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Hi
I have only built one roof where a hip was joining two different pitch roofs at the corner of a house. I was taught to split the different pitches thus coming up with the hip pitch. i.e. 3/12 and 6/12 is 4.5/17.
Is this correct?
A lead hand framer is saying go with the lower pitch (3/17) as the hip and frame 3/12 jacks into it on the one side and the 6/12 jacks into it from the other side. If that is clear.
Can some one give me a hand. Thanks
Replies
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Maurice,
Splitting the difference does NOT give the correct hip pitch.
For example, if the 2 roof pitches involved were 3/12 and 6/12, the correct hip pitch is not 4.5/17
Here's how to get the correct hip pitch.
Step 1) multiply the unit rises...3x6=18
Step 2) Find the square root of the sum of the squares of the unit rises,
square root(3²+6²)=square root(9+36)=square root(45)
= 6.7082
Step 3) Divide the result of step 1, by the result of step 2....18/6.7082=2.6833
Step 4) multiply step 3 by 17...2.6833x17=45.6161
Step 5) divide the result in step 4 by 12
45.6161/12=3.8
Step 6) put the answer in step 5 over 17. That's the hip pitch
3.8/17 or about 3 13/16 /17
For any other 2 roof pitches, just substitute the new unit rises for 3 and 6 in the above steps.
This is for 90º corners ONLY, which I assume is your case.
Ken
*Dumb DIY question. Been around a lot of years, but never saw slope in terms of xx/17. Ken's number are correct, but where did the 17 come from??
*Hi Art,No question is ever dumb."The length of hip rafters is calculated on the basis of a 17-in. run, as opposed to the 12-in. run on a common rafter. Both types of rafters have the same vertical rise, from the plates tothe ridge, but the hip comes in at a 45 degree angle, which results in a longer horizontal run. The 17-in. figure is arrived at by calculating the diagonal in a 12-in. square, which is 16.97in., rounded to 17. The roof pitch can change, but the units of run, 12 for a common and 17 for the hip remain constant."Larry Haun., The very Efficient Carpenter. pg. 160I hope that passage explains it well enough. Think of it as a diagonal line joining two planes of a dice from a lower corner to a upper corner i.e. the "one" and the "six" as compared to a diagonal line joining the lower right to upper left corner on the face of the "one" on that dice.Sincerly Maurice
*Thanks Maurice: Good ol' sq root of 2, should have guessed that, but never too old to learn. Grandpa and my dad always used "12" for everything, never calculated, just eyeballed the hips and jacks and cut in place with a handsaw, always getting within 1/4" of centers.
*Hey Art,Glad I could help. Maurice
*Maurice, All hips do not intersect the ridge at a 45 degree angle - only when they are equal pitches is that true. Only then is the diagonal approximately 17 (12*Sqr2). Ken's answer in step three of 2.6833 is correct when using 2.6833 and 12 on your framing square. His step 4 & 5 multiplying by 17 and dividing by twelve merely converts these numbers to a new base of 17 and 3.8 on your square. You could convert to any base by dividing by twelve and multiplying by the new base you want to use and using this result and the chosen base as your two numbers on the square. The result is better understood by looking at the original geometry of the problem. If we use 1 as the run for one foot it simplifies the calculation to as follows: Let R1 be one rise (3) and R2 be the other(6). One side of the hip triangle is 1 (one foot) and the other is R1/R2*1 or R1/R2 (thats why we chose one). The length of the run of the hip(per foot run) is the diagonal or SQR(1 + (R1/R2)squared). This simplifies to (SQR(R2^2+R1^2))/R2. This is Ken's square root of R1 squared plus R2 squared or the square root of 9 + 36 but is divided by R2. This is the base number on your square. The number on the blade of the square is R1. Dividing these numbers gives you the ratio of 2.6833 which gives Kens original product of R1 time R2 divided by the Square root of the sum of the squares. You don't need to multiply them out unless you want to change bases on your square. Just use R1 on one side and sqroot of the sum of the squares all divided by R2 on the other side of the square. These two numbers when squared, added, and taken the square root of also give you the length of the hip per foot run. It sounds complicated but in practice it isn't. Just diagram it out and you should be OK.Bill Liimatainen
*Hi Bill,Wow...I had to read that a couple of times. Thanks for the detailed answer......I really appreciate it. I am going to sit down with it and do some paper work on it as I am dying to know it inside out. Roof framing is a great mind tease after the somewhat simplier thought processes of building the walls and floor. Really enjoying the answers to my question. Thanks so much Bill.Maurice Doyle
*Spend the 80 bucks on a construction master 4 calculator and all of your problems will be solved.
*Thanks Steve,No problem spending the 80.00 US Steve, 110.00 Canadian eh! I guess I will have to track one down up here. Not sure if they are readily aviailable retail here in Toronto. I will check however. I have enjoyed reading the theory and practical application to a somewhat seemingly simple framing question. If I had the calculator, I wonder if I would have spent the time educating myself with the help of the kind guys who answered my query. I guess I would have, but, I am sort of glad I posted the message and received great replys. Thanks again Steve I will look into it.Maurice
*Thanks Ken and BillCutting 6/12 into 9/12 tomorrow came up with +- 5 3/4 in 12 for the hip. Now how about how to figure the hip and valley when the roofs meet at either a forty five or 135 degree angle.jim
*Woke up at three this morning. Realized made math error refigured and I'm going with a 5/12 instead.jim
*Jim,First, I want you to get the hips and valleys at the 90º corners correctly cut.The plumb cut on the hips and valleys is 5/12, not ±5 3/4 /12.
*Jim,That was pretty amazing. We both posted the same information at precisely 8:06 A.M. ( you apparently beat me by a few seconds)Anyway, I took a look at the math when a 6/12 roof intersects a 9/12 roof at a 135º outside corner, which would be one corner of an octagon. If the 2 roof pitches involved were both the same, then the hip would bisect the corner angle, forming two equal 67 1/2º angles with the plates. When we change one of the two roof pitches to make them unequal, the path of the hip will swing away from the bisected line, towards the steeper plate. ( the same thing that occurs at a 90º corner when 2 different roof pitches are involved)It just so happens, because of the ratio of the roof pitches that you have, 6:9, that the hip will swing to a position where it makes an angle of 41 3/4º with the 9/12 plate, and 93 1/4º with the 6/12 plate, as shown in the attached drawing.For all practical purposes, the run of the irregular hip, is almost identical to the run of a 6/12 common rafter. So if you make the plumb cut on the hip 6/12, it should fit nicely.Here's something really unusual.Look at the drawing. If you had to put in a hip jack on the 6/12 side of the hip, it would have to run from the ridge to the hip ( like a valley jack), not from the plate to the hip, as a normal hip jack would.
*KenSo it's true great minds think alike. Or at least at the same time. After doing the math I still checked it the old string-line, level and square way. Answer was of course 5/12. Turned out great.We also had to cut the 9 into the 6 at a 135 degree inside corner. The valley rafter was as you said close enough according to the string level and square. The top of the valley rafter went across the 6/12 common rafter just as you said.I had asked my brother how to figure these about a year ago. We (he) spent about an hour or so working out the fomula for me and I put it in my lunch box and lost it. BTW He's an electricaal engineer. He can out woodwork, drywall tape and finish me hands down. A real competent DIY.If I have any roof framing questons in the future can I feel free to ask you? Thanks in advance. I'm sure you may be hearing fromn me.jim
*Jim,No problem.Roof framing is what I do for a living Jim, and I enjoy the math that is associated with it, and enjoy talking about it with others like yourself.I worked out a formula for the Unit Rise of a hip or valley that occurs when two different roof pitches intersect at a 135º inside (valley), or outside (hip) corner. See if it reminds you of your brother's formula that you lost.Let URL = the Unit Rise of the lower pitch roofLet URH = the Unit Rise of the higher pitched roofThen the Unit Rise of the Hip or Valley is equal to= (.7071 x URL x URH)/sqrt( (URL)²+ (URH)² - 1.4142 x URL x URH)In you example, URL = 6 and URH = 9Substituting these unit rises into the formula, we getUnit Rise of Hip/Val = (.7071 x 6 x 9)/sqrt(36 + 81 - 1.4142 x 54) = 5.99Therefore, the Pitch of the hip or valley would be 5.99/12, or for all practical purposes, 6/12.Does that look familiar?
*Ken I find your formulas very interesting and helpful. Would you explain to me where the (.7071) came from.Also how would you go about figuring the hip shorting and set backs and the 2 backing angles.
*KenActually the formula that my brother worked out for me was for the ninety degree hip. And when using your steps one through three it is exactly what he came up with. The only differenc is we used P1,P2 and P3. We never got around to the 135 degree stuff. Thanks again.jim
*R Butters,I've been slow in responding to your post. Sorry about that. Have been very busy the past few days.In the process of deriving the formula that I have shown, in the next to the last step of the derivation, I ended up with the square root of 2 as a factor in the denominator of the formula. In an effort to make the formula easier for the average guy to use, I eliminated it by expressing it as .7071 instead, as a factor in the numerator of the fraction.In other words, 1/square root(2)= 1/1.4142= .7071As far as the shortening and setback go for the cut at the top of the hip or valley, let me say this. This situation that Jim has decribed, 2 different pitches intersecting at a 135º corner, rarely occurs. If I ran into this problem, I would make an accurate full scale drawing ( 1 1/2" wide hip/val, 1 1/2" wide ridge boards) to determine how to make the cut properly, and determine its length. It's possible to work out a mathematical formula for any situation, but why bother, when you only need it about once in a decade?
*Ken describe-rarelyCrazy thing is you got me through that one in February and now in March I'm faced with a similar situation, This time though it is a 9/12 into an 11/12. The good thing is this time it is all trussed and I know those pretty well.Thanks again for all your help!jim
*Jim,Thanks for writing. Good luck on your project.Ken
*I'm working on a house right now with different pitches.It's all hip with a 12/12 and a 9.75/12.The hips and valleys are offset which made things a little tricky.We pulled some strings and with a little trial and error figured out our hip and valley pitch.It ended up being a 11/12 hip and valley cut on a speed square.The jacks on one side were on a 40 degree bevel and a 50 degree on the other.Once we had our angles figured out,everything planed in perfectly.
*Tool Shed,Your figures are very close and I'm sure the roof came out nicely using the figures that you mentioned.The actual bevels are 39º for the 12/12 jacks and 51º for the 9 3/4 /12 jacks. The hip and valley pitch would be 7 9/16"/12 or on your speed square, that would be a 10.7 hip, just a little under the 11 mark.Using a framing square that would be about 10 11/16 / 17.Ken
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Hi
I have only built one roof where a hip was joining two different pitch roofs at the corner of a house. I was taught to split the different pitches thus coming up with the hip pitch. i.e. 3/12 and 6/12 is 4.5/17.
Is this correct?
A lead hand framer is saying go with the lower pitch (3/17) as the hip and frame 3/12 jacks into it on the one side and the 6/12 jacks into it from the other side. If that is clear.
Can some one give me a hand. Thanks