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Tensegrity AND MembraneStructure


Tensegrity, tensional integrity or floating compression, is a structural principle based on the use of isolated components in compression inside a net of continuous tension, in such a way that the compressed members (usually bars or struts) do not touch each other and the pre-stressed tensioned members (usually cables or tendons) delineate the system spatially.[1] 

Three men have been considered the inventors of tensegrity: Richard Buckminster Fuller, David Georges Emmerich and Kenneth D. Snelson. Although all of the three have claimed to be the first inventor, R. Motro (1987, 2003) mentions that Emmerich (1988) reported that the first proto-tensegrity system, called “Gleichgewichtkonstruktion”, was created by a certain Karl Loganson 2 in 1920. This means it was a structure consisting of three bars, seven cords and an eighth cable without tension serving to change the configuration of the system, but maintaining its equilibrium. He adds that this configuration was very simi-lar to the proto-system invented by him, the “Elementary Equilibrium”, with three struts and nine cables. All the same, the absence of pre-stress, which is one of the characteristics of tensegrity systems, does not allow Loganson‘s “sculpture-structure” to be considered the first of this kind of structures. [2] 

The most controversial point has been the personal dispute, lasting more than thirty years, between R. B. Fuller (Massachusetts, 1895-1983) and K. D.Snelson (Oregon, 1927) As the latter explains in a letter to R. Motro, during the summer of 1948, Fuller was a new professor in the Black Mountain College (North Carolina, USA), in addition to being a charismatic and a nonconforming architect, engineer, mathematician, cosmologist, poet and inventor (registering 25 patents during his life). Snelson was an art student who attended his lectures on geometric models, and after that summer, influenced by what he had learnt from Fuller and other professors, he started to study some three-dimensional models, creating different sculptures. As the artist explains, he achieved a new kind of sculpture, which can be considered the first tensegrity structure ever designed. When he showed it to Fuller, asking for his opinion, the professor realized that it was the answer to a question that he had been looking for, for so many years. At the same time, but independently, David Georges Emmerich (Debrecen-Hungary, 1925-1996), probably inspired by Ioganson‘s structure, started to study different kinds of structures as tensile prisms and more complex tensegrity systems, which he called “structures tendues et autotendants”, tensile and self-stressed structures. As a result, he defined and patented his “reseaux autotendants”, which were exactly the same kind of structures that were being studied by Fuller and Snelson.[3] 


1. Basic theoretical unit

In my opinion, the basic theoretical unit of all the tensegrity is this: Strut with two cables. The upper ridge cable and the under diagonal cable. Both cables are stressed by the strut in-between in order to make a space. Other complicated structures are different combination of the basic unit or the variations of the basic unit. Furthermore, the two supports decide which category of tensegrity the structure belongs to.
Simple combination of basic theoretical unit and variation of basic unit with the support from outside, i.e. the earth, wall and other secondary structure of earth.

2.Wire wheel system

Wire wheel system is in my eyes between open and closed system. It depends on whether one consider the supporting ring outside or inside as a part of the tensegrity structure.
The simplest wire wheel is formed through the rotation of the basic theoretical unit. The strut is at the place of the circle center. The support is the outer-press ring. This second wire wheel is formed through the rotation of the basic unit too. But the circle center is outside the basic unit. The supports are the outside ring-strut. And the inside ring-cable.
"A cable dome contains vertical struts, ridge cables, diagonal cables and hoop cables(Fig.4). Cable domes mainly include two variations: Geiger's domes and spatially triangulated domes (Fuller‘s dome)" [4]

3. Closed system

3.1 Tensegrity Prism

A tensegrity prism is a stable volume that is realized by the connection of the basic unit one by one. At the end, A is A‘and B is B‘. “It is anti-prism (occasionally, prism) composed of two layers of cables forming the upper base (by upper cables) and the bottom base (by bottom cables), stabilized by diagonal cables. Inclined struts connect opposite vertices of bases so as to brace the prism. The relative rotation angle of the two bases is dictated by the requirement for the equilibrium of the shape. For regular simplexes (i.e. having regular base polygons), this angle is 30° for a triangular prism, and 45° for a square prism, etc.”[5]

When the sides of base are more than four, there‘s more than one possibility to form a tensegrity prism. As we can see in the Fig. 7. There are two possibilities in pentagonal prism and hexagonal prism. 

Kenneth Snelson has his special understanding about the formation of tensegrity prism. „Weaving and tensegrity share the same grounding principle of alternating helical directions; of left to right; of bypasses clockwise and counterclockwise. In these figures, the column on the left shows the primary weave cells. To their right are the equivalent basic tensegrity modules. By transposing each weave filament to become a strut (stick, tube or rod) the cells transform into arrays of two, three, four, etc. compression members. They retain their original form and helical direction. And helical direction. 

3.2 Higher tensegrity polyhedra

From the tensegrity of prism, we can confirm that the point of a tensegrity should be made up of one strut and 3 cables. In order to form more complicated tensegrity, “Emmerich studied all Platonic polyhedral (regular polyhedral and Archimedean polyhedral (semi-regular polyhedral), whose vertices are inscribed into a sphere.” “The tetrahedron is unrealizable; the octahedron and the cube are variants of the triangular and square prisms, respectively.” [6] 

3.3 Cuboctahedron

“Another way to form tensegrity polyhedral is proposed by Grip. All the vertices of Platonic polyhedral are truncated (but not at the center of the edges). Each original vertex is thus transformed into three or four vertices. Struts are inserted to connect each pair of new vertices that are transformed from originally adjacent vertices but are not in the same face.” [7]

[Membrane system]:

1. Tensegrity and Membrane

A classic tensegrity structure articulates compression and tension via separate, visually discrete struts and tendons. However, no rule states that the tendons must be distinct. A continuous fabric envelope, holding all the struts apart in mutual tensile separation, would fulfill the same task. This type of fabric deployment is called a “membrane”. 

The strictest definitions of tensegrity seek the minimum use of materials. A strut and tendon structure would feature only one unique tendon for each vector of tension stress. A membrane, on the other hand, features hundreds of tendons woven together in a fabric. Most of these are not completely tensed along any given vector, thus it can be argued that minimum material usage has not been achieved. However, this lack of minimum material deployment may be compensated by the simplicity of the membrane deployment. But the membrane acts as structure and facade simultaneously. 

Tensegrity structure‘s history is very young. This 3-strut prism was probably first made either by a Lithuanian artist Karl Loganson around 1920 or by the student of Richard Buckminster Fuller at the University of North Carolina in the early 1950‘s named Ted Pope. But both Karl‘s and Ted‘s contribution towards the development of the tensegrity stops here. In fact we are not even sure they actually build this basic tensegrity. The real start of tensegrity was in a basement somewhere in Pendleton, Oregon in the autumn of 1948, where a young student called Kenneth Snelson experimented with thread, wire, clay, metal from tin cans, cardboard, etc... Or maybe it started a little earlier, when Snelson attended a summer course in North Carolina at Black Mountain College and got “electrified” by the charismatic visionary designer, architect and inventor Richard Buckminster Fuller. 

Mizuki Shigematsu, Masato Tanaka, Hirohisa Noguchi published articles regarding these types of structures, calling them “tensegrity membrane structures."[8] They thought couple tensegrity with membrane via tension loads and can be one of the rational structures achieving maximum space with minimum use of materials.“ Then Shigematsu defined tensegrity membrane structures that couple tensegrity with a tensioned membrane structure. By using the present analysis method, the self-equilibrium form of tensegrity membrane structure could be found and the basic configurations of Diamond and Zigzag models were demonstrated. The application to a structure such as a “practical tent warehouse” was illustrated to show the possibilities of tensegrity membrane structure. [9] 

2. Fabric

Fabric for tensegrity structures can be composed of various materials. Polytetrafluoroethylene or PTFE, commonly known by its trademark name Teflon, is a coating applied to a fiberglass scrim that produces a high strength tension structure fabric membrane with a life expectancy of thirty plus years. PTFE may also be expanded and woven into a fabric that can be coated with a fluoropolymer to create a high strength architectural fabric. Polyvinyl chloride or PVC, properly mixed with plasticizers for flexibility and applied to a polyester scrim, makes for a high strength and popular tension structure fabric membrane. The life expectancy and cost are proportionally lower than PTFE. [10]
The membrane in tension structures are often conceptualized purely as a surface. A fabric membrane is biaxial, meaning that it has two concurrent orthogonal, principal directions. Crimp is the extent of deformation normal to the plane of the fabric that the fill and warp yarns undergo as they are woven together. [11]
Membranes are composite material. Typically the fabric in the middle and coating two sides. Fabric is secured by means of clamps. Sectionalizing is the name of the method of field joining large fabric panels utilizing clamping hardware. A fabric clamp is a device for clamping the edge of a fabric panel, usually a bar or channel shape and made of aluminum or steel. Fabric may also fasten to tensile cable by means of pockets or cuffs. A membrane plate is the metal plate attached to a membrane corner and used to secure the membrane to the frame. A catenary pocket (aka “banana pocket”) is the pocket that is placed at the perimeter of the fabric cover to secure the catenary cable. The pocket has a curve with a ratio that is defined by the fabric patterning, but is typically close to a 1:10 ratio. This means for every 10 feet of length, there will be about a foot of bend to it. Due to the curvature of the shape, the pocket is typically fabricated by sealing together two halves of the pocket together with an overlap of 1” to 2” at the outside edge of the pocket. A cable cuff is an edge treatment in which the fabric is folded over on itself to form a pocket in which a catenary cable can be installed. Weldment is an assembly of several parts joined by welds. In tensegrity structures the weldment is usually steel, for the attachment of cables and/or fabric. If may be free-floating or connected to other membranes.
Two fabrics are joined across a seam. A lap seam is created when the two pieces being joined are overlapped by the width of the seam. A butt seam is created when the two pieces being joined are butted together and joined with a strip twice the width of the seam. 

[Pros and Cons]:

1. Advantages

“1. Due to the ability to respond as a whole, it is possible to use materials in a very economical way, offering a maximum amount of strength for a given amount of building material (Ingber, 1998). In Vesna’s and Fuller´s words (2000), tensegrity demonstrates ephemeralisation, or the capability of doing more with less. Perhaps, ‘ethereal’ is more adequate than ‘ephemeral’.
2. They don’t suffer any kind of torque or torsion, and buckling is very rare due to the short length of their components in compression.
3. Tensional forces naturally transmit them-selves over the shortest distance between two points, so the members of a tensegrity structure are precisely positioned to best withstand stress.
4. The fact that these structures vibrate readily means that they are transferring loads very rapidly, so the loads cannot become local. This is very useful in terms of absorption of shocks and seismic vibrations (Smaili, 2003). Thus, they would be desirable in areas where earthquakes are a problem.
5. The spatial definition of individual tensegrity modules, which are stable by them-selves, permits an exceptional capacity to create systems by joining them together. This conception implies the option of the endless extension of the assembled piece (Muller, 1971). Further explanations will be provided in the next chapter.
6. For large tensegrity constructions, the process would be relatively easy to carry out, since the structure is self-scaffolding (Whelan, 1981)”. [12]

2. Disadvantages

“1. According to Hanaor (1997) tensegrity arrangements need to solve the problem of bar congestion. As some designs become larger (thus, the arc length of a strut decreases), the struts start running into each other.
2. The same author stated, after experimen-tal research, “relatively high deflections and low material efficiency, as compared with conventional, geometrically rigid structures” (Hanaor, 1987, pp. 45)
3. The fabrication complexity is also a barrier for developing the floating compression structures. Spherical and domical structures are complex, which can lead to problems in production. (Burkhardt, 2004)
4. The inadequate design tools have been a limitation until now. There was a lack of design and analysis techniques for these structures. Kenner (1976) proposed shell analysis as the best way, although this is a bit distant from structural reality. In spite of this evidence, Pugh (1976) estimated, incorrectly, that as the connections between struts and tendons are pinned joints, the design and calculation of these figures was relatively simple. The past ten years, Burkhardt has been working on a computer program that, seemingly, works well enough to design and calculate tensegrities.5 and recently new software, “Tensegrité 2000”, has been developed by René Motro and his group at the Laboratoire de Génie Civil in Montpellier.
5. In order to support critical loads, the pre-stress forces should be high enough, which could be difficult in larger-size constructions (Schodeck, 1993).” [13]


Basic on the study of the precedent projects. I‘m trying to seek some possibilities to combine the tensegrity structure and membrane structure together and make it to be a movable structure. For the membrane, it could be use as a structure element as same as the tension cable in the tensegrity system, also to actuate the movable structure, change the length of the compression member might be possible. Also, there might have other solution for the movable tensegrity membrane structure. And we can see a lot of potentials of this type of structure.


[1]. Gómez-Jáuregui, Valentin. Tensegrity Structures and their Application to Architecture. Servicio de Publicaciones Universidad de Cantabria, 2010, p.19. (ISBN 9788481025750) 

[2]. Gómez-Jáuregui, Valentin. Tensegrity Structures and their Application to Architecture. Servicio de Publicaci-ones Universidad de Cantabria,2010, p.26,27. (ISBN 9788481025750)

[3]. Gómez-Jáuregui, Valentin. Tensegrity Structures and their Application to Architecture. Servicio de Publicaci-ones Universidad de Cantabria,2010, p.28,29. (ISBN 9788481025750)

[4] [5] [6] [7]. Wang Bin Bing Free-standing Tension Structures, Taylor&Francis,New York,2004,p7,8(ISBN 0-415-33595-7) 

[8] [9]. Source: http://tensegrity.wikispaces. com/membrane

[10]. Source: http://tensegrity.wikispaces. com/Fabric

[11]. Membrane Structures -workshop materials, Prof. Dr.-Ing. Lars Schiemann Source:Membrane Structures - workshop materials, Prof. Dr.-Ing. Lars Schiemann

[12] [13]. Gómez-Jáuregui, Valentin. Tensegrity Structures
and their Application to Architecture. Servicio de Publicaci-ones Universidad de Cantabria,2010, p.90,91. (ISBN 9788481025750)

List of Figures


Fig.7 Wang Bin Bing: Free-standing Tension Structures,
Taylor&Francis,New York,2004(ISBN 0-415-33595-7)

Fig.12 Prof. Dr.-Ing. Lars Schiemann
Membrane Structures workshop materials

by Yang Yu 2015

Assistant: Eike Schling
in Technische Universität München