# Tension

Tension is always accompanied by compression, its opposite. Tension and compression are co-dependent co-originating dis-similar pairs like space and matter (as opposed to to co-dependent co-originating similar-but-opposite phenomena such as chirality or convex/concave). Tension may be exerted by any construction material, but it is made most manifest by materials that can only usefully instantiate tension and collapse completely under compression. Examples include any filament such string, cables, chains, biological tendons or spider's silk.

# Tension Metrics

Read how tension is measured in the materials that compose a tensegrity structure.

## Tension is Measured in Newtons

A primary, empirical effect of tension is to exert a measurable force, so tension is measured in newtons (or pounds-force). This force is considered as parallel to the tension filament on which it applies.

## Tensile strength

Tensile strength derives from the molecular structure of the material in question, and ultimately depends on the inter-molecular bonds' resistance to being pulled asunder. A molecular material that parts quickly has low tensile strength and may be called brittle. Rocks, cast iron and soil are all brittle materials. Concrete is brittle, and it is by the addition of steel rebar pipes embedded in the concrete that enables the concrete to exert a much higher tensile force, hence the name reinforced concrete.

Given steel's prominent use in modern construction, its tensile strength has been well described with a jargon all its own. Some of these terms are ultimate strength, yield strength, proportional limit stress, rupture, strain hardening region, necking region, offset strain. (See Wikipedia article on tensile strength).

The tensile strength, or breaking strength, of rope is specified in newtons, without specifying the cross-sectional area of the rope. These units map poorly to the units we are given for metals.

Water has exceptional tensile strength, and is deployed by nature in astoundingly flexible ways. A nuclear blast wave, for example, will destroy a brittle house, while trees in its path bend over and snap back to their former height. The tree can harness this tensile strength since it houses a ubiquitous network of water tension tubes, that also draw water from the roots to the upper leaves.

### Tensile strength of sample materials

Common tension fibers in tensegrities are nylon fishing line, dacron, twine, steel cable and rubber bands.

Milliken wrote: Tensile strength correlates with the cross section area of the tendons/cables/wires. If they are small (as is typical for models), they are going to be very stretchy. If large diameter tension rods were used, the structure would be much more rigid. Twisted cables wind and unwind under load and are probably more stretchy than a solid tension member or a solid wire.

### Stress Testing

In the video below a length of steel rebar is subject to a tension test and the moment of failure is shown at normal speed and at 1/4 speed. Just before the failure, "necking" is clearly visible in the rebar.

### Difficulties of analyzing the structural strength of tensegrities

Traditional structural mensuration does not suit the analysis of tensegrities.

Snelson wrote: "My point about engineers trying to calculate these structures is that the figures anyone might come up with are only as good as the "tuning " of the tension lines. I made a sculpture years back at the Hochschule der Bundeswehr in Hamburg. There's a similar one at the San Diego Community College. Since the Bundeswehr is a military and technical school the powers-that-be decided the sculpture should undergo an analysis before I installed it. They had been given a small maquette to study. They completed their work in a couple of weeks -- offered me no copies of their figures (would have been meaningless in any case since I wouldn't have had any idea how to evaluate them) and I didn't delve into it since now I'd been given the green light to do my installation. They had found no reason to believe the sculpture would collapse.In point of fact, with the same geometry, that is, the maquette as translated into a full scale sculpture, I could have tightened the piece like a stringed instrument so that indeed it would collapse from having too tight a tension network. Since the cables don't necessarily stress in identical ways the moment one cable is heavily tightened, the figures the Bundesweher engineers came up with could no longer describe what actually was going on since my tuning the piece was determining what stress were changing where. If the Bundeswehr engineers had any grasp of that complexity they would have given me a schedule of tightings they might prescribe as the optimum tuning to avoid trouble. That's the perplexity I'm talking about. That's the reason I question the success of engineers in analyzing such structures."

# Tension Direction

Tension is usually considered as a force along a line. Fuller advocated that the tensional net of a tensegrity structure be considered as a whole, or omnidirectional, as opposed to the struts that operate in local compression.

## Bidirectional Tension (Brainstorm)

Vyom Akhil brainstormed about bi-directional tension. He wrote:

The "line" of tension - it can loop back, cross itself and intertwine - but it is not known to double back on itself. We call it a "line" of tension but it's really a 'line' that reels and pulls us back - the fishing 'line' is 'alive' responding to the moving bait or fish - and the yo-yo responds to the gravitational pull even as its 'line' uses the force to wind it up again. In the domain of 'tensional integrities' we make vectorial representations of the tensional force to observe how they keep the compressional struts vibrating in a given small domain.

But going back to the basics - can we take a 'string' and make it go through a polyhedron's tubular sides. If we find that if we do not knot it up - effectively 'cutting' the tension, we can loop it back to cross itself and even intertwine - But it is not possible to make it double back on itself. Furthermore - but I am not so sure - the Octahedron is the only one that let the tensional 'line' run through itself. All other polyhedra, including the tetrahedron - I conjecture - do not allow it , making the Octa-faced domain unique, perhaps, in this regard.

Fuller always insisted, "GRAVITY MORE EFFECTIVE THAN RADIATION" - Inspite of identical vectorial energy potential and because of single-link disintegrative patterning vs double-linked integrative patterning. He echoes Krishna who, in his song in the Gita chapter 7 verse 7, says the same thing poetically, unapologetically and simply.

# References and Links

[1] Letter from Kenneth Snelson to To: Robert W Burkhardt 3 May 1999, retrieved 18 Feb. 2010 from Burkhardt's website, http://www.trip.net/~bobwb/ts/synergetics/photos/ken4.html

 Portal To Basic Concepts A series of pages addressing critical concepts; see also the index. Tensegrity> Benefits, Chronology, Definitions, Dynamics, Force, Geodesic Dome, Humor, Mast, Nexorade, Prestress, Pneumatics, prestress, Stability, Stiffness, Stress, Videos Compression> Strut: Curved, Linear, Nucleated, Ring, Spring Tension> Floating, Tendon, Membrane, Wire Roap, Materials Forms> Bicycle wheel, Buckminsterfullerene, Folding, Musical instruments, Plane, Prism, Skew, Specific Strength, Springs, Torus, Tuning, Wall, Weaving Materials> Bone, DNA, Fabric, Glass, Inox, Integrin, Spring, Tendon Materials, Wire Roap Founders> Fuller, Snelson