Hip roof angles

[dzatto]

Okay structural guys! I need a formula. If I'm thinking of this correctly, then:

I'm designing a porte co with a hipped roof on one end (the other end will die into a wall). So, if I have a 4:12 pitch on all 3 sides, then in plan view, the peaks will be at 45 degree angles since all 3 faces have the same slope.

What I need to know is, what will the actual slope of the peak be? It can't be 4:12, that's way too steep and the beam I have there is sticking above the roof line.

There has to be a formula to figure that out. Anyone know it?

[dzatto]

Okay, I figured a way to get it. I rotated my roof 45 degrees, then switched viewports. That way, the peak was in the correct plane. It turns out a 4:12 pitch is 18.43 degrees, and the peak will be at 13.33 degrees. Go figure!

[david_peterson]

Can you shot me a screen shot? I'm a little confused. A 4:12 roof is a 4:12 roof all day long. If Are you trying to find the obtuse angle acroos the ridge line at the roof or at the angle to angle at the hip?
180 (sum of angles in a triangle) - 18.43-18.48 = 143.14 degrees.
To find the angle at the hip intersection is a little more difficult.

[dzatto]

My screen shots look like poo, so here's some pdf's. I guess I could have just uploaded the file! Oh well.........

[david_peterson]

Well I think (and I could be wrong here) that the angle in question will vary depening on the size/width of the roof. Generally speaking from a structural stand point, I'd never give the slope. You know the high point and the low point. So you know the x,y & z coords. My answer to this question on a test would be Who Cares; connect the dots.
I guess the answer is still rise over run.
So if your ridge (hp) is centered on the eve end and the eve end is say 24'. So half of the eve end is is 12' wide, you know it's 12' back to the ridge hp. (equal angles have equal opp sides). If you have a 4:12 pitch, you know that the rise on a 12' run is 4'. So you'll still have a 4' rise, now to find the run. To find the run (back to geometery) you need to find the length of c.. Since a^2+b^2=c^2 ; c=the square root of (a^2+b^2). So in the example end up with 16.97'. So your slope is 4:16.97' or the inverse tan of 4/16.97 or 13.26 degrees.
To quote Back To School "I feel like I just gave birth to an accountant".
I hope that help.
If you need more info, let me know. It's complicated, but it's really not that hard once you think about it. You just need to solve for both triangles.

[dzatto]

Well I think (and I could be wrong here) that the angle in question will vary depening on the size/width of the roof. Generally speaking from a structural stand point, I'd never give the slope. You know the high point and the low point. So you know the x,y & z coords. My answer to this question on a test would be Who Cares; connect the dots.
I guess the answer is still rise over run.
So if your ridge (hp) is centered on the eve end and the eve end is say 24'. So half of the eve end is is 12' wide, you know it's 12' back to the ridge hp. (equal angles have equal opp sides). If you have a 4:12 pitch, you know that the rise on a 12' run is 4'. So you'll still have a 4' rise, now to find the run. To find the run (back to geometery) you need to find the length of c.. Since a^2+b^2=c^2 ; c=the square root of (a^2+b^2). So in the example end up with 16.97'. So your slope is 4:16.97' or the inverse tan of 4/16.97 or 13.26 degrees.
To quote Back To School "I feel like I just gave birth to an accountant".
I hope that help.
If you need more info, let me know. It's complicated, but it's really not that hard once you think about it. You just need to solve for both triangles.

Don't you hate it when someone figures out something complicated, then when you read it, you know exactly what they are doing before you even finish? It makes total sense to me, damn Pathagorean theorum!!! Don't know why I didn't think of that.

As for calling out the angle, I'm not trying to do that. I'm drawing it in 3D with structural members and couldn't figure out what slope to put the beam at. But, alas, all is well and thanks for the answer!

[david_peterson]

Well again, it's not even something you need to know. If I was Jimbob working in a truss plant, I'd just play connect the dots. You know the start and end point. Just add a beam/brace (they are the same except that braces usually start justified at the centroid) in a 3d view and connect the dots. So much easier that having to do all the math stuff.

[dzatto]

Maybe I made it too complicated! But, during the design phase, how do I find the peak of the hip? I mean, I know where the beams in question start, but how do you know exactly where they stop so you can connect the dots? I thought I'd have to know the angle, then just miter the 2 beams and there's the point!

[reb_polum]

Speaking from an educator's standpoint, "The Great Pathagoreans!" Math is the answer!

[bhargis]

Since you are doing this in 3D, are you doing this in ADT? This may be a little more complicated than the math, but you will get the correct results...

Use the Roof with all of the info (Slope, over hang, thickness, etc.) then you may, or may not, have to convert it to Roof Slabs. Then you have the construction geometry to lay in Braces as beams... Then you can either delete the Roof or change it to a no-plot layer and move on.

I followed the math also, but why work that hard. That's why I use a computer and drawing with a CAD system....