I am about to frame a gazebo. I know that plumb cuts on a typical hip rafter (90 degree corner) run at 17. Is there a way to determine the run of a non square hip rafter. Also, if you know the answer to that question, maybe you would be able to give me some insight into how to figure valleys between varying roof pitches!
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Are you using a Scientific Calculator or Construction Master Calculator, Framing square to figure your rafters?
Is this an 8 sided Gazebo (Octagon)?
If it's an Octagon how wide is it?
What is the pitch?
Joe Carola
The Structure has eight sides and each side is nine feet long. The plans are quite vague, but we have decided to go with a 5/12.
There's nothing Mystical about the angles on this roof. Depending on what type of saw you use, if you install your commons first and then your hips in between, your saw tilt while the hip rafter is lying flat with a plumbcut scribed will be set at 67.5°.
I have a saw that cuts up to 75°. This saw will cut that in one shot, no handsaws or sawzalls.
If you don't have a saw that cuts like that you can cut your plumbcut still with your hip lying flat with the saw set at 0°. Now make the cut.
You will now scribe a center line down the face of the plumbcut which for 2x stock would be 3/4".
Using the compliment angle of 67.5° you will now set your saw tilt at 22.5° and run the bottom of your saw on that center line which is on the 1-1/2" face of the plumbcut and make one pass.
Now flip the hip rafter over and make the pass on the other side of the center line. This cut will make your 67.5° angle for your hip.
For your jack rafter you will do the same thing. The only thing different will be that you wont cut down the center line you will cut on one side of the face of the rafter.
If you don't use a 10" saw you will have to continue that cut with a handsaw or sawzall.
For an 8 sided Polygon like yours the angle will always be 67.5°
You will see how the angles are in Plan View in my drawing.
I used to use Blocks, strings,bevel squares and snap lines on the floor and eyeball these roofs too and use handsaws, sawzalls and a planer for those 67.5° cuts but I then figured out that it's only matter of figuring out a Triangle. There's absolutely nothing wrong with using all these methods I just described above.
But now that I can figure these Triangles out do to trial and era over the past 20 years, using a calculator is easy.
You can just use Pythagorean Theorem a² + b² = c² if you want when you see the drawing.
I also love my framing square and will never retire it.
I layed out an Octagon roof last summer using the 12th scale on my framing square and it worked out perfect. I was within a 1/16"-1/8" of my calculations with the calculator.
Whatever your comfortable with.
Now that I use the calculator I can do all my figuring at home.
Joe Carola
Edited 8/25/2003 12:00:27 AM ET by Framer
Hi Joe,
I started framing out my bay roof and can't thank you enough for your help and willingness to share your time and information so liberally. I printed out your advice and gave it to my brother in law who had tried to explain his way of doing it before I started searcing online. He was amazed at how clear and concise your method was. So again, thanks. Could you recommend any books you feel might help me with the math on some of the trickier roofs? And also does the construction master come with fairly explicit instructions or are you left on your own to figure out the more advanced functions? Hope all is well. I read in one post that someone was going to let your son drive a forklift? Huzzah!!!! I bought my nephew a brand new dirtbike but all he talks about to his freinds is the time I let him use the excavator I was working with. It beats the hell out of sitting inside and watching him play video games!!!
>> Could you recommend any books you feel might help me with the math on some of the trickier roofs? <<Your welcome. I'm glad I could help.Two books that you should get for cutting rafters that are the best in my mind are:Roof Cutters Secrets:(To Framing the Custom Home) by Will L. Holladay Roof Framer's Bible: by Barry D. Mussell (Author)http://www.amazon.com/Roof-Cutters-Secrets-Framing-Custom/dp/1928580149http://www.amazon.com/Roof-Framers-Bible-Complete-Reference/dp/0964335433>> And also does the construction master come with fairly explicit instructions or are you left on your own to figure out the more advanced functions? <<I would get the, "Construction Master Pro Trig" calculator if I were you and want to learn how to frame complicated roofs. Even if you don't know trig, you will know what it means after you punch in all your numbers and how it relates to trig.For some complicated roofs, punching in a few trig functions can get you to an answer you need a lot faster then going through some lengthy steps.When you look through both books you can use your calculator and come up with you on formulas to get at the same answers as the two books have and compare what you've done and write in down on paper. Every step you make with your calculator always right it down.The calculator comes with a book and a lot of information that you can use. You will realize how much more information you can come up with on your own. Everything is triangles with roof framing whether it's in plan view or the rafters are up already.When I first bought the calculator I would have 12 steps sometimes when figuring out something. I would keep trying to figure out a way to shorten those steps to arrive at my answer.The best thing that I would say to do is always draw it out in plan view and then see your triangles and then draw the rafters and see how that rafter forms a triangle. I can go on all day, but I don't want to bore you here but here's a link to the calculator. If your really interested in roof framing I would definitely get the two books and this calculator.http://www.engineersupply.com/ProductInfo.aspx?productid=ES21&affid=17Joe Carola
Edited 4/7/2007 9:46 am ET by Framer
The unit run of a typical hip roof is 17 because that is the diagonal length
thru a one foot square. So if your gazebo is octagon shape, your unit run
will be 13 because at that angle this is the length that runs through a one foot
square. To cut your jack rafters you will have to block the ends ,chain saw
or such as the cut angle will be to steep for most (all?) circular saws. Enjoy.
I'm sure that Joe can give you much more insight into framing, but I can answer your questions about determining the run of a hip.
Divide 360 by 2 times the number of sides. Find the cosine of that and take the inverse. Multiply the result by 12 to get the run of a hip rafter.
12*1/cosine(360/(2/4 sides))=16.97
12*1/cosine(360/(2/6 sides))=13.86
12*1/cosine(360/(2/8 sides))=12.98
Hope this helps. You can thank Marshall Gross (author of Roof Framing) if it does.
Mark
Yes, I am serious. And don't call me Shirley.
Buy the roof framers bible. It is a pocket reference that will tell you everything you need to know. There is about 12 pages you need to read, and the rest is all tables. Worth every penny of the price.
http://www.amazon.com/exec/obidos/tg/detail/-/0964335433/qid=1061642577/sr=1-1/ref=sr_1_1/103-6199832-5395866?v=glance&s=books
I use a Construction Master Pro Trig Plus 111 Calculator.
360/8 = 45/2 = 22.5° (Working Angle)
12/22.5 (cos) = 12.9887 (Hip Run)
Or.
22.5 [Pitch]
12" [Run]
[Diagonal] = 12.9887 (Hip Run)
As for your Hip pitch and Angle.
5" [Rise]
12.9887" [Run]
[Pitch] = 21.05° or 4-5/8/12 (Pitch)
Or.
Tan-¹ = Cos(22.5)*Tan(22.62) = 21.05° (Hip Angle)
You said that you have 8 sides at 9' or 108" with a 5/12 pitch..
That measurement will determine your common run and the total span/width of your building. For example.
Tan (22.5) * 2 = .8284
108/.8284 = 130.3718" or 130-3/8" = (Common Run)
12.9887/12 = 1.082392
1.083292 x 130.3718 = 141.1133" or 141-1/8" (Hip Run)
Tan(22.62)/ Sin(21.05) = 1.160049 (Hip Factor)
1.160 * 130.371 = 151.230" or 151-3/16" (Hip Rafter Length)
You can do this also.
22.5 [Pitch]
130.3718 [Run]
[Diagonal] = 141.113 (Hip Run)
21.05 [Pitch]
141.113" [Run]
[Diagonal] = 151.203" or 151-3/16" (Hip Rafter Length)
The easiest way for me to figure any roof is to break it all down in Triangles.
If you take your Tan(22.5) *2 = .8284. This number will always help you find your sides and your run and span of your Octagon.
If you have your side measurements as you do 108"
108/.8284 = 130.3718
Multiply that x 2 and you get your Span/Total with of your building.
130.3718 * 2= 260.7436 or 21'8-3/4" (Total Width of the Building)
If you have your Width of the building first.
21'8-3/4"/2 = 130.3718" (Your Common Run)
130.3718 * .8284 = 108" or 9' (Length of all 8 sides)
Doesn't matter how many sides your Polygon is, you can use this formula.
For Example.
Hexagon has 6 sides.
360/6 = 60/2 = 30 (Working Angle)
Tan (30) * 2 = 1.1547
Multiply Common run in inches * 1.1547 = (Length of the sides)
Divide length of the side by 1.1547 = (Common Run)
Tan (Working Angle) * 2 = (Formula for any side Polygon)
Hope this helps.
Joe Carola
Edited 8/24/2003 3:36:38 PM ET by Framer
Another way to understand the Triangles with your Construction Master Calculator.
22.5 [pitch]
130.3718" (Run)
[Rise] = 54" (Multiply that * 2 = 108 - Your Side Lengths)
[Diagonal] = 141.113" (Your Total Hip Run)
This is the way you would figure out what angle your hips would run at if your sides weren't equal. You divide the side with in half and take that answer and take the run and that's all you need.
Tim Uhler had a roof like that as do probably most of us have run into when you have the front wall of a bay that is for example 6' and the two sides can be 4'. You will not set your square on whatever pit/13 because they're not running at 22.5°.
Just another thought befor I go eat my 2 pounds of Macaroni. ;-)
Joe Carola
For any non square roof framing I find the easiest method for finding angles is a scaled drawing. For your octagon gazebo take a four foot by four foot scrap of G1S ply and draw a scaled down octagon(keep it as big as possible). Then draw in your rafter center lines. Right now in looks like a big spoked wheel. But now that you have your centerlines you can draw in your rafters actual size (do not scale these down). In doing that the intersecting angles, side cut, and shortening of all rafters will be visable. After that you can use the rafter and octagon hip tables on the framing square to calculate theoretical line lengths. you can then measure the shortening directly off the drawing. Keep in mind that all shortening measurments will be perpendicular to the plumb cut.
For something this small forget the calculations, etc. and go with the old eyball and handsaw method. The time it take you to cut with the handsaw is a lot less than try ing to figureout settings on a power tool. E.g . Lay a 2X4 across where it is supposed to go, cut one end inplace by compound eyeball angle, cut with handsaw, set that end just atop its final location, and again, cut the other end with a handsaw.
If you are really lazy. a sawzall will work too, but you don't have the width of the blade of the handsaw to give you an alignment.
Hint, its a LOT easier if your saw is sharp -- an old Disston # 196 docking saw is my favorite for rough framing cuts like this by hand.
For something this small forget the calculations, etc. and go with the old eyball and handsaw method.
What do you mean, forget the calculations,?
On every Octagon with all 8 sides equal in length that you've framed, you eyeball the cuts/angles?
Did you ever realize that you were cutting 67.5° on any Octagon with equal sides.
The time it take you to cut with the handsaw is a lot less than try ing to figureout settings on a power tool.
Why is it so hard to figure the settings on a power tool? Either you set your saw at 67.5° (provided you have one) or set your saw at 22.5°. All depends on how you cut it. It's either one or the other on any Octagon roof with equal sides.
Do you not frame with a circular saw?
Joe Carola
Joe, I need to tell you that although I do little framing and never really got into the math (algebra was never that strong for me), I enjoy every one of your posts.
I go on to your web site regularly and just learn as much as I can, then come back later to review.
Sorry to make you blush. It's a treat to read the work of a true professional.Quality repairs for your home.
Aaron the HandymanVancouver, Canada
Thank You Aaron. I hope I'm the right person you said those nice things to because I don't have a website but I'll take the compliment anyway. ;-)
Joe Carola
Thank You very much for all the detailed info. Last night, before I read the long list of E-mails, I drew out an octagon on paper with my scale rule. I drew it out with a total width of twenty four feet, twelve feet to centre, just for ease. Like your drawing I came up with a hip run of 13 feet. I divided 360 degrees by 8 to find my angles.
You know, I'm amazed out how when someone is trying to learn a new way of doing things, there is always someone who thinks they should just "cuter her till she fits". That's fine for you and I bet you do some good work.
For me, I pestered Joe and a few others over the last year and with what I have learned mathematically about roofs, I can cut that twice as fast as I used to and I understand what I am doing.
At first, it would have been faster to do it the way you describe. I did a bay roof last February in 6 hours. I cut everything on the ground and then got up there and nailed it together. Next to me was the same bay, but a little smaller and my 2 framing partners took a day, that's almost 16 man hours to do the same thing. Guess what else? They didn't know how to go any faster. (by the way, the one framer has 25 years experience, but no math and the other framer as about 10, no math) They both realized that the way I did it was better. I learned it here from Joe and a few other guys.
Thanks again Joe, I can't wait to do my next one.
The key words were "something this small" -- assumed a gazebo(w) as only about 60 sq ft -- agree, drag out the power tools for anything bigger.
Probably many don't have a hand saw anymore that can even cut straight, so power required?<G>
JunkHound,
You do have a point sometimes it’s easier just to perform the operation then to go through the entire procedure of trying to figure out all the calculations that are needed. The only problem that I have with that approach is that it’s actually a higher level technique then just using the calculations.
To use the technique you describe actually comes with years of experience and self-confidence. If you don’t have the experience to know that what you are about to do is correct, you have a tendency not to want do it. Taking the time to do all the calculations needed is just a step in becoming a better carpenter so that you eventually produce a better product.
I myself am an advocate of using hand saws to cut the complicated angles on split pitch or octagon roofs whereas some people like to use saws with swing tables on them. Either will accomplish the task, but why not use the pieces of equipment if you have available to you. There’s no question that a skilled carpenter could use just the “layout/eyeball” method to cut any of these type roofs, but using calculations will get you there just as well in my opinion.View Image
Junkhound,
I didn't mean for my post to sound like a lecture or anything like that. So I hope it didn't strike you that way.
Joe (Resurrected) is right about using handsaws, it does take confidence. I don't have any experience with handsaws, so I use a powersaw.
Those handsaws could take a finger off!! BE CAREFUL :-)
Funny you say that! The only scar I got in 20 years of carpentry was from a brand new handsaw! (Oh well, at least it wasn't a power saw!)Any jackass can kick down a barn, but it takes a carpenter to build one.
I still have the scar on my left index finger from wood shop and using a hand saw. Bled like crazy :-) I had a piece of wood in a vise and I was holding below where I was cutting so the wood wouldn't vibrate so much, well the piece broke and the saw on a pushstroke buzzed my finger. Yeeowww
The key words were "something this small" -- assumed a gazebo(w) as only about 60 sq ft
Just to clear things up. It's not that small and it's not 60s/f.
His 8 sides are 108" so therefor his building with is 21' 8-3/4".
I'm going to ask you this question not to be wise just because I'm always curious how other people figure out things.
He told us the side measurements were 108" in an earlier post, that's how I figured common run and the total width of the building and everything else.
Now how would you figure the those measurements when given the 8 equal sides first.
Also how would you figure the side measurements if you were given the common run and width of the building first.
Like I said above I did all that block and string method, eyeballing cuts, snapping lines on the floor and then using the speed square to tell me what the angle is in plan view, cutting with a handsaw, sawzall, planers and the best of all my Framing Square.
It wasn't until 1-1/2 years ago I started using the Construction Master Calculator. In my 20 years of Framing and trial and era and just putting Triangles into the Calculator it just simplifies Roof Framing and I don't have to scratch my head to figure some angle while up on a ladder.
I aslo experimented with the 12th scale on the framing square and it works great.
I'm sure any person that has to frame a roof would like to know a way to do it just from the framing square which you can or have a Formula and do it from a Calculator.
In the office or at home you can take your framing square and speed square with you and get drawing paper 18" x 24" and lay a roof out on that.
Or you can take your calculator with you and a notebook and do your figuring on that.
Why shouldn't everyone try and make they're life easier and learn something new.
I framed with my friends father who is about 64 years old and when I bring up the calculator he says "I'll do it my way kid".
He was snapping lines on the floor to figure out what the sides of a Bay Window should be when I just did it on the calcultor in 2 seconds. Or if the bay is at 45° and the projection is 2' you automatically know that a 1' run would be 16.97" or 17", so a 2' projection, you would have 33-15/16" or 34".
I jokingly called him a Stubborn Mull and told him that you can't teach an old dog new tricks and then he told me that he would throwm my calculator in the garbage. ;-)
Joe Carola
Edited 8/26/2003 6:57:35 PM ET by Framer
You're right that there are many ways to figure this out, and many ways to cut it. Which to go with depends on the equipment available and the person doing it. For a potential pro who'll do this for a living, it makes sense to invest in the calculator and learn how to use it. For an old timer who knows how to just do it by eye, that'll probably be quicker than learning a new way. For a DIY who'll do this once and then have more than enough time to completely forget how before the need arises again, the best approach is probably something very slow and simple, like clamping the piece of wood in a position parallel to and above where it needs to fit, and then transferring lines to it.
BTW, for putting together the top of a gazebo, check out the Simpson site. They have special 6 and 8 side gazebo connectors.
-- J.S.
"curious how other people figure out things"
Originally made the comments on eyeball cuts with handsaw in the same vein as Joe F's more detailed comments.
The way I figure out bigger stuff is simple trigonometry, probably have used trig in one way or another everyday for the last 45 years, usually via slide rule prior to 1972, so by now it is very easy for me to visualize and "just" calculate angles -- visualization and 'top of head' knowledge of equations acquired over decades is (as others have said) much harder to explain to others in a few paragraphs.
BTW, the way angles are figured for really big stuff (eg. 777, 7E7, space station, etc.) is often with a computer program called Catia. "Just" draw a concept on a screen, fit it with everybody else's concepts and other systems, etc. --- program does all the precise fit checks and sends the data to NC machinery.
I'm sure you all have a way to figure out all the measurements of those pesky octogons, but........
Try this
little fellow
I think you will like it.
It is downloadable and free, too.
BrianView Image
Edited 8/27/2003 12:37:49 PM ET by bee