Tensegrity,tensional integrityorfloating compression, is a structural principle based on the use of isolated components incompressioninside a net of continuoustension, in such a way that the compressed members (usually bars or struts) do not touch each other and theprestressedtensioned members (usually cables or tendons) delineate the system spatially.[1]The termtensegritywas coined byBuckminster Fullerin the 1960s as aportmanteauof "tensional integrity".[2]The other denomination of tensegrity,floating compression, was used mainly byKenneth Snelson. Tensegrity as "The Architecture of Life" is an idea developed byDonald E. Ingber, explained in a January 1998 article inScientific American.[3]Contents[hide] 1Concept 2Applications 3Biology 4History 5Mathematical explanation 6Patents 7Basic tensegrity structures 8See also 9References 9.1Gallery 10Bibliography 11Further reading 12External linksConcept[edit]

TheSkylon towerat theFestival of Britain, 1951[show]Rightframe

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AnimationA similar structure but with four compression members.

Tensegrity structures are structures based on the combination of a few simple 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 preloador tensionalprestress, which allows cables to be rigid in tension mechanical stability, which allows the members to remain in tension/compression as stress on the structure increasesBecause of these patterns, no structural member experiences abending moment. This can produce exceptionally rigid structures for their mass and for the cross section of the components.A conceptual building block of tensegrity is seen in the 1951Skylon tower. Sixcables, three at each end, hold the tower in position. The three cables connected to the bottom "define" its location. The other three cables are simply keeping it vertical.A three-rod tensegrity structure (shown) builds on this: the ends of each rod look like the bottom of the Skylon tower. As long as the angle between any two cables is smaller than 180, the position of the rod is well defined. There are also three connection points defining the position the rod tops. This makes the overall structure stable. Variations such asNeedle Towerinvolve more than three cables meeting at the end of a rod, but these can be thought of as three cables defining the position of that rod end with the additional cables simply attached to thatwell-definedpointin space.Eleanor Hartley points out visual transparency as an important aesthetic quality of these structures.[4]Korkmazet al.[5][6]put forward that the concept of tensegrity is suitable foradaptive architecturethanks to lightweight characteristics.Applications[edit]

A 12m high tensegrity structure exhibit at theScience City,Kolkata.The idea was adopted into architecture in the 1960s whenMaciej GintowtandMaciej Krasiski, architects ofSpodek, a venue inKatowice,Poland, designed it as one of the first major structures to employ the principle of tensegrity. The roof uses an inclined surface held in check by a system of cables holding up its circumference.In the 1980sDavid Geigerdesigned SeoulOlympic Gymnastics Arenafor the1988 Summer Olympics. TheGeorgia Dome, which was used for the1996 Summer Olympicsis a large tensegrity structure of similar design to the aforementioned Gymnastics Hall.Shorter columns or struts in compression are stronger than longer ones. This in turn led some, namelyFuller, to make claims that tensegrity structures could be scaled up to cover whole cities.As Harvard physician and scientistDonald E. Ingberexplains:The tension-bearing members in these structureswhether Fuller's domes or Snelson's sculpturesmap out the shortest paths between adjacent members (and are therefore, by definition, arranged geodesically) Tensional forces naturally transmit themselves over the shortest distance between two points, so the members of a tensegrity structure are precisely positioned to best withstand stress. For this reason, tensegrity structures offer a maximum amount of strength.[citation needed]On 4 October 2009, theKurilpa Bridgeopened across theBrisbane RiverinQueensland, Australia. The bridge is a multiple-mast, cable-stay structure based on the principles of tensegrity. It is also the largest tensegrity structure in existence.Biology[edit]Biotensegrity, a term coined by Dr. Stephen Levin, is the application of tensegrity principles to biologic structures.[7]Biological structures such asmuscles,bones,fascia,ligamentsandtendons, or rigid and elasticcell membranes, are made strong by the unison of tensioned and compressed parts. The muscular-skeletal system is a synergy of muscle and bone. The muscles and connective tissues provide continuous pull[8]and the bones present the discontinuous compression.A theory of tensegrity inmolecular biologyto explain cellular structure has been developed by Donald Ingber.[3]For instance, the expressed shapes of cells, whether it be their reactions to applied pressure, interactions with substrates, etc., all can be mathematically modeled if a tensegrity model is used for the cell'scytoskeleton. Furthermore, the geometric patterns found throughout nature (the helix ofDNA, the geodesic dome of avolvox,Buckminsterfullerene, and more) may also be understood based on applying the principles of tensegrity to the spontaneous self-assembly of compounds, proteins, and even organs. This view is supported by how the tension-compression interactions of tensegrity minimize material needed, add structural resiliency, and constitute the most efficient possible use of space. Therefore,natural selectionpressures would strongly favor biological systems organized in a tensegrity manner.[9]History[edit]

Kenneth Snelson's 1948 X-Module Design as embodied in a two-module column[10]The origins of tensegrity are controversial.[11]In 1948,artistKenneth Snelsonproduced his innovative "X-Piece" after artistic explorations atBlack Mountain College(whereBuckminster Fullerwas lecturing) and elsewhere. Some years later, the term "tensegrity" was coined by Fuller, who is best known for hisgeodesic domes. Throughout his career, Fuller had experimented incorporating tensile components in his work, such as in the framing of his dymaxion houses.[12]Snelson's 1948 innovation spurred Fuller to immediately commission a mast from Snelson. In 1949, Fuller developed anicosahedronbased on the technology, and he and his students quickly developed further structures and applied the technology to building domes. After a hiatus, Snelson also went on to produce a plethora ofsculpturesbased on tensegrity concepts. Snelson's main body of work began in 1959 when a pivotal exhibition at theMuseum of Modern Arttook place. At the MOMA exhibition, Fuller had shown the mast and some of his other work.[13]At this exhibition, Snelson, after a discussion with Fuller and the exhibition organizers regarding credit for the mast, also displayed some work in avitrine.[14]Snelson's best known piece is his 18-meter-highNeedle Towerof 1968.Russian artistViatcheslav Koleichukclaimed that the idea of tensegrity was invented first byKarl Ioganson, Russian artist of Latvian descent, who contributed some works to the main exhibition of Russianconstructivismin 1921.[15]Koleichuk's claim was backed up by Maria Gough for one of the works at the 1921 constructivist exhibition.[16]Snelson has acknowledged the constructivists as an influence for his work.[17]French engineer David Georges Emmerich has also noted how Ioganson's work seemed to foresee tensegrity concepts.[18]Mathematical explanation[edit]

Mathematical model of the tensegrity icosahedron

Different shapes of tensegrity icosahedra, depending on the ratio between the lengths of the tendons and the struts.The following is a mathematical model for figures related to the tensegrity icosahedron, which explains why the tensegrity icosahedron is a stable construction, albeit with infinitesimal mobility.[19]Consider a cube of side length2d, centered at the origin. Place a strut of length2lon each face of the cube, so that each strut is parallel to one edge of the face and meets the center of the face. Moreover, each strut should be parallel to the strut on the opposite face of the cube, but orthogonal to all other struts. The coordinates of one vertex of the struts are(0,d,l), the coordinates of the other vertices can be obtained by either cyclicly rotating the coordinates(0,d,l)(d,l,0)(l,0,d)(rotational symmetry in the main diagonal of the cube) or by changing the sign of the coordinates(0,d,l)(0,-d,l)(0,-d,-l)(0,d,-l)(mirror symmetries in the coordinate planes). The distancesbetween two neighbouring vertices can be obtained from the following relation

Now imagine, this figure is built from struts of length2land tendons of lengthsconnecting neighbouring endpoints. The relation tells us, that forthere are two possible values ford: one is realized by pushing the struts together, the other by pulling them apart. For example forthe minimal figure(d=0)is aregularoctahedronand the maximal figure(d=l)is aquasiregularcubeoctahedron. Whenthens = 2d, so theconvex hullof the maximal figure is aregularicosahedron.In the casethe two extremescoincide, therefore the figure is the stable tensegrity icosahedron.Since the tensegrity icosahedron represents an extremal point of the above relation, it has infinitesimal mobility: a small change in the lengthsof the tendon (e.g. by stretching the tendons) results in a much larger change of the distance2dof the struts.Patents[edit] U.S. Patent 3,063,521, "Tensile-Integrity Structures," November 13, 1962, Buckminster Fuller. French Patent No. 1,377,290,"Construction de Reseaux Autotendants", September 28, 1964, David Georges Emmerich. French Patent No. 1,377,291,"Structures Linaires Autotendants", September 28, 1964, David Georges Emmerich. U.S. Patent 3,139,957, "Suspension Building" (also called aspension), July 7, 1964, Buckminster Fuller. U.S. Patent 3,169,611, "Continuous Tension, Discontinuous Compression Structure," February 16, 1965, Kenneth Snelson. U.S. Patent 3,866,366, "Non-symmetrical Tension-Integrity Structures," February 18, 1975, Buckminster Fuller.Basic tensegrity structures[edit] The simplest tensegrity structure (a 3-prism) Another 3-prism A similar structure but with four compression members. Proto-Tensegrity Prism by Karl Ioganson, 1921[gallery 1] Tensegrity Icosahedron,Buckminster Fuller, 1949[gallery 2] Tensegrity Tetrahedron, Francesco della Salla, 1952[gallery 3] Tensegrity X-Module Tetrahedron,Kenneth Snelson, 1959[gallery 4]See also[edit] Cloud Nine Hyperboloid structure Interactions of actors theory Saddle roof Space frame Synergetics Tensairity Tensile structure Thin-shell structure