ABSTRACT
Tensegrity is a relatively new principle (50 years old) based on the use of isolated components in compression inside a net of continuous tension members, 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 and in a self-equilibrated state.
Tensegrity structures are 3-D trusses where some members are always in tension while others are in compression. The Tensegrity concept offers a high level of geometrical and structural efficiency and results in modular and lightweight structures. However, the concept of Tensegrity is still not a part of the main stream structural design wing due to various reasons.
The main aim of this work is to prove if it is possible to find some applications for such an atypical kind of structure, in spite of its particular flexibility and relatively high deflections. For that it is essential to understand the structural principles of floating compression or tensegrity, and to define the fundamental forces acting on it.
CONTENTS
| CHAPTER | TITLE | |
| 1 | INTRODUCTION | |
| 2 | CONCEPT OF TENSEGRITY STRUCTURES | |
| 3 | GENERAL CHARACTERISTICS | |
| 3.1 | SYSTEM | |
| 3.2 | STABLE SELF EQUILIBRATED STATE | |
| 3.3 | COMPONENTS | |
| 3.4 | COMPRESSED OR TENSIONED COMPONENTS | |
| 3.5 | CONTINUOUS TENSION AND DISCONTINUOUS COMPRESSION | |
| 3.6 | BOUNDARY SURFACE | |
| 4 | BENEFITS OF TENSEGRITY | |
| 4.1 | TENSION STABILIZES THE STRUCTURE | |
| 4.2 | EFFICIENCY | |
| 4.3 | DEPLOYABLE | |
| 4.4 | EASILY TUNABLE | |
| 4.5 | RELIABLY MODELLED | |
| 4.6 | PERFORM MULTIPLE FUNCTIONS | |
| 4.7 | MOTIVATION FROM BIOLOGY | |
| 5 | TENSEGRITY SIMPLEX | |
| 6 | MECHANICAL BEHAVIOUR | |
| 6.1 | BENDING | |
| 6.2 | COMPRESSION | |
| 6.3 | CHANGE OF SHAPE WITH SMALL CONTROL ENERGY | |
| 7 | CLASSES | |
| 7.1 | 3 BAR SVD CLASS 1 | |
| 7.2 | 3 BAR SD CLASS 1 | |
| 7.3 | 3 BAR SS CLASS 2 | |
| 8 | STRUCTURAL APPLICATIONS | |
| 8.1 | GENERAL | |
| 8.2 | TOWERS | |
| 8.2.1 | LIGHTENING CONDUCTORS | |
| 8.2.1 | COMMUNICATIONS | |
| 8.2.3 | WIND PARKS | |
| 8.2.4 | AESTHETIC ELEMENTS | |
| 8.3 | ROOF STRUCTURES | |
| 8.4 | OUTER SPACE STRUCTURES | |
| 8.5 | SMART STRUCTURES | |
| 8.6 | BRIDGES | |
| 10 | CASE STUDY | |
| 11 | CONCLUSION | |
| | REFERENCES | |
LIST OF FIGURES
| FIG NO. | FIGURE TITLE | |
| 1.1 | | |
| 4.1 | MOLECULAR STRUCTURE OF SPIDER SILK | |
| 5.1 | DIFFERENT TYPES OF TENSEGRITY SIMPLEXES | |
| 5.2 | TYPE 1: TENSION/COMPRESSION TRIANGLE | |
| 5.3 | TYPE 2: TENSION ONLY TRIANGLE | |
| 5.4 | 3 STRUT PRISM SHOWING TYPE 1 AND TYPE 2 | |
| 6.1 | GEDANKEN STIFFNESS PROFILE | |
| 7.1 | DIFFERENT CLASSES OF MULTI STAGE 3 BAR TENSEGRITIES | |
| 8.1 | | |
| 8.2 | | |
| 8.3 | | |
| 9.1 | THE SKYLON | |
1. INTRODUCTION
Tensegrity structures are 3-D trusses where members are assigned specific functions. Some members remain in tension while others are always in compression. Usually for compressive members, solid sections or bars are used; and string or cable type elements can be used as the tensile members.
Most bar–string configurations will not be in equilibrium. Hence, if constructed they will collapse to a different shape. Only bar–string configurations which are pre-stressed and in a stable equilibrium will be called Tensegrity structures. If well designed, the application of forces to a Tensegrity structure will deform it into a slightly different shape in a way that supports the applied forces.
The word “Tensegrity” is a contraction of the phrase “tensional integrity”. It can be traced back to Buckminster Fuller who first coined the phrase in his 1962 patent application. The construction of the first true Tensegrity structure is however attributed to the artist Kenneth Snelson who created his X- piece sculpture in 1948.
In his patent, Snelson describes Tensegrity as a “….class of structures possessing, what may be termed discontinuous compression, continuous tension characteristics.” This discontinuity was also recognized by Buckminster Fuller in his patent description, when he stated that “….the structure will have the aspect of continuous tension throughout and the compression will be subjugated so that the compression elements will become small islands in a sea of tension.”
Another important aspect is the stability. A Tensegrity system is established when a set of discontinuous compression components interact with a set of continuous tensile components to define a stable volume in space.”
A more mechanical description is given by Hanaor who describes Tensegrity structures as “internally pre-stressed, free standing pin-jointed networks, in which the cables or tendons are tensioned against a system of bars or struts.” This description introduces the fact that the system is pre-stressed and pin-jointed. This implies that there are only axial forces present in the system and there is no torque.
The general definition of a tensegrity structure is stated as:
“The geometry of a material system is in a stable equilibrium if all particles in the material system return to this geometry, as time goes to infinity, starting from any initial position arbitrarily close to this geometry”.
The bars are rigid bodies and the strings are one-dimensional elastic bodies. Hence, a material system is in equilibrium if the nodal points of the bars in the system are in equilibrium.
To summarise, the above descriptions cover most of the aspects of the Tensegrity concept which are listed as follows:
1. Pin-jointed bar frameworks: Tensegrity structures belong to the structural group of pin-jointed three-dimensional trusses.
2. Pure compressive/tensile members: Tensegrity structures contain only pure compression and tension members. And tension elements used are cables which can sustain only tension.
3. Localisation of compression: In classic Tensegrity structures the compressive elements are discontinuous. They seem to be floating in a continuous network of tension elements.
4. Pre-stressed structures: A state of pre-stress or self-stress is required for the stability of the structure since it stabilizes internal mechanisms.
Fig 1.1 Needle Tower
2. CONCEPT OF TENSEGRITY STRUCTURES
Tensegrity structures are structures based on the combination of a few simple but subtle and deep design patterns:
1. Loading members only in pure compression or pure tension, meaning the structure will only fail if the cables yield or the rods buckle.
- Preload or tensional pre-stress, which allows cables to be rigid in tension.
- Mechanical stability, which allows the members to remain in tension/compression as stress on the structure increases.
Because of these patterns, no structural member experiences a bending moment. This can produce exceptionally rigid structures for their mass and for the cross section of the components.
A conceptual building block of tensegrity is seen in the 1951 Skylon tower which follows the typical tensegrity structure concept. But there are variations such as the Needle Tower which involve more than three cables meeting at the end of a rod. These cables define the position of the end of the rod which is considered as a well-defined point in space and the other additional cables are simply attached to this well-defined point.
Eleanor Hartley points out visual transparency as an important aesthetic quality of these structures. Korkmaz put forward that the concept of tensegrity is suitable for adaptive architecture due to its lightweight characteristics.
3. GENERAL CHARACTERISTICS
3.1 System:
In relation to the theory of systems, tensegrity structures have components (two
kinds, in compression and in tension), relational structures (between the different
components), total structure (associating relational structure with characteristics of
components) and form (projected on to a three-dimensioned referenced system).
3.2 Stable Self-Equilibrated State:
It is said to be stable because the system can re-establish its equilibrium after a disturbance and it is self-equilibrated because it doesn’t need any other external condition. It is independent of external forces (even gravity) or anchorages due to its self-stress initial state.
3.3 Components:
The components used for a tensegrity structure can be struts, cables, membranes, an air volume, an assembly of elementary components, etc.
3.4 Compressed or Tensioned Components:
Instead of using compression and tensile components, the key is that the whole component has to be compressed or tensioned depending on the class of tensegrity structure.
3.5 Continuous Tension and Discontinuous Compression:
The compressed components must be disconnected, and the tensioned components should be connected to create an “ocean” of continuous tension with discontinuous compression floating in it.
3.6 Boundary Surface of Tensegrity Structures
This is a crucial point since it differentiates between the two type of structures: the conventional structures, where compression is the basis of the load support, and the tensegrities, where this role is played by the tension. In order to avoid controversial systems, such as the torus, with different “insides” and “outsides”, tensegrity system is generalised as that in which all its compressed components lie inside the system and the points at the ends of these compressed components do not belong to the boundary (or envelope). Thus, in a tensegrity system, the boundary surface has tension lines only.
4. BENEFITS OF TENSEGRITY
Tensegrity as a structural system offers many advantages over conventional structural systems. The benefits offered are elaborated as follows:
4.1 Tension Stabilizes the Structure
A compressive member loses stiffness as it is loaded, whereas a tensile member gains stiffness as it is loaded. Stiffness is lost in two ways in a compressive member: In the absence of any bending moments in the axially loaded members, the forces act exactly through the mass centre. The material spreads which increases the diameter of the central cross section; whereas tensile members reduce its cross-section under load. In the presence of bending moments since the line of application of force is away from the centre of mass, the bar becomes softer due to the bending motion. For most materials, the tensile strength of a longitudinal member is larger than its buckling strength (sand, masonry, and unreinforced concrete are exceptions to this rule). Hence, a large stiffness-to-mass ratio can be achieved by increasing the use of tensile members.
4.2 Tensegrity Structures are Efficient
Efficiency of a structure increases with the minimal mass design for a given set of stiffness properties. Tensegrity structures use longitudinal members arranged in a very unusual pattern to achieve maximum strength with small mass.
4.3 Tensegrity Structures are Deployable
Since the compressive members of Tensegrity structures are either disjoint or connected with ball joints, large displacement, deployability and stowage in a compact volume is possible in Tensegrity structures. This feature offers operational and portability advantages. A portable bridge, or a power transmission tower made as a Tensegrity structure could be manufactured in the factory, stowed on a truck or helicopter in a small volume, transported to the construction site, and deployed using only winches for erection through cable tension. Deployable structures can save transport costs by reducing the mass required, or by eliminating the requirement of humans for assembly.
4.4 Tensegrity Structures are Easily Tunable
The same deployment technique can also make small adjustments for fine tuning of the loaded structures, or adjustment of a damaged structure. Structures that are designed to allow tuning will be an important feature of next generation mechanical structures, including Civil Engineering structures.
4.5 Tensegrity Structures Can Be More Reliably Modelled
All members of a Tensegrity structure are axially loaded. Perhaps the most promising scientific feature of Tensegrity structures is that while the structure as a whole bends with external static loads, none of the individual members of the Tensegrity structure experience bending moments. Generally, members that experience deformation in two or three dimensions are much harder to model than members that experience deformation in only one dimension. Hence, increased use of tensile members is expected to yield more efficient structures.
4.6 Tensegrity Structures can Perform Multiple Fuctions
A given tensile or compressive member of a Tensegrity structure can serve multiple functions. It can simultaneously be a load-carrying member of the structure, a sensor (measuring tension or length), an actuator (such as nickel-titanium wire), a thermal insulator, or an electrical conductor. Therefore by proper choice of materials and geometry the electrical, thermal, and mechanical energy in a material or structure can be controlled.
4.7 Tensegrity Structures are Motivated from Biology
The representation of a spider fibre show that the hard β- pleated sheets are discontinuous and the tension members (amino acid matrix) form a continuous network. Hence, the nano-structure of the spider fibre is a Tensegrity structure.
Nature’s endorsement of Tensegrity structures in the form of spider fibre is the strongest natural fibre. Similarly if Tensegrity is nature’s preferred building architecture, then the same incredible efficiency possessed by natural systems can be transferred to manmade systems too.
5. TENSEGRITY SIMPLEX
The basic free standing unit within a Tensegrity structure is referred to as a Tensegrity simplex. In a Tensegrity simplex, tension lines (strings, tendons or cables) connect individually to the ends of two struts. The lines are made taut in such a manner that they bind the struts, pressing on them as a continuous tension network. The forces introduced by the tightening are permanently stored in the structure, a state known as pre-stressing. In Tensegrity structures, complete triangulation in the tension network is highly important for it decides whether the structure is firm or flaccid.
It is possible to construct any number of varied Tensegrity configurations, from simple to highly complex. Yet, only those forms whose tension network is composed entirely of triangles are truly stable.
Only the cross with its two struts and four tension members and the three-way prism have total triangulation. The square, the pentagon and the hexagon do not. They can be stabilized with additional lines but the supplemental lines necessarily will be selective in directions that will distort the form.
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| Fig 5.1 Different types of tensegrity simplexes |
If the network has squares, pentagons etc., the structure will be deformable and flaccid. This is especially true of Tensegrity spheres, none of which have triangulated tension networks.
The triangles in a Tensegrity network are formed in two different ways, designated as type 1 and type 2 triangles. Triangles of type 1 are formed with two struts and two tendons. The two tension lines run from the end of one strut to the two ends of a second strut. A Tensegrity triangle can also be formed with three tension lines attached to three different struts.
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Fig 5.4 A three-strut prism showing type 1, red and type 2 green triangles |
6. MECHANICAL BEHAVIOUR OF TENSEGRITY STRUCTURES
Stiffness of a Tensegrity structure is influenced by many parameters. However, the pretension applied to the Tensegrity is considered to be the most critical. Pretension is a method of increasing the load-bearing capacity of a structure through the use of strings that are stretched to a desired tension. This allows the structure to support greater loads without as much deflection as compared to a structure without any pretension.
For a Tensegrity structure, the role of pretension is monumental. Increasing the pretension allows for greater bending loads to be carried by the structure. In other words, the slackening of a string will occur for a larger external load if pretension is employed.
6.1 Tensegrity Structures in Bending
The bending stiffness profiles of Tensegrity structures have stiffness level Stens when all strings are in tension, Sslack1 when one string is slack, and then other levels as other strings go slack or as strong forces push the structure into radically different shapes.
More complicated Tensegrity geometries will possibly yield many stiffness levels. This inference arises from the possibility that multiple strings can become slack depending on the directions and magnitudes of the loading environment.
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| Fig 6.1 Gedanken stiffness profile |
The specific profile is heavily influenced by the geometry of the Tensegrity structure as well as of the stiffness of the strings, Kstring, and bars, Kbar.
The ratio called rigidity ratio, K
is a parameter.
6.2 Tensegrity Structures in Compression
For compressive loads, the relationships between stiffness, pretension, and applied load do not always obey the simple principles which apply to bending. In fact, qualitatively different stiffness profiles are observed in compression loading studies of different Tensegrity structures, which cannot be generalized.
6.3 Change of Shape with Small Control Energy
Tensegrity structures, even very complicated ones, can be actuated by placing pulleys at the nodes (ends of bars) and running the end of each string through a pulley. Thus, it can be thought of as two pulleys being associated with each string and the rotation of the pulleys can be used to shorten or loosen the string. Thus, in Tensegrity structures, shape changes (moving nodes changes the shape) can be achieved with little change in the potential energy of the system.
7. CLASSES OF TENSEGRITY
A Tensegrity unit comprising of three bars will be called a 3-bar Tensegrity. At a stage, 3 bar Tensegrity is constructed by using three bars in each stage which are twisted either in clockwise or in counter-clockwise direction. The top strings connecting the top of each bar support the next stage in which the bars are twisted in a direction opposite to the bars in the previous stage. In this way any number of stages can be constructed which will have an alternating clockwise and counter-clockwise rotation of the bars in each successive stage. This is the type of structure in Snelson’s Needle Tower
The strings that support the next stage are known as the “saddle strings (S)”. The strings that connect the top of bars of one stage to the top of bars of the adjacent stages or the bottom of bars of one stage to the bottom of bars of the adjacent stages are known as the “diagonal strings (D)”, whereas the strings that connect the top of the bars of one stage to the bottom of the bars of the same stage are known as the “vertical strings (V)”. Even with only three bars in one stage, which represents the simplest form of a three-dimensional Tensegrity unit, various types of Tensegrities can be constructed depending on how these bars have been held in space to form a beam that satisfies the definition of Tensegrity.
7.1 3-Bar SVD Class 1 Tensegrity
A typical two-stage 3-bar SVD Tensegrity is that in which the bars of the bottom stage are twisted in the counter-clockwise direction. These tensegrities are constructed by using all three types of strings, saddle strings(S), vertical strings (V), and the diagonal strings (D), hence the name SVD Tensegrity.
7.2 3-Bar SD Class 1 Tensegrity
These types of Tensegrities are constructed by eliminating the vertical strings to obtain a stable equilibrium with the minimal number of strings. Thus, a SD-type Tensegrity has only saddle (S) and the diagonal strings (D).
7.3 3-Bar SS Class 2 Tensegrity
In a Class 2 Tensegrity, a maximum of 2 bars are connected with a ball joint
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Fig 7.1 Different classes of multi-stage 3 bar Tensegrities |
Based on the geometrical configurations certain assumptions for the Tensegrity structures were made:
1. The projection of the top and the bottom triangles (vertices) on the horizontal plane makes a regular hexagon.
2. The projection of bars on the horizontal plane makes an angle α with the sides of the base triangle. The angle α is taken to be positive (+) if the projection of the bar lies inside the base triangle otherwise α is considered as negative (–).
3. All the bars are assumed to have the same declination angle δ.
4. All bars are of equal length, L.
8. STRUCTURAL APPLICATIONS OF TENSEGRITY
8.1 General
Kenneth Snelson, made an observation concerning the practical application of Tensegrity structures in relation to the load handling capacity of Tensegrity structures, and thus their limited practical relevance. There have been few actual implementations of the Tensegrity principle in engineering applications, which is mainly ascribed to the lack of knowledge concerning actual construction methods rather than any deficiencies in the Tensegrity concept. Tensegrity structures are certainly relevant in various areas of engineering as emphasised by the benefits mentioned in the preceding sections.
8.2 Proposals for Towers
Tensegrity towers can have the following applications:
8.2.1 Lightning conductors:
As it is not required to have these elements in a completely static situation and they tolerate certain small movements, they could serve perfectly for this application.
8.2.2 Communications:
In situations where the margin of displacements is not very strict, Tensegrity towers can be employed to support antennas, receptors, radio transmitters, mobile telephone transmitters, etc.
8.2.3 Wind parks:
The lightness of these Tensegrity towers could minimize the visual impact of these energetic installations.
8.2.4 Aesthetic elements:
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| Fig 8.1 |
Tensegrity structures can enhance the visual landscape of an area. The Tower of Rostock
8.3 Roof Structures
An important example of Tensegrity being employed in roof structures is the stadia at La Plata (Argentina
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| Fig 8.2 |
8.4 Outer Space Structures
Since the beginning of the “Tensegrity era”, one of the most recurring applications found for the floating-compression has been its speculated use in moon-colonies. In 1961, Buckminster Fuller revealed his new inventions: potential prototypes of satellite and moon-structures conceived as tensional integrity which are foldable, extremely light, omni-triangulated, pre-stressed, etc. i.e., “spherical nets in which local islands of compression act only as local sprit-stiffeners”. It is not very surprising to arrive at these conclusions, since one of the particular characteristics of Tensegrity structures is that they don’t depend on gravity, so they are stable in any position.
Recently, a very well defined project has been carried out from another approach. In this case, tensile integrity structures were not the starting point, but a resource to achieve another objective: the establishment of a self-sustainable society in the moon. This project sought the improvement of new structural concepts that experience completely different external loads (1/6 of Earth’s gravity, meteorite impacts, moonquakes, etc.), different risks (like pressure containment, radiation, etc) and different environmental conditions (atmosphere, light, wind, dehydration, etc).
8.5 Smart Structures
Most Civil Engineering structures are static. A more challenging functionality for Civil Engineering structures is active adaptation to changing requirements, such as load modifications, temperature variations, support settlements and possible damage occurrence.
The concept of active structures involves structures that include both static and active structural elements. Adaptive structures are defined as structures whose performance is controlled by a system composed of sensors, actuators and a computer that provides the ability to learn and improve response to changing environments.
Since Tensegrities can be equipped with active control systems, they have the potential to adapt to their environments.
8.6 Bridges
Advancements in the design of double grid systems has resulted in an expected interest in application of Tensegrity to bridge construction. A recent achievement in this regard is the Kurilpa Bridge in Brisbane , Australia
The Kurilpa Bridge
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| Fig 8.3 Kurilpa Bridge, Brisbane, Australia |
9. CASE STUDY
The Skylon
In 1951, just three years after the official discovery of tensegrity, the Festival of Britain's South Bank Exhibition took place in London
The long tower is held in place at one end by only three cables. At the bottom end, exactly three cables are needed to fully determine the position of the bottom end of the spire so long as the spire is loaded in compression. Two cables would be unstable, like a person on a slack-rope; one cable is just the limit case of two cables when the two cables are anchored in the same place.
A simple three-rod tensegrity structure is build on these cables: locally, each end of each rod looks like the bottom of the Skylon tower. As long as the angle between any two cables is smaller than 180° as seen looking along the rod, the position of the rod is well defined. What may not be immediately obvious is that because this is true for all six rod ends, the structure as a whole is stable.
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| Fig 9.1 The Skylon |
10. CONCLUSION
The analysis of tensegrity structures reveals the concept that lightweight is a real measure of structural effectiveness. A new architecture with new qualities is predicted which is revolutionary, elastic, light, expandable, active, mobile and dynamic which are the most important features of tensegrity structures. Tensegrity could be one of the structural systems of the future.
Recent developments show that tensegrity could be applied to Architecture and Engineering. Studies show the feasibility of tensegrity as a lightweight structure to cover large spans, bridge shorter distances or support light infrastructures. Of course, a much more detailed structural investigation would be necessary, but at least the pre-supposed idea of tensegrity as an inapplicable system should been disproved.
Investigations on foldable tensegrity structures are under process. As a result of which they could be used for disaster relief in areas devastated by earthquakes, hurricanes, floods and so on, by installing deployable systems in the form of temporal dwellings, bridges, field hospitals, etc. But further research must be carried out to develop these and many other such potential applications.
REFERENCES
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3. Buckhardt R. W. (2008), “A Practical Guide to Tensegrity Design”, http://www.angelfire.com/ma4/bob_wb/tenseg.pdf.
4. Fuller B. (1962), “Tensile-integrity structures”, U.S. Patent, 3, 063, 521.
5. Jauregui V. G. (2004), “Tensegrity Structures and their Application to Architecture”, Master’s thesis, School of Architecture , Queen’s University, Belfast , Ireland
6. Paleti Srinivas, Krishna Chaitanya Sambana, Rajesh Kumar Datti, (2010) “Finite Element Analysis using ANSYS 11.0, PHI Learning Private Limited, New Delhi.
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