How to the Optimize the Strength of a Geodesic Dome?

[mru6...@gmail.com]

Have completed a first dome.

And am In the beginning stages of designing a second dome (about 30 foot diameter).

Now deliberating which ought to be the stronger of the two.

4 frequency dome + 1 1/2 inch EMT conduit + 5 foot strut average (2 per 10ft pole)
or
8 frequency dome + 3/4 inch EMT conduit + 2.5 foot strut average (4 per 10ft pole)

I'm most curious about something like 

whether or not a 1 foot 1" EMT strut would outperform 

something like a 5 foot 2" EMT strut.
So a better question might be, what kind of frequency/strut dimensions are really best in terms of strength?

frequency type
strut material
strut wall thickness
strut diameter
strut length

-

From what I've gathered, it looks as if having the following is ideal when it comes to raising dome strength:

Higher frequency
1/2 sphere via an even frequency dome i.e. 2v, 4v, 6v, 8v (truly flat at the base)
Low strut length variance (the difference between the smallest and the largest strut)
One strut type in the base ring

Contributions appreciated,

[Dick Fischbeck]

Which strut is stronger in compression? I would start there.

[Ashok Mathur]

Most FEA analysis has shown that the weak point in a dome is rarely the strut strength.

Almost always the weakest link is the hub design and its strength.

NB: There are no standard methods of figuring out the strength of a geodesic dome as FEA/FEMA analysis is not rigorous enough to do the job.

Domerama has good articles on the subject.

Ashok

Regards

Ashok

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[thedomeguy]

The larger diameter the stronger in compression, but the failure will likely be a tension failure.

Sent from my Verizon, Samsung Galaxy smartphone

-------- Original message --------

From: Dick Fischbeck <dick.fi...@gmail.com>

Date: 12/22/16 6:40 PM (GMT-06:00)

To: Geodesic Help <geodes...@googlegroups.com>

Subject: Re: How to the Optimize the Strength of a Geodesic Dome?

Which strut is stronger in compression? I would start there.

On Thu, Dec 22, 2016 at 6:46 PM, <mru6...@gmail.com> wrote:

Have completed a first dome.

And am In the beginning stages of designing a second dome (about 30 foot diameter).

Now deliberating which ought to be the stronger of the two.

4 frequency dome + 1 1/2 inch EMT conduit + 5 foot strut average (2 per 10ft pole)
or
8 frequency dome + 3/4 inch EMT conduit + 2.5 foot strut average (4 per 10ft pole)

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[Paul Kranz]

Bucky once hung empty drums from the vertices of his "Hexa-Pent" dome and filled them with water to see how dtrong it was. Maybe you could try that.

Paul sends...

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[mru6...@gmail.com]

Was browsing through your website on geodesic domes a few days ago, very helpful. 

Also have made much use of Domerama and read article on structural analysis.  

A proper hub design has been the most thought-provoking part of designing a second dome.

There are a number of choices available, however, I have no way of distinguishing between the good and the better.

Would you happen have any recommendations on a hub design? Or at least some advice on which direction to go?

On Thursday, December 22, 2016 at 7:03:23 PM UTC-6, Ashok Mathur wrote:

Most FEA analysis has shown that the weak point in a dome is rarely the strut strength.

Almost always the weakest link is the hub design and its strength.

NB: There are no standard methods of figuring out the strength of a geodesic dome as FEA/FEMA analysis is not rigorous enough to do the job.

Domerama has good articles on the subject.

Ashok

Regards

Ashok

On Fri, Dec 23, 2016 at 5:40 AM, Dick Fischbeck <dick.fi...@gmail.com> wrote:

Which strut is stronger in compression? I would start there.

On Thu, Dec 22, 2016 at 6:46 PM, <mru6...@gmail.com> wrote:

Have completed a first dome.

And am In the beginning stages of designing a second dome (about 30 foot diameter).

Now deliberating which ought to be the stronger of the two.

4 frequency dome + 1 1/2 inch EMT conduit + 5 foot strut average (2 per 10ft pole)
or
8 frequency dome + 3/4 inch EMT conduit + 2.5 foot strut average (4 per 10ft pole)

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[mru6...@gmail.com]

Using only an empty tube of EMT conduit seems like a potential waste for reinforcing the strength of the strut.

Would adding some sort of material such as sand (fine grain) to the inside of the strut be worthwhile.

It seems that it would be significantly stronger, since sand has both high density and compression strength.

It might be analogous between trying to bend an empty drinking straw as opposed to a drinking straw filled with sand.

A drinking straw filled with sand would perform much more adequately as far as compression strength goes.

[Ashok Mathur]

Dear mru6
Let me rephrase your query as a general one as to the best relationship between the the diameter of the cross-section of a strut and its longest recommended length as a strut- i.e. when is a strut any longer than the recommended length not safe to use and therefore one must either (i) change the diameter of cross section or (ii) go for a higher frequency.

There is a fairly simple rule to help you to choose between alternative (i) and (ii) given above.
For both alternatives calculate the total cost of the struts ( Sum lengths of all struts * weight per running measure* dollar cost per running measure). Add to this total cost of hubs. Further add some measure of labor costs to get the shell cost.
Which ever alternative gives a lower shell cost is the way to go.
If you want to see this implemented in an example I can sen you a link.

Now back to the question of the recommended length for a given cross section.
Hugh Kenner attributes this solution to Fuller on page 68 of his book

"In general, in order to minmize component inventory, we use the lowest frequency we can.
How long a component we can tolerate is a function of its slenderness ratio (length divided by its diameter).
Fuller has suggested 24/1 as a slenderness ratio for wood, 30/1 for metal or prestressed concrete."

Regards
Ashok

[mru6...@gmail.com]

Thank you for the advice, though I would like clarify my query so there is no more confusion.

It is true as far as practical considerations go, cost is ultimately the deciding factor for me. (I also would like to see the link you offered, if that's still possible.)

However, my question was more theoretical in nature and asking what if strength, and only strength, were the deciding factor. 

Within the last month I was able to procure a data chart (attached below) giving the strength of EMT at different lengths, this has in the most part provided a satisfactory answer to my question.

Though the following is what remains unclear to me.

I am building a 36 foot dome.

Let's assume both strut sizes are at a safe recommended length.

And both strut sizes have an equal capability of bearing the same force/weight. 

What then would be the ideal choice:

(i) change the diameter of cross section (Ex. 4 frequency dome with 1 inch conduit)

or 

(ii) go for a higher frequency (Ex. 8 frequency dome with 3/4 inch conduit)

It seems the only additional things to distinguish (i) from (ii) is the number of hubs and the sphere-like shape of the dome.

Since these qualities would be greater in a higher frequency, would that offer more structural advantages?

Thanks

[Gerry in Quebec]

If the amount of steel in a dome frame is any indication of the building's structural integrity, it may be informative to compare the weight of the steel in the two 36' domes you mentioned: a 4v (i.e.,4 frequency) made of 1" EMT, and an 8v made of 3/4" EMT. Let's assume both are hemispheres and there are no independent hubs, i.e., the strut ends are squashed, drilled, bent to the correct axial angles, and then connected with nuts and bolts.

To simplify, let's ignore the weight of the bolts, nuts and washers, as well as the weight of steel between the ends of struts and the bolt holes (non-structural ends of the struts).

The 4v frame will weigh about 900 pounds and the 8v will weigh about 1220 pounds. With the added strength afforded by the greater amount of steel and by its higher frequency, the 8v will be significantly stronger than the 4v. But the labour requirements to build it will be far greater than for the 4v given the added geometric complexity: 980 struts, 640 triangular panels and 341 vertices in the 8v versus 250 struts, 160 triangular panels and 91 vertices in the 4v.

The weight comparison is based on an "EMT Weights and Dimensions" chart found here:

https://steeltubeinstitute.org/steel-conduit/types-of-steel-conduit/electrical-metallic-tubing-emt/

- Gerry in Québec

[mru6...@gmail.com]

Excellent answer, I never considered the added amount of steel. And even more so, it playing an important role in the dome's strength. 

So if one were to summarize, an answer to my question might go something like: There are many factors one needs to thoroughly consider when building a dome. However, if building to optimize strength and if the struts sizes in question have an equal capability of bearing the same load. Then it is a general rule, choosing a higher frequency instead of a larger strut diameter will be a superior choice. Given that in a higher frequency there is a greater redundancy, a more sphere-like structure, a greater number of intersections, and a greater amount of steel comprising the dome. These all in effect will add a substantial amount of structural integrity when compared to the equivalent dome of a lower frequency and larger strut diameter.

[Ashok Mathur]

Dear Gery

In a building that is based on only on compressive strength of steel, weight of the steel used isa fair indicator of its strength.

But when it is based on both the  compressive strength and tensional strength, the strength begins to reach proportions that are not measured bu conventional FEA measures.

As yet there is no system of measuring the strength of a geodesic dome.

That is a tall claim to make as FEA claims to do so.

Here is a example of a typical FEA analysis done by an Australian Company in 2005.

You will notice that it finds that the hubs are weaker by a factor of 10 compared to the struts. A hub deforms at about 2kN while a strut deforms at 134 kN.

The FEA analysis of the strut is a standard FEA analysis where a point force reacts only at that point.

Domes react as a whole and the FEA analysis just ignores this aspect.

When a point force is applied to a geodesic dome, it rotates to counter the point force.
Again FEA has not been modified to show that.

I would say that if a particular beam meets the slenderness ratio for two frequencies, go for the lower one, as then you minimize the chances of hub failure.

Regards

Ashok

Regards

Ashok

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[Peter Schwarzel]

Hi - FEA is definitely up to the task of estimating the strength of a dome. If the struts and connections are designed correctly to take their intended load (wind load, snow load, hung loads , dead load etc) and these are optimised correctly then the failure mode of a single skin dome is global buckling of the "skin". This is brought on by the assemble tolerances of the dome. ie the dome cannot be built perfectly spherical. When modelling such a dome the geometry needs to be perturbated in the same way it would be in practice otherwise the predicted strength would be very high as a sphere is geometrically very stable. I have modeled shells, domes and such in the past and this is the general failure mode of such structures.  ie as the element size decreases the "skin" moves towards behaving like a membrane vs a truss. In a truss the weakest element fails first and depending on the structural redundancies in place depends on what happens next. If the element size is small enough the dome "skin" behaves as a membrane and its "strength" is independent of element "strength" and becomes an elastic stability problem. There are two modes in action. 1) A local load that tries to deflect the skin inward from a point load like a hung load (or local snow load). This tries to "snap through" the skin from its outward curvature to an inward curvature shape. If this occurs its a local instability and if the load is big enough the instable "wave" or oil canning will try to turn the dome inside out. This could be a fast or slow failure. 2) A wind load tries to push the entire dome sideways. This tries to "cripple" the outsides of the dome in the transverse direction. This means the skin moves outwards and then buckles allowing the rest of the dome to collapse.

All of these mechanisms can be investigated using FEA.  Cheers Peter s

[Blair Wolfram]

Ashok;

I have found exactly the opposite from your claim of hub weakness; I've found hubs are far stronger than the struts in every case when an engineered dome is involved. On one of my earlier generations of hubs which used two bolts instead of four to secure the lumber to the hub, we had the University of Minnesota physically load a strut bolted to a hub in their science lab with both compression and tension tests, and in every case the 2"x8" douglas fir lumber failed, not the hub. The hub and the bolts stayed in form and pulled or pushed through the lumber.

Of course there are many types of hubs to consider, but generally hubs of steel (in my case aluminum) have far greater strength in compression and tension than any size lumber.

The same is true with my steel tube dome frames. A grade 5 bolt used as the hub connector has 18,000 lbs per inch of tensile strength, which is far greater than the tensile strength of the 14 gauge tubes it connects.

Blair

--

Blair F. Wolfram
Founder, Dome Inc.

thedo...@domeincorporated.com

http://www.hurricanedomes.com

888-DOME-INC or 612-333-3663

[mru6...@gmail.com]

Could it be that the hub design from this particular analysis is influencing the choice between a higher frequency or larger strut diameter?

The hub design from the FEA analysis is quite a bit different from the conventional design of connecting EMT conduit via drilling holes and bolting together. 

The dome in the FEA analysis shows that it was the ring node that contributed to the failure of the dome. And when compared to the other components of the dome, the ring node was significantly weaker under load. When they modified the node design by simply placing the lock washers further apart and making a weld, it gained a great deal more strength, yet it was still weaker than the other components. 

Simple alterations like this should be noted with hub design as there are many variations that will effect performance. And will make it difficult to confirm as to whether it is the hub that is going to fail first. This particular case seems to be an exception compared to other failures on geodesic domes I've read about. More components, this case especially, may in truth disrupt how the dome distributes loads to the rest of the structure. Connecting EMT struts via drilling holes and bolting have only two components: the struts and the bolt-nut. And with EMT conduit those struts would fail long before the bolt-nut.  Larger diameter struts may not be the solution however.

I do not have a reference but I remember reading about a test being done in which two geodesic domes were tested with differing types of struts. When compared as individual struts, one strut was significantly stronger than the other. Though that strength was given due to its stiffness. When put under load, the stronger strutted dome failed first because it was too stiff to distribute those forces to the rest of structure  The strut simply collapsed.  The weaker strutted dome, conversely, performed much better as a dome because it was able to distribute the forces to the rest of the structure more efficiently. After surpassing the stiff dome in testing, these struts did not collapse but bent gradually as more load was applied.

Either way, from what I've gathered so far is that geodesic domes can be very fickle structures indeed.

Though with the majority of answers I have received elsewhere, along with being advised by several others who have had much knowledge and experience with geodesic domes, a higher frequency would be recommended over a larger strut diameter. 'Redundancy' was a word I remember commonly being used.

Regards

Ashok

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[Ashok Mathur]

Dear Gerry,

Sometimes I wonder if I am a person full of hot stuffed air simply incapable of understanding FEA.

I know I am incapable of working out FEA given various parameters.

Peter asserts “ Hi - FEA is definitely up to the task of estimating the strength of a dome. “

Who is right and who is wrong or both are partially wrong in some ways?

Modeling a full dome in FEA and than building that dome in real life and comparing the test results of loading with the theoretical results from FEA is a complex task with the end results not easy to compare for reasons that Peter has hinted upon. Time and Cost of doing so certainly come in the way of resolution.

Anyway, there must be some way to pin prick myself so that hot air is released.

So here is a test that can be implemented in about 2 weekends and under $ 50 to pin prick me.

One of the simpler tensegrity structure with clear visual compressive and tensional elements is a six equal struts structure with 24 tensional elements called tensegrity icosahedra.(Picture enclosed)

All the six struts are of the same length - let us call it unity.

All the 24 tensional elements are of the same length -half of golden ratio or approximately 0.805.

Everything is symmetrical.

The structure is described in full mathematical detail in “ Geodesic Maths and How to Use It.”.

It is described here :

http://tensegritywiki.com/Icosahedron

It is also described here :

http://www.tensegriteit.nl/e-well-known.html

The link to EMT properties that you has recently sent talks about a half inch EMT tube of ten foot length (US Grade ½ or metric 16). With about half an hour of sawing, one such length costing under $10 will provide us 6 one foot long struts to build the tensegrity.

Most hardware stores like Lowe etc will sell a roll of galvanized wire of various grades for about $7 or thereabout. One roll will have about 25 foot of wire – just enough for our purposes. Gauge 16 or thinner Gauge like 18 will do.

There are many FEA tools available in the market and you are free to use any of them to calculate the force that will deform the one foot strut. Mark, an undergrad engineering student, had made a FEA tool that works via an excel sheet. I can send a link for its download.

Let us call the calculated deforming load as D kN.

If the actual model starts to deform near D, then I will accept FEA works for geodesic domes.

I suspect that even 5D KN will not deform the tensegrity, showing that FEA has its limitations.

Regards

Ashok

Regards

Ashok

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[Peter Schwarzel]

Hi Ashok - FEA is a small word yet it covers 100 years plous of stuff. I have been using FEA for structural analysis for over 30 years and I assure you its up to the job. There are many issues to consider and if you are using simple free tools and scripts in excel then these are severely limited and do not represent something that a competent engineer using commercial software would achieve. For instance many of the "problems" discussed here need to be solved using non linear methods. The problems have pre-load, large deformations (which cannot be estimated using linear methods) and geometric hinging issues the list goes on. But they can all be simulated using FEA if you have the experience and the program to achieve what you want to know its straightforward.  So don't say "FEA" is wrong or poor, you have to find the right person with the right software to answer your question.  The question has to be very specific as how you make the model depends on the answer you want.  Happy to answer questions of a specific nature...  I use Strand7 by the way and its very good in this area...

On Friday, December 23, 2016 at 9:46:28 AM UTC+10, mru6...@gmail.com wrote:

[mru6...@gmail.com]

Would you perhaps be able to model the strength of two geodesic domes using Strand 7? 

There are two questions based on the following information I've provided.

1) On both domes, which would fail first, the strut or hub?

2) Using standard FEA tests, which dome performed better overall as far as strength goes, the L3 or L4?

I've attached pictures of the specifications of each component below, if needed. 

Formal Specs:

Both domes are 40 feet diameter

Both domes will have a hole drilled at each end to form a connecting point for the bolt.

There is no covering, just the dome frame.

The first dome is a 4 frequency L3 variant

The struts will be 1 inch EMT conduit.

Each strut will have an additional 0.167 feet (2 inches) added to form a connecting point for the bolt.

Each strut will have 3/8 inch hole drilled 0.167 feet (2 inches) from the end.

Each strut will have 2 1/2 inches flattened at the end.

The photo shows the original calculations and then the added lengths on the right side.

The second dome is an 8 frequency L4 variant.

The struts will be 3/4 inch EMT conduit.

Each strut will have an additional 0.125 feet (1 1/2 inches) added to form a connecting point for the bolt.

Each strut will have 3/8 inch hole drilled 0.125 feet (1 1/2 inches) from the end.

Each strut will have 2 inches flattened at the end.

The photo shows the original calculations and then the added lengths on the right side.

Material Specs:

If you are feeling up to the challenge.

[Peter Schwarzel]

Hi Ashok - That's a large job so no. But you also need to think about what you mean by strength? Are you hanging something from a node/hub? is it a snow load? a 100mph wind load? All of these things change how the dome behaves and changes the strength required for each component.  The process would go as follows.

1) make a beam model of the dome. This assumes the hubs are rigid or free to rotate depending on your design (ie "welded ends" or pin ends. single bolted hub would be pin ended) then the required load is placed upon the dome and the model is run in a linear solver. Then a linear buckling run is done to establish the structure does not buckle at the design load. If it buckles at a load near the design load then you have to move to non linear domain. So then you run the non linear solver to establish that large deflections do not occur. Once your happy that the linear and NL solutions are similar then you run a NL solution to check it does not cripple or oil can or warp in some way. Then now we understand its global behavior we can model the hubs discreetly to establish their strength, Hubs can be manually calculated probably.  Then we run a model that is not perfect ie it is out of round say 2%. Then rerun to establish if this eccentricity is a problem. Maybe even at 4% out of round to find out how tolerant the structure is as in the real world it wont;t be perfect.  Once all this is done then we make solid models to check the local effects of the tube buckling. Then its pretty much done.  So it s a bit of work to answer your question...  Peter

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[Peter Schwarzel]

thinking about this problem and trying to establish a way to do it relatively easily. 1) If we have designed an optimum solution the failure mode is global buckling or a "snap through" mechanism.l This is usually from an uplift (wind load) that straightens out part of the dome. When the dome recovers this area snaps through and collapses. Another mode is if the dome is quite flat it can snap through locally from a hub or strut load which again leads to a global failure as the dome tries to turn inside out. To overcome these issues the hub needs to be as stiff as the members that connect to it. So if you built a row of struts and their connections say 3 or 4 of them and placed them across some sort of gap and looked at their deflection you would be able to establish the "continuity" of the stiffness of the structure. ie the connections need to be the same stiffness as the struts. So if the strut assembly was 8 feet long then if you place a continuous strut next to it the deflection needs to be the same. Plus under a load the hub needs to behave the same as the strut. 2) This is the usual failure mode of a squashed and bolted connection as the connection is no where near the stiffness of the strut. The in-plane stiffness of a triangular structure is huge and with a dome we are depending on the double curvature to save the day. Maybe this helps??  3) so if you build a small scale flat representation of your domes and compare them the stiffest out of plane one is the go, all other things being equal.  Peter

On Friday, December 23, 2016 at 9:46:28 AM UTC+10, mru6...@gmail.com wrote:

[Ashok Mathur]

Dear Peter,

I like the deft touch with which my request for a specific comparison between the theoretical output of FEA with actual test results has been brushed aside.

It takes an expert to do it.

When a young Mechanical engineer starts his learning he is quickly taught that the mechanical world is divided into two binary halves.

One half is rigid structures where the component parts do not move relative to any other part and it is correct to assume that all reactions are local. FEA rules this world.

The second half is the world of machines where parts do move in relationship to other parts. Dynamics, Kinematics and tribology rule this world but FEA is not far away when it comes to analyzing each individual component of the machine as that can be seen as a rigid structure in most cases (except for springs and hydraulic devices).

Geodesic domes violate this neat binary division.

They have properties of a rigid body as well as properties of machines i.e.
the struts are not rigid; they move like parts of a machine even when no force is being externally applied to them.
they rotate when pressed;
the structure does not react only locally but reacts as a whole;
they have varying modulus of elasticity etc.

Analysis by Hugh Kenner suggests that their strength may be 300 to 600 times the FEA calculations because of varying modules of elasticity.

I guess it may be 5 to 6 times the strength calculated by FEA.

I guess I will have to wait and see till a FEA expert checks out the six strut tensegrity.

Regards

​ ​

Ashok

---------- Forwarded message ----------
From: Peter Schwarzel <carbonfi...@gmail.com>
Date: Tue, Feb 14, 2017 at 2:33 AM
Subject: Re: How to the Optimize the Strength of a Geodesic Dome?

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[Ashok Mathur]

Dear Peter,

I like the deft touch with which my request for a specific comparison between the theoretical output of FEA with actual test results has been brushed aside.

It takes an expert to do it.

When a young Mechanical engineer starts his learning he is quickly taught that the mechanical world is divided into two binary halves.

One half is rigid structures where the component parts do not move relative to any other part and it is correct to assume that all reactions are local. FEA rules this world.

Regards

Ashok

---------- Forwarded message ----------
From: Peter Schwarzel <carbonfi...@gmail.com>
Date: Tue, Feb 14, 2017 at 2:33 AM
Subject: Re: How to the Optimize the Strength of a Geodesic Dome?
To: Geodesic Help Group <geodes...@googlegroups.com>

[mru6...@gmail.com]

I was hoping there could be some clarification as to who was being referred to; I feel like there has been a misunderstanding.

First, there's been two proposals.

I recently made one to do an in-depth FEA analysis of two geodesic domes, not long after Peter offered to answer a specific question regarding geodesic structures.

Ashok has also made one to construct a small tensegrity structure.

From the previous posts, it's my impression that Peter was declining my proposal, seeing that there would be a considerable amount of work and data involved.

I do not believe he was brushing your proposal aside, Ashok.

Second, when Ashok first proposed his tensegrity structure to be tested, it was in reference to the previous post questioning the pdf of FEA analysis.

There were 3 posts in response, none of which were written by Gerry, and I believe you were referring to my response, Ashok.

[Peter Schwarzel]

Hi All - We need to clarify what is being requested in terms of "Strength" Tensegrity and geodesic structures are not limited by material "strength" (unless poorly designed). They are limited by their membrane elastic stability limits. So we need to know what loading is to be applied before we start modelling.  The strength to resist a snow load, a wind load or a hung load from a node are three entirely different issues. So once the loading is defined we can progress to the modelling. Are dxf files of these structures available?

Peter

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[Gerry in Quebec]

Yes, it would be good to clear up the confusion. 

This discussion group has been heavily focused on geodesic polyhedra/geometry over the years, with relatively little said about the structural integrity of those polyhedra when built as dome shelters. To his credit, Ashok has often pushed us in the direction of finding out more about physical strengths & weaknesses of triangulated domes. I, for one, welcome the chance to get some engineering input/insight from someone like Peter who has actually done many Finite Element Analyses. But, as has become clear, the specific aspects of each dome, including expected loads, need to be nailed down first.

Ashok, sorry I didn't respond to your posts, but, coincidentally, I've been busy dealing a series of urgent structural issues of my own -- shoveling snow off the roofs of a few rectilinear buildings. Thankfully, my domes don't require snow removal. Our snow load this winter has been huge, with public warnings to get out that ladder & shovel asap! Well, I more or less finished the rooftop work late this afternoon. It wasn't much fun, but at least I had a wonderful view of the lake and hills.

Peter, you asked about getting dxf files. I expect there are a number of people in the group who can provide dome models in that format. I can do so by converting off files (created in Excel) to dxf via MeshLab. But the input file must be triangles only as far as I know.

Here in West Québec, Canada, I have a steel-framework dome project (5/9 truncation, 26 ft. spherical diameter) on the back burner. I'd love to know whether it will stand up to the local snow and wind conditions.

I really hope this discussion on structural integrity takes off. 

- Gerry in Québec, with snow above the window sills

[Peter Schwarzel]

Hi Gerry and others,

Happy to compare two or three domes with a hung load and dead load plus a snow load  pick one to start with. A single loadcase is easier to discuss and compare vs multiple load cases.  The limitations are as follows.  1) I need to get a dxf file of the proposed domes to compare plus a description of the tube dimensions and materials used. The length is defined by the dxf file 2) Is the general assumption that the ends of the struts are "pinned" or "fixed".  We can run both ways if needed to establish top and bottom boundaries of the design 3) I shall limit the analysis to a beam model which means the struts are analytical beams not actual "plate or solid" geometry, but they will give use the global performance of the dome.  Beams will not predict tube crippling but they will predict euler buckling. Strut geometry is usually picked so cripple type buckles are unlikely. ie the tube wall to diameter ratio is over 50 usually.  The optimum stut is the lightest that does not euler buckle 4) so get working on a couple of dxfs for some tests  5) this model does not include anything about the hubs, it assumes the struts all connect at the intersection perfectly.  6) the analysis will include linear and non linear effects as much as a beam model can. If there is a dome out there that has been physically tested and someone knows its behavior and limit strengths then it maybe a good one to start with ??  Peter  carbon-works.com.au if you want to look at what I do

--

[Ashok Mathur]

Dear Peter,

I am glad that some amount of confusion that had crept in has been removed.

If there is a choice to be made between doing FEA of the two domes that "mru" wants to be done and doing the six strut tensegrity, then I will urge you to do the "mru" request first as that looks like something that "mru" wants to build.

Within that analysis, I will urge you to first do only the deadload forces at either hubs or deployed along the struts. Ignore snow and windload calculations as they are important only when the wind and snow forces are significant at the location of the dome. You will need to get many years of snow and wind data from "mru" before you can seriously model those at a location. Additionally, I believe if the two alternate domes are to be ranked as per their strength, then the ranking will be the same for all three types of forces.Only difference may be that a model that can comply with deadloads, may not be able to deal with the combined deadload, snow and wind loads.

In proposing the six strut model for FEA analysis, I was hoping to settle in my mind the issue if FEA can predict buckling strength results that match with the built model buckling strength results of a tensegrity.

In past, I had no resources of a workshop and sharp mathematical brains to do this analysis.
But I have lived a philosophy that all resources needed to solve a problem are to be found near you if you look sharp enough.
I think near me I can locate a workshop that will build the physical model and an engineering college where FEA analysis will be carried out.

Regards

Ashok

Regards

Ashok

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[Peter Schwarzel]

A dome will support much more than its dead load, even if its made of paper so we need to apply some realistic load. Gerry how deep is the snow you want to support. Sorry I'm metric so 1m? 39 inches of snow? I'm on the Gold Coast of australia and have never had to design to a snow load, so I imagine that it falls off at a certain angle so the sides will be clear unless it builds up on these, then there will be a hydrostatic load on the sides and a weight load on the top? Propose some loading and then its apples to apples. It will come out as a ratio of load to failure called the reserve. For the comparison.

Peter

[Peter Schwarzel]

Hi Ashok - I think you mean live loads at hubs not deadloads? The deadload is the load distributed via gravity (self weight) and any permanent installed masses or forces?  So you are proposing to apply specific loads at two or three hubs?

Peter

[Ashok Mathur]

Dear Peter,

I erred in using the term deadload.

What I had in mind is a load that is not fluctuating like the wind forces are.

Once the load is applied neither the value of the load changes nor does the point of application change.

Of course in the next itreation, a different load could be applied at another point or at the same point.

What would be the correct name for such a load?

Regards

Ashok

Regards

Ashok

[Peter Schwarzel]

This would be a point load or action. Or a live load. A live load does not mean it necessarily moves it just means its a load that is applied and goes away. eg we may have a block and tackle at a hub or a hanging wall.  Some may call it an imposed load.  A hung load is a little different to a block and tackle attched to the floor. The hung load will continue to apply its force as it descends. A B&T will unload as the structure deflects then it will reload as the B&T is tightened more and the force trajectory may change as the roof moves sideways slightly. If its hung its always down and directly under the hub no matter how the roof moves.  Initially we will just apply a load and see what happens. Ideally we are trying to make a structure with no non linear behaviours so its very stiff well beyond its service loads.   Structures are either strain stiffening or strain softening. It its strain softening then we are heading for a callapse. Peter

[Ashok Mathur]

Dear Peter,

Cheers to point load or action!

Ashok

Regards

Ashok

[Peter Schwarzel]

Hi All - So we are going to compare two domes. Each of same radii and height. We shall place a unit load centric to the dome and a unit load eccentric and run them to see what happens. Someone needs to give me a dxf of the contesting domes.  Is someone starting a book on this?  They shall also run with fixed and pinned ends to see the difference. Don't be surprised if its not much different. Peter

[Peter Schwarzel]

I meant to mention that by applying a unit load we can see the load multiplier in each member. All you out there watching can download the strand7 viewer and I can publish the results so you can interrogate the model to your hearts content. Peter

[Ashok Mathur]

Dear Taff

Your sketchup warehouse is sure to have images of both types of domes, albeit with unit radius.

I see that there is a plugin for converting sketchup files to dxf files.

See https://www.guitar-list.com/download-software/convert-sketchup-skp-files-dxf-or-stl

You may already know better solutions to convert to dxf.

May I request you to supply the needed data to Peter.

Thanks

Ashok

Regards

Ashok

[Mr U]

What software would be ideal for drawing up the geodesic domes in dxf format needed for this experiment?

I've browsed through several but none seemed capable of modeling the level of detail needed for the geodesic domes. 

I will attempt to learn whatever program necessary however it might be a while before I can draw up the models for this experiment.

[Peter Schwarzel]

Hi Ashok - I use rhino3d (NURBS modeller) and geomagic mechanical designer (similar to solidworks). There are two/three paths to follow maybe more:

1) wireframe ie calculate the nodes (x,y,z) then join the dots with a line. The result is called a wireframe and can be exported as a dxf

2) This wireframe can be converted into a solid or parasolid. ie the lines create faces which are geometric entities. This solid can be exported in iges format or step format and then I can extract the edges to make the beam model

3) Some CAD systems like solidworks build solids directly and do not understand wireframes so you would build a solid directly then export as step or iges

Since it seems you have some sort of code that calculates hub coordinates I'd find a program that can join these up into a wireframe. I'm sure someone in the group can supply a suitable CAD file for investigation.  If you can generate a txt file of the co-ords I can import this (comma delimited or space delimited) and join the dots manually. this is called a cloud data file. Its more labour intensive but if its  simple dome then no probs. If it has hundreds of struts I'd prefer a line dxf file. For the dxf start with release 14 lines and arcs flavour if possible. This is very reliable dxf. Some of the new autocad dxfs give me grief.

If your new to CAD and can afford rhino3d then I suggest you get it. There is a free add on called grasshopper (parametric programmer) which you would have lots of fun with making exquisite domes and structures.  Peter

[Peter Schwarzel]

Ops this was for Mt U - Peter

[Gerry in Quebec]

Mr mru, Peter. Ashok & others,

I don't wish to jump the queue for Peter's FEA help, but here are two images that may illustrate why I'm so interested in the effects of snow load on dome design. One of the pix was taken a few hours ago. More snow is on its way to this region.

More later, including some simple dxf files of domes if still needed.

- Gerry in Québec

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[TaffGoch]

DXF and SketchUp files attached:

-Taff

[TaffGoch]

I forgot to attach the SketchUp files.

-Taff

[Gerry in Quebec]

Great, Taff.

Meanwhile, I've downloaded the dxf plugin for SketchUp as Ashok suggested and will now try it out.

(It was easier than I thought.)

- Gerry in Québec

[TaffGoch]

Gerry,

I'm eager to hear-about/see your results.

Since I use a PRO version of the SketchUp program, a DXF export option is already included, in the main menu. (I, therefore, did not need a plugin, such as linked by Ashok.)

-Taff

[Peter Schwarzel]

Hi Taff,

Thank you for the dxf. came into rhino and strand perfect. So its a 39 ft dome?. Now need to know the materials tube spec that you want to use.  Same in both or do we optimise down until it fails?  Peter

--

[TaffGoch]

Peter,

My import testings come in as domes of 40.000000-foot diameter.

-Taff

[Peter Schwarzel]

Hi - Checked scales etc and its now 40ft in diameter across its base.  Do you want Aluminium, steel or titanium struts? I'll optimise the strut size down till we get a collapse or do you want to compare same weight domes for strength?  Next step please!!   Peter

[Bryan L]

Hi Peter, because Mr U is the OP of this thread, and he has also provided the data sheets for EMT, that could be a good starting point?

Bryan

On 16 Feb 2017 12:31 pm, "Peter Schwarzel" <carbonfi...@gmail.com> wrote:
>
> Hi - Checked scales etc and its now 40ft in diameter across its base.  Do you want Aluminium, steel or titanium struts? I'll optimise the strut size down till we get a collapse or do you want to compare same weight domes for strength?  Next step please!!   Peter
>
> On Thu, Feb 16, 2017 at 11:18 AM, Peter Schwarzel <carbonfi...@gmail.com> wrote:
>>
>> Hi Taff,
>> Thank you for the dxf. came into rhino and strand perfect. So its a 39 ft dome?. Now need to know the materials tube spec that you want to use.  Same in both or do we optimise down until it fails?  Peter
>>
>> On Thu, Feb 16, 2017 at 10:58 AM, TaffGoch <taff...@gmail.com> wrote:
>>>
>>> Gerry,
>>>
>>> I'm eager to hear-about/see your results.
>>>
>>> Since I use a PRO version of the SketchUp program, a DXF export option is already included, in the main menu. (I, therefore, did not need a plugin, such as linked by Ashok.)
>>>
>>> -Taff
>>>
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>>
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[Peter Schwarzel]

Hi - I have created aluminium tubes and equal weight domes The L4 is 443kg the L3 is 449kg. Sorry you guys i'm metric.  the L3 struts are Dia60x2mm and the L3 is Dia32x2mm.  There is a great difference in the linear and non linear results. For instance the linear buckling shows that as the load is applied the dome pushes up the middle panels ie the dome is strain stiffening. But the non linear applies a small load then corrects the geometry then another small load slowly climbing up to the full load. This shows the structure fails by tension and compressive stress in the struts before it gets to the buckling load. I'll run a few more tests and then write a small paper on it and publish it here. Need to do some other things today.  I've attached an avi showing the dome pushing up against the load.  This is called strain stiffening. The difference between pin ended beams (truss elements) and fixed end elements ) beams is about a factor of 2 for global buckling. But it seems we will get to element failure before we get to callapse. So need to make the elements smaller to optimise them in this case. So we can hang about 500kg at the moment without damaging anything.  Dos someone have a target hung load in mind?  and the L3 is doing better as its tubes are bigger so provide better bending strength as the dome deforms. Peter

On Thu, Feb 16, 2017 at 11:41 AM, Bryan L <bhla...@gmail.com> wrote:

Hi Peter, because Mr U is the OP of this thread, and he has also provided the data sheets for EMT, that could be a good starting point?

Bryan

On 16 Feb 2017 12:31 pm, "Peter Schwarzel" <carbonfi...@gmail.com> wrote:
>
> Hi - Checked scales etc and its now 40ft in diameter across its base.  Do you want Aluminium, steel or titanium struts? I'll optimise the strut size down till we get a collapse or do you want to compare same weight domes for strength?  Next step please!!   Peter
>
> On Thu, Feb 16, 2017 at 11:18 AM, Peter Schwarzel <carbonfi...@gmail.com> wrote:
>>
>> Hi Taff,
>> Thank you for the dxf. came into rhino and strand perfect. So its a 39 ft dome?. Now need to know the materials tube spec that you want to use.  Same in both or do we optimise down until it fails?  Peter
>>
>> On Thu, Feb 16, 2017 at 10:58 AM, TaffGoch <taff...@gmail.com> wrote:
>>>
>>> Gerry,
>>>
>>> I'm eager to hear-about/see your results.
>>>
>>> Since I use a PRO version of the SketchUp program, a DXF export option is already included, in the main menu. (I, therefore, did not need a plugin, such as linked by Ashok.)
>>>
>>> -Taff
>>>
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[Peter Schwarzel]

this gets back to my comment that as the tube gets smaller the membrane (and thru thickness) stiffness gets less. So there is a trade off, so far my bets are on the L3 being better. Peter

eg the L4 globally buckles at 2166kgf and the L3 buckles at 7943kgf. 60mm tube is much stiffer then 31mm in bending. You may say that it should not bend but at point of instability it has to bend just like a sail changes sides on a boat or an oil can pops. Peter

[Peter Schwarzel]

what material is EMT tube? PVC?

[Bryan L]

EMT is the steel tube used for electrical conduit in the US (I believe). Not so strong but relatively cheap. Mr U posted it's specs earlier in the thread.

[Bryan L]

https://lh3.googleusercontent.com/-flT1mE0SDso/WJ90zXkXKLI/AAAAAAAAAAM/WXig5-PHfJgBXA3A-_obgt4daff6r0ocwCLcB/s1600/Screen%2Bshot%2B2017-02-11%2Bat%2B2.13.37%2BPM.png

[Bryan L]

The above link was the EMT spacing / buckling data.

Following link is diameter, ID and OD

https://lh3.googleusercontent.com/-x22m0akaqTg/WKJiTWG0TdI/AAAAAAAAABE/g4hcQVZShC8h5XUEBYI8bM6wObH7Y17hgCLcB/s1600/emt.png

[Peter Schwarzel]

Ok thanks but none of those mention material so I shall assume steel. Peter

[mru6...@gmail.com]

EMT conduit (Electrical Metallic Tubing) is used for protecting electrical wiring inside buildings. From the manufacturers website (also in attached document), it states that EMT conduit is made from mild carbon steel and so I've attached a document listing mild carbon steel's mechanical properties. The information I was unable to provide are the properties associated with EMT's malleability since is designed to bend. I did find the document listing the National Electrical Standards for EMT conduit but it requires a bit of money to see, far more than I'm willing to pay for. So instead I hope the attached pdf will be sufficient.

https://lh3.googleusercontent.com/-flT1mE0SDso/WJ90zXkXKLI/AAAAAAAAAAM/WXig5-PHfJgBXA3A-_obgt4daff6r0ocwCLcB/s1600/Screen%2Bshot%2B2017-02-11%2Bat%2B2.13.37%2BPM.png

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[Peter Schwarzel]

Hi All - heres a summary doc. The strand files are here if you want to look at them, use the strand veiwer. I may expand the doc when I can. Ask questions. Peter

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[Bryan L]

Only empirical, but the last reply to this question on Reddit gives a good insight in what a dome is capable of...

https://www.reddit.com/r/AskEngineers/comments/3bud37/need_help_calculating_the_max_load_for_a_geodesic/

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[Bryan L]

How do you provide a clickable link that shows the content of the web page in the email / forum post?

[Bryan L]

This what was the reply posted in the Reddit thread I linked to...

" I've done around 40-50 dome builds, all for the purposes of hammocking, and all using EMT. I usually use 3/4" EMT for the 2v 17ft domes like you are building. I've gotten up to 9 hammocks in them before. You can hang up to 2 hammocks from any single joint & things will hold up. Once you get 3 or 4 hammocks on a single joint, you start to have problems. A bar will bend, corner will pop in, and the hammocks connected to that joint will fall a few inches.

I've never did any calculations as far as load goes, but I have plenty of practical experience with how much these things can handle.

now, what /u/spthirtythree said about EMT(and even rigid) conduit not being rated for structural is correct. however, it still works pretty damn well as a cheap solution.

I actually just finished building a 17ft v2 out of 1" EMT today, but haven't gotten to load test it yet. I would imagine it could easily hold 3 hammocks per node. I've used 1" EMT on some of my bigger domes. I have a 21 ft v4 dome that has held up 25 people sitting on top of it and 15 hammocks hanging inside it."

[mru6...@gmail.com]

Before a clear victor is confirmed, I would like to note a discrepancy made.

It seems that in my hastiness to provide a proposal for FEA, I've failed to provide a set of fair measurements. 

In order to do this, the strut lengths comprising the dome ought to be capable of bearing an equal load. 

In the measurements I posted earlier, the L3 is expected to be superior seeing that its strut is capable of bearing much more the L4. Since the load was hung was from the center of the dome, this would imply that it is being hung from the pentagon at the top which is formed from the shortest strut lengths. 

According to the math the chart supplies, those struts should euler buckle as follows:

L3: strut A = 5.518 feet (0.84 m) = 2,222 lbs (1007.882 kg)               - 1 inch EMT conduit

L4: strut A = 2.7656 feet (1.62 m) = 1,731 lbs (785.168 kg)               - 3/4 inch EMT conduit

At first glance this may not appear to be significant, but the strength is different by 491 lbs (222.714 kg) 

For the particular test being done, considering that there 5 struts at the top sharing a load and as these are geodesic structures that are being tested, this difference in strut strength could be substantial.

My suggestion would be to scale down both of the dome sizes so that the strut lengths are matched in capability. 

In reference to the chart (I've attached as a pdf this time around), I've chosen strut lengths that are rated at a Force Class IV of 2,000 lbs (907.184 kg).

These strut lengths are the struts that form the inner section of the pentagons, also known as the A strut, the shortest strut.

The diameters of each dome then should be as follows:

L3: 42.624 feet 

L4: 37.171 feet

[Gerry in Quebec]

Hi Taff,

I opened your L4; 8v.skp file in SketchUp Make, version 17.1.174, and exported it using the export-to-dxf plugin. One thing to note: when the plugin asked for a file name, I had to manually add the dxf extension. Without the extension, the file can't be opened in my dxf file viewer, eDawings (by SolidWorks).

The output DXF file is attached, along with a screen shot of the result in eDrawings.. 

- Gerry

[TaffGoch]

Gerry

Good to hear that the plugin works smoothly. (Actually, knowing the internal structure of a DXF file, I would not expect such a plugin to be too complex or difficult to code.)

For SketchUp users, here are a couple of other plugins you might want to try:

DXF In - Ruby Library Depot

DXF Export - Ruby Library Depot

(I am certain that there are others that can also be found online.)

-Taff

[TaffGoch]

Gerry,

I downloaded and imported your DXF file into SketchUp, with no errors -- so, it looks like you're all set, with SketchUp import/export capabilities.

-Taff

[Gerry in Quebec]

Thanks, Taff.

I'll check out the two plugins you mentioned.

- Gerry

[Peter Schwarzel]

Hi MRU - The Euler load of the strut is not the defining failure mode. The dome "surface" is behaving as a continuum and it moves globally and locally. I will look at the models and try to image the effect.  It is acting as a membrane and is just like a single skin balloon (with no internal pressure) So if you had a balloon and pushed your finger into it this is what the domes are doing (nearly). I suggest you download the S7 veiwer and have a look at the models. There's a lot of info in what I have provided before we make new models. I don't think its fair to compare different radii domes. One way to look at it is that if we smear the material into a skin and figure out its equivalent thickness. This gives us the rigidity of the skin. The more rigid the skin at the same areal weight the better the dome will perform. eg like a thin plastic dome vs an aluminium dome. Peter

The more elements you have the "flatter" the local geometry is and the easier it is for the dome to snap through (oil-can then start turning inside out) In the case of a wind load (uplift) the dome is already on the load side so its easy to elongate the dome and the girth becomes unstable. The dome designer tries to add more elements so they can use smaller struts but this reduces the thru thickness stiffness so you end up under designed if you use eulers as the guide.  So we need another way to determine the "ideal" skin stiffness to size our optimum dome. Have to think about that one...

The 1" tube is 2.85x stiffer in bending then the 3/4" tube (see calcs attached) This is why the 1" does better. If you smear the tube to a single thickness the 1" is 0.712" thick and the 3/4" is 0.54" thick.  Round tubes have been used historically because they are easy to get and they are easy to analyse. If I wanted to use rectangles in the FE model I'd have to figure a way to align the axis to the centre of the dome a bit hard with over a 1000 struts... If you really want to optimise you need to think about I beams or rectangular sections that improve the through thickness stiffness but decrease the inplane thickness/stiffness. Because the inplane geometry is very stiff (triangulated) we do not need material in-plane we need it thru thickness. This is sometimes called the short transverse direction.  Peter

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[Gerry in Quebec]

Hi Peter,

I'm putting together some info on a plywood covered steel tube dome, with snow load info and a dxf file. I need to check a few bits and pieces of info before posting. Thanks for the comments and analysis so far on the L3 (4v) and L4 (8v) domes.

- Gerry in Québec

On Tuesday, February 14, 2017 at 10:13:22 PM UTC-5, Peter Schwarzel wrote:

Hi Gerry and others,

Happy to compare two or three domes with a hung load and dead load plus a snow load  pick one to start with. A single loadcase is easier to discuss and compare vs multiple load cases.  The limitations are as follows.  1) I need to get a dxf file of the proposed domes to compare plus a description of the tube dimensions and materials used. The length is defined by the dxf file 2) Is the general assumption that the ends of the struts are "pinned" or "fixed".  We can run both ways if needed to establish top and bottom boundaries of the design 3) I shall limit the analysis to a beam model which means the struts are analytical beams not actual "plate or solid" geometry, but they will give use the global performance of the dome.  Beams will not predict tube crippling but they will predict euler buckling. Strut geometry is usually picked so cripple type buckles are unlikely. ie the tube wall to diameter ratio is over 50 usually.  The optimum stut is the lightest that does not euler buckle 4) so get working on a couple of dxfs for some tests  5) this model does not include anything about the hubs, it assumes the struts all connect at the intersection perfectly.  6) the analysis will include linear and non linear effects as much as a beam model can. If there is a dome out there that has been physically tested and someone knows its behavior and limit strengths then it maybe a good one to start with ??  Peter  carbon-works.com.au if you want to look at what I do

On Wed, Feb 15, 2017 at 12:27 PM, Gerry in Quebec <toomey...@gmail.com> wrote:

Yes, it would be good to clear up the confusion. 

This discussion group has been heavily focused on geodesic polyhedra/geometry over the years, with relatively little said about the structural integrity of those polyhedra when built as dome shelters. To his credit, Ashok has often pushed us in the direction of finding out more about physical strengths & weaknesses of triangulated domes. I, for one, welcome the chance to get some engineering input/insight from someone like Peter who has actually done many Finite Element Analyses. But, as has become clear, the specific aspects of each dome, including expected loads, need to be nailed down first.

Ashok, sorry I didn't respond to your posts, but, coincidentally, I've been busy dealing a series of urgent structural issues of my own -- shoveling snow off the roofs of a few rectilinear buildings. Thankfully, my domes don't require snow removal. Our snow load this winter has been huge, with public warnings to get out that ladder & shovel asap! Well, I more or less finished the rooftop work late this afternoon. It wasn't much fun, but at least I had a wonderful view of the lake and hills.

Peter, you asked about getting dxf files. I expect there are a number of people in the group who can provide dome models in that format. I can do so by converting off files (created in Excel) to dxf via MeshLab. But the input file must be triangles only as far as I know.

Here in West Québec, Canada, I have a steel-framework dome project (5/9 truncation, 26 ft. spherical diameter) on the back burner. I'd love to know whether it will stand up to the local snow and wind conditions.

I really hope this discussion on structural integrity takes off. 

- Gerry in Québec, with snow above the window sills

On Tuesday, February 14, 2017 at 2:05:03 PM UTC-5, mru6...@gmail.com wrote:

I was hoping there could be some clarification as to who was being referred to; I feel like there has been a misunderstanding.

First, there's been two proposals.

I recently made one to do an in-depth FEA analysis of two geodesic domes, not long after Peter offered to answer a specific question regarding geodesic structures.

Ashok has also made one to construct a small tensegrity structure.

From the previous posts, it's my impression that Peter was declining my proposal, seeing that there would be a considerable amount of work and data involved.

I do not believe he was brushing your proposal aside, Ashok.

Second, when Ashok first proposed his tensegrity structure to be tested, it was in reference to the previous post questioning the pdf of FEA analysis.

There were 3 posts in response, none of which were written by Gerry, and I believe you were referring to my response, Ashok.

On Thursday, December 22, 2016 at 3:46:28 PM UTC-8, mru6...@gmail.com wrote:

Have completed a first dome.

And am In the beginning stages of designing a second dome (about 30 foot diameter).

Now deliberating which ought to be the stronger of the two.

4 frequency dome + 1 1/2 inch EMT conduit + 5 foot strut average (2 per 10ft pole)
or
8 frequency dome + 3/4 inch EMT conduit + 2.5 foot strut average (4 per 10ft pole)

I'm most curious about something like 

whether or not a 1 foot 1" EMT strut would outperform 

something like a 5 foot 2" EMT strut.
So a better question might be, what kind of frequency/strut dimensions are really best in terms of strength?

frequency type
strut material
strut wall thickness
strut diameter
strut length

-

From what I've gathered, it looks as if having the following is ideal when it comes to raising dome strength:

Higher frequency
1/2 sphere via an even frequency dome i.e. 2v, 4v, 6v, 8v (truly flat at the base)
Low strut length variance (the difference between the smallest and the largest strut)
One strut type in the base ring

Contributions appreciated,

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[mru6...@gmail.com]

Peter, your most recent post was very insightful for me. Especially, elaborating upon the thru stiffness and the in-plane stiffness.

"How to determine ideal skin stiffness?" 

Would space frames be suited to the task of providing increased thru stiffness? 

As for making a fair assessment of the L3 and L4, I wasn't sure what else could be changed other than radii. If the frequency of either dome is compensated, then the benefit of the low strut variance (difference between the longest and shortest struts) provided by either the L3 or L4 would be lost. 

Though, a third option was considered when you spoke of the analogy about smearing the material into a skin. I began thinking about the given weight of the domes from the experiment; the L3: 563kg and L4: 593kg. 

If more material=more thickness=more rigidity, then perhaps the domes were equally matched after all, seeing they contained nearly the same amount of material. Since the L3 claimed superiority, it may be further proof to the notion that a larger strut diameter is a better choice.

I am still convinced however that a higher frequency ought to hold some advantages over a larger diameter. As to what conditions would render this possible, remains an open question.

On Thursday, February 16, 2017 at 4:24:32 PM UTC-8, Peter Schwarzel wrote:

Hi MRU - The Euler load of the strut is not the defining failure mode. The dome "surface" is behaving as a continuum and it moves globally and locally. I will look at the models and try to image the effect.  It is acting as a membrane and is just like a single skin balloon (with no internal pressure) So if you had a balloon and pushed your finger into it this is what the domes are doing (nearly). I suggest you download the S7 veiwer and have a look at the models. There's a lot of info in what I have provided before we make new models. I don't think its fair to compare different radii domes. One way to look at it is that if we smear the material into a skin and figure out its equivalent thickness. This gives us the rigidity of the skin. The more rigid the skin at the same areal weight the better the dome will perform. eg like a thin plastic dome vs an aluminium dome. Peter

The more elements you have the "flatter" the local geometry is and the easier it is for the dome to snap through (oil-can then start turning inside out) In the case of a wind load (uplift) the dome is already on the load side so its easy to elongate the dome and the girth becomes unstable. The dome designer tries to add more elements so they can use smaller struts but this reduces the thru thickness stiffness so you end up under designed if you use eulers as the guide.  So we need another way to determine the "ideal" skin stiffness to size our optimum dome. Have to think about that one...

The 1" tube is 2.85x stiffer in bending then the 3/4" tube (see calcs attached) This is why the 1" does better. If you smear the tube to a single thickness the 1" is 0.712" thick and the 3/4" is 0.54" thick.  Round tubes have been used historically because they are easy to get and they are easy to analyse. If I wanted to use rectangles in the FE model I'd have to figure a way to align the axis to the centre of the dome a bit hard with over a 1000 struts... If you really want to optimise you need to think about I beams or rectangular sections that improve the through thickness stiffness but decrease the inplane thickness/stiffness. Because the inplane geometry is very stiff (triangulated) we do not need material in-plane we need it thru thickness. This is sometimes called the short transverse direction.  Peter

On Fri, Feb 17, 2017 at 7:40 AM, TaffGoch <taff...@gmail.com> wrote:

Gerry

Good to hear that the plugin works smoothly. (Actually, knowing the internal structure of a DXF file, I would not expect such a plugin to be too complex or difficult to code.)

For SketchUp users, here are a couple of other plugins you might want to try:

DXF In - Ruby Library Depot

DXF Export - Ruby Library Depot

(I am certain that there are others that can also be found online.)

-Taff

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[Peter Schwarzel]

Hi MRU _ Yes a truss is very useful in strategic places but this gets away from the dome principle. I designed several semi circular buildings some years ago and had to put trusses at the ends and the middle to stop the hemi from lozenging at the wind load. More on the L3 and L4 see attached.  Peter

[Peter Schwarzel]

MRU - Graham mentioned earlier that large domes have to go to double skins to get the thru thickness stiffness. This is the traditional way to go once you get to this sort of area. The EMT tube is not structurally optimised. It has a very small D/T ratio mainly to allow it to be bent in a simple bender. The optimum ratio is about D/t = 50 but these are 1" 16 and 3/4" 19.5 so you need to find thinner and bigger tubes to take advantage of the material better in this application. So a 1mm thick tube can be 50mm in diameter and this would be great.  Perhaps look for some thin aluminium tube?  Plus EMT is very weak to allow bending, again this limits the ultimate strength of the structure. In the L4 case we see that its material low strength does not allow it to get to its elastic capacity.  Peter

[Peter Schwarzel]

MRU - FYI the image of Robert Clarks plywoood dome is the (I think I called him Graham last post) stimulus for me to get into this forum. I've been working on a similiar idea and he has made it. I think you need to go down this path. Using tube has so many limitations especially making hubs. Roberts idea opens up so many opportunities its great. It can become double skinned as we scale up, and we can control our materials properties by width and thickness so easily. Plus its pre-stressed as we bend the material into shape so it has a predisposition to not 'dimple" or snap through.  In my head is making fibreglass elements vs plywood that are super strong and weather resistant (plywood needs maintenance). I can control the thickness and the stiffness its a great thing... is it still a geodesic?  I can see these as isogrids and diagrids and any polyhedra you like. etc Peter

[Peter Schwarzel]

Updated dome doc again.  Peter

[Peter Schwarzel]

updated again with EMT strength comments and now woring on non linear material model. Then I'll call it a day for this stuff. Peter

[mru6...@gmail.com]

This is very good stuff. Would be ok to post this pdf and the model viewing files on another forum. There was a discussion on geodesic domes about this same question and I know the people partaking would be thrilled to have the data available from an actual FEA analysis. With your approval, before I post, I wanted to edit any spelling and/or grammar within the document.

[Peter Schwarzel]

MRU _ yes its a public doc now.  Tidy as needed, I have fixed a few things. Its not written and reviewed as a tech doc its a train of thought. But if you download the viewer you can look at these direct. I'll publish the latest models when done as well.  The pin ended models and fixed models are behaving quite differently need to understand them before I put my foot in my mouth.  Peter

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[Peter Schwarzel]

Looking at further optimisation - If we look at tube weight the 1" is 1.19kg/m and the 3/4" is 0.65kg/m. So lets say we want a linear weight of <1kg/m. I look at local tube sizes and want to find the thinnest biggest tube at 1kg/m. So this is Dia38.1x1.2 at 0.9 or 35x1.2 at 0.99kg/m The inertia of the dia38 is 23509mm4 and the 1" emt is 14743mm4 so is a big step fwd and its lighter.  Cheers PeterS  If we look at the 3/4" emt then we aim at 0.65kg/m and this looks like a 25.4x1.0 (0.6kg/m) or 28.6x1.0 (0.68kg/m) which both are much stiffer. These tubes are typically used for furniture construction.  We really need 0.5mm thick tube to make a big gain in these tube sizes....Can do much better in weight loss and strength in aluminum if you want to go there. 

[Peter Schwarzel]

I have the NL material pinned model running, Heres a video. Some of the struts have failed in the L4 which means I have to find out when they failed and then remove them from the model to establish what really happens. But I won't do that. I think the L3 wins which was the object of the exercise.  Peter

[Bryan L]

Hi Peter, thx for all your effort.

I wonder if the pinned analysis is necessary?
Although there is the odd hub / strut design with threaded rod, even they have some sort of lock nut or just wound in tight. So in the main, the struts aren't free to spin.
That's my understanding of the difference between the pinned and fixed analysis. Correct me if I am wrong...

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[Peter Schwarzel]

Hi Bryan -  for the purposes of the model a fixed end is absolutely fixed ie able to resist a moment in any direction. Also the pinned end is absolutely free to rotate in any direction. A single bolt at a hub is practically free to rotate in at least one direction so in terms of Eulers buckling it can buckle in that direction. Which is in-plane of the element. We can model frictional effects but this takes an effort. So by running pinned and fixed we can see the difference this makes easily. In many of these analyses the difference is negligible as the failure mode is global not local, so we can say that the end fixing is not relevant in the beam model at least. Once we go to a more detailed model it could be different. This is not a strength thing its a stiffness thing. The next issue to overcome is that the beam model has perfect alignment of the struts to a centre point. In reality this is eccentric and can make it buckle at even lower loads. Thats why once we understand the global behaviour of the dome we would go to a more sophisticated model and include eccentrities of the dome itself and its connections.   We have now established the possible elastic limits of the domes and have found that we can't acheive this as the material is too weak in the L4 but the L3 is OK... I currently have two models one with pinned and one with fixed ends. The next step is to combine these so all the variations are in one model so its easy to compare them... the to do list goes on...Peter

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[Bryan L]

Yep understand. My reading of Euler buckling / critical load (Wikipedia) wrt end fixing didn't include the case of tubes squashed at the ends, drilled for a bolt and bent to the vertex tangent (the simplest form of hub). The strut can't spin on its axis, but can rotate around the bolt. Perhaps a unique case?

[Peter Schwarzel]

Hi - Heres a video of the results so far. It includes the yielding of the material. The domes behind have fixed ends the domes in front have free ends. The L3 fixed and free behaves very similiarly but the L4 free ends fails fast because its locally very flat. I've loaded them to 4500kgf to establish the elastic limits of the structures. So the video does not mean the actual structure can get to 4000kgf. This just means its elastically capable if the material can hold it together. The L3 does appear to be able to hold this load whether its free or rigid ended. The L3 however fails quite early at <500kg pinned and around 2500kgf fixed.  So hands together for L3!!  Cheers Peter S

[Peter Schwarzel]

Not sure how to edit these things - but the last L3 should be an L4 fails at <500kgf not the L3 Peter

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[mru6...@gmail.com]

My budget is between $1000-$2000 (1304.80 - 2609.60 AU dollars) for the frame. I'm looking to invest in materials and design that will provide the most structurally sound 40 foot (12m) diameter --or possibly less-- dome design for the cost. I've been focusing most of my time into researching in order to fulfill that standard. 

My plan after creating the frame is to cover the dome with a fiberglass mesh and then cast a thin concrete shell into this.  What I've found so far is to use an acrylic/latex additive and/or fiberglass strands for reinforcement, diminishing any potential failures due to the concrete cracking. 

After looking into Robert Clark's idea I'm in agreement with you. This might likely be a better investment and I would seriously consider going this route. But it would also require skills and tools that I don't believe I have access to currently. Though I'm still open to it if it becomes something within my means. 

As far as the shape of the strut goes, what design would be recommended. Round vs. square vs. rectangle…

I will most likely be mashing ends and bolting since I have yet to encounter a hub design that's as easy and reliable to fashion.

Aluminum tubing is still a strong option for me at this point. The major disadvantage is that aluminum is chemically reactive. This could be a problem if a thin concrete shell were applied to the dome. Not sure how it will fair with the steel bolts or the high alkalinity of cement. Other than aluminum, I see steel as the only other likely candidate... maybe thin-wall titanium is a possibility even. 

[Peter Schwarzel]

Hi MRU,

How thin will the concrete be? Concrete is cheap but does crack. Plastic or metal fibres is the way to go if you choose concrete. In Australia fibre reinforced concrete is taking on quite well. Why not go all fibreglass? Concrete and aluminium don't mix I agree.  Why not make it in fibreglass panels, flat on a table nice and easy then lift panels into place and glue together like a boat?  Why make a frame then turn it into a monocoque? Go straight to monocoque?  Your budget is small and your thinking is big!  There used to be architects that made organic shaped concrete buildings using chicken wire and concrete amazing shapes. Peter

--

[mru6...@gmail.com]

The weight of concrete over 2500 sq ft (232 sq m) could be immense. So I was advised not to let it exceed more than necessary, from what I've calculated so far that's around 1/4 inch (6mm). Use more lightweight aggregate such fiberglass strands to cut down on weight. It could essentially end up being composed of more fiberglass than concrete. Then I would have something close to fiberglass panels as suggested. If there is a binder cheaper than concrete, I would consider that. Also considered casting thin shell panels first, then attaching to dome. Experiments will be coming up soon, once warm weather arrives. This will ensure that a proper curing process can take place. The shell won't be much more than a covering to repel the elements, I wouldn't intend for the thin shell to be a structure on its own. There were many other options for a covering, many of which were lightweight compared to concrete. Along with cost, degradation caused by sun and UV narrowed my options down to thin shell concrete or painted fabric. Going straight to monocoque was something I thought early on. Given my limited grasp of structural engineering, I thought that not a good idea. Geodesic structures were found to be most promising as they were a structure that could provide a roof and have a very good reputation for their integrity, plus very easy to build. Dumbfounded really, how easy it was to construct something of that caliber. Although not ideal, EMT conduit might suffice for required integrity of building, will attempt to find large diameter, thin wall tubing that gets close to a d/t ratio of 50. Will update findings once available. If I would consider Robert's Clark's idea, I'd need to find a better material than plywood, fiberglass panels appear to be quite expensive. Both would also need to cut accordingly, this might be difficult. Could perhaps cast some material into mold to make panels then I could commence with that approach. I'd need a recipe for a stiff material and that is just flexible enough, not sure if a combination of acrylic, cement, and fiberglass would be up to the task. Marine applications of fiberglass mesh and resin could prove to be an elegant solution.

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[Peter Schwarzel]

Hi MRU - 6mm concrete sounds a difficult thing to do? Is there a precedent on this? Crack control is your issue I wouldn't go there. Fibreglass is same density as concrete so by volume no weight reduction in the combination. The more mixed media you go the more open to issues you will have. I think monocoque is the go or use building grade membrane over your steel structure. Or make flat panels at ground level lift them up zip tie in place and adhesive bond like a boat, then remove zips and seal. You make the panels to correct size from fibreglass and foam to minimise wastage. Look up composite infusion as a process some call it VIP. Vacuum infusion process. The other route is as you are going but find a membrane that works. eg building grade PVC. But you'll have to do the research. I think you will be let down by 6mm concrete. I helped a friend some 30 years ago build a ferro-cement 50ft boat. Chicken wire armature, 50mm thick concrete still had to be epoxied to seal it. Your epoxy cost will be big.  My latest model of the L3 weighs 458kg and uses Dia35x1.2 furniture ERW steel tube. Don't disregard plywood, been building boats from plywood forever. Just needs a good paint system done right and since you will be pulling a membrane over it UV not a problem. Can cut the elements with a jig saw either as per Roberts idea or as a monocoque. But why not 100% timber or plywood? This is very acceptable given what you want to do and there are structural design rules for timber?  Plywood is rated and its density is 650kg.m3 vs steel at 7800kg/m3 so you can use a lot of timber to get to the same place and you can control properties by size of member and lamination. Look up Roskilde Dome for ideas. Peter

Askok what about your tensegrity structure? Happy to look at it now if you can get a dxf of it?

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[Dick Fischbeck]

If you build a sheet metal dome, all the numbers change. Lightweight membrane structure like a plydome, only easier.

http://randomeshelter.blogspot.com/

[Peter Schwarzel]

Yes Dick, agree on the steel. Attached is image from latest model. In summary of MRU questions and Ashoks comments

1) To analyse domes requires non linear FE techniques. Linear gets it wrong and linear buckling gets it wrong but they are useful to get some sort of load capacity as a starting point for the NL work

2) The L3 is the superior dome to the L4 in this case

3) The NL FE needs to use very small increments so it does not miss a possible elastic path. Beam elements are good for first round design

4) The fixed vs free end models have similiar results in the L3 mode. So design hubs to the euler load plus a design factor

5) The L3 weighs 563kg using furniture tube of Dia31.8x1.2 gets it down to 412kg at similiar load.

6) We have used a single loadcase to do the comparison work. Need to have more loadcases to check other loading conditions

7) Using NL materials for the beams adds more information to the output and is easy to run

8) Obviously if this was a commercial task several checks and balances would be done through this process.

9) Hope this info was useful...

I'll write a small closing doc to publish here.  Peter

[Ashok Mathur]

Dear mru,

Plain concrete may crack and may not be suitable for a dome skin as the the whole structure is always in slow motion.

However we have successfully used ferro-cement for dome skin for last 30 years or so.

It also adds more strength to the dome being a thin shell structure with its own inherent strengths over and above the strength of the struts.

Using a blower it can easily be applied over the dome.

If you are interested I can end you links to such structures that I have built.

Regards

Ashok

Regards

Ashok

On Sun, Feb 19, 2017 at 12:02 PM, Peter Schwarzel <carbonfi...@gmail.com> wrote:

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[Ashok Mathur]

Dear Peter
 I shall soon post a note giving all the details and the arguments in a more cogent way.

Thanks

Ashok

Regards

Ashok

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[mru6...@gmail.com]

Peter, though still an estimate, the precedent for 6mm concrete was the closest I could get to what I thought was a reasonable thickness without over-weighing the structure. Upcoming experiments will determine of whether reinforced concrete is a good candidate or not, and next is what minimum thickness is required to repel the elements. If 3mm works, then I will go with that. Thin shell concrete at previous estimated thicknesses will no doubt crumble standalone. So crack control is definitely a primary concern along with weight. I heard many good things about acrylic-latex additives in cement which will improve elasticity, along with fiberglass strands for tensile strength. There are recipes --some using dozens of ingredients-- that have shown great success for many who have worked with concrete. I believe under the proper guidance thin shell concrete could prove to be a versatile material.  Limewash/whitewash coating will be applied to exterior, once cured ought to seal of concrete shell, hopefully it won't be seeing as much water as a ferrocement boat. However this is all one option so far. 

Have been looking into suggested alternatives, and if anymore are suggested, will dig for information on them. Have been looking into material for frame, ERW as mentioned could be a very good replacement for EMT. Would like to build Clark's idea, though I have concerns about plywood's longevity, if wet can warp, and insects as well as other fauna may find it attractive in some way, though these are minor concerns. Agreed plywood/timber can be a good option, though mostly I'm thinking there are likely to be better materials. I will still have read more about it and what is possible with wood based material.. Was mentioned previously by Dick, if sheet metal would perform as well plywood in Clark's dome, I would be more inclined.

Ashok, I would very much like to see links offered. 

[Peter Schwarzel]

what is the purpose of the dome? Is it for habitation or storage or shelter?  Whats your required lifetime?By precedent I mean an example of someone else that has done 6mm concrete? fibreglass/resin seems to be the natural material for me. Peter

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[mru6...@gmail.com]

I plan on using the dome for a house, ideally something once built, will need very little maintenance if any at all. Lifetime I'm hoping should exceed 50 years. I had initially decided that ferrocement was the way to go but was hard-pressed for a reliable frame design. Then spotted the use of domes, both monolithic and geodesic, as being very efficient structures in many respects. That along with the concept of thin shell application from ferrocement has been the inspiration for current designs. Have even considered forming thin shell tubes to serve for framework geodesic dome as well. Would scrap metal tubing work for struts? This would lower my costs significantly and would have access to much stronger and larger diameter struts i.e. fence gate railing. The only problem I have found is whether or not tubing of different sizes and/or shapes and materials would be compatible with one another in a geodesic structure? Or might there be a minimum difference that is acceptable?

[Peter Schwarzel]

Scrap metal is fine. Do you have to meet building codes? Current modelling is base on weight reduction as product is effectively bought by weight. But if the member is bigger and cheaper (per metre for instance)  then all's good as long as the product is not rusty/bent/ugly etc. So recycled material is fine. ie the modelling establishes minimum dimensions. Peter

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[mru6...@gmail.com]

There aren't any building codes where I'm building, so that has opened up a whole range of design possibilities. Will most likely explore and experiment with other designs once a permanent home is constructed. Just wanted to make sure, using both a small aluminum square tube and large steel round tube on the same dome shouldn't pose any problems as long as they're strong enough; they won't have a major effect on the integrity of the dome? 

Were you going to build a Clark's dome or your own variation? If so frequency, size, type/thickness of plywood?

Also, before I post the FEA results pdf elsewhere, there was only thing that might be confusing. (Would've edited this myself, but do not have access to pdf editor.) On the 2nd page of the pdf, under Stress Analysis, the second paragraph mentions L4 again, I believe it was meant for L3. 

[Peter Schwarzel]

Yes I'll fix that and republish. I noted it in the forum. I've been thinking and mucking about with domes for over 30 years on and off. Was going to make a shelter over a veranda I have here. Just small but have always had trouble with various things, hubs, suitable materials, lack of elegance. Now we look like moving so won't put up the shelter,  but using fibreglass opens up huge opportunities going the Clark way. I had a similar design with more complex connection as I want the outside to be flat.  Learning "grasshopper" a rhino add on that can draw all of this stuff automatically. Plus I'm building a cnc router at the moment so I can cut this sort of thing. Lifes busy.  Peter

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[Peter Schwarzel]

Hi GMU heres Issue 6 for public review

[Ashok Mathur]

Dear Peter

The case for studying the six strut tensegrity now spans over many pages and with its appendices is over 10 pages in length.

It would be impolite for me to thrust it down the throat of all the readers of this wonderful group.

So it is attached as a text file to this email.

In the note I have written that your results are attached but for this group that already has access to them, I have not attached your results.

I have embedded as an excel sheet the calculation of coordinates of the six strut ends. The calculations are enclosed for a unit length of the strut and 10 unit lengths of the struts.

I have made a drawing in Geo Gebra that is able to export it as eps file and png file.

I can send the eps file if you can convert that into a dxf file. But overall the geometry of the six strut tensegrity s so simple that you will find it much simpler to draw it fresh in a CAD program.

In the note I have not said anything about the material of the six struts and 24 tendons. This is because I want you to be free to use the materials you have at hand to first calculate the strength and then build the six strut tensegrity and then compare the two results.

Any tube of about half inch radius of mild steel will do for struts whose lengths could be 12 inches. The 24 tendons of 0.612 times strut length could be fabricated from either 16 gauge GI wire or the thinner 18 gauge GI wire.

I end with a direct quote from Hugh Kenner that I discovered re-reading him in connection with this debate.

"It follows that calculations pertaining to such a system, taking into account the known characteristics of the materials but presuming the usual methods of assembling them, are certain to be wrong."

Regards

Ashok

Regards

Ashok

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