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Jul. 29th, 2009 @ 12:18 am Zometool structural analysis
Attendees of the Bridges 2009 Math & Art conference are in the process of building the largest Zometool sculpture ever. It will be ~12 feet high and wide if completed, and consume 24000 parts IIRC. There isn't a master digital model yet, but the portion of the model that I do have was run through a simple structural analysis program of mine and shows significant tensional stresses at the narrow junctions.



Red is for segments in tension, blue is for compression. Since the magnitudes of the peak tension and compression forces are roughly equivalent, I have to conclude that if the structure does break, it will be a tensional pull-out failure, and will occur on the undersides of the narrow junction regions.

(cross-posted to my own journal, apologies to those who have to see it twice)
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manheadphones v1
technolope:
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From:don_t_know_how
Date:July 29th, 2009 03:18 pm (UTC)

2 questions

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1. why notice that tension and compression are of same magnitude?
2. ... and if it doesn't?
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From:technolope
Date:July 29th, 2009 05:03 pm (UTC)

Re: 2 questions

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1. It just seemed worth mentioning. I'm a fluids guy, so maybe all structures exhibit this property (second thought---there can be a large variation). The physical shape of Zometool objects is such that tension is much more likely to cause failure than compression.

2. We could make much larger zometool structures if we could design for compression instead of tension---more arches, say.
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From:don_t_know_how
Date:July 29th, 2009 05:20 pm (UTC)

Re: 2 questions

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indeed i think arches would be a good choice...

i don't actually know zometool, it seems a sort of truss assembly... anyway, these "truss" structures remain an approximation of solids, and in complex slender (and many other) solids under weight loads you often have to have parts under tension... or you build columns, pyramids.. and arches.

imho the question is curious: are there any other [more or less common?] types of structures subject only to compression stress under weight load?

PS nice colormap, makes your bridge quite aerospaceengnry ;)
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From:don_t_know_how
Date:July 29th, 2009 05:22 pm (UTC)

Re: 2 questions

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i think the trick would be to find a way to leave the tension part to the base (as in the case of the arches)
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From:technolope
Date:July 29th, 2009 11:19 pm (UTC)

Re: 2 questions

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I suppose an upside-down parabola would be in perfect compression (adjusted slightly to account for the weight). I'm not sure what other shapes would be tension-free.

Unfortunately, Zometool's connection mechanisms don't allow arbitrary connections.
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From:don_t_know_how
Date:July 30th, 2009 04:58 am (UTC)

Re: 2 questions

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"Unfortunately, Zometool's connection mechanisms don't allow arbitrary connections."

are parts (almost absolutely) rigid? i think that when it comes to thousands of them, you can use.. ahem.. a long straight beam and then bend it.
it could be ok if bending tension remains under the level of the weight compression.

however, when you make it big enough, compression might bring about buckling problems.
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From:technolope
Date:July 30th, 2009 05:57 am (UTC)

Re: 2 questions

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Right---each node has 24 (or 30, or something) rigid holes, accepting one of three types of rod end-shapes (triangle, rectangle, pentagon). The design is such that there is a great variety of constructions possible, though the angles are fixed.

I would suspect that any structure with beams long enough to bend also have beams long enough to buckle---as you note. The strongest parts of the structure were the zones with lots of nodes and lots of very short connecting segments. Those were little rocks.
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From:don_t_know_how
Date:July 30th, 2009 06:10 am (UTC)

Re: 2 questions

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another solution(?) might be to make in the respect of the connection angles, with as many bars as possible and it HUGE enough for the "microscopic" geometry not to matter. (there are many buildings withe carved walls or arches built with rectangular bricks)

once again, the basis elements resistance to buckling would have to be ensured

good luck