Can’t get my head around this… have run into it in the past and just boogered my way through.
Picture this….. a 45 degree three sided bay on the front of a house. Bay extends out into the covered front porch area. I need to frame the bay walls up to the 3 pitch porch roof. The porch roof continues past this wall plane into the interior of the house where it is cathedral and exposed so it needs to look decent.
How do I figure out the compound miter angles of the studs making up the two flanking bay walls that run at 45 degrees to the roof framing? And the miters for the top plates?
Don’t make me booger this one! LOL…. I’ve got time… about a week…. to wrap my head around this thing but a nudge in the right direction would be much appreciated.
Replies
I figure the miter cuts on your top plates, if they're nailed flat to the underside of the roof framing, is 23 degrees, plus or minus. Miter and bevel settings on the saw are 10 degrees for both.
Maybe over Christmas, you can play around with SketchUp. It took about 5 minutes to figure, just by drawing it out. Real nice for me, since I hate figuring the math! Merry Christmas!
Mike
That's a good idea Mike. I've been meaning to find the time to play around with Sketchup and this might be just the right opportunity. Thanks.View Image
Brian, I would Sketchup this one for you, but we are in Chicagoland for the holidays, visiting kids and grandson. I'm typing this out on our daughter's laptop.
But lemme ask, just to clarify. You've got a firstfloor bay, three sides of an octagon in plan view, running up and terminating against the bottomside of a 3:12 roof frame?
Right?
To plane correctly, if this is your situation, your top plates for the skew walls and the wall perp to the rafters are not rectangular in x-section. But you know that.
If I had a CM and knew how to use it, I would start with a sketch and start doing some trig. But I gotta go.
Merry Christmas!
Diesel: Prow Peak Framing.
Another way to think of the diagrams in the link is as a "half-Valley" rafter. The studs aren't cut at an actual compound angle; there's no miter angle, the blade bevel is the Hip pitch angle.
Difference in stud length = Spacing O.C. × tan 10.02499° (Hip Pitch Angle for 3/12 Common at 45°)
Plate Bevel = 9.87496° (Backing Angle)
I'm running out of computer time here so I hope I don't "booger" this on you. I'll be back next week to post the solution to the following. For now, just the numbers ... these are for different from the figures above because they are for a true compound angle:
Saw Miter Angle on wide face = 10.02499° (the "Plumb Backing Angle" ... for the 45° Plan Angle this equals the Hip pitch angle).
Saw Blade Bevel = 9.87496° ... for a 45° Plan Angle this equals the Backing Angle
The miter angle on the narrow face of the studs remains the 10.02499° (Hip pitch angle).
Saw Blade Bevel on the narrow face
= arctan(cos 10.02499° × tan 10.02499°) = 9.87496° ... the Backing Angle.
Again, this last set of cuts creates a compound angle and if you set your plate on it it will be tilted to the correct angle. But now the narrow edges of your plate will need to be ripped (at the backing angle) because they will project beyond the studs.
Whew! Hope I didn't frig that all up. And btw, Merry Christmas to everyone! Gotta go ...
Joe Bartok
Edited 12/24/2006 2:40 pm ET by JoeBartok
Edited 12/24/2006 2:43 pm ET by JoeBartok
Edited 12/24/2006 2:59 pm ET by JoeBartok
Edited 12/24/2006 3:29 pm ET by JoeBartok
Joe,
Thank You for posting that link. I guess maybe I can actually try to learn something over the holiday.
Diesel, notice how many edits are included on Joe's explanation.
Now you know why I booger, instead of figure!
hey...I think I've found my motto!
booger, instead of figure!
lol blue
"Diesel, notice how many edits are included on Joe's explanation."
Sorry to get off topic here, but I tend to make a lot of typos for good reason. That's why whenever possible I'll use a hyperlink.
Accuracy is important. If anyone finds errors in the final edits please let me know.Joe Bartok
Joe, I hope you didn't take that post of mine as a shot at your work. I was just making a funny about myself. I fully understand how important it is to understand the math and geometry of complex roof angles. At one time, I was interested enough to explore them too, just as you have done and have actually used them onsite to accurately cut most (I've avoided curved and round things) of the stuff that is talked about in here. I would have loved to have you as a resource back in my days when I was learning about this stuff. Your posts and links are extraordinarily helpful.
Knowing how to do the geometry is critical for overall developement but in the field, I've found that I can booger most of the stuff much faster than I can calculate it, mainly because I have to "relearn" it because it doesn't come up enough to stay in my conscious mind. After my first few technical calculations, to prove to myself that I could do it, I lost interest in the technicalities and focused more on the economics of the situation.
Boogerin' is the technical term for getting it done economically, usually by eye. It normally would take me only two trys to get most cuts right, but sometimes I need three and occasionally it takes me four. There aint no way I ccould calculate that fast LOL!
blue
Blue,
With a Construction Master Trig calculator, it really only takes a few seconds to figure the miter and bevel. I'm not saying this to be contrary, but from experience. But I know what you mean about "relearning". I think what I'm going to do to minimize that, is print out the forumulas with small font and tape them to the inside of my calculator case.
I had them memorized for a long time, then didn't have the situation for awhile, and have forgotten.
The nice thing is that the formulas for the miter and bevel are the same as the you'd use on the roof, so the formulas have a lot of use (they work for birdblocks with some minor changes). So it isn't like you have to remember a dozen formulas or something.
So it isn't like you have to remember a dozen formulas or something
Tim, I agree. In most cases, the angles and bevels are the same simple ratios that are created by holding two commonly known numbers on the framing square. You CM types go immediately to your calculator to find the angles and I pick up my framing square if I need to do an accurate angle.
To see if I'm close to knowing what I'm talking about, start converting some of your angles into simple ratios and I think you'll be surprised at the results. Quite often the same numbers pop up.
blue
Blue: Don't even worry about it. I didn't take you out of context or personally. I too noticed that the edits in this forum ... ALL the edits ... show up and knew it was just a matter of time before someone or other nailed me.
We do a lot of "boogering" in my corner of the world as well. It's often easier, quicker and just as accurate to do a layout using projection, geometry or by scribing.
All: We don't have to remember dozens of formulas. The key is in those developed tetrahedra in the links I posted a couple of days ago. If you ever need a formula it can be solved from scratch, even if for "new" angle or intersection.
Joe Bartok
Edited 12/30/2006 11:16 am ET by JoeBartok
Tim,I had a little note book I got from a supplier about 20 years ago that I kept all my formula in. It was about 20 5x3 pages. . . The problem with paper is it burns. . . .About 15 years ago I bought a Sharp Scientific Calc that was programmable and I programmed the formulas into it. That works.
Joe's got something there with the programmable calculator. As far as I'm concerned they are the mutts nuts. It's like carrying an infinitely variable table of angles with you at all times. Just enter pitch, pitch, and total plan angle between the eaves and no more cyphering, just keep pressing the "=" or "EXE" key.
My Casio (not an advertisment ... there are all kinds of makes and models just as good) is over 10 years old and has paid many times over the 120 bucks it cost.
Joe Bartok
Tim
I have more experience with the math than the actual framing (I'm not a pro framer). But I'm curious as to what the CM pro calculator does for the extra $70 bucks over the $10 scientific calculator that does all trig functions. The obvious thing is the conversions to feet & inches.
BTW: nice article on floor framing in the JLC
Mike
Thanks.
The trig calculator has all the roof, stair, arc etc functions built in. It is just easier to use on the job than a scientific calc. I used to use one when I was still in school and we kept one in the truck, but the CM is just easier to use for construction.
Since your flanking walls are 45 deg, their run is 1.414 x the extension of the bay (hypotenuse of 45 deg triangle is leg times sq root of 2), so the pitch is 3:12 divided by 1.414 or 2.12:12 = 2 1/8:12. The bevel of the top plate is at 90 deg to the flanking wall, therefor also at 45 deg to the roof pitch, so it too will be 2 1/8:12.
My 7" speed square is not big enough to give me an accurate angle for 2 1/8:12 pitch (somewhere around 11 degrees, looks like), but you could work it out with a framing square and miter angle gauge.
arctan(2.125/12) = 10.04202° ... looking goodJoe Bartok
JLC Wall Framing ThreadJoe Bartok
dp,
Use this formula to first determine the “miter” cut:
Miter setting = Tan-1 ( tan (roof angle) * cos (plane angle))
Use this formula to first determine the “bevel” cut:
Bevel setting = Tan-1 ( sin (miter setting) * tan (plane angle))
This should get you where you need to be. . .
Numbers are still looking good; they all agree. Whew, I typing at maximim speed and afraid I screwed up!
See you all next week. :)Joe Bartok
I gotta fly..... gotta go do the 'family holiday thing' for awhile.... but you guys are the best! We'll talk more about this in upcoming days I'm sure.
Happy Holidays everyone!View Image
Brain,The angle on the stud is the hip angle.The saw setting angle when you cut the stud is the hip/valley backing bevel angle.Using your CM Trig.3 [Inch] [Pitch]1[Inch] [Run] (Doesn’t matter what number you use, 1 is the fastest)[Hip/Val] (Twice)-Returns - 10.02° (Angle on stud and also Hip/Valley Pitch Angle)[Sine][Conv][Tan] Returns - 9.874962° (Saw Setting and also Hip/Valley Backing Bevel)So basically you mark a 10° angle on the stud and set your saw to 10° because it’s so close.Some books actually say that the backing bevel is the same as the hip/valley pitch angle and it’s not.Merry Christmas!
Joe Carola
Hey Joe, Is there a way to get that backing bevel without a CM trig ? I guess it's tim e for me to upgrade my calculator again if not. JK
>> Is there a way to get that backing bevel without a CM trig ? <<John,I have a drawing that I made a while back showing how to get it without Trig using an 8/12 pitch roof.I just come in level half the thickness of the hip and then plumb up and that's the hip drop amount. That plumb line is a 25.24° same as the hip. It's not the same angle as the backing bevel which some people and some books say they are.That line is Plumb for the hip drop and the correct line for the backing bevel is Square off the top of the hip. That's the correct measurement. That measurement you enter as the rise and enter half the thickness as the run and press pitch, that gives you the correct backing bevel.This is for an 8/12 pitch.25.24 [Pitch] .75 [Inch][Diag]
[Rise] = .319808" [=] [Rise]
.75 [Inch] [Run] [Pitch] = 23.09° (Backing Bevel)25.24 [Pitch] .75 [Inch] [Run]
[Rise] = .353563" (Hip Drop)This is for an 3/12 pitch.10.02 [Pitch] .75 [Inch][Diag]
[Rise] = .130494" [=] [Rise]
.75 [Inch] [Run] [Pitch] = 9.87? (Backing Bevel)10.02 [Pitch] .75 [Inch] [Run]
[Rise] = .132515" (Hip Drop)The CM Trig is alot faster and I would get one if I were you since you do so much framing and it takes a lot less steps to figure anything with it.This is the backing bevel for an 8/12 pitch using the hip pitch angle.25.24 [Sine] [Conv] [Tan] = 23.09°Joe Carola
Edited 12/27/2006 4:14 pm ET by Framer
Hip Rafter Shift and Drop: Pages #2 and #3 illustrate the difference between the Backing Angle and Plumb Backing Angle. Like Joe Carola says they are not the same thing.
I'm surprised to learn that some books also say that the backing angle is the same as the Hip pitch angle! For an irregular roof, the angle of the Hip rafter, the backing angle and the angle viewed along the plumb cut are three different values.
Question: Is there another name for this "Plumb Backing Angle"? I was told that this was what it was called about fourteen years ago. This is the same as the Hawkindale angle labelled A7 at the Timber Framers Guild website.Joe Bartok
Example: 7/12 and 10/12 slopes intersecting, the angle in plan = 90°
Hip Pitch Angle = 25.54245°
7/12 Side of Roof:
Backing Angle = 16.79517°
Plumb Backing Angle = 18.49610°
10/12 Side of Roof:
Backing Angle = 31.63186°
Plumb Backing Angle = 34.32109°
Joe Bartok
>> Pages #2 and #3 illustrate the difference between the Backing Angle and Plumb Backing Angle. Like Joe Carola says they are not the same thing.I'm surprised to learn that some books also say that the backing angle is the same as the Hip pitch angle! <<Joe,I have two books that say that the backing angle is the same as the hip angle. One book is "Roof Framing" by Marshall Gross, Page 134.The other one is "Measuring Marking & Layout" by John Carroll, Page 144 and 145 with a drawing backing the bottom of a valley.The angles are close on lower pitched roofs, but when you get higher up they change.For example the 8/12 pitch, the hip plumbcut is 25.24°, the backing angle is 23.09°.For a 12/12 pitch the hip angle is 35.26° and the backing angle is 30°.Joe Carola
Edited 12/27/2006 4:23 pm ET by Framer
I scratched this out on paper today while eating lunch and concluded that Marshall Gross' book was in error. Thought I was going nuts. Came home and saw you reached the same conclusion. I learned a lot. So where's the book that's right? Carroll's discussion of hip drop is weak.
This is a good thread.
I for one have gotten lost in the different names of the drops, shifts, angles etc. Can someone do a very simple drawing lableing just which is which. Hate it when the terminology isn't the same everywhere gets very confusing to an old mans brain.
This is why I usually suggest that if one wants to really understand the math ... do your own work! It's not that books and forums aren't excellent teaching and learning tools, they are. But people make typos and honest mistakes. And a formula from a book or the Internet is ... just a formula. Take the familiar formula for the Backing angle:
Backing Angle = arctan (sin Hip Pitch Angle / tan Plan Angle)
If someone wants to back a Hip or Valley that's good enough. But how do we derive this formula, why those terms? How does the Backing angle relate to shifting and dropping the Hip rafter? Are there other formulas for the backing angle? Can they be used for other purposes, such as sizing or projecting the depth of a common rafter or purlin to the plumb face of a Hip-Valley rafter?
With as little as a child's geometry set and a cereal box or bristol board a person can teach themselves more about how to solve complex roof framing problems and how to find formulas for angles than they can learn from a dozen books.
Extract a section of a Hip Roof and split it along the plane or triangle representing the Hip-Valley Pitch Angle. Now try these developments:
Development of a Hip Roof
Development of a Compound Angle
Comparison of a Compound Angle of a Hip Roof
Extracted and Developed Model of a Compound Angle
Once the tetrahedron is developed we can assign values to the sides of the triangles in terms of the trig functions of the angles:
Scaled Models of a Hip Roof ... now we're all set to rock'n'roll! All kinds of formulas.
That's a beginning ... :)
PS: Don't just click on the links and look at the pictures and take my word for the drawings and sketches ... grab a compass, ruler and protractor and DO IT!
Joe Bartok
Edited 12/28/2006 9:07 am ET by JoeBartok
Joe, what program are you using to make your line drawings?
All the drawings are done on the Windows 98 bitmap. Line drawings are saved as GIF for economy (i.e. smaller files size). Shaded drawings that require a bit more of a 3D look are saved as JPG.Joe Bartok
Joe, Thank you for a desktop full of links and attributes that I can find at a moments notice, your work is awesome.!!!!!
Spheramid Enterprises Architectural Woodworks
I have irriatable Vowel syndrome.
Enjoy! A lot of the recent math and calculators are the result of attempts to answer questions posted in online forums such as this one. It's only fair to put back some of what I have received.
As a result of the Q&A in BT, JLC and other online resources, should similar problems arise in my little corner of the world I'll be a little better prepared.
Joe Bartok
Edited 12/28/2006 1:56 pm ET by JoeBartok
Being of the curious sort...what's up with you? You in prison with a limited allotment of internet access or what?
I saw the hands, mine aint far behind, we work with what we have.
Spheramid Enterprises Architectural Woodworks
I have irriatable Vowel syndrome.
Nope, not in prison or wanted by the authorities (not as far as I know!).
I don't bother with Internet access on my PC at home. It's too much to keep up with protection against all the malware out there even if a lot of the digital prophylatics are free. The public library is across the street from me and they have all the best and latest armament against anything nasty. It only takes me half a minute to get there. This does limit my time on a daily basis. There are also times when I can't get online for long. I'm a volunteer; I'm supposed to be helping the library patrons on the computers (some of who drive in from the country) and not hog them for my own use.
The hands (and feet and upper spine to match) are the result of natural causes. Google up other links related to this:
http://www.medicinenet.com/psoriatic_arthritis/article.htm
A downhill and losing struggle for the last fifteen years. I don't think I could get along without the power of modern computers and the ability to manipulate large amounts of data, cut and paste, and GUIs. Typing sucks! Oh well, things could be worse. :)
Joe Bartok
Edited 12/28/2006 3:51 pm ET by JoeBartok
Your work is, well, fantastic. Just an under appreciated, due to lack of exposure, or deef audiance.
So, uh...you have a hobby? LOL.
Spheramid Enterprises Architectural Woodworks
I have irriatable Vowel syndrome.
The hip length is from the ridge to the outside corner of the building. Since the hip sits at 45°, the outside of the hip where the plumbcut length is marked will be off the top plate by half the thickness of the hip. If you have a 2x hip you will be off the plate 3/4" as a run and you will have a small rise. That rise is how much higher your hip would be then the common H.A.P. at (Height above Plate) the plate line. That is what I call the Hip Drop amount.Regardless of how anyone cuts their hip, there has to be an adjustment for this in order for the top of the hip to plane in with the top of the common rafter at the plate line. Therefore if you mark the HAP cut at the outside corner the same as the common HAP. cut, the top of the hip won't plane in the same height as the top of the common HAP cut at the plate line.When you mark the length of the hip at the outside corner, all you have to do is come in level towards the ridge half the thickness of the hip and make a plumbcut there and just come down from the top of the hip the same HAP cut as the common rafter HAP cut.Here’s a drawing that I hope will show you.
Joe Carola
So by what name is the cheek cut ( the bevel put on the jack rafter at the plumb cut where the jack meets the hip) in your labeling scheme.
I Know what the hip drop, the shift , the ridge backing bevel all are but can't decide what you are calling the cheek cut .
Interestingly enough the first dwelling I contracted way back when was an Octagon that was longer than it was wide. Some real headscratching and lots of string lines for a none mathematician back then.
From that building I learned that I don't have to know the answers , but as my Dad used to say, I just have to know where to look for them or the person who does know them .
I have 3 questions I ask prospective framers who claim they are the best...
1) Can you do a cut roof? (Eliminates 90 %)
2) Can you cut a set of stair jacks? (Eliminates another 9%)
3) If you know the pitch of a roof expressed in inches you know that on a Framing sq. you use 12" as the run for commons, 17" as the run for hips on an equal pitch roof. What # do you use for the hip on an equal pitch Octagon?
Only once in 40 yrs. has a man answered correctly . I hired him on the spot and at his named price.
Edited 12/28/2006 8:53 pm ET by dovetail97128
>> I Know what the hip drop, the shift , the ridge backing bevel all are but can't decide what you are calling the cheek cut . <<The blue circled ares in the picture and drawing is what I call cheek cuts.Joe Carola
>> 3) If you know the pitch of a roof expressed in inches you know that on a Framing sq. you use 12" as the run for commons, 17" as the run for hips on an equal pitch roof. What # do you use for the hip on an equal pitch Octagon? <<Did he tell you 13 or 12.98871.......;-)Joe Carola
13... ;-)
I have a great old book ..
" Radfords Cyclopedia of Construction", The Steel Framing Square and it's Uses" Volume V111, published in 1921, Radford Architectural Company , Chicago Il.
That I use as my roof framing reference when all else fails. I have spent many a night up till the wee hrs. trying to learn things.
Sphere wrote: "So, uh...you have a hobby? LOL."
Yeah, framing. Ha! Ha!
Seriously, no it isn't. My construction background is mostly prestressed/precast concrete. I learned some framing during my tenure as a log builder (over twenty years ago) and other random jobs helping build houses but my experience in this area of construction is limited.
Joe Bartok
13 was my guess too Joe, but I wasn't sure about the question.
The first and last time I thought about the unit run on an octogon hip was back in the 80's when I framed my first bay roof and thought it was important to technically calculate the parts. It took me hours to figure. Now I just booger them in using much simpler methods and guess what? They actually look and function better today LOL!
All this info would be critical if I was framing an exposed post and beam octogon, but it becomes totally irrelevant out in the field on a simple octogan roof frame.
blue
Blue,
Curious how you "booger" the birds mouth and plumb cut on those octagon hips..Can you explain it. Always seemed the fascia alignment and eave height was noticeably off when I didn't use the correct run dimension on the sq.
I went and sketched it with a pencil, and lacking a calculator, went and used an online triangle solver.
I got the miter and bevel settings both alike at 9.875 degrees. Maybe I did something wrong, but my sketch tells me they are both the same angle.
I looked in one of my rafter books. Listed under hip bevel cuts for 3/12... 10 deg. No data entry needed.
OK, back to the book! Quick!
We'll need to detail the top plates. Those that parallel the rafters are 2x6s, but the others we'll need to bevel-rip from 2x8s. Give us the bevel settings for the skews and the top cross, plus the compound miters for joining them together.
I'm gonna try to use my cell phone for this one.
""Those that parallel the rafters are 2x6s, but the others we'll need to bevel-rip from 2x8s.""
I don't see the "parallel " aspect, perpindicular to the 3/12 rafters yes, but parallel no.
I wouldn't rip 2x8, just off set 2x6 plates slightly to each other, I am guessing that at that slight a pitch I may not even have to trim those with a bevel. I wouldn't butt top top plates, lap them instead myself at the outside corners.
But if I was to mitre and butt I "think" the cuts would be 22 1/2 deg. mitre, 5 deg. bevel.
I actually never was any good with math,(why I stayed poor my whole life, easier to count my money that way ) so I stayed good friends with my engineers. ;-)
Here is a start for you. The 2x6 top plates that are tracking the 3:12 rafter slope, paralleling the rafters, have their bottom ends compound cut by setting the miter at 23.1 degrees, and the bevel at 14. Ins or outs depend on which side you're cutting.
To make the stock that is used for the plates for the two diags, take some 2x8, set your tablesaw to slice at 10 degrees, and rip two sides so the flat is a heavy 5-9/16.
For the plate capping the octagon, the one that runs at 90 across the rafter bottoms, take some more 2x8, and as anybody with a speedsquare can tell us in a NY second, tilt the tablesaw for the rip at 14 degrees. The flat should be 5-11/16". Your endcuts, the compound miters, will be cut with the chopsaw set to miter at 21.9 degrees, and the bevel at 4.9 degrees.
To cut the meeting miter for the skewplate stock to join the parts cut in paragraph one, above, take the bevel-ripped stock (10 deg x 5-9/16), set your miter at 21 degrees, and WAITAMINUTE! Don't set the bevel yet!
I'll let the CM guys tell us how to proceed from here.
Here is a pic of the SU workout model for this. One plate thickness is shown.
View Image
Edited 12/26/2006 11:01 am ET by Gene_Davis
Edited 12/26/2006 11:27 am ET by Gene_Davis
Gene,
diesel is looking at only 3 sides of the octagonal shape. Cuts will be the same but you have 2 extra plates in the drawing.
Later today I think I can get access to a scanner and will post some drawings of an example solution for the compound angles for a similar sloped wall. The roof slope will be 11/12, with a plan angle of 40°. It's interesting that the compound angles are the same as required to make the square or chamfer cuts along the plumb line for the housing and tenon on a jack rafter-to-Valley intersection.
And I'll try to dig up my notes and find a drawing of the triangles scaled in terms of the trig functions of the angles.
Be back soon ... ! :)Joe Bartok
The attached images detail another way of cutting the compound angle on the studs. The unbacked plate set on the studs will be canted to the correct angle. On the minus side, the 1½" faces of the plate will be out of plumb. So this may not be the optimal method.
The "Plumb Backing Angle" is a miter angle, not a saw blade setting. It's the angle we would see on a backed Hip-Valley along the plumb cut. The formula is:
Plumb Backing Angle = arctan (tan Hip Pitch Angle / tan Plan Angle)Joe Bartok
Joe,
(and others posting) I just wanted to pop in for a second and thank you guys for your replies. I'm currently on what I hope is the backside of a nasty stomach flu. This is my first time out of the bedroom/bathroom since Christmas night. Hopefully I'll be feeling much better soon and will be able to continue this conversation.
So much for my big vacation.View Image
Gene,
Try that same method, but use a 10-12 roof instead and see if the numbers get a little farther apart.
dieselpig,
If you get a angle that's confusing you staple a string at the corner point of where the board is going to be and take your angle readings from the string to surface.