Tensegrity

=Tensegrity=

Tensegrity or tensional integrity is a property of structures with an integrity based on a balance between tension and compression components.

=Concept=

Tensegrity structures are structures based on the combination of a few simple but subtle and deep design patterns:


 * loading members only in pure compression or pure tension, meaning the structure will only fail if the cables yield or the rods buckle
 * preload, which allows cables to be rigid in tension
 * mechanical stability, which allows the members to remain in tension/compression as stress on the structure increases

Because of these patterns, no structural member experiences a bending moment. This produces exceptionally rigid structures for their mass and for the cross section of the components.

Connelly contrasts this operational definition with a mathematical, theoretical definition. Structurally, "It is a structure that joins nodes (points) with inextendibile cables and incompressible struts. The cable can be made from string, wire, or rope, and struts can be made from tubes, dowel rods, or just sticks. See wikipedia for a reasonable definition." Mathematically, "It is a finite configuration of points, the nodes, in space or the plane where some pairs of the nodes are designated cables, constrained not to get further apart, and some pairs are designated struts, constrained not to get closer together. Note with this definition cables and struts are allowed to intersect and cross."

=Typologies= There is no one widely accepted method of classifying tensegrities.

By Similarity to Polyhedra
The similarity of a given tensegrity to a given polyhedron is not a simple issue, as sometimes the faces are implied or asymmetrical.

Pugh's catalog
Anthony Pugh (1976) attempted a comprehensive typology in the 1970's. His typology is polyhedra-centered. "First, he described the simplest figures superficially (both 2D and 3D), depending on the relative position of their tendons (passing through their centres or not), on the complexity of the compressed components (single elements or groups of struts), on the number of layers or stages, etc. Then, he described the three basic patterns that can be used to configure spherical or cylindrical tensegrity structure: Diamond pattern, Circuit pattern and Zigzag pattern. This classification was based on the relative position of the struts of the figures, as is explained in fig. 5.1. Finally, he related the way of joining systems together and the construction of larger figures. In that section some grids, masts and domes were described, but not in an in-depth manner."

Motro's refinement of Pugh
Motro refined Pugh's classification in his book, “Tensegrity, Structural Systems for the Future” (2003). His category highlights are
 * **Spherical systems**: systems homeomorphic to a sphere, e.g. all cables can be mapped on a sphere without intersections between them and all the struts are inside the sphere
 * **T-prism and Rhombic configuration**, corresponds to the Diamond Pattern established by Pugh. Tensegrity prisms (T-Prisms) are included in this section. Also includes the “simplex” and the “expanded octahedron” (also so-called “icosahedric tensegrity”).
 * **“Circuit” configuration**, where compressed components are conformed by circuits of struts, closing the rhombus generated by the struts and cables of the diamond pattern tensegrities. Many regular and semiregular polyhedra can be built in this class, such as cuboctahedron, icosidodecahedron, snub cube, snub icosahedron, etc. Pugh notes that a circuit system is more rigid than a rhombic one with the same number of struts. This is understandable since the former evolves from the latter, but it becomes more compact and there is contact between its compressed elements.
 * **“Zigzag” configuration** or “Type Z”. To build the zig-zag, take a rhombic system as a basisand change cables in such a way as to form a ‘Z’ of three non aligned tendons. Note that substitution of the cables must be done in such a way so as to preserve the stability of the system. Example: the “expanded octahedron” when rearranged into zig-zag pattern, becomes the “truncated tetrahedron”.
 * **Star systems.** Though also spherical, stars are considered a derivation of zigzag. For example, taking as a basis one of the rhombic system, if a vertical strut is inserted in the centre following the main axis of symmetry and linked to the rest of the cables by means of tendons, a star system is created. Another possibility could be proposed by inserting a small spherical node instead of the central strut.
 * **Cylindrical systems:** also a variation of the rhombic configuration, obtained by adding other layers of struts to the initial layer. For example, adding a second line to a four-strut rhombic cell that subsequently closes all around itself again, creates a cylindrical mast.
 * **Irregular systems.** A catch-all class for everything that does not fit the above. It is here that Motro classifies most of Snelson’s sculptures
 * **Assemblies:** Combinations of the above. They include Vertical Masts (or horizontal beams) that feature assembly along a single axis, or Grids, extension in two directions that describe a surface.

=Bibliography=

Today there are thousands of publications on tensegrity in the fields of architecture, structural engineering and cell biology.

Some excellent bibliographies: Bibliography written by Valentín Gómez Jáuregui