Above are two models, one built on my desktop from junk found in my desk, one built on my desktop p.c.
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Cubes (constructed with beams) and houses can and do collapse when a sufficient horizontal
(shearing) force is applied above the foundation.
The walls act as levers, creating torque, and the house deals with the stress by destroying itself.
Beams and cables have strength in compression and tension respectively,
but both are poor in resisting torque.
Can a lightweight structure be designed so that a horizontal force above the base creates
compression and tension but no torque?
Buckminster Fuller asked: "What's the minimal structure that can support a weight and oppose horizontal forces, that uses compression and tension, but experiences no torque?" His answer to (his own) question was: |
Above are two models,
one built on my desktop from junk found in my desk,
one built on my desktop p.c.
These are 'Tensegrity' structures. The rubber bands are all in tension and paradoxically have the dual roles of holding the beams apart, and the structure together, in a flexible and stable equilibrium.
This is a fun model to build and play with. It can be squashed flat against a table top with the palm of your hand, and if you pull your hand away quickly it jumps up off the table, springing back into its original shape.
This model can be hard to visualize. None of the beams or tension members are parallel, or perpindicular. The rubber bands form two triangular faces, and they lie on parallel planes and give the structure a twisted appearance because the triangles differ by a rotation relative an axis perpendicular to the planes and the beams all have the same tilt, relative to that same axis.
Euler's equation does NOT hold for this structure ( v + f - e = 2 is not true ). An additional three (exterior) edges could be added to the existing verticies. If these were added, it would have the topography of an octahedron ( 8 faces, 6 verticies, 12 edges ) and Euler's equation would apply (and of course would be true).
I was going to write that this is the simplest possible 'tensegrity' structure, and it is in the sense that you can't create a tensegrity structure with only two beams, or only one, but it occured to me that you can create a tensegrity structure with no beams and two, count 'em two, elastic (and completely non-ridged) members in tension. I'll leave that as a riddle. ( The answer is non-digenerate: it is an elastic structure in a stable equilibrium and is not a collapsed structure like a ball of rubber bands. )
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