A friend and I are having a debate; which shape is the strongest?
Our defintion of strongest is rather vague, but is essentially the mount of external force the shape can resist - be it a single force acting in a single direction or multiple forces in multiple directions.
We are arguing seperately for both the 2D scenario, and the 3D scenario.
I am unable to find much about this online - so I am hoping someone here can help settle the argument.
Many thanks!
Buckminster Fuller's geodesic domes were made of triangles. So 2D, I'd say triangles. For 3D, TPH's pyramid sounds good, but then what about those domes? Hmmm, isn't a pyramid the geodesic dome with the minimal number of faces?Originally Posted by TigerTom
I think you and your friend are making a category error, shapes as such do
not have strength, a structure fabricated out of some particular material
may well have strength, but even then you may need to define exactly what
you mean and under what loads you want to measure/compare this.
RonL
(Smiles) OK, that is analogous to what I said. But, not knowing any better, I just read the definition from here and conclude the minimal geodesic dome would be 1 tetrahedron and 0 octahedrons.
A geodesic dome is a spherical building in which the supporting structure is a lattice of interconnecting tetrahedrons (a pyramid with three sides and a base) and octahedrons (an eight sided figure—two pyramids with four sides and a base, placed base to base).
I have always learned that a domes, spheres, and ellipsoids are the srongest.
It certainly depends on the application. A triangle is a strong design in some areas. Bridges, for example.
As for domes, look at the Hajia Sofia. Fantastic piece of architecture.
One may look in nature for some strongest designs. Sometimes those are the best designs for strength.
The dome of Hagia Sophia is strong because stone and concrete (though there
is no significant concrete in the structure of Hagia Sophia apparently but there
is in the Pantheon) are strong in compression (though brittle and weak in tension)
and the structure is designed to keep the stone work and concrete in compression.
If built of rubber the dome would probably not be able to bear its own weight. The
strength is due to using a structure that exploits the strength of the materials
while avoiding their weaknesses.
RonL
Yes, we had discussed that to the extent that joints on a triangle could be weak, but the argument dismisses the idea that the shape could be weakened by poor construction. Whilst it is impossible to do, we are trying to dismiss the impact that various contruction methods or different materials bring to the table.
I argued a triangle would be strongest, and he argued for a circle.
My logic was a triangle would dissipate a single force acting on it over the largest possible area for a shape constructed with a set perimeter. I though a circle, resting on a surface, would have an infinitely small area though which the force would act.
Yes, I realise it is a silly argument and there are a million factors to consider...
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