[bmartin]

I have to frame a rake wall that comes of 45 degrees from the outside wall to a 3 and 12 ceiling. Does anyone know how to do the math with a construction master pro for the miter and bevel for the stud and the backing cut for the top plate. Also how to figure common difference for each stud. I have it pretty close but would like to understand the math for future.

 

[loneframer]

Miter and bevel angle can be found by holding a speed square on the 3 on the hip/val scale. Both angle and bevel will be the same, because the studs will be oriented at 45 degrees to the rafter, similar to a hip or valley. Same with rip on backing. Common difference of studs on 16" centers is 2.825"by my math.....

Can't help you with the CM. I used old-school math.

Someone please check my math?

 

[Timuhler]

I have to frame a rake wall that comes of 45 degrees from the outside wall to a 3 and 12 ceiling. Does anyone know how to do the math with a construction master pro for the miter and bevel for the stud and the backing cut for the top plate. Also how to figure common difference for each stud. I have it pretty close but would like to understand the math for future.

There was an old thread at JLC where Ken Drake posted the formulas and they work great.

Now that we all have smart phones, I'd try Sim's app http://raftertools.com/

I've used it and it works great.

 

[mathman]

From Ken Drake ( mathman )

I just posted this on the JLC forum:

"The angle for the top of the studs is just the pitch of a regular hip in a 3/12 roof, 10.025 degrees. Just a hair over 10 degrees.
The bevel for the top of the studs, and the top plate, is the backing bevel for a regular hip in a 3/12 roof, 9.875 degrees. Just a hair under 10 degrees.
If you want the increase in length for each stud, just enter the hip pitch in your CM, 10.025 degrees, then 16" for RUN, and press Rise. Result is 2 13/16". Press diagonal, and you see 16 1/4", which would be the layout increase on the top plate."

 

[bmartin]

Thanks for the info everyone. If the wall came off at an angle other than 45 would the angles be different?

 

[mathman]

Thanks for the info everyone. If the wall came off at an angle other than 45 would the angles be different?

Absolutely.

Think about it. Think about the extreme cases. Suppose the wall was running square to the plate and ridge. What angle and what bevel would be on the studs? Pretty simple, the angle would be = 0, and the bevel would be = to the roof pitch, right?

Now, let's look at the opposite extreme, where the wall is running parallel to the plate and ridge. What angle and what bevel would be on the studs? This time, the angle would be = to the roof pitch, and the bevel would be = 0.

What does this tell you? It tells you that everywhere in between, there is a different angle and different bevel for the studs, as you change the angle that the plate is making with respect to the roof plane.

You need to find the pitch of the hip and the backing bevel on the hip, to cut the studs properly.

 

[Birch]

From Ken Drake ( mathman )

I just posted this on the JLC forum:

"The angle for the top of the studs is just the pitch of a regular hip in a 3/12 roof, 10.025 degrees. Just a hair over 10 degrees.
The bevel for the top of the studs is the backing bevel for a regular hip in a 3/12 roof, 9.875 degrees. Just a hair under 10 degrees.
If you want the increase in length for each stud, just enter the hip pitch in your CM, 10.025 degrees, then 16" for RUN, and press Rise. Result is 2 13/16". Press diagonal, and you see 16 1/4", which would be the layout increase on the top plate."

Ken,


It is good to see you posting again. Hope this is not just a fleeting visit.

Do you have a formula for the non 45* rake-head walls?


Regards, Richard

 

[mathman]

I just posted this in the JLC forum. Let's see what responses it get's here also.

"Okay, let's try another one. 12 milkbones to the first person with the correct answers.
This time, the roof pitch is 12/12. The rake wall is running at 67 1/2degrees to the rafter plate in the plan view.

1) what is the angle and the bevel for cutting the top of the studs?
2) What is the bevel on the edges of the top plate so that the top plate planes with the sides of the studs?
3) If the studs are 16" On Center, what is the increase in stud length?
4) What is the increase in layout on the top plate?"

 

[kiteman]

I'll take a quick stab at it.

1) Angle is at 7/12 and bevel at 30.26 degrees
2)Bevel top plate at 22 1/2 degrees
3)Add 9 5/16" per stud
4) 17 1/3" for the layout

 

[mathman]

kiteman,

I don't think any of your results are correct, but thanks for your response. Can I make a suggestion? Take 2 short 2x4's and cut the angle and bevel on the tops that you found for your studs. Make one of the pieces 9 5/16" longer than the other, like you suggest. Then bevel a small piece of 2x4 on one edge at 22 1/2 deg as you suggest for the top plate, and see how it comes out.

Ken

 

[kiteman]

I was doing it in my kitchen with no lumber at hand, just kinda off the top of my head.

Back to school for me , I guess.

 

[mathman]

Think about it again. I usually solve these type of problems in bed at 2 in the morning when it's dark, my eyes are closed, and I'm lying on my back. The kitchen doesn't work for me either.

 

[kiteman]

Well, to start, did you mean that 67 1/2 degrees from rafter plate is the same as 22 1/2 degrees from the perpendicular, or the other way?

 

[Birch]

I just posted this in the JLC forum. Let's see what responses it get's here also.

"Okay, let's try another one. 12 milkbones to the first person with the correct answers.
This time, the roof pitch is 12/12. The rake wall is running at 67 1/2degrees to the rafter plate in the plan view.

1) what is the angle and the bevel for cutting the top of the studs?
2) What is the bevel on the edges of the top plate so that the top plate planes with the sides of the studs?
3) If the studs are 16" On Center, what is the increase in stud length?
4) What is the increase in layout on the top plate?"

Hi Ken,

I have another solution that I use a lot and am not posting since it is not what this inadvertent math challenge I stirred up is about. And depending on whether you use 67.5* or 22.5* as the Rake-head wall angle, :blink: :whistling


1) what is the angle and the bevel for cutting the top of the studs? 42.73* (Hip Pitch) = Bevel, Miter Angle= 15.7*

2) What is the bevel on the edges of the top plate so that the top plate planes with the sides of the studs? = 15.7*

3) If the studs are 16" On Center, what is the increase in stud length? = 14 3/4"

4) What is the increase in layout on the top plate? = 21 13/16"


*Hypothetical Irregular Hip Pitch/ Rake-head wall slope angle:

= 90* - Atan [(Tan Pitch angle) / (Sine Plan angle)]

 

[mathman]

kiteman,

Just think about it like the hip rafter angle in a regular octagon. The hip runs at a 67 1/2 degree angle with the plate in plan view. In other words, it's not that far away from being a common rafter, only 22 1/2 deg. If the pitch of a common is 12/12, then the pitch of the hip is close to being 12/13 ( 12/12.9887 ). If you think about that, it can help you with the top plate bevel.

Hmmmmmm.........

 

[mathman]

Richard,

I'm not 100% sure that your answer to question 1) is incorrect, but the angle and bevel that you found are not what I came up with. Otherwise, I agree with your answers to 2), 3), and 4), with the minor exception that I believe the increase in stud length is a hair closer to 14 13/16", rather than 14 3/4"

I'm finding more angle, and less bevel, than you found for the studs. We'll get to the bottom of this soon. Until then, no milkbones,

 

[kiteman]

Ok, off the top of my head, we 're bisecting the angle between a 12/12 common and 12/17 hip. Isn't that pretty much the same as a 12/12-5/-12 irregular hip?

 

[mathman]

kiteman,

yes, I suppose that's one way to look at it. If you do that, you find that the pitch of the hip is 12/13, like a regular octagon hip pitch, as I mentioned before.

ken

 

[Birch]

Richard,

I'm not 100% sure that your answer to question 1) is incorrect, but the angle and bevel that you found are not what I came up with. Otherwise, I agree with your answers to 2), 3), and 4), with the minor exception that I believe the increase in stud length is a hair closer to 14 13/16", rather than 14 3/4"

I'm finding more angle, and less bevel, than you found for the studs. We'll get to the bottom of this soon. Until then, no milkbones,

My CM Pro DT returns 14-13/16" on my last double check. (?) :whistling


As far as the answer to No. 1, I would think it would depend on what the plate was meeting. Sheathing angles and either plumb or square miters would be a good guess? Friday night, got to go Fairlane'n.

 

[mathman]

Richard,

I suppose you could just think of the top plate being nailed to the underside of the 12/12 jack and common rafters, or any other surface that has a 12/12 pitch.

Have fun at Fairlane'n.

Ken