# Design and Construction of a Tensegrity Tower. A Visual and Statistical Case Study of a Tensegrity System

## Project Report, 2017

Excerpt

Part I - Research
Tensegrity structures
1.1 Definition
1.2 Use of tensegrity systems
1.3 Open vs. closed tensegrity systems
1.4 Tensegrity tower
1.5 Simplex module
1.6 Importance of Eurocode
1.6.1 Basis of structural design (EN 1990)
1.6.2 Actions on structures (EN 1991)
1.6.3 Design of concrete structures (EN 1992)
1.6.4 Design of steel structures (EN 1993)
1.6.5 Design of composite steel and concrete structures (EN 1994)
1.6.6 Design of timber structures (EN 1995)
1.6.7 Design of masonry structures (EN 1996)
1.6.8 Geotechnical design (EN 1997)
1.6.9 Design of structures for earthquake resistance (EN 1998)
1.6.10 Design of aluminium structures (EN 1999)

Part II - Construction and Dimensioning C2
Calculation
2.1 Basis of calculation
2.1.1 Terms
2.2 Static methods
2.2.1 Analytical solution
2.3 Kinematic methods
2.3.1 Analytical solution
2.3.2 Definition of the overlap ho
2.3.4 Determination of the additional twisting angle
2.5 Tensegrity modell
2.5.1 Prototyping
2.5.2 Final modell
2.5.3 Modell photos

Part III - Programming and Simulation S7
Visual Study and Conclusion
3.1 Calculation with python
3.2 Visual study
3.3 Grasshopper
3.4 Conclusion
4.1 Source directory

## Part I

### Tensegrity structures

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#### 1.1 Definition

The term tensegrity is a portmanteau of “tensional integrity” and it was coined by the architect and inventor Richard Buckminster Fuller. Searching on short, sufficient definitions I came across a definition by Valentin Gomez-Jauregui:

»Tensegrity is a structural principle based on the use of isolated components in compression inside a net of continuous tension, in such a way that the compressed members (usually rods or struts) do not touch each other and the prestressed tensioned members (usually cables or tendons) delineate the system spatially.«

A lot of originally definitions of tensegrity emphasize that the pressure rods do not touch each other.

#### 1.2 Use of tensegrity systems

Until now, tensegrity structures receive less importance in civil engineering, but they are more popular with the visual arts. Tensegrities are of interest in structural design studies because of their lightweight property, aesthetic and modern look. Usually, the structures are built in such a way that struts are connected, which might not be the original definition for tensegrity.

#### 1.3 Open vs. closed tensegrity systems

Open tensegrity systems must, in order to be stable, provide forces to the foundation or to secondary constructions that are beyond the scope of the forces resulting from their own weight and the external loads. Open systems have the advantage that the pressure elements don’t have to be used as diagonals, as in closed systems. As a result, shorter pressure sections are possible with open systems, which can be executed with a smaller cross section.

A closed tensegrity system is a self-sufficient array of struts and tendons, arranged in such a way that the struts and tendons enforce an ongoing structural integrity in the overall assemblage. These are termed as “real” tensegrity systems. Closed systems are, regardless of their storage, inherently stable.

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Figure 1.1: Examples for an open tensegrity system (left) and a closed tensegrity systems (right)

#### 1.4 Tensegrity tower

The American artist and pioneer of the tensegrity idea Kenneth Snelson, in contrast to Richard Buckminster Fuller, has dealt more with the artistic design than with the constructional utility of tensegrity structures. An example is his 30 m high Needle-Tower (Figure 1.2) which is neither walkable nor resilient. It can be classified as a pure art object.

In 1965, Snelson was granted the patent for a number of topologies developed by him under the title “Continuous tension, discontinuous compression structures”. It also contains the topology of the “Needle Tower” by which Snelson became known worldwide as an artist. For the first time in a large scale such a tower was built in 1968 in Washington D.C on the premises of the “Hirshhorn Museum and Sculpture Garden”. The tower is made of aluminum rods and stainless steel ropes and can be lifted by only three persons despite its considerable dimensions (18.3 x 6.2 x 5.4 m).

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Figure 1.2: Needle-Tower

#### 1.5 Simplex module

In this project I will examine a two-way column which consists of two simplex modules. One simplex module is composed of three struts and nine tendons (Figure 1.3).

It is important, as in all tensegrity structures, to esta- blish the optimum lengths for the tension members in this simple structure so it will be firm and tightly pre- stressed. This can only be done by successive adjust- ments, by trial and error. If the length of one line is changed the tension on all lines are effected.

#### 1.6 Importance of Eurocode

»For the EU, the overriding policy objective linked to the Eurocodes is the creation of an Internal Figure 1.3: Simplex module Market with the free circulation of products and services while guaranteeing a high level of safety in construction works. Eurocodes will enhance competitiveness of European civil engineering firms, contrac- tors, designers and producers of structural products also in a global context. Indeed, there is a high potential for them being a recognized international reference beyond Europe. Being the result of cross-border cooperation between scientists, experts and national standardization bo- dies, they can be assumed to correspond to the best and latest state of knowledge, to be univer- sally applicable and to be simply superior to internationally competing standards.«

This is why it's necessary to confront all Eurocodes (1-10) for my tensegrity project. With the use of Eurocodes I can calculate a working construction. Nevertheless it’s obligatory to check the Na- tional Annex because it may contain provisions which complement the Eurocode without inconsis- tency.

##### 1.6.1 Basis of structural design (EN 1990)

The Eurocode 1990 can be used as a guidance document for design of structures outside the scope of the Eurocodes, so there is the possibility to assess other actions and their combinations.

At first I define the design working life category 1 for my tensegrity tower depending on its planned useful life (Figure 1.4). As a closed tensegrity system my tensegrity tower should be lifted by only two persons, that’s why it will be a temporary structure.

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Figure 1.4: Indicative design working life

##### 1.6.2 Actions on structures (EN 1991)

In this case the calculation of snow load isn’t necessary. The tensegrity tower is a sculpture without a roof. But the weight of ice loads plays an important role for the tensegrity system. Furthermore there are special cases in regard to snow load. Ice loads are generally to be considered with regard to the increased dead weight as well as with regard to their effects on the winds. As a vertical surface load, the maximum ice load can be set at 0.9 kN/m2 in Germany. National Annex contains information on ice loads, ice thicknesses, ice densities and ice distributions as well as load case combinations and combination factors for wind and ice effects on towers. The application of Annex C is recommended.

The Eurocode does not give guidance on specialist aspects of snow loading, for example: Effect of wind and ice loading on sag and tension. In cold places there is a ice coating formed on the ten- don and also wind pressure nets horizontally on the tendon. Consequently, the ice coating on the tendon increases the total diameter of the tendon and also the weight of the tendon increases. The total weight of the tendon e.g., both the tendon weight and the weight of the ice acts vertically downwards whereas the wind force acts horizontally on the conductor. Therefore, the vector sum of horizontal and vertical forces acting on the conductor gives the total force shown in Figure 1.5.

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Figure 1.5: Effect of wind and ice loading on sag and tension

Total weight wt of conductor per unit length is

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Wind pressure

The wind impacts are as a rule described in EN 1991-1-4.

Also the national annex may provide information on the extension of EN 1991-1-4 for towers and masts. The application of the additional rules in Annex B is recommended. Nevertheless it is more important to take a closer look into the German Codes DIN 4131 and DIN 1055-4.

The starting point for the determination of the wind velocity is the map of fundamental basic wind velocity. It is based on a 10-minute mean velocity.

Basic wind velocity:[illustration not visible in this excerpt]

where [illustration not visible in this excerpt]

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Figure 1.6: Basic wind velocity in Germany

The wind loads should be treated as linear distributed loads on all cable and tube sections and be calculated using the German Code DIN 4131 Anhang A and the draft of the DIN 1055-4 from March 2001. The Codes also regulate by law that wind loads are also to act on cable and tube sec- tion covered with ice. That is why it will be necessary to use increased sections, so the wind velocity can be reduced.

The dead weight is usually determined according to EN 1991-1-1.

In addition to that the dead weight of guy ropes must, as a rule, be determined in accordance with EN 1993-1-11.

As a rule, the required pre-stresses must be set so that the load-bearing structure achieves the required geometrical shape and stress distribution after applying all permanent effects. The stiffness of my tensegrity tower depends heavily on the preloading. Low preloading would lead to large deflections due to wind and earlier cable drop-out, and possibly to a reduction of bearing capacity of the system. On the other hand, high preloading can also reduce the bearing capacity, e.g. highly compressed tubes might buckle earlier.

Temperature changes

It is of vital importance for the planning of a tensegrity structure to chose the right materials. Temperature changes could have negative effects on the stiffness of the tensegrity structure. In addition to this aspect there should be materials which heat constantly (Figure 1.7). Nevertheless, in the reality where can’t be a perfect temperature profile in an outstanding sculpture because of variously solar radiation and shadows.

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Figure 1.7: Temperature changes

##### 1.6.3 Design of concrete structures (EN 1992)

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Figure 1.8: Tensegrity System with foundations

##### 1.6.4 Design of steel structures (EN 1993)

EN 1993-1-1 contains rules for the design, calculation and dimensioning of steel structures with sheet thicknesses t ≥ 3 mm. In addition, application rules for building construction are specified.

Section 5 relates to the calculation of the load bearing capacity of bar support structures, and section 6 contains detailed rules for the design of cross-sections and components in the limit of load-bearing capacity. For the tensegrity sculpture it is possible to take steel structure with a smaller sheet thickness.

##### 1.6.5 Design of composite steel and concrete structures (EN 1994)

This Eurocode isn’t useful for the tensegrity tower because this project can’t deal with composite steel.

##### 1.6.6 Design of timber structures (EN 1995)

EN 1995 addresses the requirements for load-bearing capacity, usability, durability and fire resis- tance of wooden structures. Other requirements, such as heat and noise protection, are not cover- ed. In regard to the tensegrity tower the mechanical properties of timber are moisture depended. A change of moisture content from 12% to 20 % leads to significant reduction (Figure 1.9).

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Figure 1.9: Wood moisture

##### 1.6.7 Design of masonry structures (EN 1996)

This Eurocode isn’t useful for the tensegrity tower because this project can’t deal with masonry structures.

##### 1.6.8 Geotechnical design (EN 1997)

The Eurocode 1997 has useful hints for tensegrity structures with foundations. In the planning of supporting structures, the temporal and spatial effects of unusual temperature changes must be taken into account. In order to prevent the formation of ice lenses in the ground behind the supporting structure, special precautions such as, for example, the selection of suitable filling material, drainage or insulation must be taken.

##### 1.6.9 Design of structures for earthquake resistance (EN 1998)

The stiffness of the foundations shall be adequate for transmitting the actions received from the superstructure to the ground as uniformly as possible. With the exception of bridges, only one foundation type should in general be used for the same structure, unless the latter consists of dynamically independent units.

##### 1.6.10 Design of aluminium structures (EN 1999)

The Eurocode EN 1999 shows several characteristic attributes of aluminium structures. In the selection of material for the rods, it could be helpful to take a closer look in to this table (Figure 1.10).

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Figure 1.10: Table with characteristic attributes of aluminium structures

## Part II - Construction and Dimensioning C2

### Calculation

Excerpt out of 38 pages

Details

Title
Design and Construction of a Tensegrity Tower. A Visual and Statistical Case Study of a Tensegrity System
College
Hochschule Ostwestfalen-Lippe - University of Applied Sciences
1,7
Author
Year
2017
Pages
38
Catalog Number
V374508
ISBN (eBook)
9783668518643
ISBN (Book)
9783668518650
File size
2489 KB
Language
English
Tags
design, construction, tensegrity, tower, visual, statistical, case, study, system
Quote paper
Angelina Aziz (Author), 2017, Design and Construction of a Tensegrity Tower. A Visual and Statistical Case Study of a Tensegrity System, Munich, GRIN Verlag, https://www.grin.com/document/374508