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Discussion Forum

Valley rafter bevels and angels???

bhendrix | Posted in Construction Techniques on September 5, 2005 06:12am

Hi Folks,

I’m helping a friend with his a home addition.  He has a new 8/12 pitch roof (adjacent) intersecting an existing 12/12 pitch roof (main).  The ridge of the new 8/12 is going to be about 21″ higher than the existing 12/12 ridge, due to the greater span (building width).  The top plate on all walls is the same height and perpendicular.  Can someone help me with the calculations for the angles and bevels for the valley rafter?

Thanks,

Bill Hendrix

Reply

Replies

  1. Piffin | Sep 05, 2005 07:12pm | #1

    I don't even have to look that up. A 12/12 is 45°. It sounds like he will be laying the addition roof atop the 12/12 existing california style.

    So layout the new rafter seat cut with the framing square for the 8/12 and cut it with the saw bevel set at 45°

     

     

    Welcome to the
    Taunton University of
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  2. Piffin | Sep 05, 2005 07:24pm | #2

    So how does he plan to deal with the additional height where ridge does not intersect? I would cahnge the pitch down to 6 or 7/12 maybe, depending on overall design. Otherwise, there willbe a funky hip interupting the original ridge or a small dutch gable with a vent in it. neither ever really look good in that application.

     

     

    Welcome to the
    Taunton University of
    Knowledge FHB Campus at Breaktime.
     where ...
    Excellence is its own reward!

  3. olle | Sep 05, 2005 09:44pm | #3

    will you be flat framing the valley or will you be framing actual valley into the roof system?

    1. wolverine | Sep 05, 2005 10:31pm | #5

      Good question olle. Big difference in the difficulty of the project and the amount of time it will take to complete.  As mentioned, the 45 degree bevel and 8/12 pitch is correct for flat valley framing.

      wolverine

       

      1. Piffin | Sep 05, 2005 10:42pm | #6

        I assumed the overlaid because it is an addition and to rebuild the existing would increase costs. 

         

        Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!

        1. wolverine | Sep 05, 2005 11:12pm | #7

          I totally agree with the design issues you mentioned piffin. The new roof would have to hang over the existing ridge so that the gable is flush to the ridge.

        2. MrJalapeno | Sep 05, 2005 11:42pm | #8

          I agree with your evaluation of the new roof to existing with reference to keeping the new roof’s ridge below the existing 12/12 roof’s ridge too.  It's usually a better visual design scenario for a tie-in roof.

           <!----><!----><!---->

          Fwiw, I would frame the new roof’s valleys directly over the uncut existing roof’s shingles too.  I would not cut into the existing roof until the new roof is ready to dry in.  The shingles should then be done as soon as possible too.  (assuming this is a shingled roof, of course)

          1. Piffin | Sep 06, 2005 12:29am | #9

            I would tear off the shingles along that line so that I have a more direct bearing. leaving just the tarpaper there is enough for he temporary dry-in 

             

            Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!

          2. MrJalapeno | Sep 06, 2005 12:50am | #11

            I know what you’re saying but there is always a chance you’ll leave the roof like that overnight and a storm will come a haunting.  It is just a matter of preference as far as I’m concerned and I like to play it safe, and you really can’t get much safer than not cutting the existing roofing.

             <!----><!----><!---->

            It seems like around here that tearing a roof off is like doing a rain dance.  It’s a sure bet, you’re gonna get wet. 

          3. Piffin | Sep 06, 2005 01:07am | #12

            In thirty five years of this, I've only had one small leak, so I must do it safe enoughly.Reason I get concrened about taking the shingles off is that unless they are thin three tabs, with no curling and cupping, there will be some compression after the fact. only 1/8" or so, but that can be ebnough to mess up some rooflines, plus if it settles after the roof and valley work is all done, the seals can be tweaked open to leak later. So I'd rather built it like a rock to begin with, wood to wood. 

             

            Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!

          4. User avater
            dieselpig | Sep 06, 2005 01:56am | #15

            Piffin, I agree with you that stripping along the valley lines is a good idea when tieing new into old.  Not only is it better framing practice (just in my opinion), but it gives you a chance to inspect the existing roof sheathing for damage or tell tale signs of leaks and what-not. 

          5. MrJalapeno | Sep 06, 2005 01:57am | #16

            Lets see………well, in the 34 years I’ve been doing it I’ve never had a leak. Not one!  Not even when the new roof was left without paper over night, which has happened a few times.  I feel the 1/8”, or even the ¼” settling concerns are not enough to cause any future problems.  I am more concerned with damage to existing interiors while I am on the job than with minute, rough framing measurements that “may” occur after I leave.   

             <!----><!----><!---->

            I can guarantee that the only reason for any HO’s complaints that could have occurred would have been from preexisting problems of the roof I have tied into.  Not cutting into these roofs to further expose a problem has also been a concern.  To date, no leaks and no complaints.   I always make it clear that I am not responsible for pre-existing roof problems and I will charge extra to address them if needed.  Otherwise, the roofs I frame will be flat and they will not leak.

             <!----><!---->

            Btw, I haven’t encountered to many “perfect roofs” in my 34 years either.  I mean other than the ones I built. Lol.  I have flat turned down some jobs due to horrible preexisting roof conditions.  Sound like a good thread topic, “Why I wouldn’t take that Job”

          6. Piffin | Sep 06, 2005 02:36am | #19

            to each his own. 

             

            Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!

          7. MrJalapeno | Sep 06, 2005 04:04am | #29

            I agree, to each their own.  Like I said, "Matter of prefference".

             I have done it the way you describe but not for about 28 or 29 years or so.  It worked then, and it will still work today, I just don't do it like that anymore.  The heavy shake style shingles do require some top tabs removed from time to time to help keep the valley flatter to the roof but the light three tabs are no problem at all.  But it is quite a bit faster to frame the roof too if you don't have to cut the shingles though.

            Like olle said, I'm not looking for a who knows the most whizzing fest,  Just here BS'n with ya.

            I'm looking forward to what olle has to share with us.

          8. olle | Sep 06, 2005 12:38am | #10

            nobody has said any thing about overhangs do you want them equal ? if so you will have ####plate hight adjustment ,or do you want the valley to spring from the inside corner and look nice inside. I have seen way to many unequal hips and valleys done wrong it frustrates me . I agreee with the laid over but folks may need to know how to figure out where a unequal valley or hip can spring from and an easy way to devolepe angles . what do you guys think

          9. MrJalapeno | Sep 06, 2005 01:14am | #13

            I have actually built the scenario you describe, as it relates to an irregular chamfered ceiling, and the method I used to accomplish the task was to rip the steeper side’s jacks down so I would have an equal plate height line for the ceiling on the inside and the HAP for the rafters is equal too, outside.   A flat ceiling will not matter and I build them basically the same but with out the ripped jacks.  The plans I deal with regionally rarely have equal overhangs on irregular hip roofs and usually have equal pitches for the chamfered ceilings too.  (Iow, the shallow pitch is framed under the irregular steeper pitch.)

          10. olle | Sep 06, 2005 01:42am | #14

            Good idea hope you dont have to do this with tgis . what then ? In our area if you rip dimenisional lumber it is then not up to span ratings . lesson # 42 in apprentice school. I have been framing super high end houses for the last 18 years and in the housing tracts for 15 years before that. I always belive that I can learn somthing from sombody else. As far as I have been able to figure out there three senarios for un equal pitch no overhang, equal overhang and plate hight adjustmant, and equal plate hight and unequal overhang . I dont mean to be a curmongen but I would like guys to learn an simple and elegant way to figure these things out , and has anybody checked my math? please do I only do the math to the 1/8 " for stickstuff but I will go much farther for timber stuff. are you guys with me?

          11. MrJalapeno | Sep 06, 2005 02:14am | #18

            One of the things about ripping the steeper jacks is that they are always shorter than the adjacent shallow side and usually are over built for their span strength needs anyway.  Your concern is also why they often frame the ceiling below to match the shallow pitch.

             <!----><!----><!---->

            I have not encountered this scenario with a TJI constructed roof yet, but I have thought about it.  The bigger/taller the rafter the greater the difference would be for ripping so If the designer did his home work he might find the two different size TJI’s might work for a specific combination of irregular pitches to work from the interior plate height and have equal HAPs, other wise the HAP would have to be different for each rafter and the hip would be likewise adjusted or backed to match the HAPs..

          12. olle | Sep 06, 2005 02:50am | #20

            In europe the roof pitches work in degrees so the carpenters must learn to do anything. The european carpenters even have a simple way of shifting the hip or valley rafter so that both sides of the hip or valley are equal on the backing cut. somthing called grundshibundgen in german, I hope I spelled that right . I must still say have you checked the math I have done many of these roofs and have been around awhile The first one i did as an apprentice was in 1973. All I want to know is if folks want to know how to really figure out how to do this. Its great to hear that you are thinking about the problems , and we have the answers. I always say to young carpenters that a simple gable roof is #101 and a hip and valley is #201 and unequal hips and valleys are #801 as in collage courses. lets get folks in the know

          13. Piffin | Sep 06, 2005 03:00am | #21

            I must be about a 410. glad to seee someojne who knows something and can teach it. 

             

            Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!

          14. olle | Sep 06, 2005 03:05am | #22

            410 better than 101

          15. olle | Sep 06, 2005 03:29am | #24

            in order to calc. an unequal pitch you must firstpick a therotical hight above either plate or eave assuming those at 0' . say for this example 12" we will then do a horizontial cut at 12" above the 0 line for both pitches. with me? here we go 8/12 = .666. 12"/.66=18 1/32, and 12/12= 1 . 12"/1 = 1 . so lets draw it out in 1 /12 scale for you square guys or 1 to 1 for all the rest of us. when you do this it shows an intersetion from 0 to 12" above 0 and gives a line for our valley or hip. got it or did I lose you guys? It is easy you just have to understand the horizontial roof cut. I can also post a simple spread sheat for the roof cut for all common pitches.

          16. Piffin | Sep 06, 2005 03:43am | #27

            I guess I got lost with out a drawing. HAP i get. varied overhangs i get. Angle isa what I have trouble with. notice the mis-spelled title of this thread - are you the angel of valley angles 

             

            Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!

          17. olle | Sep 06, 2005 03:51am | #28

            I will do a drawing for a simple unequal pitch hip or valley with equal overhang and post it Just tell me the roof pitches you want and I will do it hip or valley . Do you want the math or just the develpoed drawing, or both. It seems that this needs to be written about soon. I will pass that along to the powers that be. all the best

          18. Piffin | Sep 06, 2005 10:59pm | #31

            sounds like a good way to do an article - step by step figuring process, for the magazine. 

             

            Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!

          19. Piffin | Sep 06, 2005 03:38am | #26

            also means i'm a litle scattergun. There are holes in what I know. 

             

            Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!

          20. User avater
            dieselpig | Sep 06, 2005 03:11am | #23

            I, for one, would love a review of the unequal pitch roof relationship.  Let's do an unequal pitch hip with equal overhangs.

            This is something that I can and have done, but usually have to do some real head scratching along with some homework in Roof Cutter's Secrets and Roof Framer's Bible.  Maybe someone else's perspective and explanation will make a few more lights come on for me.  I've only been framing roofs for about 7 years and while I do have a good foundation... there's always room for improvement and a desire to learn.

            By all means.... teach away.... I'm listening intently.

          21. olle | Sep 06, 2005 03:35am | #25

            hey email me and we can talk its simple and fun you will blow them away with this

      2. olle | Sep 08, 2005 10:35pm | #42

        I have made a simple drawing of what is called the roof cut, and attached it I hope it works. It shows a profile of a 12 pitch and a 8 pitch and a 12 " cut and then a plan view showing the relationship. If you want to show plates then draw them in at equal distances into the building from the 0 line and you will also have the hip corner offset. Make sense ?

        1. bhendrix | Sep 10, 2005 07:59am | #43

          Thanks everyone.  Got the valleys and rafters cut with your help with the angles.  Everything worked out great.

          1. JBartok | Sep 10, 2005 07:06pm | #45

            Hello all:

            This discussion has piqued my interest. For those who like to frame a roof by calculation here are some links to Hip-Valley framing math.

            Main Page: Timber Framing and Joinery Math

            Online Calculators and Worksheets

            A limited version of Roof Framing Angles, better suited to stick framing.

            Browse the site, I hope you folks here find the info useful.

          2. JBartok | Sep 10, 2005 07:22pm | #46

            Valley Angle: 29.01714°

            Plan Angles:

            8÷12 SIDE: 56.30993°

            12÷12 SIDE: 33.69007°

            Backing Angles:

            8÷12 SIDE: 17.92021°

            12÷12 SIDE: 36.03989°

            I don't understand what the 18.34° and 37.87° angles are for or how they were determined.

            Edited 9/10/2005 3:07 pm ET by JBartok

          3. MrJalapeno | Sep 10, 2005 11:41pm | #47

            Welcome Joe Bartok,

             <!----><!----><!---->

            I’m pleased to see you’ve made it over to BT.

             <!----><!---->

            My spreadsheet agrees with Joe Carola’s and your figures too.  It also does the Sleeper’s bevel at the same time, which is the sum of the backing bevels for both pitches taken from 90 = 36.04 degs.  I’m just curious about the coincidence of the sleeper’s angle being equal to the 12 pitch’s hip backing angle.  Does that always happen with combinations of 12 and any pitch?  (I’ll bet it does.  It was just something I noticed when I looked back.)

          4. User avater
            Timuhler | Sep 14, 2005 04:44am | #53

            If I remember correctly, the sleeper angle will be the same as the 12 side.  I figured a bunch of them when the original thread at JLC was going strong a few years ago :-)

            Edit,

            I found Ken's post  http://forums.jlconline.com/forums/showpost.php?p=96750&postcount=169

             

            man was that some fun reading :-)

            Edited 9/13/2005 10:02 pm ET by Timuhler

          5. MrJalapeno | Sep 14, 2005 06:24am | #54

            Yes, those were some fun forum times weren't they?  I miss ole Ken, Chippy and Boyd (and a few others too).  They were all great carpenters to exchange thoughts with.  It hasn’t been quite like that since.  Thanks for the memories Tim.  I didn’t remember that specific post till I reread it.  I wasn’t looking that far back.  Almost three years now, man time flies!

  4. olle | Sep 05, 2005 10:24pm | #4

    if you are framing convential the valley will be at a roughly 33.69 deg angle from one plate and a 56.30 for the other side assuming you make these as plumb cuts for the jacks these are tool angles. the valley is then roughly 29.02 deg piths and the backing angles are 18.34 for one side and 37.87 for the other side good luckemail me for more info if you want

    1. FramerJoe | Sep 10, 2005 06:38pm | #44

       f you are framing convential the valley will be at a roughly 33.69 deg angle from one plate and a 56.30 for the other side assuming you make these as plumb cuts for the jacks these are tool angles. the valley is then roughly 29.02 deg piths and the backing angles are 18.34 for one side and 37.87 for the other side good luckemail me for more info if you want

       

       I dont mean to be a curmongen but I would like guys to learn an simple and elegant way to figure these things out , and has anybody checked my math? please do I only do the math to the 1/8 " for stickstuff but I will go much farther for timber stuff. are you guys with me?

       

      For the bevels, I get 17.92168° and 36.04242°

       

      Tan-¹(sin(29.02) / Tan(56.31) = 17.92168°

       

      Tan-¹(sin(29.02) / Tan(33.69) = 36.04242°

       

       

      Joe Carola

      1. olle | Sep 10, 2005 11:56pm | #48

        Hey great thanks for checking the math I am no mathamtician, and did the backing angles from a scale drawing I need to learn more trig to be as accurate as you I will check
        the sites you mention and thanks for putting them up. I have found that most folks can get the simple angles yet have difficuty plotting { especially valleys that are conventionaly framed } where the framing members actually go. Which is why I showed the drawing of the roof cut did it make sense to you?
        Hey are you a timber framer ? I don't uasually figure backing angles, I have a simple drawing method of obtianing them so I don't use the math. Its is easier for me and I don't make make the mistakes like you picked up in my math.1 or 1.5 degrees out won't be so bad in a backing cut with stick framing or in a very rough timber frame but in a hip or valley run it will kill you. what do you think

        1. JoeBartok | Sep 12, 2005 04:57pm | #49

          Thanks for the welcome guys.

          Mr. Jalapeno: I just calculate from Backing angles from whatever parameters are given and to be honest I've never thought about the sleeper angle with regard to a 12/12 pitch meeting another pitch. I'll play around with the math today and see what the geometry says.

          olle: Here's how I determine the angles for complex roof systems by Development. The trig shown on the diagrams can be disregarded and the angles determined solely with compass and straightedge. The web page contains links to "slideshows" showing the developments of the angles directly "on the stick". I'm not a timber framer but I did learn log building about twenty years ago. My experience at stick framing is more limited. Timber framed, log, or stick roof: the angles are all the same. In a timber or log roof the joinery is visible inside and appearance is everything. It takes a lot less than a degree to "kill" a roof especially over a long span. I carry out my calcs to five decimal places in degrees and inches and round off to the nearest 1/32nd of an inch on the final dimensions.

          There's a link to an Excel worksheet titled Log Angle Generator.xls on the Framing Angle Calculators page: anyone's welcome to download a copy. Many of the angles referenced, those most apt to be used for framing, use Hawkindale angle names. The next incarnation of this worksheet will include angles for cutting square tail fascia.

          Joe Bartok

          Edited 9/12/2005 10:00 am ET by JoeBartok

          Edited 9/12/2005 10:22 am ET by JoeBartok

          Edited 9/12/2005 10:23 am ET by JoeBartok

          Edited 9/12/2005 4:48 pm ET by JoeBartok

          Edited 9/12/2005 4:48 pm ET by JoeBartok

          Edited 9/12/2005 4:49 pm ET by JoeBartok

          1. JoeBartok | Sep 12, 2005 08:56pm | #50

            I won't get a chance today to tackle the sleeper bevel angle math, but here's where I intend to begin and perhaps someone else can work this out.  We can determine the following angles geometrically as per the Developments web page in my last post.

            The formula for the Backing angle is:

            tan Backing Angle = sin Hip Pitch Angle ÷ tan Plan Angle

            The term sin Hip Pitch Angle will be constant for the Backing angles on both sides of the roof. If the Hip eaves or Valley ridges meets at 90° in plan: geometry guarantees that the 12/12 side Plan Angle equals the Common Rafter Pitch angle for the adjoining side. The adjoining side Plan Angle equals the complement of its own Common Rafter Pitch angle.

            Based on this we should be able show why the sleeper bevel equals the Backing angle on the 12/12 side of the roof.Joe Bartok

          2. JoeBartok | Sep 13, 2005 05:42pm | #51

            I had a chance to think about the Backing Angle and Sleeper Bevel last night after all. I still think there’s a really simple way to do this with just geometry or maybe an easier way with trigonometry. For now here’s a solution using the sum of the cosines of two angles. The sum/difference formulas for sines and tangents also work but they involve trig functions of the Hip-Valley pitch angle and the equations become even more convoluted.

            These equations are true only if:

            The plan angle between the Hip eaves or Valley ridges = 90°

            One of the pitches is 12/12

            If the plan angle is other than a right angle and/or the one of the pitches is not 12/12 … don’t try this at home!Joe Bartok

          3. olle | Sep 14, 2005 03:39am | #52

            olle: Here's how I determine the angles for complex roof systems by Development. The trig shown on the diagrams can be disregarded and the angles determined solely with compass and straightedge. The web page contains links to "slideshows" showing the developments of the angles directly "on the stick". I'm not a timber framer but I did learn log building about twenty years ago. My experience at stick framing is more limited. Timber framed, log, or stick roof: the angles are all the same. In a timber or log roof the joinery is visible inside and appearance is everything. It takes a lot less than a degree to "kill" a roof especially over a long span. I carry out my calcs to five decimal places in degrees and inches and round off to the nearest 1/32nd of an inch on the final dimensions. Joe thanks for helping me with the math I have been learning the math and I always check with a drawing. I learned developed drawing in apprentice school and have always relied on these for the angles. The pages you recomended are terrific and I will study them over the next few weeks. how do you deal with backing angles or sleeper angles mathamatily when roofs don't intersect at 90 degrees? I can draw the angles very easy but I would love to know how to do it with math. Also will you reccomend a better calculator than a const. master? thanks

          4. JoeBartok | Sep 14, 2005 07:42pm | #55

            olle: To tackle any combination of Irregular pitches and plan angle between Hip eaves or Valley ridges we first have to extract values for the plan angles as measured from the eaves (or ridges) to the Hip-Valley run. This is how I do it: Solution of General Plan Angle

            Once we have determined these angles (they're also called cheek cut angles or Deck angles) we can proceed to solve the remaining angles: Hip-Valley Pitch, Backing angles ... etc.

            Calculators: I've used programmable graphing calculators from the get-go. The capacity of some of the newer models does justice to a small computer. Mine is several years old; it's a Casio 7700-fx. It only has a 4K RAM, but that's sufficient to store all the calculations currently posted at my weblog and has room to spare for programs for engineering beams "in the round" (logs, that is).

            Advantages: Constantly pushing buttons is a thing of the past. You save your formulas as a program and if you wish to edit the program and add new formulas you can do so. For example, on my calculator I would simply enter values for Major Pitch, Minor Pitch and Plan angle between eaves. Then all I keep pressing is the EXE button and read the results of the calculations. I currently use about 38 different angles (generally with different values on the Major and Minor Spans, which effectively doubles that number!). As you can imagine it would get a little onerous keying in each calculation one at a time.

            Another bonus is that the calculator has a "REPLAY" or "EDIT" function. (Actually most calculators, programmable or not, have this built in them nowadays). You see your formula on-screen as you enter it. After your calculation has been carried out you can hit the "REPLAY" key - and there's your formula on-screen again. It's great for folks like me who make a lot of typos. Or, if you're calculating jack rafter lengths you can enter your formula, solve, then produce the formula again and enter a new dimension ... as many times as you like.

            The greatest advantage of programmable calculators is that they're adaptable for any purpose: framing angles, volumes, areas, engineering, financial calcs, you name it, the calculator can do it.

            Joe Bartok

            Edited 9/14/2005 12:47 pm ET by JoeBartok

            Edited 9/14/2005 12:48 pm ET by JoeBartok

          5. olle | Sep 15, 2005 02:59am | #56

            Once again thanks, I spent some time with you web pages this afternoon and realized I that your drawing is exactaly like mine . When I draw a intersetion kernel I draw both sides, and develope the backing angles for both sides at a time . Have you ever seen Eric Sloane"s book on barns. There is a great old drawing of old barn and its rafter developement, also showing backing angle fully developed just as you have done.
            I also have a book whhich is a text for the french Compagon it is called "La Charpentte En Bois " isbn # 2-85101-022-0. which is in french but if you can draw and understand drawing is invaluable.
            I will be shopping for a new calculator soon and follow you recomendations .
            Lets keep this up

          6. JoeBartok | Sep 15, 2005 06:56pm | #57

            olle: By all means "keep this up". I find discussing math applied to real life construction problems keeps my skills sharpened.

            I don't really have any timber framing or joinery literature to speak of. I was well into my own analysis of the math when a friend in the log building industry learned of my interest and gave me a copy of the Hawkindale angles. It's pretty much what's posted at the Timber Framers Guild website.

            I found these Hip and Valley Books a couple of years ago. There's a copy of the Martindale book. And check out the "analytic proofs" in the McKibben-Gray book ... wow! That's what I call an analysis!Joe Bartok

          7. olle | Sep 16, 2005 01:47am | #58

            I do have those both and I am learning the math and having a ball. I found them after working with the hawks. If you can find the french book it is great. Try abebooks.com, I find myself looking at it several times aweek.

          8. JoeBartok | Sep 20, 2005 09:02pm | #59

            olle, check out this Development of Backing Angles. Someday I'm going to do a series of these with a state-of-the-art program, perhaps  in VRML (this is just a series of "Paint" bitmaps saved as GIFS).Joe Bartok

          9. olle | Sep 20, 2005 11:19pm | #60

            Joe , that is sweet. I use the same method for all backing angles . It is simple and elegant for polygon roofs as well. I hope others will look at it as well. What about the math for backing angles for unequal pitch roofs that don't intersect at 90 degrees?

          10. JoeBartok | Sep 20, 2005 11:58pm | #61

            The formula Backing Angle = arctan (sin Hip-Valley Pitch Angle ÷ tan Plan Angle) will work for any roof configuration of irregular pitches, any angle between Hip eaves or Valley ridges. The "slideshow" shows a 90° eave or ridge angle (or "wall" angle W) but the development and trig will work regardless of the value of this angle.

            I wanted to keep the "slideshow" strictly geometric so I didn't label or define the following lengths and angles:

            The Major and Minor, or Main and Adjacent Plan Angles (DD and D respectively) are measured from the Hip eave to Hip run, or Valley ridge to the Valley run (near the upper right corner of the diagram). Angular values depend only on ratio and proportion and remain the same regardless of scale. So, let's set the value of our Hip run = 1. (If the Hip run is set at some other value, all lengths are increased proportionally).

            If the Hip run =1, then the line being drawn perpendicular to the Hip length, which eventually forms the rise of the Backing angles, equals sin Hip-Valley Pitch Angle (or sin R1). The lines produced through the Hip rise until they intercept the lines of the eaves (or ridges), the runs of the Backing angles, equal tan Major Plan Angle and tan Minor Plan Angle (or, tan DD and tan D).

            And there are our Backing angle formula(s). The tangent of an angle equals Rise ÷ Run, therefore:

            Main or Major Side: tan C5m = sin R1 ÷ tan DD

            Adjacent or Minor Side: tan C5a = sin R1 ÷ tan D

            Or re-arranging the equations:

            C5m = arctan (sin R1 ÷ tan DD)

            C5a = arctan (sin R1 ÷ tan D)

            And ... we made no assumptions or placed any special restrictions on the values of W, or the Main and Adjacent Pitch Angles SS and S, the values of which determine the Plan Angles DD and D. The formulas are true under ALL conditions.

            Joe Bartok

            Edited 9/20/2005 5:01 pm ET by JoeBartok

            Edited 9/20/2005 5:20 pm ET by JoeBartok

            Edited 9/20/2005 5:23 pm ET by JoeBartok

          11. olle | Sep 22, 2005 03:04am | #62

            joe so if I get this right if the plan angle is 45 degs. and the tan is 1 then the hip or valley pitch is the same as the backing angle for an equal pitch hip or valley?

          12. JoeBartok | Sep 22, 2005 05:04pm | #63

            Not quite! The number one removes the divisor tan Plan Angle from the equation but we're left with the following expression for the Backing angle for regular pitches meeting at a 90° angle between eaves (or ridges):

            Backing Angle = arctan (sin Hip-Valley Pitch Angle)

            We are taking the arctan of the sine of the Hip-Valley Pitch Angle and this makes a difference in the value returned by the formula.

            However, the Plumb Backing Angle (Hawkindale A7) will be equal to the Hip-Valley Pitch Angle under the above conditions because:

            Plumb Backing Angle = arctan (tan Hip-Valley Pitch Angle ÷ tan Plan Angle)

            At 45° tan Plan Angle = 1 and the formula reduces to:

            Plumb Backing Angle = arctan (tan Hip-Valley Pitch Angle)

            Taking the arctan of the tangent of an angle returns the original angle.

            Joe Bartok

            Edited 9/22/2005 10:13 am ET by JoeBartok

  5. User avater
    maddog3 | Sep 06, 2005 02:10am | #17

    I see you made it here,

    welcome aboard !

    Lot of good folks here,

    "
  6. MrJalapeno | Sep 06, 2005 04:33am | #30

    Olle,

     

    I too use a spreadsheet to create my rafters cut list.  I try to keep it kind of simple so I don’t get lost with information overload.  I am very interested in seeing your spreadsheet.  It would be great if you could attach a screenshot of it to a post.  I have attached a file shot of mine.  I have become lazy with my math because f it too.

     

    One thing I can tell you about the 8/12 and 12/12 dual pitch roof is that the tangents/ratios for this combination is 2/3’s and 3/2’s.

     

    One of the other things that I find fascinating is the method people might use to actually mark and cut the irregular Hip/Val rafters.   I read a lot about the “Hip Drop”.    A technique to plane the unbacked hip. 

    1. olle | Sep 07, 2005 12:52am | #32

      hey thats a great spread sheet. Have you ever seen the hawkingdale angles at the timber framers guild website? tfguild.org I use it all the time for weird stuff, you can change afew cells and get the magic #s. Its is a easy download and a great teaching tool. With it you can get some great drawings that show where all the angles are. If you are astick builder you can ignore the stuff about housings but you never know when you will need it . If you were able to make your sheet you will love the hawks . Its is great to hear that some one is as interested as I am in this kinda stuff. Did you understand the horizontal roof cut to plot hip or valley runs? or did I not explain it well enough? I am still trying to figure out how to get a drawing into the system any ideas?

      1. MrJalapeno | Sep 07, 2005 02:02am | #34

        I have heard and read references to the Hawkindale angles but I have not studied them.  I did just get the download, and the instructions too, from the tfguild.org site.  Thanks for the link.  I recognize some of what is going on in their spreadsheet.  I would like mine to be able to work with intersecting walls that are other than square/90 degs.  As it is now, it only does squares.  Oh boy! Another project!  The answer is right in front of me too.  I wish I were more Trig-literate.  I’ll be getting the text books back out too.

         <!----><!----><!---->

        “Did you understand the horizontal roof cut to plot hip or valley runs? or did I not explain it well enough?”<!----><!---->

         <!----><!---->

        Are you asking about how to find the plumb and level cuts for the Irregular Hip using a random common height dimension? (12")  Or are you trying to explain how to find a ratio of the irregular Hip/Val effective length to an effective run for one of the two pitches?  That probably answers the question about whether or not I’m confused.<!----><!---->

         <!----><!---->

        As far as posting pictures of drawings, I’m a little clumsy with that myself.  I get my AutoCAD drawing on screen and press the “Alt” key and the “PrtScn” (Print Screen) key to copy a picture of my monitor’s screen to the clipboard and then I open Paint or my Photo editing suite to a blank document and paste (press “Ctrl  V” keys) the picture to that.  Then I crop and resize the picture to as small a file that is still readable and save it as a .jpg file.  Then I can use the attachment tools with the message “reply” button tool to share/attach it here on the forum.  I don’t know if that is the help you want, but that’s how I do it.<!----><!---->

         <!----><!---->

        I’m going to go play with the Excel Hawks SS for a while.  I hope you can get some pics posted.  I look forward to them.  Good luck.<!----><!---->

        1. olle | Sep 07, 2005 02:20am | #36

          hey thanks for looking at the hawks I am with you about the trig. As to the roof plot I use that to draw aplan view of the h or v system. I sratr with a profile imagine a roof starting at 0 and another roof also starting at 0 interseting at 90 degs. at 1 ' above the 0 line one roof travles in to the building 1' for a 12 pitch and then 18 " for the 8 pitch. I then draw this out in plan view showing the two intercetion points 1 at 0 and 1 at 12' above the 0 which is the point where the twodiffrent pitches meet at 12" above. boy it sounds crazy but it works I have to get a drawing out to you please be patient with me I will get it out. thanks

    2. blue_eyed_devil | Sep 07, 2005 01:57am | #33

      Mr Japapeno, that is a very impressive spreadsheet. Too bad I don't have a clue as to what it means or what you'd use it for.

      A very long time ago, we were taught how to cut "bastarrd" hips in my apprenticeship school. I can't remember how to do it, but when I have need for the information, I manage to re-create the math using my calculator and framing square. If memory serves me correctly, we never once talked about degrees. YOu really don't need to know anything about degrees to cut a bastard hip, valley, and jacks, but of course after determining the cuts, we automatically memorize the degree cuts for the cheek cuts.

      By the way, all our cuts were done with handsaws.

      blue

      ps I'm on the same page with you regarding the layons over existing roofs. I've done tons of them both ways. In my earlier, more idealistic years, I stripped the roofs, then layed on the valley board. In my older wiser years, I layed the valley board over the shingles. Piffin might be right, it might crush down an 1/8'', but I really don't care because I know an 1/8" won't matter, no how, no way.

      pps I often use 2x valley stock when I'm doing a re-mod layover. Depending on the pitch, I might lay two 2x6's on the flat next to each other or maybe just one 2x8. In either case, the beefiness of the 2x stock presents a very stable anchoring foundation for my rafters.

      blue 

      1. MrJalapeno | Sep 07, 2005 02:32am | #37

        Blue,<!----><!----><!---->

         <!----><!---->

        How’d that Lot-Look’n trip to Tx go?  Did you see any rocks?<!----><!---->

         <!----><!---->

        I don’t have any degree marks on my handsaws either.  Finding the miter angles for the cheek cuts is as simple as drawing a diagonal through a rectangle with sides equal to the two pitches of a bastard hip.  You could read the degrees with you speed square or transfer the bevels to the saw by bevel square.<!----><!---->

         <!----><!---->

        If you were to study my SS for a while you might find some use for it.  But if you are setting trusses most of the time then it might make better wall paper in the blue lagoon.<!----><!---->

         <!----><!---->

        I’m with you totally on the layons.  Btw, did you notice the SS pages/tabs labeled “Sleepers”?

         

        Mr J<!----><!---->

        1. blue_eyed_devil | Sep 07, 2005 06:14am | #40

          What are "sleepers"?

          blue 

          1. MrJalapeno | Sep 07, 2005 06:39am | #41

            "Sleeper" is another name/term for the lay-on flat valley board(s).  Aka, California Valley.

            That sheet of my SS calculates the valley jacks lengths from the unadjusted ridge length.

            My SS is only used to do "Homework" prior to starting the frame.  I still use the old fashioned CM Pro, Riecher's FLRF, Swanson's Blue Book, or the Framing Square for onsite calcs.  I don't have a laptop and probably wouldn't use it if I did.

            Hey, I'm looking forward to your next visit,  It sounds like you got to see a few of the primo sites while you were here.  Feel free to email me.

            Mr. J

    3. olle | Sep 07, 2005 02:02am | #35

      I forgot to mention hip drop. When doing wide hips or valleys I find it better to back rather than drop a hip, and I always back a valley, to many timesthe jacks get held to high or to low and I like just lining up planes. and with unequal hips and valleys this is really helpful. Do you understand the diffrence between backing and dropping? many folks don't. In Dropping the level cut at the seat of the rafter is cut deeper to equal the amount of the backing. does this make sense? With backing the top of the hip is beveled to the coresponding pitch and with unequal this means that both sides are diffrent, does that help?

      1. User avater
        Timuhler | Sep 07, 2005 03:18am | #38

        Olle,

        We set 4 hip beams on Friday.  2 of them were 5 1/4x 11 7/8" LVL and two were 3 1/2 x 11 7/8 LVL.  My plan was to back all 4 of them, but the lumber company goofed up the order and set us back 3 days, so I elected not to back them.  Here are the pics.  Engineer spec'd them.

        The hips were about 25' long and the easiest way to get them to the back yard was to set it the length of the forklift and drive it around the back :-)

        http://pic9.picturetrail.com/VOL293/2163851/7154567/111217505.jpg

        http://pic9.picturetrail.com/VOL293/2163851/7154567/111217523.jpg

        Yours truly http://pic9.picturetrail.com/VOL293/2163851/7154567/111217527.jpg  I'm on a mission to lose some weight :-)

        http://pic9.picturetrail.com/VOL293/2163851/7154567/111217537.jpg

        http://pic9.picturetrail.com/VOL293/2163851/7154567/111217542.jpg

        I think you should start a new thread.  I feel comfortable calculating bastard roofs and irregular corners, but greater number of approaches I can get my hand on, the better my understanding. 

        1. MrJalapeno | Sep 07, 2005 04:56am | #39

          Well,,,,,Tim "Thunder Hips" Uhler,

          Looks good!  I mean very good! Perfect!

          8)  Mr J

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