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Advanced Geodesic Dome Question
This summer I plan on building an elliptical geodesic dome.
I based it off an octahedron frequency 5. I stretched my face triangle so that the corners all matched up with a 20 by 30 ellipse. I then projected lines from the center to every intersection on my face triangle.
I used spherical coordinates to find all my points, built an excel spreadsheet to calculate strut lengths, central angles, plotted them in AutoCAD......DOME.
See picture:
www.lostmachine.com/images/m...pdome.jpg
Here is my Question.
When I kept the divisions on my equilateral triangle proportionally correct while I manipulated it to fit into the ellipsoid the projections give huge differences in Strut length, varying from 2.5’ in the corners to over 6’ in the middle.
The engineer in me says that if my strut lengths were closer to the same length I’d have a stronger dome. I look at my face triangle and I think I could shrink the triangles near the center and that would help when I do my projection...
So, what is the best way to go about this?
Should I feel responsible for coming up with a relationship for the projected strut lengths and that of the face triangle and then manipulate accordantly?
Is there any written material covering this problem?
I know if I have all my struts the same length, I end up with all my points on a plane. I want to keep the same general curvature but would like more uniform struts.
I’m tempted to simply estimate, pull the inner triangles in and recalculate.
Then there is my other question.
If I do this, is it going to mess with the dome's ability to transfer forces throughout the structure? Is my gain in strength from shorter strut lengths going to be negated by odd angles?
Here is a link to the AutoCAD drawings in you would like to see them.
www.lostmachine.com/images/m...tower.dwg
Thanks for the Help.
LM
X-posted to
Mathematics
Dome Home
sacred geometry
This summer I plan on building an elliptical geodesic dome.
I based it off an octahedron frequency 5. I stretched my face triangle so that the corners all matched up with a 20 by 30 ellipse. I then projected lines from the center to every intersection on my face triangle.
I used spherical coordinates to find all my points, built an excel spreadsheet to calculate strut lengths, central angles, plotted them in AutoCAD......DOME.
See picture:
www.lostmachine.com/images/m...pdome.jpg
Here is my Question.
When I kept the divisions on my equilateral triangle proportionally correct while I manipulated it to fit into the ellipsoid the projections give huge differences in Strut length, varying from 2.5’ in the corners to over 6’ in the middle.
The engineer in me says that if my strut lengths were closer to the same length I’d have a stronger dome. I look at my face triangle and I think I could shrink the triangles near the center and that would help when I do my projection...
So, what is the best way to go about this?
Should I feel responsible for coming up with a relationship for the projected strut lengths and that of the face triangle and then manipulate accordantly?
Is there any written material covering this problem?
I know if I have all my struts the same length, I end up with all my points on a plane. I want to keep the same general curvature but would like more uniform struts.
I’m tempted to simply estimate, pull the inner triangles in and recalculate.
Then there is my other question.
If I do this, is it going to mess with the dome's ability to transfer forces throughout the structure? Is my gain in strength from shorter strut lengths going to be negated by odd angles?
Here is a link to the AutoCAD drawings in you would like to see them.
www.lostmachine.com/images/m...tower.dwg
Thanks for the Help.
LM
X-posted to
Mathematics
Dome Home
sacred geometry
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Re: Advanced Geodesic Dome Question
Fri, April 22, 2005 - 11:03 AMHey there Lost Machine,
First, thanks for all the good content you've added to this tribe! (I am definitely going to look at your dual boom dome crane in much more detail).
I will take a stab at your questions, but please understand that my answers are based on my half-a$$ed grasp of theory, experience building a normal conduit dome, and experience building my own experimental designs of PVC tensegrity structures.
I think the long struts are mainly a problem when they have lateral force applied to them, like if someone was to climb or hang from them, for instance. I am not at all sure that wildly variant strut lengths will compromise the strength of your dome given normal loading from gravity, since it is tension rather than compression that holds a dome up.
That said, in some of the different experimental tensegrity PVC pieces I have built over the last couple of years, 2" od PVC will bend before you think it will-- strut length is a very critical factor in the bendability.
I think you mentioned on another post you were going to build out of 1" od PVC. That stuff will definitely bend at a 6' strut length given a moderate amount of force, maybe even the dome's weight itself if it is big enough. If the dome is skinned it will have much more flex in it than if you made it from metal (ridiculously expensive now, I know), especially when the wind hits it. So take that into account with the skin and the way you fasten it. Arguably the skin could be used to give it extra strength if it was the right stuff....
Bruce :-) -
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Re: Advanced Geodesic Dome Question
Fri, April 22, 2005 - 12:56 PMBruce thank you for your response.
You’re right I am worried about the lateral forces.
I’m sure the 1”PVC can take the tensile and compression loading. As I’m sure you know accurate vertices are extremely important. If I were to get some side loading the bend in the PVC will shorten the length between vertices. This could allow the intersection to pop inward.
Because I already have a lot of 1” PVC I want to use it to build my dome. I’m planning on sleeving 8” lengths of 3/4”OD steel Conduit into the ends. I’ll leave a few inches out to press and drill for my connections. One thought is on the longer length inserting a full length of EMT into the PCV. I would have to glue it in otherwise the benefit of having both materials would be diminished.
In order to keep the price down I think I’ll be skinning the dome with old Hotel bed sheets again. So they won’t help with strength.
Over on the Mathematics tribe I think we are working on a solution to shrinking the struts.
Thanks again, I’ll be sure to post my progress.
LM -
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Re: Advanced Geodesic Dome Question
Sat, April 23, 2005 - 1:50 PMThanks-- I'm interested to hear how you solve this.
I'd also like to check it out on the playa-- I love it when people do nontraditional domes.
I saw the pictures of your dome from last year- the bedsheets look really good, nice design (and let in breeze too, I am sure, which is very helpful in the daytime).
How were you going to fasten the conduit to the pvc? Screws or pins? Glue? What kind of glue do you use for galvanized metal to pvc?
Thanks,
Bruce :-) -
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Re: Advanced Geodesic Dome Question
Sat, April 23, 2005 - 11:22 PMThe sheets worked great last year, they were a lot of work but I would do it all over again. They let a lot of air in, they cut the wind down, and they made no noise. Another nice thing about them is you get to see a lot of what is going on outside, we could see people walking up from a block away, but from the outside it was hard to see in. You had to be standing next to the dome to see inside, almost like a one way mirror.
As for the struts:
Instead of cutting everything to the right length, I’m going to cut the PCV within 1/2” of the length it needs to be in order to have enough EMT sticking out the ends.
The conduit I’ll press, drill, and file clean before it gets glued in.
As for glue my first choice is Lexel it comes in a tube that fits into a caulking gun dries clear and is awesome.
The glue I’m going to use is “Liquid Nails”. I have a case of it left over from an old job, I want to use it before it goes bad. The OD of the 3/4” conduit is about a 1/16th smaller than the ID of the 1” PVC, which is why I want to use a glue that can fill a gap.
After glue has been applied, I’ll adjust the lengths so that the distance between holes is where it needs to be and then I’ll put two small self taping machine screws into each end.
I’ll make some test pieces before I commit to the project. I’ll post pics when I do.
LM -
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Re: Advanced Geodesic Dome Question
Mon, April 25, 2005 - 10:39 AMThanks again for the info!
Bruce :-)
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Re: Advanced Geodesic Dome Question
Wed, April 27, 2005 - 3:56 PMEMT. Spend the money, collect the scrap, whatever. Forget PVC for you application. It just doesn't do the trick well and will make more work for you.
Free advice indeed,
Andrew
(Former Director fo Development, Pacific Domes) -
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Re: Advanced Geodesic Dome Question
Wed, April 27, 2005 - 6:02 PMI don’t mind don’t mind doing extra work to save money.
So what about PVC makes it bad?
Right now my biggest concern is getting too much flex and having vertices pop inward. Not counting the extra work, with the price of PVC I could build two domes about the same size, one slightly larger than the other then connect the two in a space frame.
I have about 150’ of 1” PVC that was given to me. I’m going to use it for something, and if I can use it for a dome then I will.
You say it won’t work; I need to know why it won’t work.
Thanks in advance,
LM -
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Re: Advanced Geodesic Dome Question
Thu, April 28, 2005 - 12:02 PMA couple of thoughts on the PVC question:
1) you should certainly use the stuff since you've got it.
2) I am still worried about compression, though I know you mentioned this is not a concern. In the ideal math world of the dome that doesn't happen, but just the weight of the dome and the force of the wind on it could put some of your 6' struts into too much compression. You definitely don't want people climbing it.
FWIW I had compression problems with approx 500 lbs. I had a sort of loose tensegrity structure holding up hammocks, and four 2" od 10' long PVC struts ended up taking too much of the weight and bent until the weight was on the ground. Yes, only 125 lbs bent each 2" od strut, possibly less than 125 lbs since the rest of the structure gave some support.
Non critical failure, just had to take out one of the hammocks and all was fine. So definitely do your experiment, since there shouldn't be anyone hurt as a result.
3) While shorter strut lengths will do wonders for your pvc strut bending problems, there is a factor in geodesic construction that is often not talked about: the closer it gets to a sphere, the easier it is for vertices to pop.
[digression: I witnessed a nice new freshly (and professionally, it was your dome at Blue House, Andrew, which was certainly very lovely, functional, and filled with lovely and functional people) constructed strong huge high frequency dome exhibit vertex pucker when someone climbed it. The problem being that the near sphericity made the wiggle necessary for puckering close enough that it happened easily.]
[Note also the gigantic dome Fuller built for the world expo. It had two layers because it is the =thickness= of the dome shell that gives it stability. Low freq domes have a "thicker shell" because all those corners stick out farther in and out, high freq domes thinner.]
[I believe this issue is addressed in the Kenner Geodesic Math book, in case someone thinks I am totally crazy]
One solution to the pucker problem is to increase the thickness of the dome shell by reducing the frequency. Of course this then gives you longer struts... Seems like you should be able to selectively alter the dome frequency in different sections of the dome to acheive your desired result. I've done some design work on Maya (personal learning edition = free) to this end, but have not tried it in practice yet.
Bruce :-) -
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Re: Advanced Geodesic Dome Question
Fri, April 29, 2005 - 12:33 PMBruce,
I think you and I are worried about the same thing. When I say compression I think about the strut being loaded axially. As if a piece of all-thread was running down the length of the PVC and some nuts and washers were added and tightened. In a perfect environment this wouldn’t be a problem, it would take a lot of force to break it.
My worry and yours is that compression along with any force added laterally (a climber) will cause the strut to buckle. If I do end up using 6’ struts I think I’ll insert a full length of conduit into the PCV not just on the end like the smaller struts.
As far as the High Frequency part, I don’t think you’re crazy ; )
The greater the frequency the smaller your dihedral angles become. When they get too low it doesn’t take much bending (or improper construction) to pop the vertices inward.
I still have a few months left before I settle on a design. I may end up building a smaller dome this year and saving up for a big one the year after. Now that I’m really getting into the spherical math, more shapes are available to play with. I’m tempted to buy a lump of clay and go at it for a while to see what I really like, and then do the math. As of right now I’m going about it the other way, (crunch numbers then looking). It doesn’t seem to be working very well. We’ll see how it goes.
LM -
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Re: Advanced Geodesic Dome Question
Sat, April 30, 2005 - 12:34 PMYes, I agree, I think we are talking about the same thing as far as compression goes. Let me add though that it wouldn't take any sort of thing added to a strut to apply any lateral force-- the struts all pull eachother through three dimensional space, and of course there is gravity, working both through the struts and on them. Add a little wind (or a lot sometimes on the playa) and you already have plenty of lateral forces on the struts.
If you put conduit through the 6' struts I think you will definitely be OK. In that case you could just use conduit and not even use the pvc over it...?
It occured to me this morning, and perhaps this was obvious to you from my earlier post (though it was not obvious to me <grin>) that you could do what fuller did-- build a two layer dome. In fact, since you are playing with nontraditional shapes you could build two layers on the top and bring the innermost layer down to meet the wallish part of the dome halfway down, and just do one layer from there.
Yes, I am totally with you there on the difficulty of modeling. For a while I was visualizing mentally, then doing a lot of math so that I could make paper cutouts and then assembling those with scissors and tape. It took forever!
What I do now is use Maya, the 3-d animation platform that is behind a lot of the special effects in movies nowadays. There is a personal learning edition that is free to download. The only caveat is that it requires a somewhat expensive graphics card, and a reasonably contemporary processor in your computer. You can also find cracks of the software out there, but that doesn't solve your system requirement issues if you have them.
But with Maya modeling is fast and easy! (faster and easier, anyway). You can easily create shapes and twist and bend and warp them, connect them with other shapes and move your viewpoint around to see it from different angles.
It is also possible, depending on your degree of measurement tolerance, to build a shape in Maya and then extract the strut length measurements directly from maya without ever having to do the math.
There might be some other software tool out there that is easier to use than maya-- it has a lot of functionality that is not used in the wire frame modeling work that I am doing, and all that other stuff gets in the way. Nor is Maya totally optimized toward what I am doing with it-- if there was something out there that was did less but was directed towards doing this specifically...
On the other hand, the lump of clay has an easy interface and you can do pretty much anything with it!
Oh, one other thing: this is the site of a guy in New Zealand who has been building nonspherical domes for a long time, some interesting info... I also have his book pdf if you want to check it out:
www.geocities.com/geodesics...ex.htm#idx
Bruce :-) -
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Re: Advanced Geodesic Dome Question
Thu, May 5, 2005 - 4:23 PMSorry it has taken so long to respond. I’ve got a lot of projects on my plate right now and some intense deadlines approaching.
One of the reasons I would still sleeve PVC over conduit is purely aesthetics. I like the look of clean large diameter struts. I would paint the conduit ends to match the PCV and clean the PVC with acetone. I think a dome should look good as well as function well. I want to do some testing but I’m sure the PVC over a full piece of conduit will add a lot more strength.
The duel Dome idea is pretty good, but it is a lot more work. Not to mention the extra material. With the added material and the extra work I would be willing to spend the money for EMT.
Your hammock stands got me thinking of some geodesic sculptures.
I’m thinking of some non weight bearing, not covered towers. I’m thinking this might be a better idea for my supply of PVC.
My girlfriend reminded me of one of the goals of this years shade structure was a quick dome that we could use over and over again. Orbbject (last years dome) take a full day to set up. I’m going to keep looking for other options for now.
Maya sounds cool, I’m going to have to check it out. I just got 3-D studio max but haven’t played with it yet. I was told there are a thousand different ways you can manipulate an object.
That guys site is pretty neat, I wish he had better photos. I would love to see his book it you can send it to me that would be great.
LM -
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Re: Advanced Geodesic Dome Question
Fri, May 6, 2005 - 11:13 AMNo worries on the response time! I have a relatively large amount of unstructured time, so I can get carried away on the internet occasionally. Feel free to respond or not as your time and interest allows...
Yes, domes are slow. My dome went unbuilt last year because I camped with a lot fewer people and didn't have the peoplepower to put it up along with the other (new) stuff I wanted to do.
You may be able to see from the pictures in my profile I've had some success using those tensegrity structures for tarp suspending frameworks. They work quite well, since the relatively large amount of flex in the structures allows them to dissipate a lot of the wind's force, and of course their tensegrity nature allows a more effective distribution of the forces on the structure to different parts of it, as opposed to post and beam.
Those are 2" od pvc struts in the picture of the tent shade structure. The long struts are 14' 7" and they manage not to bend excessively.
I wouldn't try that kind of strut length with 1" od pvc, but if you use prisms with more uniform sides I think you could definitely use them as the basis for a shade structure.
You could do quite a lot with your pvc if it's not weight bearing. Since it's so lightweight you should be able to assemble something fairly large/high on the ground and get it standing up by yourself or with one or two people to help.
I used to use rope threaded through holes at the ends of the pvc struts to attach them, but I switched to nylon straps with metal cam buckles (got them at www.ahh.biz, though I keep thinking there must be somewhere less expensive to buy them). The straps are much faster, and don't require the continual tightening that the rope does. I did have an unexplained vertex failure in the high winds one night last year, and I don't know if the strap slipped or if something else happened.
I like using the tensegrity structures for things that allow people to have a physical kinesthetic experience of the way that it behaves differently from post and beam. Hammocks already have a nice floaty feeling to them, but you get just a little bit more when they are hung on a structure with lots of flex in it. It's a nice feeling. Also cool is the way the structure responds differently when there is more than one full hammock. People can kind of swing around and get the other hammock moving quite a bit. People can climb all over them, too.
I'm still really exploring the basics of this construction method. At this point I've made myself a giant erector set that I can use to make different things.
I'm definitely interested in seeing what you end up doing.
Book details by personal message...
Bruce :-)
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