Hello,
I am new to posting questions because I really like to read everyone else’s comments and questions. I have a roof to frame that has some curved rafters on an upstairs room. The length from ridge to plate is 12 feet and the depth of curve is 12 inches. Is there a geometric formula for figuring the radius. I seem to remember something about how a chord cuts a circle but I can not find a formula. When I do aches I usually take some plywood and a chalkline to the street and pull some tapes until I find the radius. That is certainly trial and error. It works well but I know there has to be a better way.
Replies
You said your rafter length is 144" and the depth or height of the curve is 12".
You would take your Chord Squared ÷ 8 x Height + Height ÷ 2
Chord = 144"
Height = 12"
Formula - [C² ÷ 8xH] + [H ÷ 2] = Radius
144 x 144 = 20736
8 x 12 = 96
20736/96 = 216
12/2 = 6
Answer - 20736/96 = 216 + 6 = 222" = Radius
Using a Construction Master Pro Trig Plus III.
Enter 144 [Inch] [Run]
Enter 12 [Inch] [Rise]
Press [Conv] [Diag] Returns 222" = Radius
Joe Carola
Thanks a lot. I have one question. We recently framed a house with 33 arches inside and out. I did the pull the tapes trick and the arches turned out very well. Does this formula work on arches as well? If I know the width of the arch and the height can I arrive at the radius with the formula you gave me? I do not own a construction calculator as of yet.
James Hart
Thanks for that formula Framer.
On monday I'm going to have to put in a few arches myself. Like nextlevel, I really never calculated the arches, I just do a trial and error thing...now I will look like a friggin genius!
I'll have to print the formula out and sneak a peek at it while I'm doing it...then brag about how good I am at this sort of thing to the kids.....
Actually, maybe I'll just let Frank run the trig on it...
blue FRAMING ADVICE ALERT!!!! DON'T TAKE ANY FRAMING ADVICE FROM ME. I DON'T KNOW ANYTHING ABOUT IT. IF YOU WANT GOOD FRAMING ADVICE, JUST ASK GABE. DON'T ASK ANYONE ELSE....JUST ASK GABE! REMEMBER, I DON'T KNOW ANYTHING ABOUT FRAMING...I JUST BS ABOUT IT.
END OF ALERT!
Oh Great!
I got U not allowing speed squares on one job ...
and my buddy Joe not allowing calculators on another(ok ... on roofs) ...
how am I ever supposed to build anything nice!
Jeff
construction master will make you a mathematical genious! I always used the "blue book" to cut roof and figured out the rest with a tape like you guys were saying. I even refined the tape measure-arc thing down to a science. Lets see if i can write this out- you can let me know if my technical writing skills are worth a darn. I know i could show someone, but writing is a different story. Here goes...first snap a long line, set up a square line off of that like a "T" with a long vertical. mark your center of arch height off of the top of the "T" square up off the intersection. pull over from center line 1/2 the span of your arc along the top of the "T" and mark the beginning of your arc on the top "T" line. put a nail at each point, hook a tape on each nail and pull them down the long snap line with them intersecting (crossing) on the long snap line. when both tapes at the intersection point have the same measurement, there is your radius. This way, I could find the radius measurement without all the hit and miss stuff. I thought i was really smart untill i got the arc formula and did it mathematicly. Then comes the smart guy with the calculator and i just had to break down and buy one. They are great, and remarkably tough too. I have had mine for years now and carry it about half the time in my bags!
After all that, i am going to try to draw the radious method out and attach it to my post.. I just love technology!!
Edited 10/31/2004 2:14 am ET by robzan
I was wondering what you would cut your curved rafters out of? this is something i haven't had to do yet and have been wondering how you would go about it. If you could put perlins in i could see using a couple of different rafters, but you couldn't cut too much curve on dimentional lumber of course because at a certian point you will have cut across the grain and it would fall apart. How did those old guys do it back in the day? steam bent those old dense full dimention 2x4s? I talked to one old builder, and he did a room addition on a house with curved 2x6 rafters. He said that they actually set up a jig, wet and slowly bent the lumber?? I saw pictures of the finished product and it looked all right, but that sounds a little slow and unpredictable. I guess if you got some clear lumber......hard to find out here. So do any of you Old Guys have a good answer? I love all the knowledge that you guys share on this site and look forward to your answers. Sincerely, RZ
Blue,
If you view that 144" Chord as the span of a roof you can divide it in half to get the run of 72" and use the 12" height as the rise to get the Radius by creating Triangles.
72" Run 12" Rise with a 73" Rafter Length.
Tan-¹(12/72) = 9.46°
12/Sin(9.46) = 73"
73/2 = 36.5
36.5/Sin(9.46) = 222" - Radius
Or a Construction Master Calculator.
12 [Inch] [Rise]
72 [Inch] [Run]
Press [Pitch]= 9.46°
Press [Diag] = 73
73/2 = 36.5
36.5 [Inch] [Rise]
9.46 [Inch] [Pitch]
Press [Diag] = 222" - Radius
Joe Carola
I hope I made myself clear from the beginning. The actual run is 10.5 feet and the actual rise is 55.5 inches. The 12 foot dimension I gave is from the ridge to the end of the tail on the rafter measured on the top. This is the actual rafter length. The curved drop is 12 inches. I plan to cut a pattern out of plywood and then cut the actual rafter out of 2x12 and then cut plywood for each side, glue and staple the plywood on like a sandwhich. I will put a full length 2x6 under the 2x12 pieces for support. The other option was to cut the rafters out of 16 inch LVLs. That could get expensive. But it might be worth the money saved on labor. What does anybody think?
James Hart
Is this what your talking about? If so I did one 2 years ago and we use 14" lvl's but the arc was only 4" yours is 12" you should go with a bigger lvl than a 16". Or can you put a header at the center point under the rafters or sister rafters along side the lvl's?
Sorry the run is in the wrong spot in this picture. I corrected it in my next post.
Joe Carola
Edited 10/31/2004 7:52 am ET by Framer
Yes!
That is exactly what I have. The plans call for shingles and for the rafters to be 16 on center. I suppose I could use bendable plywood for the decking. If I use 16 inch LVLs I could certainly use a center header for support. That would save me a lot of time cutting plywood and gluing and stapling. Do you think I could use regular plywood on that radius and screw it down or would it not bend that much? Thanks for all the help. I glad for guys who have been there and can share there knowledge.
James Hart
Next, weve added the curves to 2x6s. It works fine.
Here a pic of some bent osb. The radius wall is probably much tighter radius that you will be using. The strength axis of the ply or osb will work in your favor on the roof.
blue FRAMING ADVICE ALERT!!!! DON'T TAKE ANY FRAMING ADVICE FROM ME. I DON'T KNOW ANYTHING ABOUT IT. IF YOU WANT GOOD FRAMING ADVICE, JUST ASK GABE. DON'T ASK ANYONE ELSE....JUST ASK GABE! REMEMBER, I DON'T KNOW ANYTHING ABOUT FRAMING...I JUST BS ABOUT IT.
END OF ALERT!
If you are going to put a beam in midspan then you can just use 2"x12".
(See Image)
The measurements that you gave did not specify to what point they were to. Did the rise include the H.A.P. and did the run include 1/2 the ridge?
Without knowing I went to the same points as in the previous image.
Also the beam shown is a double 2"x12". Of coarse I do not know what size you actually need.
Kyle,
I flipped your drawing around for you.
Joe Carola
Thanks Joe,
I thought I already did. New scanner, ain't figured it out yet.
Kyle.
What are you going to cover the roof with? That pitch at the bottom is going to be almost flat.
The plans call for shingles. You do have the HAP correct. I am not sure what you are joining the two pieces with but I suppose a piece of 2x12 will work. I did not think of trying to make the rafters out of two pieces. That would certainly save on material. SEtting a double 2x12 for support is no problem. It is great to have guys to run this stuff by for advice. I have thought about the shedding water problem. This curved roof joins to a ridge at which point a 1412 roof comes down to. I think the velocity of water flow will help this situation. I tried to talk the builder into a sloped roof since this is a spec house but he thought the curve would look good. Well, I've got to go to work and cut out curved rafters. And by the way, the rest of this roof is a 1012 meeting a 1412. That is always fun.
Fixed the run in this drawing.
Joe Carola
Joe, thanks for that visual...it helps me tremendously to understand.
I dropped out of trig class after one day. I didn't like the teacher...I didn't understand a word he said the first day!
I rely of simple basic geometry...and your original formula was just as easy for me to use as the trig thing.
I know that I could perform the trig functions if I would pick up the booklet or use a construction master...but I use a very simple calculator...one of those $5 jobs....I keep it in my pouch at all times...it has to have a separate memory clear button and I can whiz along as fast any any Construction master (I own one...it's on the dash of slowguys truck...been there for a year...).
I've argued with guys like Joe (hes gone now) that my simple calculator is more efficient....and I believe I won the argument...but he didn't believe me. Heres how I won: I was able to derive the answer faster by using less pushes of the button! Less button pushes means getting back to the actual construction quicker!
blue FRAMING ADVICE ALERT!!!! DON'T TAKE ANY FRAMING ADVICE FROM ME. I DON'T KNOW ANYTHING ABOUT IT. IF YOU WANT GOOD FRAMING ADVICE, JUST ASK GABE. DON'T ASK ANYONE ELSE....JUST ASK GABE! REMEMBER, I DON'T KNOW ANYTHING ABOUT FRAMING...I JUST BS ABOUT IT.
END OF ALERT!
Joe, I used your formula today and it worked to perfection! Thank you again. I gave a copy to Frank and he is equally thankful.
We haven't been doing the big customs for several years now and knowing this formula has had a high priority, but now...we're going to need it constantly!
blueWarning! Be cautious when taking any advice from me. Although I have a lifetime of framing experience, some of it is viewed as boogerin and not consistent with views of those who prefer to overbuild everything...including their own egos
Additionally, don't take any political advice from me. I'm just a parrot for the Republican talking points. I get all my news from Rush Limbaugh and Fox and Friends (they are funny...try them out)!
I'm glad it worked out for you Blue. Does Frank work for you?
If you want to figure the Radius out faster use the Construction Master you said someone has in there truck. I just figured the Radius in 5 seconds with it. That's a lot faster then the formula I gave you.
Take some pictures and post them when you get a chance.
Joe Carola
Edited 11/1/2004 7:15 pm ET by Framer
Frank used to work for me, now we are partners.
Five seconds aint bad...you gotta count the punches though...thats what really matters.
I actually hate that construction master. Too many buttons.
blueWarning! Be cautious when taking any advice from me. Although I have a lifetime of framing experience, some of it is viewed as boogerin and not consistent with views of those who prefer to overbuild everything...including their own egos
Additionally, don't take any political advice from me. I'm just a parrot for the Republican talking points. I get all my news from Rush Limbaugh and Fox and Friends (they are funny...try them out)!
Joe, I want to let you know that we used the formula today and it worked great. I showed it to my oldest son and he laid the rafters out and cut out two of them and set them up on the wall to see how they looked. The formula made the job easier. When they get all the rafters up I'll send you some pictures.
James Hart
James, Joe is my hero too!
I've put in about 8 arches in this house and his formula makes the job a cinch!
blueWarning! Be cautious when taking any advice from me. Although I have a lifetime of framing experience, some of it is viewed as boogerin and not consistent with views of those who prefer to overbuild everything...including their own egos
Additionally, don't take any political advice from me. I'm just a parrot for the Republican talking points. I get all my news from Rush Limbaugh and Fox and Friends (they are funny...try them out)!
I wish my wife would tell me I'm her Hero. Maybe I'll try to figure out some kind of Formula on my Construction Master to give her so that I'll be her Hero......;-)
Joe Carola
James,
Glad to here that it worked out. Definitely post some pictures when you get a chance.
Joe Carola
thanks for the algebra tutorial...Scribe once, cut once!