It should be pointed out to everyone that this type of trussed dome appears to be the kind of dome that Buckminster Fuller used for all of his big dome projects, but this method of stiffening the dome has been forgotten, and none of the dome enthusiasts out there today appear to have preserved this insight. Do any image search for the domes made by Bucky Fuller, and you'll see that they are trussed domes. A single layer dome does not get stronger as you build larger because of the risk of buckling due to the vertices becoming very shallow, but the trusses protect against the risk of buckling.
Yes you are totally right, Oh just thought it could also be possible to connect to the WangerFlange lugs for the trussed portion which would half the number needed.....
@@Geo-Dome, it seems to me that your thought is correct but I just cannot get my head around it. It would be great if you did a follow-up showing the hardware and how you would go about assembling it without wearing it, if you get my drift.
I asked Paul, and he said that the inner set of struts isn't a 2v dome. It is actually a Pentakis dodecahedron (en.wikipedia.org/wiki/Pentakis_dodecahedron ), which is not a 2v dome. It is a dodecahedron where each pentagonal face is turned into five triangles, with the vertex pushed out to conform to the containing sphere.
Great, you have applied tensegrity to the structure by rotating each node (I've seen it that way since it finally delivers the same figure, but rotated). It would be interesting to make a script to rotate the nodes (see as coordinates in space). Super strong geodesic dome. Greetings from Chile 💪🏻
Not gonna lie, Paul, I'm a little bummed you've moved away from beveled construction but the wanger flanges are cool too. Just can't really see myself using them. That being said, I can't stress enough how informative and awesome your videos continue to be! Thanks for all you do!
Don't be bummed, I'm still working with beveled frame structures, I just have to explore a few more possibilities with WangerFlanges. I have fully optimised plans for most sizes in Beveled frame but if there is anything you think I've missed by all means give me a shout.
@@Geo-Dome You rock, Paul. One thing I think could be a great video idea that would also help folks with WangerFlanges projects: Tutorial / ideas for laying out a foundation for the domes. I struggle with the idea of pre building an accurate concrete or block foundation that the dome will then line up with perfectly. It's a bit easier to do on wood, but something like laying out a concrete form? Anyways, I'm not bummed anymore. Thanks again.
I'd be interested in seeing a shot of this dome which somehow highlights only the extra struts -- either with all the regular struts invisible, or dialed back so they're almost see-through.
Interesting . This was the style made on the old houes i bought. it didnt last the winter snows so i need to think of another roof but maybe i could make a bigger one with your designs. eitherway im glad i found this video. thanks !
@Paul Robinson: I just noticed one feature of this geometry that may contribute to the strength of the truss. Look at 2:39. You can see that every strut seems to lie on a long arc (not sure if they're all great circles); pick any strut, inner or outer, and trace it's path; the outer ones all lie along a path that connects them to the long struts inside the dome. I imagine that this would transfer any pushing or pulling forces on this dome along that line, down to the foundation. The inner struts all lie along lines that transition to the outer struts when they pass through the centers of the pentagons.
I'm particularly interested in the 10-way and 12-way connections using wanger flanges. Will they be strong enough as a ring of connections, or does every other strut need an extender to reach in for a 5/6 way connection in the gap to give it rigidity? If extenders are used for the 10 and 12 way connections, it would seem to me that the greatest strength that could be achieved would be to extend the inner struts, since they would meet at a sharper angle. In your booklet, you explained that very flat verticies are at risk of buckling in if pressure is applied to them. By extending the inner struts to meet at a 5 or 6 way connection in the middle of a 10 or 12 way connection, the inner struts would meet at a sharper vertex, and would confer more strength to the structure.
The trick will be how to keep all of the 12 way connections stable until you have completely assembled the dome. ruclips.net/video/sW2czmTEx4s/видео.html
It just occurred to me that you could technically truss a 2-frequency dome as well, but the trussing would look rather different. Even frequency domes might not truss the same way as odd frequency domes. If you take a 2 frequency sphere, and connect all of the pentagon vertices to each other, you would end up with a trussed sphere, and the inner shell of struts would essentially be an icosahedron (a 1-frequency sphere). But the visually odd thing about that manner of trussing is that the inner struts align with rows of outer struts. Instead of subdividing the sphere into a bunch of tetrahedra, the inner set of struts would turn the sphere into a shell of shallow octahedra. I suspect any trussed even frequency dome would end up with this characteristic.
Yes I looked at the 2v first, I would go from centre of pentagon to centre of the equilateral, you would need three struts from the corners of the equilateral, in a upside down pyramid. i'll maybe do something with a 2v also
@@Geo-Dome what I meant was that you could truss from the center of one pentagon to the center of another pentagon in a 2v geodesic sphere. Try trussing that way in even frequency geodesic spheres. A sphere trussed this way looks very different, but might still be stuff enough.
Paul I really like what your are doing and will be in touch with you. I like the way you are sharing your ideas and assisting others to do domes. You will always be welcome in my place in Northern Ireland. I will purchase flanges and do some experiments. I did a program using a hp calculator to do domes and drew them in 3d and really want to get back into it. I was able to produce elliptical domes of any breakdown would be interested in doing the program again and useThe wangerflanges which are exciting. WELL DONE I ADMIRE YOUR WORK.
Great design. I look forward to more data. Didn’t mention any specific sizes would this data be in any future video? Thanks again your channel is a fabulous resource.
Paul, could you show the various ways of inserting a door into a dome that you've shown in your previous videos adapted to a trussed dome? It would seem to me that the two layers of struts would offer more options, since the door could be built from any appropriate half-hexagon whether from the inner shell outer shell of struts.
The inner set of struts is what forms the truss. The entire dome then ends up being made of shallow tetrahedra. See this: fab.cba.mit.edu/classes/863.19/CBA/people/joaowilbert/week1/ This was one of Buckminster Fuller's original domes. All of his domes were trussed domes; this appears to be the insight that has largely been forgotten.
Excited to see more applications. I am working on studying and building model Zomes. Have you seen or worked with them before? Since they are not as stable of a structure, I wonder if the trusses would solve there problem, however, I am not sure how one would truss a zome. Any ideas?
Could the additional interior truss struts be replaced by cables? My first thought was that "no, cables would not help", but consider this. When a regular single layer dome fails, as one vertex pops inward, the surrounding vertices pop outward. Would interior cables strengthen the dome by preventing the outward popping of vertices?
Yes that would totally work! It would be like a pre-stressed system, the tension on the cables holding the solid frame under compression. A node inversion is much less likely because to push the vertex inwards all the vertices around it need to move outward a little, cable tension would prevent this. Great observation.
The True Nolan. Given that the geodesic dome is one of the strongest possible structural designs, the only way a failure can occur is through total incompetence of the builder. Look at 'prior art', there are many successful designs out there and strut strengthened domes are not required until you are exceeding 30 metres diameter.
@@biomechanique6874 Hey Bio! Yes, one of the strongest designs, but is optimized for a distributed, radially inward load. Of all likely failure modes, a point source inward load is the most likely to induce collapse. This can occur on any size dome, large or small, if the frequency is high enough. In fact, for a single layer design, as frequency goes higher and higher, the needed point load to pop a vertex inward approaches zero. the appeal of the inside truss design is that it redirects a point load sideways so that the load is once again diverted into a compression.
@ The True Nolan It is good that you have given these factors some thought. However, solid hub design combined with adequately sized structural strut material selection for any given usage criteria is far superior to a design that would flex and deform enough for vertex inversion. Paul's wangers are too small for domicile applications - even with bracing.
I have an additional pair of questions. 1) I'm trying to visualize what the inner set of struts forms. I imagine it forms a sphere with a lower frequency, but I can't figure out what it is. It doesn't appear to be a simple icosahedron because an icosahedron doesn't have 6-way verticies. What does the inner set of struts look like by itself? Is it just a 2-frequency geodesic sphere? That's what I think it might be, but I'm not sure. 2) In this video (ruclips.net/video/WlDntcslkmE/видео.html ), you explained that a 2-frequency dome is trivial to get a flat bottom with. This trussed dome, if it has a 2-frequency inner shell of struts, should be able to be divided right in half for a flat bottom, but also offers the possibility of modifying the 3-frequency shell of struts so that the undulating row of verticies get straightened out, permitting two different planes at which the sphere can be divided to make a flat bottomed dome (per this video of yours: ruclips.net/video/EU449-HhDeo/видео.html ). With these two possibilities, what would you recommend for producing a flat-bottomed dome from this trussed dome idea? It seems like there are three planes at which the dome could be divided to leave the verticies of one of the shells all lying in a plane, but either the inner or outer shell of struts necessarily gets cut. How would all of those cut pieces elegantly mount to a flat base?
OK to answer your questions: The inner framework forms a pentakis dodecahedron, simply a dodecahedron with the pentagon faces made into shallow 5 sided pyramids. This is the dual to icosahedral symmetry again often forgotten this was mostly used by Bucky in the early days until he discovered icosahedral geometry which he called "alternative method" I'll model the plans on a Kruschke flat bottom 3v so you have all the choices, I don't often use this geometry because it doesn't work well with beveled frame construction but for WangerFlanges I think it would only add one extra length of strut. I'll try and get this done tonight.
@@Geo-Dome isn't a pentakis dodecahedron the same as a 2v geodesic sphere? *EDIT* Upon further examination of a 2v geo-sphere with a pentakis dodecahedron, they do not appear to be the same. Can the pentakis dodecahedron be classified on the frequency scale?
@@Geo-Dome there is no frequency... its perfectly round (or can be any shape that you make with the airform)... its an airform!! using air to fill up the airform. the shape of a dome. made of fabric of some kind. covered with cement and wire or basalt rope or something to keep it strong. like the monolithic dome company does. similar but cheaper and easier to build.
Thanks Paul! I really appreciate your videos and insights and CAD skills. Thanks for making this!
My pleasure! Thanks for this great idea, I think it has loads of possibilities
Bucky is proud of ya , lad !
It should be pointed out to everyone that this type of trussed dome appears to be the kind of dome that Buckminster Fuller used for all of his big dome projects, but this method of stiffening the dome has been forgotten, and none of the dome enthusiasts out there today appear to have preserved this insight. Do any image search for the domes made by Bucky Fuller, and you'll see that they are trussed domes. A single layer dome does not get stronger as you build larger because of the risk of buckling due to the vertices becoming very shallow, but the trusses protect against the risk of buckling.
Yes you are totally right, Oh just thought it could also be possible to connect to the WangerFlange lugs for the trussed portion which would half the number needed.....
@@Geo-Dome Could you show what this means in your next video? I'm not sure what a WangerFlange lug is.
@@Geo-Dome, it seems to me that your thought is correct but I just cannot get my head around it. It would be great if you did a follow-up showing the hardware and how you would go about assembling it without wearing it, if you get my drift.
@@seanflanagan5674
Assembly video backed by Benny Hill music would be perfect.
This is equivalent of having a 2v and a 3v dome at the same time. Very inspiring!
I asked Paul, and he said that the inner set of struts isn't a 2v dome. It is actually a Pentakis dodecahedron (en.wikipedia.org/wiki/Pentakis_dodecahedron ), which is not a 2v dome. It is a dodecahedron where each pentagonal face is turned into five triangles, with the vertex pushed out to conform to the containing sphere.
Fascinating. It would be interesting to see two of these joined at the cut-out. From the look of the above the cut-out could be even higher.
Great, you have applied tensegrity to the structure by rotating each node (I've seen it that way since it finally delivers the same figure, but rotated). It would be interesting to make a script to rotate the nodes (see as coordinates in space). Super strong geodesic dome. Greetings from Chile 💪🏻
This design looks extremely sturdy. Seems like the two layers might allow for insulation as well. Very nicely done. Thank you!
Not gonna lie, Paul, I'm a little bummed you've moved away from beveled construction but the wanger flanges are cool too. Just can't really see myself using them. That being said, I can't stress enough how informative and awesome your videos continue to be! Thanks for all you do!
Don't be bummed, I'm still working with beveled frame structures, I just have to explore a few more possibilities with WangerFlanges. I have fully optimised plans for most sizes in Beveled frame but if there is anything you think I've missed by all means give me a shout.
@@Geo-Dome You rock, Paul. One thing I think could be a great video idea that would also help folks with WangerFlanges projects: Tutorial / ideas for laying out a foundation for the domes. I struggle with the idea of pre building an accurate concrete or block foundation that the dome will then line up with perfectly. It's a bit easier to do on wood, but something like laying out a concrete form?
Anyways, I'm not bummed anymore. Thanks again.
Wow I love this, Adds strength if you are using smaller diameter struts. great idea!
I'd be interested in seeing a shot of this dome which somehow highlights only the extra struts -- either with all the regular struts invisible, or dialed back so they're almost see-through.
Sorry. I didn't see that the follow-up video was ready.
Interesting . This was the style made on the old houes i bought. it didnt last the winter snows so i need to think of another roof but maybe i could make a bigger one with your designs. eitherway im glad i found this video. thanks !
Yes, that done is a good reason to invest in the flanges.
@Paul Robinson: I just noticed one feature of this geometry that may contribute to the strength of the truss. Look at 2:39. You can see that every strut seems to lie on a long arc (not sure if they're all great circles); pick any strut, inner or outer, and trace it's path; the outer ones all lie along a path that connects them to the long struts inside the dome. I imagine that this would transfer any pushing or pulling forces on this dome along that line, down to the foundation. The inner struts all lie along lines that transition to the outer struts when they pass through the centers of the pentagons.
Yes they are great circles in it, but the two rows at ground level are not quite.
This is basically Bucky Fuller's Triacon dome from 1949. Ziptie Domes has a very informative video on this.
I'm particularly interested in the 10-way and 12-way connections using wanger flanges. Will they be strong enough as a ring of connections, or does every other strut need an extender to reach in for a 5/6 way connection in the gap to give it rigidity?
If extenders are used for the 10 and 12 way connections, it would seem to me that the greatest strength that could be achieved would be to extend the inner struts, since they would meet at a sharper angle. In your booklet, you explained that very flat verticies are at risk of buckling in if pressure is applied to them. By extending the inner struts to meet at a 5 or 6 way connection in the middle of a 10 or 12 way connection, the inner struts would meet at a sharper vertex, and would confer more strength to the structure.
I've done 8 way and had no problems, I'll have to make a structure this way to fully test but I don't see any problems.
The trick will be how to keep all of the 12 way connections stable until you have completely assembled the dome.
ruclips.net/video/sW2czmTEx4s/видео.html
It just occurred to me that you could technically truss a 2-frequency dome as well, but the trussing would look rather different. Even frequency domes might not truss the same way as odd frequency domes.
If you take a 2 frequency sphere, and connect all of the pentagon vertices to each other, you would end up with a trussed sphere, and the inner shell of struts would essentially be an icosahedron (a 1-frequency sphere). But the visually odd thing about that manner of trussing is that the inner struts align with rows of outer struts. Instead of subdividing the sphere into a bunch of tetrahedra, the inner set of struts would turn the sphere into a shell of shallow octahedra. I suspect any trussed even frequency dome would end up with this characteristic.
Yes I looked at the 2v first, I would go from centre of pentagon to centre of the equilateral, you would need three struts from the corners of the equilateral, in a upside down pyramid. i'll maybe do something with a 2v also
@@Geo-Dome what I meant was that you could truss from the center of one pentagon to the center of another pentagon in a 2v geodesic sphere. Try trussing that way in even frequency geodesic spheres. A sphere trussed this way looks very different, but might still be stuff enough.
AWESOME
Paul I really like what your are doing and will be in touch with you. I like the way you are sharing your ideas and assisting others to do domes. You will always be welcome in my place in Northern Ireland. I will purchase flanges and do some experiments. I did a program using a hp calculator to do domes and drew them in 3d and really want to get back into it. I was able to produce elliptical domes of any breakdown would be interested in doing the program again and useThe wangerflanges which are exciting. WELL DONE I ADMIRE YOUR WORK.
What CAD application are you using to do this modeling?
I use sketchup, I think it's the 2019 version. Not liking how they are going subscription based so maybe will move to Blender.
Great design. I look forward to more data. Didn’t mention any specific sizes would this data be in any future video? Thanks again your channel is a fabulous resource.
Paul, could you show the various ways of inserting a door into a dome that you've shown in your previous videos adapted to a trussed dome? It would seem to me that the two layers of struts would offer more options, since the door could be built from any appropriate half-hexagon whether from the inner shell outer shell of struts.
Can you show an image of just the trusses? I am very curious about the lines, and had a hard time seeing them in the image you showed??
The inner set of struts is what forms the truss. The entire dome then ends up being made of shallow tetrahedra. See this: fab.cba.mit.edu/classes/863.19/CBA/people/joaowilbert/week1/
This was one of Buckminster Fuller's original domes. All of his domes were trussed domes; this appears to be the insight that has largely been forgotten.
Yes I will, this was to test the theory, when I do full plans I'll make nice diagrams that show everything clearly
Very interesting! Would you be able to make your sketchup file available?
Yes I can, let me finish it properly with all the wangerflanges, nudge me if I don't get this done in a week
I don't understand how to make all the tubes at once from picking up only one, can you please explain?
Good job boss
Impressive!
Paul, could this not be made in your unity dome style? In a way, I see the kite inside of this.
Hi Paul, would you ever consider building out the full polygon? As in, a dome on top, connected to a half underground upsidedown dome?
Excited to see more applications. I am working on studying and building model Zomes. Have you seen or worked with them before? Since they are not as stable of a structure, I wonder if the trusses would solve there problem, however, I am not sure how one would truss a zome. Any ideas?
Yes working on zomes now and will be doing a video shortly,
Hi Paul would it be possible to trussed only one « middle line « ? To reduce wood /connection and so cost and weight
Regards
Could the additional interior truss struts be replaced by cables? My first thought was that "no, cables would not help", but consider this. When a regular single layer dome fails, as one vertex pops inward, the surrounding vertices pop outward. Would interior cables strengthen the dome by preventing the outward popping of vertices?
Yes that would totally work! It would be like a pre-stressed system, the tension on the cables holding the solid frame under compression. A node inversion is much less likely because to push the vertex inwards all the vertices around it need to move outward a little, cable tension would prevent this. Great observation.
In the case of a 3v you`ll find no vertex moves inwards at the point of failure because they are all under load.
The True Nolan. Given that the geodesic dome is one of the strongest possible structural designs, the only way a failure can occur is through total incompetence of the builder. Look at 'prior art', there are many successful designs out there and strut strengthened domes are not required until you are exceeding 30 metres diameter.
@@biomechanique6874 Hey Bio! Yes, one of the strongest designs, but is optimized for a distributed, radially inward load. Of all likely failure modes, a point source inward load is the most likely to induce collapse. This can occur on any size dome, large or small, if the frequency is high enough. In fact, for a single layer design, as frequency goes higher and higher, the needed point load to pop a vertex inward approaches zero. the appeal of the inside truss design is that it redirects a point load sideways so that the load is once again diverted into a compression.
@ The True Nolan It is good that you have given these factors some thought. However, solid hub design combined with adequately sized structural strut material selection for any given usage criteria is far superior to a design that would flex and deform enough for vertex inversion. Paul's wangers are too small for domicile applications - even with bracing.
Paul, are you shipping to the states ?
Yes, Royal mail for orders under 150(takes ages) and UPS for larger ones should get them in around 7 days
I have an additional pair of questions.
1) I'm trying to visualize what the inner set of struts forms. I imagine it forms a sphere with a lower frequency, but I can't figure out what it is. It doesn't appear to be a simple icosahedron because an icosahedron doesn't have 6-way verticies. What does the inner set of struts look like by itself? Is it just a 2-frequency geodesic sphere? That's what I think it might be, but I'm not sure.
2) In this video (ruclips.net/video/WlDntcslkmE/видео.html ), you explained that a 2-frequency dome is trivial to get a flat bottom with. This trussed dome, if it has a 2-frequency inner shell of struts, should be able to be divided right in half for a flat bottom, but also offers the possibility of modifying the 3-frequency shell of struts so that the undulating row of verticies get straightened out, permitting two different planes at which the sphere can be divided to make a flat bottomed dome (per this video of yours: ruclips.net/video/EU449-HhDeo/видео.html ). With these two possibilities, what would you recommend for producing a flat-bottomed dome from this trussed dome idea? It seems like there are three planes at which the dome could be divided to leave the verticies of one of the shells all lying in a plane, but either the inner or outer shell of struts necessarily gets cut. How would all of those cut pieces elegantly mount to a flat base?
OK to answer your questions: The inner framework forms a pentakis dodecahedron, simply a dodecahedron with the pentagon faces made into shallow 5 sided pyramids. This is the dual to icosahedral symmetry again often forgotten this was mostly used by Bucky in the early days until he discovered icosahedral geometry which he called "alternative method" I'll model the plans on a Kruschke flat bottom 3v so you have all the choices, I don't often use this geometry because it doesn't work well with beveled frame construction but for WangerFlanges I think it would only add one extra length of strut. I'll try and get this done tonight.
@@Geo-Dome isn't a pentakis dodecahedron the same as a 2v geodesic sphere?
*EDIT* Upon further examination of a 2v geo-sphere with a pentakis dodecahedron, they do not appear to be the same. Can the pentakis dodecahedron be classified on the frequency scale?
MAKE A AIRFORM CEMENT DOME MAN!!
OK I'll throw something together with a very simple 2v just to test the theory.
@@Geo-Dome oh man!!! your awesome!!
@@Geo-Dome there is no frequency... its perfectly round (or can be any shape that you make with the airform)... its an airform!! using air to fill up the airform. the shape of a dome. made of fabric of some kind. covered with cement and wire or basalt rope or something to keep it strong. like the monolithic dome company does. similar but cheaper and easier to build.