The math, please

[Bob Dylan]

Take a look here, and get out your CMs, or your CM Pros, or even your CM Pro Trigs. Or anything that works.

Shown are the upper walls of a little 2-story place, with a principal pitch of 12:12 bearing on the 4'-0" kneewalls. All rafters are 2x12s.

A shed dormer runs across much of the front and back, each with a different pitch. Front and back wall heights at the shed rafter seats are shown.

The ridge won't be structural, as we will do collar ties as ceiling joists. To get toenail purchase along most of the rafter plumb cuts, we might use an LVL at 16 or 18 deep. But that's overkill, right? How about just a 2x12 with a 2x6 under it? But, ridge doesn't come into play for this question.

Calculate for me the pitches of the shed roof rafters, but please, show me the development of the math. Thanks.

I can work it out graphically with CAD, to get real close, and I get 7.578:12 for the front and 9.016:12 for the rear, but I am wanting to see how math is used to get them exactly.

[Joe Bartok]

Re: The math, please

Gene, this is what I get based on the widths and heights only in your diagram:
7.53409/12 (front) and 8.97727/12 (rear)

[TWhite]

Re: The math, please

Joe I got the same, but the drawing is not clear. Do we need to account for the rafter height above birdsmouth at the 4' high wall?

[Joe Bartok]

Re: The math, please

Joe I got the same, but the drawing is not clear. Do we need to account for the rafter height above birdsmouth at the 4' high wall?

I'm uncertain of this as well. That's why I used only the widths and heights given for the time being.

[Bob Dylan]

Re: The math, please

Here is my diagram, Joe. How did you get your answers? I was hoping to get the method, not the results.

[Ed Michnick]

Re: The math, please

Rise of 22’-0” span with 12/12 pitch = 11’0” total rise
Height difference of front wall plate height (8’-1.125”) less 11’-0 total rise = 6-10.875”
6-10.875”(rise)/11’-0”(run) = 7.5625/12

Height difference of rear wall plate height (6’-9.25”) less 11’-0” total rise = 8’-2.75”
8’-2.75”(rise)/11’-0”(run)= 9/12

[Joe Bartok]

Re: The math, please

Hope I type this correctly on my first attempt ... :)

This is based on the first diagram, I'll try to get back to look at the new drawing. Calculations are in decimal inches as entered in my scientific calculator.

Front difference in rise = (8 × 12 + 1.125) – 4 × 12 = 49.125
Rise = 12 × (11 ×12 – 49.125) ÷ (11 × 12) = 7.53409

Rear difference in rise = (6 × 12 + 9.25) – 4 × 12 = 33.25
Rise = 12 × (11 ×12 – 33.25) ÷ (11 × 12) = 8.97727

Gotta run, one of my sibs is coming over with some cool rock and mineral samples we want to identify.

[Bob Dylan]

Re: The math, please

Thanks, Joe. Now that I can see it relates strictly to the rise diff, I can think like a framer, instead of a CAD operator.

Now, can you dive into Ed's reply a little, and explain why he comes close, but not exact like you?

[Joe Carola]

Re: The math, please

Guys,

We all have to be on the same page here. He has a fixed ridge height.

Gene,

1) Are you figuring for a 2x4 wall using a 3-`1/2” level seatcut for the 12/12 commons and the two shed rafters?

2) Will the top of the shed rafters be flush with the top of the 12/12 main ridge?

3) Are you using a 2x ridge or 1-3/4” lvl ridge?

All this has to be taken in consideration because of the different pitchers and the H.A.P. cuts (height above plates). You already said that the rafters are all 2x12’s.

As of right now figuring a 2x for a ridge using an 11-1/2” 2x12, your ridge height will be exactly 12’ from the top of the 4’ kneewalls. That’s deducting ½ the thickness of the ridge and the height above the plate.

Joe, this is exactly the same thing as my fixed ridge height thread and the way I figure out the rafters, do you remember that thread? You even posted it on your site.

[Bob Dylan]

Re: The math, please

I was too quick to thank Joe, thinking prematurely that his method gave the exact answer.

Thus far I have gotten three replies all done using calculators. Two came here, and one came in response to the same Q over at another forum.

I used my CAD program to plug all into the 2D model I built, and as can be seen in the attached zoom-in up at the ridge, none are exactly right. I did not show my graphical solution pitches of 9.016 (front) and 7.578 (rear), which by the way came closer to having the tops all meet at the peak.

I am wondering what the math is to get it right, exactly.

[Bob Dylan]

Re: The math, please

You are on the right track, Joe. More info is needed, and here it is.

Wall thickness = 5-1/2"

Our 2x12s come from either Europe or Canada, and all measure 11-1/4". Where do those beefy ones come from that measure 11-1/2"?

Ridge thickness = 1-1/2" (it ain't structural, I could probably use a 1x12, but let's do it with a 2x)

Seat cuts for all rafters have them springing from inside wall line. In other words, horizontal cut of seat equals 5-1/2"

All rafter peaks must come to top edge of ridge member.

[Joe Bartok]

Re: The math, please

Guys,

We all have to be on the same page here. He has a fixed ridge height.

Joe, you're right. I barely had time to look at the drawing and that's why I was cautious and stated that I was using only the widths and heights and not taking anything else into consideration.
I remember the fixed ridge height thread. This is a link to the Fixed Ridge Height Calculator based on Joe Carolas math and diagrams (hopefully I've got it right. And it requires an MSIE6 or earlier browser ... it's a mess viewed with Firefox).
Guess I'll have to wait 'til tomorrow to pursue this thread in detail; got to get off this computer and I didn't bring a floppy to save whatever information everyone has posted so far.

[Joe Bartok]

Re: The math, please

Another "speed calculation" using the web based digital cheater:
7.56112/12 and 9.00283/12
These results may be a bit off because of rounding off the calculator entries. Even if I have the answers wrong (only got a couple of minutes to do this) check out Joe Carola's method and see what you get. My "new" numbers (sorry, no time to type everthing up) are based not on making the rafters meet at the same theoretical point, but at the face of the ridge board.
This isn't the first time I flubbed this!
Fixed Ridge Thread in Joe Fusco's Forum.
As I recall I tried solving the pitches by beginning with the HAP or heel height ... which is unknown at this point in the game and made it a bit tough to come up with some numbers.
See you all tomorrow.

[Joe Carola]

Re: The math, please

Joe,


The front shed roof, the pitch angle I get is 32.22° or 7.562655/12 or 7-9/16 pitch.

The back shed roof, the pitch angle I get is 36.87° or 9.000034/12 or 9” pitch.

I'd say that's close enough..............;-)

[Joe Bartok]

Re: The math, please

That's close enough for me. I got 32.21476° and 36.87855° for the pitch angles from the web calculator. They aren't spot on to five decimal places because the entries were rounded to the nearest 1/32nd of an inch.
Gene is probably still waiting for a step-by-step calculation. :)