluded me so I chose the easy way, every thing came out fine.
Here and now the solution popped right into my head!!
I will probably not be able to recall it if I every have to do it again!!!
Mr T
Do not try this at home!
I am an Experienced Professional!
T i may be using the wrong terminology in calling that a compound angle but it is definitely not a single bevel. as you look at the picture it angles down from back to front and angles down from left to right. thats why i call it a compound angle, the cut is made by marking the stud at an angle and cutting with a skilsaw foot set at an angle. i believe that previous posters are correct that hips and therefore top cuts on studs in walls at 45 degree angle to cathedral ceiling are X in 17 as opposed to the common run of X in 12, but that changes if the wall is more or less than 45 degree.
just framed a masterbed/bath with the same deal....
used my usual method....
Got up on the ladder with a level and a tape....held the level level....measurered up from my 12" mark......read 3.5"...
so I knew I had a 3.5/ 12 pitch roof to deal with.
one angle down...now for the other.
I couldn't even tell ya what angle the walls ran at......I had to measure from an existing wall...so I didn't need that info.
So..all I did was another trip up the ladder with a small 2x with the 3.5/12 end cut.....taped to my level. Held it plumb with one hand and measured the gap with the other....
1/2 inch...along the short side.
Back down on the floor......make a tick mark at 1/2 down....
take out the speed square and read that line......15 deg...or so.
So all those studs were cut at what ever angle the 3.5/12 is...with the circular saw set at 15deg...
and everything fit.
Even the top plates that had have a corner ripped off at 15 deg so the drywall will set flush.
My point...don't over complicate things.....if a quick trial and error got ya there...
Like I used to tell my buddy that was an excellent trim carp but the worlds slowest roof framer....
Just nail it...we ain't building cabinets today.
He'd wanna recut something that was off by an 8th! Like the wood would still be that same length tomorrow.....
Jeff
Buck Construction Pittsburgh,PA
Fine Carpentery.....While U Waite
Thanks for the ideas, everyone. As much as I'd like to know how to do the math on these, I think Jeff's got the simple answer that will work for any configuration. It's very close to what I did, btw.