Greenhouses forum: Paul's geodesic dome, part 1: Design and Preparation

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Imagepsa
Feb 9, 2010 12:59 AM CST
Name: Paul
Eastern WA
DG: tropicalaria
[Extracted, edited, and increased from posts originally made at http://davesgarden.com/community/forums/t/652446/ starting in September 2006.
The first parts are mostly repeated as published, the middle parts heavily edited, and the last parts entirely new. ]

Part 1: Design and Preparation
Part 2: Frame construction
Part 3: Plastic covering
Part 4: Door, Ventilation, and more
_________

I have been looking at a number of ways to do this for quite some time now, and I think I'm going to go ahead and put up a simple hub-strut wooden structure. Most of my calculations derive from the groundwork at http://www.tekstaronline.com/monkeyhouse/ [Defunct now, unfortunately] -- though the calculator and tips at http://desertdomes.com/ are quite valuable as well. Feel free to skip to later posts as I hope to post progress and pictures as I go along, but the planning stages require a bit of math that I realize may only be of interest to a select few.

I'm building a 20' frequency 3 dome, 3/5 (or 4/7) sphere using cedar 2x4s. Since eight foot lengths are the most economical, I've adjusted my strut lengths to fit this with two struts per eight foot section. 3 frequency domes have three different strut lengths, each with their own vertex angle. Since I will be connecting these together with hubs for simplicity, I also have to factor the hub size into the strut lengths.

The angles are
A - 10.038 degrees from a right angle
B - 11.641 degrees
C - 11.9 degrees

For practicality with my miter saw, I will simplify these to 10, 11.5, and 12 and expect my hub attachment to give enough to make up the difference.
I will use 3" sch 80 pvc pipe cut to 3" lengths for the hubs, attached with perforated steel strips. This adds three inches total to the effective lengths of all struts. This is actually a simplification, since the hub widths are not measured at the same angle as the struts will be, but it's close enough. I can't afford to produce materials at greater tolerances, anyway.

3.5" tan 12 degrees = .75", which is the effective overlap obtained when I cut two C struts out of the same 8' 2x4. So, measuring all strut lengths from the outside (longest) edge, I can cut struts up to 8' 3/4" / 2 = 4' 3/8"

Add 3" for the hub, and the effective C strut length will be 4' 3 3/8". I can now work backwards from the reverse strut calculator at http://desertdomes.com/rev3calc.html to find the appropriate lengths for the other two, shorter, strut types. I calculated with decimals for the math:

Laid out as Effective Decimal, Actual Decimal, and Actual Inches:

C - 4.281 - 4.031 - 4' 3/8"

B - 4.189 - 3.939 - 3' 11 1/4"

A - 3.619 - 3.369 - 3' 4 3/8"

So these are the measurements to which I will cut the lumber on the longer edge, mitering at the angles listed above.

There are some fine graphics of the layout of these struts in the sites listed above, so I won't attempt to illustrate it here. I will need numbers of struts as follows:

A 30
B 55
C 80

In reality, I'm warping the bottom layer of struts slightly, both to give a more even bottom edge and to normalize the height of the first tier of triangles on the dome. The bottom of a 3 frequency dome isn't quite flat; it bulges and pulls up an inch or so every couple of vertices. In practice we can expect this small bit of warping to cause few problems. Additionally, the edge isn't flat on the ground; it contacts at an angle, since the sphere it projects would be expected to continue at an angle under the ground.

Internal angles of a regular polygon are given by 180 - 360/n, where n is the number of sides. In this dome, there are 15 sides, so the angle is 180 - 24, or 24 degrees from being flat. Split in two for the contribution from the miter on each strut, gives 12 degrees, which fits nicely with the calculated 11.9 degrees on the C strut which makes up most of the middle circles. The difference comes from the insertion of an occasional B strut and the contribution of the extra-planar tilt which I want to correct for. In this case, all I'm going to do is not angle the bottom of the vertical struts at the bottom and maintain this 12 degree angle between the ground struts in order to keep it flat. I'm not going to bother reprojecting the vertices in order to get strut lengths for a flat bottom since the variance is in fractions of an inch and I don't think it will make a difference.

I also need a door in this greenhouse, and after much examination I'm going to put it in one of the hexagons, removing the six internal C struts. I will drop two vertical posts between the top and bottom of the hexagon with joist hangers and use half-sized C struts to brace on either side to the midline vertices. This will connect at a 12 degree angle with the bottom strut of the hexagon. I'll then add horizontal extensions from the side posts to hold a vertical door.

The final bill of cut pieces:
30 A
45 B
10 B flat end
54 C
20 C flat end
2 B half struts
2 vertical door posts

This will be cut as
2@
1 vertical door post each

27@
2 C struts each

20@
1 B strut, one C flat end each

10@
1 B strut, one B flat end each

1@
1 B strut, two 1/2 B struts

7@
2 B struts each

15@
2 A struts each

horizontal door braces will come from scraps from A brace cuts

This adds up to 82 8' 2x4s. Cedar is not the strongest material, but I don't think it will have to be in this structure, and it should hold up to the damp better than fir. It runs $6 at Lowes, for a total of $492, plus tax, not counting any extras I have to purchase for mistakes and the occasional bad section. Redwood is much more expensive here. Pressure treated isn't much cheaper, requires more expensive hardware to resist corrosion, and introduces chemicals that I really don't want. I don't really want to paint this whole thing, but I am still a bit worried about the UV exposure.

The plan is to glaze with greenhouse film inside and outside (two layers separated by 3.5") the first year and consider things like polycarbonate down the road. I want to insulate the north wall, probably with a standard fill backed internally with a radiant barrier.

Ground contact is still a bit up in the air. Since the dome itself is a rigid structure, ground motion is less of an issue than with other structures. I will probably set sub-frost line anchor piers at each of the 15 vertices and rest the ground struts on something like compacted gravel. I'd like to put raised beds around the inside edge of the dome with radiant heating through them, but I'm not sure what to line the inner edge of the dome with for contact with the soil. I may also decide to use ground contact rated pressure treated lumber for the ground struts.

Thumbnail by psa

Imagepsa
Feb 9, 2010 1:00 AM CST
Name: Paul
Eastern WA
DG: tropicalaria
The door frame timbers will be the only members receiving forces other than tensile and compression. In addition the tensile force on the top and bottom struts will be greater than normal. For this reason I've considered making these pieces out of something more sturdy--either 2x6, which could be problematic for the 3" hub connections, or pressure treated fir which I'm still not fond of, but would be much stronger. It's worth noting that the geodesic dome structure is very impressive in its distribution of load, and the whole thing could easily be sturdy with much thinner members.

Although this wasn't the source of my decisions on the door, it is remarkably similar to both the dome and the door that I plan to build:
http://www.gardendome.com/gd3_door/gd3_door1.html

I feel more like I know what I'm doing when I find others with similar plans online to what I've come up with, but I suppose it is a tenuous validation at best, since there's no telling whether theirs is a *good* solution.

Note also in the illustrations that this kind of dome has a nearly vertical wall for the first level of triangles, extending 3.7' for the strut calculation given in my first post. The second set of triangles is at a 12 degree angle for another 3.5-3.7', giving a height of seven feet at less than a foot out from the wall. (These are the same calculations used to compute the door placement and framing).
Imagepsa
Feb 9, 2010 1:13 AM CST
Name: Paul
Eastern WA
DG: tropicalaria
72 8'x2"x4" cedar
11 8'x2"x4" structural pressure-treated

Doesn't look like much in this photo, but it felt like a lot when loading and unloading it (and it felt like even more when paying for it!).

Thumbnail by psa

Imagepsa
Feb 9, 2010 1:15 AM CST
Name: Paul
Eastern WA
DG: tropicalaria
Most of the pieces are 3/16" longer than 8'. Cutting at a diagonal of 12 degrees turns 1/16" into sawdust and yields 8' 1/8" on the longer side and 7' 11 3/8" on the shorter side -- a difference of 3/4", as predicted. Apparently I can still do trig after all!

This is good, as I did all my calculations based on overlapping 3/4" on the struts. Also, the extra length in original pieces allows for loss from the sawblade, which I hadn't really thought through.

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Imagepsa
Feb 9, 2010 1:19 AM CST
Name: Paul
Eastern WA
DG: tropicalaria
Here's the first 15 struts: 10 C and 5 B all out of the pressure-treated lumber. You can see the chemical penetration on the cut ends. This consitutes everything that will be on the ground. Besides these, the doorway will be made out of pressure treated lumber, consisting of top, sides, and side braces. This stuff must have a stain included because it is orange, rather than the sickly green I associate with ground-contact pressure-treated, especially in the newer high copper formulations.

Since I took this picture I have moved on to cedar, cutting all 20 of the flat-ended C struts, plus 20 more regular C struts. Once I cut the 10 flat-ended B struts, plus 20 regular B struts, I'll be ready to construct the half and whole hexagons that will ring the bottom of the structure.

It's taking about an hour to do 30 struts, mostly because I'm being meticulous about the measurements and marking all of the struts on both ends to ensure I can tell them all apart. I've got about 3 1/2 hours of cutting to go at that pace.

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Imagepsa
Feb 9, 2010 1:28 AM CST
Name: Paul
Eastern WA
DG: tropicalaria
The only material for screws that I could find which was approved by the manufacturer for use with pressure-treated wood and cedar is stainless steel. Many sites on the web say hot-dipped galvanized would work as well, but every package I looked at said specifically not to use it in this way. Stainless steel is expensive.

I looked at the box, poked through it, and then dumped everything out looking for the included bit to screw these in. Reminds me of those "I Spy" books.

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Imagepsa
Feb 9, 2010 1:29 AM CST
Name: Paul
Eastern WA
DG: tropicalaria
I called my DW over to help.

I only started looking through the screws when I determined that the bit had come loose and was no longer attached to the inside of the lid. Yet when my DW came over, she had no trouble locating the bit.

Still scratching my head over this one.

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Imagepsa
Feb 9, 2010 1:31 AM CST
Name: Paul
Eastern WA
DG: tropicalaria
So here's the plan for the hubs. Schedule 80 PVC pipe, 3" diameter, cut to 1/4" less than the width of the struts. Perforated hanger strap, 22 gauge, held with two screws on each side. The one farthest out is to hold the strap onto the strut and the one closer to the edge is to control pivoting. For the most part, these joints will take compression, rather than tension, so the straps maintain integrity but don't carry much load. Distortion forces should be transmitted through the structure as well, with all parts reinforcing each other. Nonetheless, each strut should be good for up to 320lbs hanging load individually, based on the ratings of the strapping and the pipe. This is important since I want to be able to hang things off of the inside of the frame.

3" sch 80 PVC is very cool stuff--solid, but expensive. Good thing I don't need much (~16').

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Imagepsa
Feb 9, 2010 1:34 AM CST
Name: Paul
Eastern WA
DG: tropicalaria
Here's a set of hubs and straps. I've precut and bent the strapping because it's too stiff to bend acutely without a tool.

Thumbnail by psa

Imagepsa
Feb 9, 2010 2:26 AM CST
Name: Paul
Eastern WA
DG: tropicalaria
Construction details in Part 2: Frame Construction
http://cubits.org/midcolumbiagardens/thread/view/3094/


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brennanblue
Aug 10, 2011 11:17 AM CST
Thanks Paul! your step by step instructions made this possible.
Thumb of 2011-08-10/brennanblue/7dc881
I have found it difficult to locate thick pipe and strong sch. 80 PVC in Alaska, but as you can see, it is still strong enough to support my weight using off-the shelf hardware from lowes.

Thumb of 2011-08-10/brennanblue/932c7a
looking forward to trying the plastic triangle sheeting method next. I am also going to try a version with 2x6's to support insulation, and plywood for a complete shell.
Imagepsa
Sep 15, 2011 6:00 PM CST
Name: Paul
Eastern WA
DG: tropicalaria
Hey, that's great! I haven't been by this site lately and it was a wonderful surprise to see your pictures. I'm about to reglaze mine and am looking at various alternate strategies, so I look forward to hearing about your experiences with that as well.

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