Architectural Dissertation/Tensegrity Structure/Himanshi Nigam

TENSEGRITY STRUCTURE IN ARCHITECTURE

Dissertation, AR 415

January 2022

Submitted by:

HIMANSHI NIGAM 0842AR181017

Under the Guidance of:

Ar. Ridhima Madan Seth

SDPS COLLEGE OF ARCHITECTURE SDPS GROUP OF INSTITUTIONS

© RAJIV GANDHI PRODYOGIKI VISWAVIDYALAYA BHOPAL – 462003 (M.P.), INDIA ALL RIGHTS RESERVED

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DECLARATION The Dissertation report in the subject UP-611 entitled “Tensegrity Structure in Architecture” is being submitted in partial fulfillment of the requirement for the award of Degree of Bachelor of Architecture by the undersigned for evaluation.

The matter embodied in this project (drawings and report submitted for evaluation) is a record of my own work. If, in future, it is found that the above statement is false, then I have no objection in withdrawal of Bachelor of Architecture degree awarded to me by the Institute.

HIMANSHI NIGAM 0842AR181017 B. ARCH, SEM VII SDPS COLLEGE OF ARCHITECTURE Date: Place:

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RECOMMENDATION Based on the above declaration of the student, the undersigned recommends that the work submitted by the candidate may be considered for the final end term viva of the subject Dissertation (AR 415)

AR. RIDHIMA MADAN SETH DISSERTATION GUIDE Date: Place:

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CERTIFICATE

This is to certify that the above declaration of HIMANSHI NIGAM is true to the best of my knowledge and that she has worked for one semester for preparing this Dissertation Report.

GUIDED BY: AR. RIDHIMA MADAN SETH

ACCEPTED AND CO-ORDINATED BY: AR. ASTHA JAISWAL

Date: Place:

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ACKNOWLEDGEMENT A dissertation cannot be completed without the help of many people who contribute directly or indirectly through there constructive criticism in the evolution and preparation of this work. It would not be fair on my part, if I don't say a word of thanks to all those whose sincere advice made this period a real educative, enlightening, pleasurable and memorable one. First and foremost, I would like to express my deepest appreciation to my dissertation supervisor Prof. Ar. Ridhima Madan Seth, Department of Architecture, SDPS College, Indore for her gracious efforts and keen pursuits, this has remained as a valuable asset for the successful instrument of my dissertation Report. Her dynamism and diligent enthusiasm have been highly instrumental in keeping my spirit high. Her flawless and forthright suggestions blended with an innate intelligent application have crowned my task a success. My thanks are due to Ar. Ruchira Jain, Head of the Department of Architecture of this institute for providing excellent facilities and aid in preparation of the report. Finally, I would like to express my gratitude to my family, for their unconditional support and prayers at all time and constant encouragement during the entire course of my dissertation work. I would also like to offer my sincere thanks to all faculty, teaching and non-teaching staff of Department of Architecture for their assistance.

Thank you

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ABSTRACT The concept of tensegrity is relatively new not more than 50-year-old. The basic principle of tensegrity is continuous tension and discontinuous compression, thereby creating an internal prestress which stabilize the entire structure.

The main aim of this work is to find possible application of tensegrity structure. With this establishment, extensive research has been done, trying to make origins controversy clear and the progress of its evolution.

Some reference shows the development of tensegrity with regrades to nature. And to study the classification of different type of tensegrity configuration.

Himanshi Nigam 0842AR181017 B.Arch., Sem VII SDPS College of Architecture, Indore

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List of Figures Figure 1 ................................................................................................................................. 13 Figure 2 ................................................................................................................................. 14 Figure 3 ................................................................................................................................. 15 Figure 4 ................................................................................................................................. 15 Figure 5 ................................................................................................................................. 19 Figure 6 ................................................................................................................................. 21 Figure 7 ................................................................................................................................. 22 Figure 8 ................................................................................................................................. 23 Figure 9 ................................................................................................................................. 25 Figure 10 ............................................................................................................................... 25 Figure 11 ............................................................................................................................... 26 Figure 12 ............................................................................................................................... 26 Figure 13 ............................................................................................................................... 27 Figure 14 ............................................................................................................................... 28 Figure 15 ............................................................................................................................... 28 Figure 16 ............................................................................................................................... 28 Figure 17 ............................................................................................................................... 29 Figure 18 ............................................................................................................................... 29 Figure 19 ............................................................................................................................... 29 Figure 20 ............................................................................................................................... 30 Figure 21 ............................................................................................................................... 30 Figure 22 ............................................................................................................................... 31 Figure 23 ............................................................................................................................... 32 Figure 24 ............................................................................................................................... 32 Figure 25 ............................................................................................................................... 33 Figure 26 ............................................................................................................................... 33 Figure 27 ............................................................................................................................... 33 Figure 28 ............................................................................................................................... 33 Figure 29 ............................................................................................................................... 34 Figure 30 ............................................................................................................................... 34 Figure 31 ............................................................................................................................... 34 Figure 32 ............................................................................................................................... 35 Figure 33 ............................................................................................................................... 35 Figure 34 ............................................................................................................................... 35 Figure 35 ............................................................................................................................... 36 Figure 36 ............................................................................................................................... 36 7

Figure 37 ............................................................................................................................... 36 Figure 38 ............................................................................................................................... 37 Figure 39 ............................................................................................................................... 37 Figure 40 ............................................................................................................................... 37 Figure 41 ............................................................................................................................... 38 Figure 42 ............................................................................................................................... 39 Figure 43 ............................................................................................................................... 39 Figure 45 ............................................................................................................................... 40 Figure 44 ............................................................................................................................... 40

List of Tables Table 1 .................................................................................................................................. 12

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CONTENTS List of Figures…………………………………………………………………………………….7 List of Tables…………………………………………………….………………...……………. 8 CHAPTER 1

SYNOPSIS .................................................................................................. 11

INTRODUCTION: .............................................................................................................. 11 NEED: ............................................................................................................................... 11 AIM: ................................................................................................................................... 11 OBJECTIVE: ..................................................................................................................... 11 SCOPE: ............................................................................................................................. 11 LIMITATION: ..................................................................................................................... 11 METHODOLOGY: ............................................................................................................. 11 CHAPTER 2

INTRODUCTION: ........................................................................................ 13

1.1 WHAT IS TENSEGIRTY STRUCTURE? .................................................................... 13 CHAPTER 3

HISTORY ..................................................................................................... 14

2.1 THE INCEPTION OF TENSEGRITY ........................................................................... 14 CHAPTER 4

EVOLUTION ................................................................................................ 17

CHAPTER 5

TENSEGRITY AS A UNVIVERSAL PRINCIPLE ......................................... 19

5.1 TENSEGRITY IN MACROCOSM AND MICROCOSM ............................................... 19 5.2 TENSEGRITY IN BIOLOGY ........................................................................................ 19 5.3 TENSEGRITY IN INORGANIC CHEMISTRY ............................................................. 20 5.4 TENSEGRITY IN ANATOMY ...................................................................................... 20 CHAPTER 6

DEFINITIONS AND BASIC PRINCIPLES ................................................... 22

6.1 DEFINITIONS .............................................................................................................. 22 6.2 GENERAL CHARACTERISTICS ................................................................................ 24 6.3 MAIN CONCEPTS ...................................................................................................... 25 6.4 GEOMETRY AND STABILITY .................................................................................... 25 CHAPTER 7

CLASSIFICATION OF TENSEGRITY STRUCTURE .................................. 27 9

7.1 SPHERICAL SYSTEMS .............................................................................................. 27 7.1.1 Rhombic configuration .............................................................................................. 27 7.1.2 Circuit configuration .................................................................................................. 28 7.1.3 Zigzag configuration ................................................................................................. 28 7.2 STAR SYSTEMS ......................................................................................................... 29 7.3 CYLINDRICAL SYSTEMS .......................................................................................... 29 7.4 IRREGULAR SYSTEMS ............................................................................................. 30 CHAPTER 8

APPLICATION OF TENSEGRITY STRUCTURE ........................................ 31

8.1 DOMES ....................................................................................................................... 31 8.2 SOME OTHER APPLICATION OF TENSEGRITY SYSTEM ...................................... 32 8.3 SOME OTHER APPLICATION OF TENSEGRITY STRUCUTRE OTHER THAN ARCHITECTURE .............................................................................................................. 32 8.4 EXAMPLE OF TENSEGRITY DOMES IN DETAIL ..................................................... 33 8.4.1 SEOUL OLYMPIC GYMNASTICS HALL (1988) .................................................. 33 8.4.2 ATLANTA OLYMPIC GEORGIA DOME ............................................................... 37 CHAPTER 9

CONCLUSIONS .......................................................................................... 41

References and Bibliography ................................................................................................ 42 BOOKS ................................................................................................................................. 42

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CHAPTER 1

SYNOPSIS

TENSEGIRTY STRUCTURE IN ARCHITECTURE: INTRODUCTION: Tensegrity is a structural design principle that applies to a structure which can be stabilized entirely by internal pre-stress. This pre-stress is created by a discontinuous set of compression elements being opposed and balanced by a continuous tensile force. An early example of tensegrity structures is Snelson’s X-piece.

NEED: Tensegrity structures are strong and resilient, with multiple paths for force transmission. There is no shear and no bending moments, and prestress can be adjusted to suit different circumstances. Tensegrities are transparent both in structure and design. It’s possible for a significant section of a tensegrity to be damaged and yet still be able to maintain structural integrity. The whole purpose of selecting a tensegrity structure for a purpose is to deflect and disperse loads rather than compound them.

AIM: To study about fabrication and analysis of tensegrity structure OBJECTIVE: •

To study about origin of tensegrity

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To study about history and evolution of tensegrity

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To study about structural characterizes and fundamental concept of tensegrity

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To study about classification of different type of tensegrity

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To study about how Tensegrity is used in architecture

SCOPE: The scope of this research is to study about origin and evolution of tensegrity structure and its application in architecture and to study its fundamental concept LIMITATION: This dissertation is limited to study of tensegrity used in domes and its use in architecture. Study only include the structural formation of tensegrity structure.

METHODOLOGY:

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INTRODUCTION

HISTORY OF TENSEGRITY STRUCUTRE

EVOLUTION OF TENSEGRITY

PRINCPLES OF TENSEGRITY

CLASSIFICATION OF TENSEGRITY

APPLICATION OF TENSEGRITY IN ARCHITERTURE

ANALYSIS OF CASE STUDIES

CONCLUSION Table 1 12

CHAPTER 2

INTRODUCTION

1.1 WHAT IS TENSEGIRTY STRUCTURE? Firstly, it is important to understand the term tensegrity structure. So, the definition of tensegrity which is proposed by expert to give complete and finish understanding of the term: - “Tensegrity describes a structural relationship principle in which structural shape is guaranteed by the finitely closed comprehensively continuous, tensional behaviours of the system and not by the discontinuous and exclusively local compressional member behaviours” – BUCKMINSTER FULLER To interpret the idea of tensegrity we can describe it as structure that is in the state of steady self- balancing uninterrupted network with components that support tension (usually cables) and components that support compression (normally bars or struts) without connecting to each other.

To understand tensegrity in a better way we can look at example given in figure 1.1. The most appealing thing about these structures is how bars are suspended in the air and how forces made as obvious it. In the Snelson sculpture, components in red are compressed and components in blue are tensioned.

Figure 1

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CHAPTER 3

HISTORY

2.1 THE INCEPTION OF TENSEGRITY Tensegrity is relative new concept (less than fifty year) this concept was recognized in the end of 40’s century. It is not the prominent type of the structure, so knowledge about its mechanism and physical principles is not widely known by architects and engineers. The concept of tensegrity has always been surrounded by arguments about its authorships.

Usually the authors are named according to the year they published their patents; Buckminster Fuller (November 13, 1962), David Emmerich (September 28,1964), and Kenneth Snelson (February 16, 1965).

Rene Motro in his book “tensegrity Structural Systems for the Future” pointed that Emmerich mentioned that the first pro-tensegrity was called GLECHGEWICHT KONSTRUKTION (Balance of Construction) and it was created by Karl Loganson show in figure 1.2. Emmerich express Loganson structure as abnormal structure comprehending of three bars and seven wires that can contort the structure. Loganson viewpoint is fascinating with regard to the relationship established between the form and strength as it simply pictorial how to create a self-balancing geometry. In spite of everything, unavailability of prestress, which is one of the characteristics of tensegrity structure, does not allow Loganson’s structure to be considered.

Figure 2

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The biggest argument about the concept of tensegrity has been always between Fuller and Snelson. In the summer of 1948 Fuller was a visiting professor in the black mountain college (Carolina, USA). The college was a new kind of school in which study of art was seen to be central to be liberal arts education. Kenneth Snelson was a student in these school who attended Fuller classes. He was deeply influenced by geometric Fuller approach to art. After attending these school Snelson started to generate some three- dimensional models designing different sculptures and the first tensegrity model ever existed which was consisted of two XSHAPED plywood modules, one floating miraculously above the other, held in place only by tensed nylon wires, anchored to a plywood base as shown in figure 1.3. This configuration is a tensegrity system where the compression from the rigid bodies is stabilised by the tension in the strings.

Figure 4

Figure 3

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 which was how can a structure be stabilized.

Despite in the beginning Fuller recognised Snelson has the inventor of tensegrity, then he started calling it “my tensegrity” and he was the one that give it that name, that means, “tensional-integrity”, letting people think that it was his invention.

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Almost at the same time, David Emmerich was developing his “structure tendues (tense) and autotendants (self-tending)”, most likely influenced by Karl Loganson’s structure. He began to study different types of structure as tensile prisms and more complicated tensegrity systems. As a result, he defined his patent which were exactly the same kind of structure that were being studied by Fuller and Snelson.

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CHAPTER 4

EVOLUTION

As previously mentioned, tensegrity structure still required more advanced study especially in the field of architecture. After the concept of tensegrity was invented, Snelson, Fuller and Emmerich directed their investigation differently.

Snelson took more sculptural approach, thought he was the one who began to study about principles of tensegrities, he avoided very deep mathematical and physical approaches, it was due to his background of artist and he also analysed that the application of tensegrity system is complicated. This process provided him the facility to develop very different configurations, asymmetrical and non-conventional, applying his intuitive knowledge and achieving impressive sculptures. On the other hand, Fuller and Emmerich took a distinct approach, by studying different achievable classification of tensegrity system. They did it by making models and practical experiments as their main tools and in contradiction to Snelson, they look for feasible applications in architecture and engineering.

In 1961 Fuller started to develop a series of tensegrity structure with vertical faces of three, four, five and six each. He also discovered the “six-islanded-strut icosahedron Tensegrity” (expanded octahedron). He been searching for new designs, method and application of tensegrities for construction. He made a variety of experiments to design geodesic tensegrity domes which is a hemispherical thin -shell structure (lattice -shell) based on geodesic polyhedron, although they lacked of stability due to the absence of triangulation.

Rene Motro, most likely one of the primary specialists in tensegrity at present, started to publish his studies on the subject in 1973: topolgie deestructures discretes (topology of discrete structures). Incidence sur leur comportement mecanique (impact on their mechanical behaviour). Autotendent icosaedrique (self-tending icosahedron). It was an internal note about the mechanical behaviour of this kind of structure. From this time forth, Civil Engineering of the University of Montpelier (France) laboratory and engineer became a reference in terms of tensegrity research.

Couple year later, in 1976, Anthony Pugh and Hugh Kenner continued this work with different approach. On the one hand, Pugh wrote the “Introduction to Tensegrity” which is fascinating for the various of models that it outlines and his strict classification and typology.

On the other hand, Kenner developed the useful “geodesic math (curve representing in some sense the shortest oath between two points in a surface) and how to use it” which shows how to calculate “to any degree of accuracy”. The suitable details of geometry (length and angles of the framing systems), and explores their potentials.

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During the 1980s, some authors tried to develop the field opened for them previously. Robert Burkhardt started complete analysis and maintain similarity with Fuller (1982) in order to acquire more details about the geometry and mathematics of tensegrity. The final output, 20 years later, is very complete, useful, and continuously revised Practical Guide to Design Tensegrity. Other important researches have been Ariel Hanaor, who explain the main bidimensional assemblies of elementary self-equilibrated cell and Nestorovic with his presentation of metallic integrally tensioned cupola (a small dome on the top of a roof).

In the following year, Connelly and Back have aimed to find a proper three- dimensional generalization for tensegrities. Using the mathematical tools of group theory and representation theory and the capabilities of computers, they have drawn up a complete catalogue of tensegrities with detailed prescribed types of stability and symmetry, including some that have never been seen before.

A lot of other authors such as, S. Pellegrino, A.G. Tibert, A.M. Watt, W.O. Willams, D. Willamson, R.E. Skelton, Y. Kono, Passera, M. Pedretti, etc. have also studied the physics, mathematics (from geometrical, topological and algebraical point of view) and mechanics of tensegrity structure.

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CHAPTER 5

TENSEGRITY AS A UNVIVERSAL PRINCIPLE

All structures, properly understood, from the solar system to the atom, are tensegrity structure. Universe is omnitensional integrity – BUCKMINSTER FULLER The origins of tensegrity were associated to sculpture; eventually, it was connected to architecture and mathematics; and at present, mainly civil and mechanical engineers are trying to research its properties and applications.

5.1 TENSEGRITY IN MACROCOSM AND MICROCOSM In order to understand tensegrity subject other than material, it is important to understand some concept, Stephen Kurtz (1968) mentioned that Snelson notice all ways that can connect tensegrity to universe: in astronomy (a planet to the sun), in atomic physics (an electron to the nucleus), and in mechanics (a cable to a rod).

To Fuller, tensegrity is structural strategy of nature, according to fuller there is no limit ratio in tension, so we could have very great lengths and no section at all; which is the game that the universe is playing: gravitation. At the cosmic level he saw, the earth and the moon are invisibly cohered, this is the same manner in which the solar system coheres. That is, compression of solar system is continuously controlled in their ongoing relocation in respect to one another by absolute tension of the system, which is called gravity by Newton. On another scale, he was assured that the atomic attraction (peculiarly the invisible interaction between atoms, nuclei and electrons) is another type of tensegrity, where compression and tension are always separated, and always coexist.

5.2 TENSEGRITY IN BIOLOGY In addition to the last proposal, several suggestions were made by different specialist from different field. The one of the main contributions was by Donald E. Ingber, professor of pathology at Harvard medical school, in the early 80s. it occurred to him that the view of cell is like tensegrity structure.

Figure 5

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Ingber describe in, “The tensegrity model”, “that the structure of the cell's cytoskeleton can be changed by altering the balance of physical forces transmitted across the cell surface”.

Based on several experimental work, some new discoveries have proved that the proposition is valid and mathematical formulations of the model predict many aspects of cell behaviour (Ingber, 2003a). Ingber discovered that, not only cells but also an incredibly large variety of natural systems are created following the tensegrity model: carbon atoms, water molecules, proteins, viruses, tissues, and other living creatures.

5.3 TENSEGRITY IN INORGANIC CHEMISTRY Based on some new finding, interesting even inorganic substance can show floating compression. Author Tsu et al (2003), has introduce a new model of tensegrity for an amorphous silicone (a-Si:H) which has tensile and compressive agents that act to globally redistribute the effect of locally created defects. Which can lead to volume changes that appear to be experimentally confirms by recent measurements.

5.4 TENSEGRITY IN ANATOMY It is very common to find the term “tensegrity” applied to biomechanics and especially, to anatomy. some sources (Heller, 2002; Wikipedia, 2004; Meyers, cited by Gordon, 2004) make use of the term to explain the relationship between muscles, tendons and bones in animals and humans. They claim that the skeleton is not just a frame of support to which the muscles, ligaments and tendons attach, but a set of compression components suspended within a continuous tension network.

The first reference to tensegrity in this subject was proposed by Stephen M. Levin in the early 1980s, when he wrote “Continuous Tension, Discontinuous Compression. A Model for Biomechanical Support of the Body”. He focused his reflection in the system of the human spine, and indeed the remainder of the body.

Finally, it has been lately presented that the central nervous system also functions as a tensegrity. According to Wilken (2001), the sensory neurons are always sensing information (continuously pulling) while the motor neurons are only occasionally involved in some motor action (discontinuously pushing).

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Figure 6

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CHAPTER 6

DEFINITIONS AND BASIC PRINCIPLES

For several year, some authors have been trying to find definite definition of tensegrity, which is clear and acknowledged by the whole scientific community.

6.1 DEFINITIONS In order to exhibit the development of the analysis of these systems, different definitions will be given in chronological order.

The first interpretation was given by the author of the patents, describing their discovery. In the article called tensegrity, Buckminster Fuller (1961) describe the very important principles and main concepts that govern the tensegrity system, he has explained these kind of structure as “a plurality of discontinuous compression columns arranged in groups of three nonconjunctive columns connected by tension elements forming tension triangles” (Fuller, 1962, p.1). To explain this, he wrote in synergetics: “Tensegrity describes a structural relationship principle in which structural shape is guaranteed by the finitely closed, comprehensively continuous, tensional behaviours of the system and not by the discontinuous and exclusively local compressional member behaviours” (1975b, 700.011)

Figure 7

The other “father” of tensegrity, David G. Emmerich, declared in his patent that his invention could be further described in a non-limitative manner with reference to several examples,

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shown by accompanying drawings. In this way, he avoided the difficult task of giving a strict description.

Perhaps Kenneth Snelson is clearer in his definition. In his patent, he describes: “The present invention relates to structural framework and more particularly, to a novel and improved structure of elongate members which are separately placed either in tension or in compression to form a lattice, the compression members being separated from each other and the tension members being interconnected to form a continuous tension network.” (1965, p.1) Some year later, Anthony Pugh gave the following definition of tensegrity, which was accepted by specialists, “A tensegrity system is established when a set of discontinuous compressive components interacts with a set of continuous tensile components to define a stable volume in space” (1976, p.3).

Figure 8

It was not until the 90s that Daniel L. Schodesk (1993) explain tensegrity as rigid structure made of discontinuous rods in compression and continuous cords in tension in which each component has one degree of member redundancy.

Bin-Bing Wang, Li-Yan-Yun (1998,2003) went ahead with pervious definition, identifying other important characteristics: “Tensegrity systems are free-standing pin-jointed cable networks in which a connected system of cables is stressed against a disconnected system of struts and extensively, any free-standing pin-jointed cable networks composed of building units that satisfy aforesaid definition.” (pp. 93) There are further and more complex definitions depending on the perspective of the authors.

Kanchanasaratool and Williamson (2002) state that a tensegrity system is a stable connection of axially-loaded members, being a Class k tensegrity structure if at most “k” compressive 23

members are connected to any node. E.g., a traditional tensegrity structure is a class 1 structure because only one compression member makes a node.

Ariel Hanaor explain tensegrity structures as “internally prestressed, free-standing pin-jointed networks, in which the cables or tendons are tensioned against a system of bars or struts”.

While Miura and Pellegrino (cited in Tibert, 2002) describe tensegrity as: “A tensegrity structure is any structure realised from cables and struts, to which a state of prestress is imposed that imparts tension to all cables” later added, “as well as imparting tension to all cables, the state of prestress serves the purpose of stabilising the structure.

Finally, Rene Motro (2003) tried to distinction between two concepts, he first established definition based on patent and then the extended definition.

“Patent based definition: 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. Each node receives one and only one compressed element.” (p.18) “Extended definition: Tensegrity system is a system in a stable self-equilibrated state comprising a discontinuous set of compressed components inside a continuum of tensioned components.” (p.19) 6.2 GENERAL CHARACTERISTICS Here we will explain the essential element of tensegrity structure. Trying to characterize this type of structure.

“Tensegrity is a structural system in a state of stable self- balancing, in a continuous net, with components that supports 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: In relation to the theory of systems, it has components (two kinds, in compression and in 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).

Stable self-equilibrated state: Stable because the system can re-establish its equilibrium after a disturbance, and self-equilibrated because it doesn’t need any other external condition,

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it is independent of external forces (even gravity) or anchorages due to its self-stress initial state. It is stable even in orbit.

Components: In contrast to the term “element”, it can be a strut, a cable, a membrane, an air volume, an assembly of elementary components, etc.

Compressed or tensioned components: Instead of compression and tensile 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.

Figure 10

Figure 9

6.3 MAIN CONCEPTS Until the last century, the technique of construction and the philosophy of building have been very simple: everything was held in place by weight, so the continuities of stress were basically compressive. Tensegrity structures are based on a completely different approach.

Instead of the “weight and support” strategy, they are made as a “system of equilibrated omnidirectional stresses” (Kenner, 1976). Furthermore, they do not have to be supported as they are self-equilibrated and pre-stressed, so they are not depending on gravity factors for their own equilibrium; the tension created by the attraction of the Earth is replaced by the multidirectional tension of their members.

6.4 GEOMETRY AND STABILITY The stability of tensegrity can only be shown by geometry which can established static selfequilibrium. the analogy of balloon will make as understand tensegrity system and its relationship with geometry and stability.

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A balloon contains of envelope whose shape is fixed by its manufacture. A balloon can be related to tensegrity system as it is in the stable self- balancing system, which has two components, the air as compression component and the membrane as tensional component.

Figure 12

Figure 11

The relation between balloon and tensegrity system can be established by associating the membrane component of the envelope element as in tension and by replacing the include air by internal element capable to be compressed.

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CHAPTER 7 CLASSIFICATION OF TENSEGRITY STRUCTURE It is expected that the first classification of tensegrity was given by Fuller and his term, but has only given general division based on pre-stressed and geodesic tensegrities.

Anthony Pugh (1976) was the first one to give classification of tensegrity structure. Though his classification was based on polyhedral, still it was very useful.

First, he characterizes on the bases of simplest figures in both 2D and 3D bases on the relative position of their tendons and bars, how the structure connects together, the number of layers, the composition of the compressed membrane. Then he characterizes three basic types of tensegrity structure which can be used on the bases of its configuration: the diamond pattern, the circuit pattern, and the zig-zag pattern. These classifications were bases on the position of the struts.

7.1 SPHERICAL SYSTEMS These systems are similar to a sphere, e.g. all cables can be plot on a sphere without making any contact between each other and all the struts which are inside this cable network are making a spherical cell.

7.1.1 Rhombic configuration This type of configuration is name based on the way it is constructed. Each struts of the structure act as a longest diagonal of a rhombus formed by four other cables. Other classification of these type of structure is that cables are horizontal or vertical and the struts are diagonal between the vertices of the two different levels. One of the examples for rhombic configuration can be T-Prism

Figure 13

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7.1.2 Circuit configuration In circuit configuration the compressed elements are followed by circuits of structs, as give in figure 6.1.2.1, which consist of four circuit of struts and the cables representing the edge of the polyhedron as given in figure 6.1.2.2. The one use of circuit configuration can be in generating geodesic tensegrity domes. Some example of circuit configuration can be cuboctahedron, icosidodecahedron, snub cube, snub icosahedron, etc.

Figure 14

Figure 15

7.1.3 Zigzag configuration The basic structure of zig-zag configuration is derived from rhombic configuration, it can be archive by changing the position of cables which forms Z-shape of three non-aligned tendons.

This can be archive by removing two tendons of the opposite sides of a non-planar rhombus.

By doing so, the number of tendons will be reducing and the change in the formation will be in a wat that three non-aligned tendons joining both struts to form a z- shape

Figure 16

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7.2 STAR SYSTEMS Star system are also spherical cells, but they are obtained from previous class. For example, if we have basic rhombic configuration, if vertical strut is placed in the centre forming main axis of symmetry and connects to the rest of the cables by means of tendons, a star system is created.

Figure 17

7.3 CYLINDRICAL SYSTEMS Cylindrical system is another variation of rhombic configuration, it can be derived by adding other layers of struts to the initial layer. Figure 6.3.1 shows initial branch of bars and tendons of a four-strut rhombic cell. If the second line is added, as shown in figure 6.3.2, and if it eventually closed all around itself again, a cylindrical mast will be created.

Figure 18

Figure 19 29

7.4 IRREGULAR SYSTEMS Irregular system is not governed by any rule which are defined in any other classification.

Most of Kenneth Snelson’s sculptures comes under irregular system.

Figure 21

Figure 20

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CHAPTER 8

APPLICATION OF TENSEGRITY STRUCTURE

As we have understood basic concept and basic classification of tensegrity system, now we will try to understand the application of this system with the help of some examples.

The examples will be presented on the bases of both real and false tensegrity. Firstly, it is necessary to recall the difference between real and false tensegrity. So, in pure tensegrity one compressed member touches only 3 or more tensioned members. The rhombic configuration and the zig-zag configuration comes under real or pure tensegrity whereas, the circuit configuration is considered to be false tensegrity.

8.1 DOMES The major work and studies on tensegrity system are done so the bases of spherical and polyhedral configuration. Most of the authors have applied the concept of tensegrity “the continuous tension-discontinuous compression” to different kind of domes from a sphere or spherical polyhedral configuration.

The first one to apply tensegrity in domes was Buckminster Fuller in 1953. Which was also first where geodesic tensegrity domes every constructed but, it lacked in stability due to the absence of triangulation.

Figure 22

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In Kenneth Snelson patent of 1965, he has shown different kind of domes which uses floating compression. These domes were not based on polyhedral or spherical configuration, but on the bases of x-shape tower which he first discovered; each of the arches is formed by this tower bending adequately. This kind of domes were not very successful, and was abandoned and this concept was never used for practical purpose.

Figure 23

Robert W. Burkhardt research is important to mention as he started develop “A Technology for Designing Tensegrity Domes and Spheres” (1999-2004), in which he considers doublelayer domes, where an outer and inner layer of cables are inter-connected by bars, as well as, additional wires in order to obtain the crucial triangulation which contributes to the stability of the structure.

8.2 SOME OTHER APPLICATION OF TENSEGRITY SYSTEM The concept of tensegrity can be applied to roof structure, arches, tent-like structure, but there are not many examples of these structure, as it is new concept the researchers are still trying to study about how to use tensegrity grid which can provide loading bending capacity and can also provide structural stability.

8.3 SOME OTHER APPLICATION OF TENSEGRITY STRUCUTRE OTHER THAN ARCHITECTURE Some of the other application of tensegrity structure beside architecture are, chairs, tables, lambs, ornaments, puzzles, toys, leisure, submarines and sculptures.

Figure 24

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Figure 27

Figure 26

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8.4 EXAMPLE OF TENSEGRITY DOMES IN DETAIL •

Seoul Olympic Gymnastics hall dome

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Atlanta Olympic Georgia dome

8.4.1 SEOUL OLYMPIC GYMNASTICS HALL (1988) Basic Information Project: Olympic hall Architect: Kang Kum-Hee Engineer: David Geiger Location: Bangi-Dong, Seoul South Korea

Figure 28

The gymnastics hall is largest out four stadiums in Seoul Olympic park which were main stadium for the 1988. Olympic games. The gymnastics hall was the world's first erected supporting "cable dome fabric roof. The main concept of making cable dome is continuous tension throughout the roof with tension cables and discontinuous compression posts. The ultra-lightweight cable domes system has given new way to fabric structures by removing the demands of air -Supporting structures, such as mechanical system. Which provide possible pressure to avoid deflection of the roof by wind and show.

The layout of cable dome is radical layout, the benefit of using this layout is it, simplify the flow of force which helps in the domes statically determinant, it has low curves and it is also feasible which helps in lower wind uplift and there will be less drifting of snow, hence, low snow and wind load and this layout use minimal surface area which reduce fabric costs. A cable dome consists of vertical struts, ridge cable, diagonal cable and hoop cables.

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Figure 29

Figure 30

Carbon steel struts and tension ring Cast steel nodes 0.6-inch steel cable, made up of bundles of 7 wires prestressed tendons Reinforced concrete compression ring

Figure 31

PLAN Height: 29.4 m Span: 120 m Membrane covered area: 11310 m2 Building area: 14016.8 m2 The ridge and diagonal cable separate the roof into sixteen equal segments. These segments have equal hoop spacing, equal load distribution and corresponding vertical geometry, the corresponding members of cable domes of different diameters carry the same loads as one moves from the centre of the dome to outward direction.

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Figure 33

Figure 32

Figure 34

CONSTRUCTION Design period – October 1983-November 1984 Construction period – August 1984-May 1986 The way tensegrity domes are constructed, is main advantage of cable domes. The level can be built differently without any need of external structure as each level is self-stable.

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With ridge cables spanning from the reinforced concrete compression ring to the support tension ring, the strands of the outermost tension hoop were laid in position on the ground with castings for the compression posts in position. The bottom of the post themselves were then bolted to the castings and the hoop and hosts were lifted and attached to the casting of the already erected ridge cables.

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Figure 37

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8.4.2 ATLANTA OLYMPIC GEORGIA DOME Basic Information Project: Olympic hall Architect: Heery International Engineer: Matthys levy Location: Atlanta Georgia, United states Figure 38

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The Georgia dome is the largest cable-supported stadium dome which was built in 1992 in downtown of Atlanta. In 1996 Olympics games event of gymnastics and basketball was hosted in this stadium.

The patented ten-star dome structure, whose roof weight only 68 pounds, but it has the enough strength to support a fully loaded pickup truck (approximately 20 + tons). The construction was based on tensegrity principles which allows for a “pull and push” cable support system. Hence, the roof structure is lightweight, yet it is structurally strong.

The short posts support the weight of the roof, which are hold in place by cables attached on either end. The pull of the cables on the posts creates the series of tightly-stretched triangles that gives the concept of tensegrity.

The entire perimeter of the dome supports a 2750-foot reinforced concrete ring of the roof.

The concrete ring helps in sustaining the movement of roof from the extreme wind condition with the help of Teflon pads.

Figure 41

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 allow for no distortion of view for stadium spectators.Due to translucent Teflon-coated fibreglass roof, minimum light is needed during daytime and during night the dome glows, creating a radiant landmark which is visible from all parts of the city.

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Figure 43

Figure 42 39

Figure 45

Seoul Olympic Gymnastics hall dome

Figure 44

Atlanta Olympic Georgia dome

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CHAPTER 9

CONCLUSIONS

From the beginning of the research work, we have come across various example of tensegrity and other structure with reference to nature. So, we can conclude that floating compression is applied to every single atom present on our universe. While studying about tensegrity we not only studied the relation between tensegrity and nature, but we also understand the use of tensegrity in history of architecture. From the above study we can also say that tensegrity structure is light-weighted structure but it has enough strength do to self-stability. And from the above study we can understood that principles of tensegrity are currently applied to spherical and polyhedron configuration but researcher are still researching on tensegrity grid and its stability.

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References and Bibliography https://issuu.com/aneferreiro/docs/tensegritystructures_aneferreirosis https://issuu.com/irjet/docs/irjet-v4i275 http://kennethsnelson.net/ https://en.wikipedia.org/wiki/Tensegrity http://www.scholarpedia.org/article/Tensegrity https://civilsguide.com/tensegrity-structure/ https://en.wikipedia.org/wiki/Cupola https://en.wikipedia.org/wiki/Geodesic https://en.wikipedia.org/wiki/Geodesic_dome http://www.engineeringmechanics.cz/pdf/21_5_355.pdf https://issuu.com/clinhvu/docs/15._tensegrity_report_2_

BOOKS Tensegrity: Structural-Systems-for-the-Future - René Motro Tensegrity Structures and their Application to Architecture - Valentin Gomez Jauregui

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