A late post of a test I did looking into a hyperboloid and how it behaves. If you’re wondering what one is and where you might have come across one before, think of a stretched Chinese finger trap. This is a hyperboloid.
As you can see from above the strands of the shape are formed from straight members to create a curved form, one which has 3 axis of symmetry. The finger trap works as when you pull the cylinder apart it forms a hyperboloid as the internal column diameter narrows and the straight strands clamp down on your fingers, to release you have to squash the hyperboloid, and widen the internal diameter.
Further tests will look at the structural properties of this shape as it can be found in many places in nature. I will be looking at how the shape fairs by making it into a straight column by effectively bending each strand to wrap around the cylindrical shape of a traditional column. From what I remember the shape is pretty resilient.
Tensile strength seems a given: by pulling the shape down (lengthening the column) you are tightening the centre radius and effectively trying to return the strands back to their natural straight shape.
Compressive strength is less obvious: you will be bending each individual strand further, stretching their elastic limit until they either break or don’t return back to their original form. But each strand is supported by the strand next to it, so I anticipate it still being quite strong, and probably a more economical use of material to build columns of, hopefully equal in strength to a bunch of straight strands simply bundled together?? Wishful thinking maybe. Think it should be more stable as a shape.
Bending strength is also meant to be enhanced: where the form is used horizontally as a beam – the forces applied on lower (beam base) strands are wanting to bend them more, but these are supported by upper (beam top) strands which are effectively being straightened, hence the structure is self-supporting… I hope.
Can be employed as a form of tensegrity structure, whereby it in effect gets stronger the more load is put on it, as the force is distributed evenly across all members even though the applied force is local. Reminds me of a stool design I had (but never explored properly) at uni studying furniture design. Never refined it enough to make it work. The materials I was using weren;t really up to the job; a let friend sit on it, it broke. It wasn’t a final piece, just an experiment, one of several maquettes exploring a particular theme. I developed another idea further in the end, probably because the work involved in trying to work that one out scared me!