Let’s consider the beams for the 20 foot yurt. For the book I used a 4.5/12 slope and for practical reasons I would use it for your project. I’ve walked on many different sloped roofs and on some that couldn’t be walked on without ropes. I can say that you can comfortably walk or work on a roof that is a 4.5/12 slope.
One thing that you may not immediately notice is that I assign the slope to the beam and not the roof plane. Why do that? If you use the roof plane you subsequently have to calculate the “hip” (that joint that joins the adjacent abutting planes) of the roof structure; i.e. directly over where the beams run. Why make things more complicated? Because the beam’s lengths are determined using a slope calculation, it simplifies your calculations. So now to that calculation.
When you solve for the hypotenuse of your 4.5/12 slope (triangle) you have a 4.5” leg perpendicular to a 12” base leg (level). Both squared (20.25+ 144) gives you 164.25 and the square root of that is 12.816 (your hypotenuse). How does all of this relate to the beam? Two things: first for every foot on the level that the beam travels the beam rises by 4 1/2 inches (so for a theoretical beam of 10 feet the “up” end is 45 inches higher) and second, for every foot traveled horizontally (on the level) the beam’s length increases by X 1.068 (so in our 10 feet run the beam grows to (10 X 1.068) or 10.68’ which is just over 10’-8”.
So to complete the beam length calculations you have to subtract the skylight ring assembly and add the overhang you want (here beams are assumed to go all the way to the center of the yurt). Both of these are accomplished in the same manner as above.
For the skylight, take the diagonal of the framing of the skylight ring (a level measurement from one corner to the opposite corner) and then halve that. That is then taken from the beam overall length, after calculating the “sloping” length.
The overhang is a bit different. To make it simple just consider the overhang equal to whatever you extend the beam tail (whatever is hanging past the walls). So, if you wanted a two foot overhang, just extend the beam out two feet (using the slope calculation, of course). This will be close enough for a two foot overhang.
Otherwise, if you want a more precise dimension for your overhang you will need to do some more calculations. This requires a bit of trigonometry. It goes like this: Say you want a two foot overhang. This is a two foot projection that is horizontal (level) from the wall and parallel to the wall. Since we know the number of sides we have, we get the number of divisions in the 360 degree circle. That gives us the peak angle for our triangle. We will use 1/2 of that angle (see drawing below). Our long side of the triangle is 2’ (our overhang). So solving for the hypotenuse: recalling our trig formulas: CAH — cosine of the angle = adjacent side divided by the hypotenuse. Solving for H we divided through by A to get H=C/A. Now do the “rise” calculation from above to get the actual beam overhang length. This sounds like a lot of work, but honestly, it’s easier than reading this entire article!
Be sure to get a copy of the book which explains the rest of building a wood-framed panelized yurt. It’s available on Amazon in color paperback, color ebook, and b&w paperback. And hey, if you build a yurt after reading our book, please send photos to share, thanks!
Here are the links to purchase the book: