Tensegrity Structures by Ane Ferreiro Sistiaga

TENSEGRITY

STRUCTURES ARCH 487. FALL 2013 Professor Peter Land Ane Ferreiro Sistiaga

TABLE OF CONTENTS: 1. Introduction:

1.1. What are the objectives of these work? 1.2. What is tensegrity?

2. Background and History:

2.1. The origins of tensegrity. 2.2. The evolution. 2.3. Tensegrity as an universal principle.

3. Basic principles. 3.1. General CharacterĂstics. 3.2. Geometry and Stability. 3.3. Relational Structure. 3.4. Classification. 3.4.1. Diamond pattern. 3.4.2. Circuit pattern. 3.4.3. Zig Zag pattern. *How to build a simplex. 4. Applications. 4.1. Domes. 4.1.1. Gymnastic Hall. 4.1.2. Georgia dome. 5. Bibliography.

1. INTRODUCTION. 1.1. What are the main objectives of these work? The main objective of this paper is to outline the tensegrities. Throughout my study in this area I realized that you can find lots of information but or this is very specific and difficult (only speaks of a specific part of the subject) or very general (without delving into interesting aspects of the tensegrity).

- Classify the diferent types of tensegrity. - Give some exemples related to architecture that can inspire us to develop these kind of structures.

I want to create a document of an overview on the subject, delving into interesting aspects for architects. The aim is to compile the information in one text useful for people wishing to enter the tensegrities So that from here to further the issues that concern them knowing the basics of the subject. As a result the objectives of these work are: - Investigating the origins of tensegrity, who were its creators and talk about the controversy over its authorship. - Take a look at the history and evolution of tensegrity giving a timeline and point out some important authors for the people who wants to continue investigating. - Define structural characteristics and fundamental concepts. Figure 1.1.1. E.C. Tower. Kenneth Snelson.

1.2. What is Tensegrity? Is important, from the beggining, stablish a clear definition of tensegrity to understand wich structures are tensegrity. During the last decades a lot of structures, systems and natural phenomena have been classified as tensegrities when they were not. First we are going to give some definitions proposed by tensegrity experts to finish giving a complete and simply as possible definition of the term: - “Tensegrity describes a structural-relationship principle in which structural shape is guaranteed by the finitely closed, comprehensively continuous, tensional behaviors of the system and not by the discontinuous and exclusively local compressional member behaviours.” Buckminster Fuller.

- “Tensegrity describes a closed structural system composed of a set of three or more elongate compression struts within a network of tension tendons, the combined parts mutually supportive in such a way that the struts do not touch one another, but press outwardly against nodal points in the tension network to form a firm, triangulated, prestressed, tension and compression unit.” Kenneth Snelson. - “Tensegrity systems are spatial reticulate systems in a state of selfstress. All their elements have a straight middle fibre and are of equivalent size. Tensioned elements have no rigidity in compression and constitute a continuous set. Compressed elements constitute a discontinuous set. René Motro. As we see some key-words start to appear. Those concepts are important in thensegrity that why we will try to explain them later.

KEY-WORDS: - Structural-relationship.

- Closed structural system.

- Selfstress.

- Continuos.

- Compression struts.

- Tensional elements.

-Tensional.

- Network.

- Continuos set.

- Discontinuos.

- Tensional tendons.

- Compressed elements.

- Compressional.

- Nodal points.

- Discontinuos set.

Figure 1.2.1. The skylon. South Bank Exhibition in Britain 1951.

To simplify the concept we will define tensegrity as a structure that is in a state of stable self-balancing in a continuous net with components that support tension (normally cables or tendons) and components that support compression (usually bars or struts) without touching each other.

The better way to understand tensegrity is to look a model as the exemple we give in figure 1.1. The most attractive thing about these structures is how bars are hanging in the air and how forces made visible to us. In the Snelson sculpture, elements in red are compressed and elements in blue are tensioned.

COMPRESSIONAL ELEMENTS TENSIONAL ELEMENTS

Figure 1.2.2. Flat Out. Kenneth Snelson.

2. BACKGROUND AND HISTORY. 2.1. The origins of tensegrity. Tensegrity is a relative new invention (less than fifty years) that was discovered in the ends of 40’s century. It is not a commonly known type of structure, so knowledge of its mechanism and physical principles is not very widespread among architects and engineers.The invention of tensegrity has always been surrounded by great controversy about its authorship. Usually the authors are named acording to the year they published their patents; Buckmister Fuller (November 13, 1962), David Emmerich (September 28, 1964) and Kenneth Snelson (February 16, 1965). René Montro in his book “tensegrity systems” pointed that Emmerich mentioned that the first pro-tensegrity system was called “Gleichgewichtkonstruktion” and was created by Karl Iaganson. Emmerich described Ioganson structure as an unusual structure consisting of three bars and seven wires which are manipulated by an eighth wire that can deform the structure. Ioganson approach is interesting with regard to the relationship established between the form and strength as it simply illustrates how to create a self-balancing geometry. All the same, the absence of prestress, that is one of the characteristics of tensegrity systems, does not allow Ioganson’s structure to be considered the

The biggest controversy about the invention of tensegrity has been always between Fuller and Snelson. In the summer of 1948 Fuller was a visiting professor in the Black Mountain Collage (Carolina, USA). The school was a new kind of college in which the study of art was seen to be central to a liberal arts education. Many of the school’s students and faculty were influential in the arts or other fields, or went on to become influential. Kenneth Snelson was a student in these school who attended Fuller classes. He was heavily influenced by geometric Fuller approach to art. After attended these school Snelson started to develelop some three-dimensional models creating different sculptures and the first tensegrity model ever existed. The next year Snelson shown his sculpture to Fuller and he realized that was the answer to the question he had looking for many years. Despite in the beginning Fuller reconigsed Snelson has the inventor of tensegrity, then he started to call it “my tensegrity” and he was the one that give it that name, that meas “tensional-integrity”, letting people think that it was his invention.

Almost at the same time, David Emmerich was developing his “structures tendues and autotendants”, probably inspired by Ioganson’s structure. He started to study different kinds of structures as tensile prisms and more complex tensegrity systems. As a result he defined his patent which were exactly the same kind of structures that were being studied by Fuller and Snelson.

Figure 2.1.1. Scheme of “Gleichgewichtkonstruktion” . Karl Ioganson.

2.2. The evolution. As stated above, the tensegrities are structures that still need further study, especially in the field of architecture. After his invention, Snelson, Fuller and Emmerich directed their investigations differently. Snelson took a more sculptural approach, even thounght he began studying the principles of tensegrities, he avoided very deep mathematical physicaland approaches, due to his artistic background and his review difficult in relation to the application of tensegrity systems. In the other hand Fuller and Emmerich took a different approach, studying the differentpossible typologies of tensegrity. They did it using models and empiric experiments as their main tools, and in contrast to Snelson, they looked for possible applications to architecture and engineering. Fuller started to develop a family of tensegrities with vertical side faces of three, four, five and six each. He kept on looking for new designs, applications and methods of construction. He made several attempts to design geodesic tensegrity domes, although they lacked of stability due to the absence of triangulation. René Motro, probably one of the most important specialists in tensegrity at present, started to publish his studies on the

subject in 1973: Topologie desstructures discrètes. Incidence sur leur comportement mécanique. Autotendant icosaédrique. It was an internal note about the mechanical behaviour of this kind of structure. From this time forth, this laboratory and engineer became a reference in terms of tensegrity research. Some years later, in 1976, Anthony Pugh and Hugh Kenner continued this work with different lines of attack. On the one hand, Pugh wrote the “Introduction to Tensegrity”, which is interesting for the variety of models that it outlines and his strict classification and typology. On the other hand, Kenner developed the useful “Geodesic Math and How to Use It”, which shows how to calculate “to any degree of accuracy” the pertinent details of geodesic and tensegrity regular structure’s geometry (lengths and angles of the framing system), and explores their potentials. During the 1980s, some authors made an effort to develop the field opened by their predecessors. Robert Burkhardt started an in-depth investigation and maintained a correspondence with Fuller (1982) inorder to obtain more details about the geometry and mathematics of tensegrity. The final result, 20 years later, is a very complete, useful and continuously revi-

Figure 2.2.1. Fuller holding his tensegrity.

Figure 2.2.2. First Kenneth Snelson sculpture.

Figure 2.2.3. Emmerich first patent.

sed Practical Guide to Tensegrity Design. Other important investigators have been Ariel Hanaor, who defined the main bidimensional assemblies of elementary self-equilibrated cells and Nestorovic with his proposal of a metallic integrally tensioned cupola. In the following years a lot authord have also studied the physics, mathematics (from geometrical, topological and algebraical points of view) and mechanics of tensegrity structures as Connelly and Back, S. Pellegrino, A.G. Tibert, A.M. Watt, W.O. Williams, D. Williamson, R.E. Skelton, Y. Kono, Passera, M. Pedretti, etc.

“All structures, properly understood, from the solar system to the atom, are tensegrity structures. Universe is omnitensional integrity.” Buckminster Fuller.

Some years later, in 1976, Anthony Pugh and Hugh Kenner continued this work with different lines of attack. On the one hand, Pugh wrote the “Introduction to Tensegrity”, which is interesting for the variety of models that it outlines and his strict classification and typology. On the other hand, Kenner developed the useful “Geodesic Math and How to Use It”, which shows how to calculate “to any degree of accuracy” the pertinent details of geodesic and tensegrity regular structure’s geometry (lengths and angles of the framing system), and explores their potentials.

To Fuller, tensegrity is nature’s grand structural strategy. At the cosmic level, he saw that the spherical astro-islands of compression of the solar system are continuously controlled in their progressive repositioning in respect to one another by comprehensive tension of the system which Newton called ‘gravity’. At the atomic level, man’s probing within the atom disclosed the same bind of dicontinuous compression, continuous tension appa-

During the 1980s, some authors made an effort to develop the field opened by their predecessors. Robert Burkhardt started an in-depth investigation and maintained a correspondence with Fuller (1982) inorder to obtain more details about the geometry and mathematics of tensegrity. The final result, 20 years later, is a very complete, useful and continuously revised Practical Guide to Tensegrity Design. Other important investigators have been

2.3. Tensegrity as universal principle.

Ariel Hanaor, who defined the main bidimensional assemblies of elementary self-equilibrated cells and Nestorovic with his proposal of a metallic integrally tensioned cupola. In the following years a lot authord have also studied the physics, mathematics (from geometrical, topological and algebraical points of view) and mechanics of tensegrity structures as Connelly and Back, S. Pellegrino, A.G. Tibert, A.M. Watt, W.O. Williams, D. Williamson, R.E. Skelton, Y. Kono, Passera, M. Pedretti, etc.

Figure 2.3.1. Image of microspcope. Cells.

3. BASIC PRINCIPLES. 3.1. General Characteristics. Here we will make a description of the basic elements of a tensegrity structure. Trying to better describe these kind of the structures. “Tensegrity is a structural system in a state of stable self-balancing, in a continuous net, with components that support tension and components that support compression without touching each other.” If this last definition is accepted as being sufficiently comprehensive and concise to define the term, it is possible to distinguish true and false tensegrity due to their respective characteristics. - System: we can consider tensegrity as a system becouse it has components (in compresion and tension), relational structure (between the different components), total structure (associating relational structure with characteristics of components) and form (projected on to a three-dimensioned referenced system).

ty) or anchorages due to its self-stress initial state. - Components: it can be a strut, a cable, a membrane, an air volume, an assembly of elementary components, etc. - Compressed or tensioned components: because the key is that the whole component has to be compressed or tensioned depending on its class. - Continuous tension and discontinuous compression: because the compressed components must be disconnected, and the tensioned components are creating an “ocean” of continuous tension. 3.2. Geometry and Stability.

tuation of stable static self-equilibrium can be established. The ballon analogy can help us to better understand the functioning of a tensegrity system and the relationship berween geometry and stability. A ballon consists of an envelope whose shape is determined by its manufacture. A ballon can be considered a tensegrity system since it is a stable self-balancing system made up of two components: a compressed component, the air and a tensioned component, the membrane. The analogy that have been described fot a ballon and a tensegrity system can be established by associating with the membrane a system of envelope element net that could be tensioned, and by replacing the include air by internal elements susceptible to be compressed.

The stability of tensegrity systems can be satisfied only for geometry in which a si-

- Stable: because the system can reestablish its equilibrium after a disturbance. - Self-equilibrated: because it doesn’t need any other external condition, it is independent of external forces (even gravity) or

Figure 3.2.1. Indeterminated shape for a non-equilibrium membrane

Figure 3.2.2. Equilibrium geometry.

3.3. Relational Structure. All reticulate systems being created by an assembly of components, it is necessary to define this mode of asssembly. The number of nodes characterises the tensegrity systems. If this number is “n” (atending to a spacial case) the minimal value of n is n ( n=2, corresponds a linear system, n=3 to a bi dimensional system). In the basic configurations three links are sufficient to ensure he necessary condition of spatial stability for a node which will receive one (and only one) crompressed element. This last element will be placed inside a solid angle which must not be coplanar to preserve spatiality.

Figure 3.3.1. Fork connectors. Tensile structure.

Figure 3.3.2. Connectors of Giorgia Atlanta Dome. David Geiger

Figure 3.3.4. Kurilpa bridge. Connectors. Cox Rayner.

Figure 3.3.3. Connectors of Warnor tower. Kenneth Snelson.

Figure 3.3.5. Seccions des aurees. Juan S. Pérez i Parra y José L. Frías Wamra.

3.4.Classification. Anthony Pugh was the first person that did a clear classfication of tensegrities. It’s true that he almost related to polyhedral but still is very helpful to classified them.

pink and blue) and the cables defining the edge of the polyhedron. Circuit systems are able to generate geodesiv tensegrity as spheres or domes.

First he described the simplest configurations in 2D and 3D depending on the relative position of their tendons and bars, how the systems joins together, the number of layers, the composition of the compressed elements... Then he described the three basic types tat can be used to configure spherical or cylindrical tensegrity sturcture: the diamond pattern, the circuit pattern and the zig zag pattern. These classification is based on the possition of the struts.

- Zig–Zag pattern: Zig zag systems uses diamond systems as basis but some of the cables changed their position forming a Z of three non aligned tendons. It’s important to say that elimination of the cables must be coherent in order to preserve the stability of the system.

SPHERICAL SYSTEMS: - Diamond pattern: The name of these types of figures correspond to the way thery are constucted. Each strut of the system represent the longest diagonal of a rhombus formed by four other cables. In these type. Other characteristic of these type of tensegrity is that the cables are horizontal and vertical and the struts are diagonal as in the Simplex. - Circuit pattern: The components are confermed by circuits of struts. As it’s seen in the image below the figure is composed of four circuits of struts. (yellow, green,

Figure 3.4.2. Circuit pattern.

Figure 3.4.1. Diamond pattern.

Figure 3.4.3. Zig-Zag pattern.

WHICH

BUILD A SIMPLEX.

SIMPLEX.

ARE THE BASIC STRUCTURES OF

One of the most basic tensegrity structure is call Simplex. The simplex is compose for 3 bars (in red) and 9 cables Cables from the top (blue) and the bottom (green) of the structures create a triangle. Then the in between cables (pink) help with the stability of the structure. Simplex is based, SIMPLEX. like all the tensegrity structures, in geometry.

TENSEGRITY?

Bars Top cables Bottom cables In-between cables

Steps: 1. Build a regular prism with a dodecagonal base. Nominate edges from 1 to 12. 2. Build a triangle on the bottom (cables). Join 1 - 5 - 9.

3. Build a triangle on the top (cables). Join 2 Bars Top cables 6 - 10. Bottom cables In-between 4. Place the struts. (1 - 6), (5 -cables 10), (9 - 2). 5. Join the in-between cables. (1 - 2), (5 - 6), (9 - 10)

Step 1

Step 2

Figure 3.4.4. Developement of a tensegrity Simplex. Wikepedia.

Step 3

Step 2

Step 4

Step 3

Step 5

Step 4

Step

pointed out and that the author took into account for the design of some domes in section 6.3.

4. APLICATIONS. Once the basic fundaments and basic systems have been described, this chapter will deal with the task of showing the applications of this material with exemplars. First, the most important examples of works already built will be presented, both the “real” and the “false” tensegrity structures, according to the things that we have been explaining in the paper. It’s important to remember the difference between “real” and “false” tensegrity again: pure tensegrities are those where one compressed element touches only 3 or morenly tensioned elements. The diamond pattern and de zig-zag pattern are considered pure tensegrities meanwhile the circuit pattern is considered as “false” tensegrity.

connections of the struts forming a polygon different of the triangle. In the example

compression was the one shown by Kenneth Snelson in his patent of 1965. It was not based on polyhedra, but on the x-shaped towers that he first discovered; each of the arches is formed by these towers bending adequately. Obviously, it was not very successful, as it was abandoned and never used for practical purposes. Now we are going to summariza some of the advantages of tensegrity domes, for instance: use of equal-length struts and simple joints, improved rigidity, extreme resilience, high lightness, etc. The following are some of the possible applications that Burkhardt points out:

4.1. Domes.

- Superstructures for embedded substructures in order to escape terrestrial confines where this is convenient (e.g. in congested or dangerous areas, urban areas, flood plains or irregular, delicate or rugged terrains).

Most of the works and studies in tensegrity have been done in relation to spherical or polyhedral configurations. Several authors have proposed different kinds of domes following the continuous tension-discontinuous compression fundaments. That’s why all off the “pure” domes addopt geodesic configurations.

- Economic large-scale protection for storage, archaeological, agricultural, construction, electrical or electromagnetic shielding or other delicate sites. Refugee or hiking shelters. Some similar proposals, following the tensile skin domes projected by Pugh, although some of their constructionsare not pure tensegrity.

A different kind of dome using floating

Some of the domes obtained from truncated polyhedra, have the

of fig. 6.1, each apex is formed by five struts creating a pentagon of tendons. This - Frames over cities for environmental control,

energyistransformation and situation not very convenient, but food can be resolved by adding more wires between production.

them and connecting other apexes of the dome.

- Exclusion or containment of flying A different kind of dome using floating animals compression was the one shown or other objects, similar to the Snowdon by Kenneth Snelson in his patent of 1965. It was not based on polyhedra, but on the Aviary in London, by Tony Armstrong-Jox-shaped towers that he first discovered; each ofPrice the arches is formed by these towers nes (Lord Snowdon), Cedric and Frank Newby.

Figure 4.1.1. Kenneth Snelson propposal for a dome. Dome projected by Snelson

3 4

Illustration taken from Snelson (1965)

Kenneth Snelson: excerpt from an e-mail to the author, 3 Aug 2004. (See Appendix D) Kenneth Snelson: excerpt from an e-mail to the author, 23 Aug 2004. (See Appendix D)

Figure 4.1.2.. Tensinle dome by Buckmister Fuller.

4.1.1. GYMNASTIC HALL DOMEs. Seul Olympics. Bangi-dong, Songpa-gu, Seoul South Korea.

BASIC INFORMATION Project: Olympic Hall. Archiect: Kang Kum-Hee Engineer: David Geiger. Location: Bangi-dong, Seoul South Korea. Construction system: Tensegrity. DOME - I

304 ft.

DOME - II

256 ft.

PROJECT DESCRIPTION

PRODUCED BY AN EDUCATIONAL PRODUCT Figure 4.1.1.2. Components ofAUTODESK the dome.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Compresion Ring PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Tendons

Tensional Rings Struts Tensional Ring

PRODUCED BY AUTODESK EDUCATIONAL PRODUCT Figure 4.1.1.3. Distribution ofANthe loads.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

BY AN AUTODESK EDUCATIONAL PRODUCT Figure 4.1.1.1. ThePRODUCED dome working as trushes.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Compression Elements Tensegrity working as trushes

Tension Elements

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

De dome sits in a hexadecagonis composed of one exterior rign, that works in compression (this compresion ring is the reason that we can not call these dome “pure” tensegrity becouse in those ones the compresion elements “doesn’t touch

With this configuration, the dome behaves like a series of paired cantilever trusses not quite touching at the center. One of the system’s advantages is that, as the length of span increases, the weight, 2 psf, remains constant and the cost per sq ft increases very little.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Perhaps, the main in novation of these dome is that the approach that the engineer David Geiger did. Meanwhile Fuller try to triangulate all the dome in the exterior using the tensegrity system, Geiger makes the tensegrity system work as trushes, notabily simplifying it.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

each other), interior tension rings and cables and compresion post, in the middle , a small tension ring closes the structure.

The Gymnastics Hall is the largest of the five stadiums in Seoul Olympic Park which were used as the main facility for the 1988 Olympic games.The gymnastics Hall developed a structural system that had never before been built: the world’s first erected self-supporting “CABLE-DOME” fabric roof. The essential concept of the cable dome is making a continuous tension throughout the roof with tension cables and discontinuous compression posts.The ultra-lightweight cable dome system opened a new vision of fabric structures by eliminating the operational demands of air-supported structures, such as the need for mechanical systems which supply to provide possible pressure to avoid deflation of the roof by wind and snow.

1. Hang tension ring, then hang post and hoop cables.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

2. Tension first diagonal to 69 kips.

3. Tension second diagonal to 84 kips.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

4. Tension third diagonal to 65 kips.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

5.Tension fourth diagonal.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

PRODUCED BY AN AUTODESK PRODUCED EDUCATIONAL BY ANPRODUCT AUTODESK EDUCATIONAL PRODUCT PRODUCED BY AN AUTODESK EDUCATION CED BY AN AUTODESK EDUCATIONAL PRODUCT PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

One of the main advantages of these tensegrity domes is the way they are constructed. The difirente levels can be build without the need of a external structure becouse each level is self stable. With ridge cables spanning from the reinforced-concrete compression ring to the supported tension ring, the strands of the outermost tension hoop were laid in position on the ground with the bottom castings for the compression posts in position. The bottoms of the posts themselves were then bolted to the castings, and the hoop and posts were lifted and attached to the castings of the already erected ridge cables.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT PRODUCED BY AN AUTODESK EDUCATIONAL PROD Y AN AUTODESK EDUCATIONAL PRODUCT PRODUCED BY AN AUTODESK PRODUCED EDUCATIONAL BY ANPRODUCT AUTODESK EDUCATIONAL PRODUCT

CONSTRUCTION.

DETAILS. Upper Cables threaded through Upper Castings PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT Cable Saddle Plate

Rigid Cables

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Top Diagonal Cables

Top Casting

Steel Post

Top Diagonal Cables

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Lower Casting

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Top Diagonal Cables

Ring Cables

H - Beam

Cat Walk and Casting

4.1.2. GEORGIA DOME. Atlanta Olympics. Atlanta, Georgia. United States.

BASIC INFORMATION Project: Olympic Hall. Archiect: Heery International. Engineer: Matthys Levy. Location: Atlanta, Georgia, EE.UU. Construction system: Tensegrity.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

746 ft.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

607 ft.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

PROJECT DESCRIPTION

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Tensional Rings Struts

Figure 3.3.1. Distribution of the loads.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

A 2,750 foot reinforced concrete ring secures the roof to the entire perimeter of the dome. The Teflon pads on which the concrete ring is placed help to sustain movement of the roof due to extreme wind conditions.

Tendons

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

The weight of the roof is supported by short posts which are held in place by cables attached on either end. The pull of the cables on the posts creates the sequence of tightly-stretched triangles that embodies the conception of tensegrity.

Compresion Ring

Compression Elements

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

The roof weighs only 68 pounds, but it is strong enough to support a fully-loaded pickup truck (approx. 20+ tons). This is because of its construction being based on tensegrity principles which allow for a “pull and push” cable support system. The structure of the roof is therefore remarkably lightweight yet very structurally sound.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

The patented Tenstar Dome structure, the first of its kind to be built, adapts tensegrity geometry to the standard oval of stadium design.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

The “hyper tensegrity” construction of the roof incorporates reinforced fabric positioned over tensioned cables so that it only requires being secured at the edges. This allows for no distortion of views for stadium spectators. The structure is easily converted to other uses from the network of catwalks that form part of the roof structure. Despite the airy and festive atmosphere created by the tent-like roof, the impression is one of permanence and security. Minimal light is needed for daytime use due to the translucency of the Teflon-coated fiberglass fabric roof, and at night the dome glows, creating a radiant landmark visible from all parts of the city.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

The Georgia Dome, opened in 1992 as the largest cable-supported domed stadium in the world, is located in downtown Atlanta. Host of the gymnastics and basketball events for the 1996 Olympic Games.

Figure 4.1.2.1. Elements of the structure.

Tension Elements

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

DETAILS. Detail Plans of a typical Join.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

DETAILS.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Corner Union in the Top.

PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Union with the Compression Ring. PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT

Atlanta Olympics. Atlanta, Georgia. United States.

GEORGIA DOME.

Seul Olympics. Bangi-dong, Songpa-gu, Seoul South Korea.

GYMNASTIC HALL DOMEs.

5. BIBLIOGRAPHY Books

1. Tensegrity Concepts. Rene Motro.

2. Biotensegridad. Garcia Barreno.

3. Mallas tensegriticas de doble capa y manipulaciones de Rot-Umbela. Gómez Jauregui.

4. Inventions. The patented works of R. Buckmister Fuller.

5. Systemes legers pliables/despliables: cas des systemes de tensegrite. Ali el Smaili.

6. Tensegrity Structures and their Application to Architecture. Valentín Gómez Jáuregui

Web Pages

7. http://www.kennethsnelson.net/

8. http://tensegrity.wikispaces.com

9. http://www.columbia.edu/cu/gsapp/BT/DOMES/GEORGIA/georgia.html

10. http://www.columbia.edu/cu/gsapp/BT/DOMES/SEOUL/s-struc.html

11. http://www.tensinet.com/database/viewProject/3755.html