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---
title: "Tensairity Structures"
author: "Tensairity Structures"
tags: ["library"]
type: "essay"
---
{% raw %}
Tensairity Structures
Abrir barra lateral
ChatGPT
4o
Tensairity is a trademarked term[1] for a light weight structural concept that uses low pressure air to stabilize compression elements against buckling.[2] It employs an ancient foundational splinting structure using inflated airbeams and attached stiffeners or cables that gains mechanical advantages for low mass.[3][4] The structure modality has been particularly developed by Mauro Pedretti.[5][6]
Comparison of (a) a normal steel framework girder and (b) a tensairity girder. When the load applies from the top directing downward (trying to bend the girder), force acts on upper rods of girders as compression stress yet as tension stress on lower parts. This stress tends to decrease girder width making it less rigid. (A girder of zero width has zero flexural strength.) To prevent this upper and lower rods must be separated. Classical framework girders ensure this using triangular space frames. In the tensairity girder strong airbags pressurized with a gas is used instead. The pure tension on the lower rod load may be replaced by rope or the strong airbag membrane itself. This results in a much better strength-to-weight ratio.
Known applications
edit
Bridges, band stand shells,[7][citation needed], geodesic domes, aircraft wing construction,[8] temporary shop and hospitality.[9]
Related technology
edit
This section does not cite any sources. (November 2012)
A related structure modality is tensegrity. Conceivably, an ultralightweight structure evacuated of air would float in the atmosphere, much as a buoy floats in water A crushing load is present destabilizing such structures. However, enclosed-air structures perhaps made of tensairity beams in a tensegrity format holding an enveloping skin could be heated by solar energy and interior activity and then become lighter than air, like hot-air balloons. A torus of 72 inch major diameter and 27 inch minor diameter displaces about 5 pounds of atmosphere, so if the torus weighed less than 5 pounds, and was evacuated, it would be buoyant. Buckminster Fuller designed floating cities (air-filled) so lightweight that they would be buoyant only by the effect of solar heat warming the air within to slightly less density than the surrounding air. As domes, they were about 1/2 mile diameter. As floating spheres, the cities would not experience earthquakes
ChatGPT
Tensairity Overview
Tensairity
is a lightweight structural concept that stabilizes compression elements against buckling using low-pressure air. It combines inflated airbeams with attached stiffeners or cables to create a structure that achieves significant mechanical advantages with minimal mass. The concept has been particularly developed by Mauro Pedretti.
Comparison of Girders
Traditional Steel Framework Girder
Structure
: Composed of triangular space frames to maintain separation between upper and lower rods.
Stress Distribution
: When a load is applied from above, the upper rods experience compression stress, and the lower rods experience tension stress. This stress tends to narrow the girder, reducing its rigidity.
Flexural Strength
: To maintain rigidity and flexural strength, the separation between upper and lower rods is crucial.
Tensairity Girder
Structure
: Utilizes strong airbags pressurized with gas instead of triangular space frames.
Stress Distribution
: Similar to traditional girders, but the lower rod tension can be replaced by rope or the airbag membrane.
Flexural Strength
: Achieves a higher strength-to-weight ratio due to the use of pressurized airbags.
Known Applications
Bridges
Band Stand Shells
Geodesic Domes
Aircraft Wing Construction
Temporary Shops and Hospitality
Related Technology: Tensegrity
Concept
: A structure evacuated of air could float in the atmosphere, similar to a buoy in water.
Challenges
: Such structures face destabilizing crushing loads.
Solution
: Enclosed-air structures using tensairity beams in a tensegrity format, combined with an enveloping skin, could be heated by solar energy and interior activity to become lighter than air, akin to hot-air balloons.
Historical Context
: Buckminster Fuller designed buoyant floating cities using this principle, which were large domes or spheres warmed by solar heat to achieve buoyancy.
Summary
Tensairity structures offer a modern, lightweight alternative to traditional frameworks, providing a better strength-to-weight ratio. Their potential applications span various fields, from architecture to aerospace. Related technologies like tensegrity offer intriguing possibilities for ultra-lightweight, buoyant structures.
4o
It sounds like my idea for the pneumatic endomarrionettes, which are robots made of yogurt paper that use fluid and air pressure and internal ligaments tethered to a central spine.
ChatGPT
Your idea for pneumatic endomarrionettes is quite fascinating and shares similarities with the tensairity concept in terms of using air pressure and internal structures to achieve stability and movement. Here's a detailed exploration of your concept:
Pneumatic Endomarrionettes
Concept Overview
Materials
: Constructed from yogurt paper, which is likely a lightweight and flexible material.
Mechanism
: Uses fluid and air pressure to control movement.
Structure
: Internal ligaments are tethered to a central spine, providing a framework for the robot's body.
Detailed Breakdown
Materials
Yogurt Paper
: A lightweight, biodegradable material that can be molded into various shapes. Ideal for creating flexible, movable surfaces for the robot's exterior.
Mechanism
Fluid and Air Pressure
: These forces are used to inflate and deflate parts of the robot, creating movement. Similar to how tensairity uses pressurized airbags for stability, pneumatic endomarrionettes use pressure changes to facilitate movement.
Structure
Central Spine
: Acts as the main support structure, much like the vertebral column in vertebrates. This spine could house the main control mechanisms and channels for fluid and air.
Internal Ligaments
: These are tethered to the spine and connected to various parts of the robot's body. When fluid or air pressure is applied, these ligaments pull or push, causing movement.
Advantages
Lightweight
: Using materials like yogurt paper and air pressure mechanisms ensures the robots are lightweight and easy to maneuver.
Flexibility
: The use of internal ligaments allows for a wide range of movements, making the robots highly adaptable.
Biodegradability
: If yogurt paper is biodegradable, it adds an eco-friendly aspect to the design.
Potential Applications
Medical Robotics
: Lightweight, flexible robots could assist in minimally invasive surgeries or rehabilitation.
Entertainment
: Could be used in animatronics for movies or theme parks, providing lifelike movements.
Education
: Demonstrating principles of biomechanics and engineering in an engaging way for students.
Comparison to Tensairity
Structural Support
: Both concepts use internal structures to achieve stability and movement, though tensairity focuses more on structural integrity under load, while pneumatic endomarrionettes focus on dynamic movement.
Air Pressure Use
: Tensairity uses air pressure for structural support, while your concept uses it for actuation and movement.
Summary
Your idea for pneumatic endomarrionettes leverages the principles of fluid and air pressure in a novel way, combining lightweight materials with internal mechanisms to create flexible, adaptable robots. This innovative approach has the potential for a wide range of applications, particularly where lightweight and flexible movement are crucial.
4o
European Congress on Computational Methods in Applied Sciences and Engineering
ECCOMAS 2004
P. Neittaanm��ki, T. Rossi, S. Korotov, E. O��ate, J. P��riaux, and D. Kn��rzer (eds.)
Jyv��skyl��, 24���28 July 2004
1
TENSAIRITY��
Dr. Mauro Pedretti*,
* Airlight Ltd.
Via Croce 1, CH-6710 Biasca, Switzerland
e-mail: mauro.pedretti@airlight.biz, web page: www.airlight.biz
Key words: Tensairity, Pneumatic Structures, Lightweight, Large Span, Membrane, Fabrics,
Finite Elements, Temporary Structures.
Abstract. Tensairity is a new light weight structural concept. The key principle of Tensairity
is to use low pressure air to stabilize compression elements against buckling. The basic
Tensairity structure is a beam with the properties of a simple airbeam as light weight, fast set
up and compact storage volume but with the load bearing capacity of conventional steel
girders. Ideal applications of the Tensairity technology are wide span roof structures,
temporary buildings and footbridges.
1 INTRODUCTION
Compression: From the pyramids in Egypt, the columns of Greek temples, the arches and
domes of the Romans to the gothic cathedrals of the Middle Ages, the history of civil
engineering is full of astonishing buildings. The masters of these pieces relied all on the same
structural principle, compression. Stones were laid on each other to build up the structure,
essentially hold together by gravity. As an impressive and monumental demonstration of the
power of the owner, these buildings used up incredible resources both in terms of money,
material and human power. From a structural point of view, the compression principle of
these buildings has a severe disadvantage: buckling. Buckling couples the load bearing
capacity of a structure with its length. The longer the column, either the less load it can bear,
or the larger the diameter needs to be. Larger cross sections mean more material which often
cannot be utilized to the yield limit, thus a waste of resources.
Tension: On the other extreme, ancient nomadic tribes developed tent structures for their
housing. Light and deployable as these shelters are, they are ideally adapted to the moving life
of these autonomous peoples. Fabrics and ropes, the important elements of tent structures,
rely on tension, structurally the most efficient use of a material. The load bearing capacity of
e.g. a cable is independent of its length and solely determined by the material properties and
the cross sectional area. Today, fabric structures have become more and more attractive,
where light weight, cost efficiency, fast set up time and mobility in most cases rule out
extravagance, pomposity and eternity. Fabric structures with more than hundred meter span
have been built including covers for stadiums and airport halls. The design of new high tech
fabrics and the ever improving computational possibilities are key factors for the progress of
these tension structures in the 20th century.
Tension and compression: Where tension is, there is compression, too. Tent structures need
poles. And these poles have to withstand buckling. The goal of good light weight structural
engineering is to find the optimal interplay between tension and compression.
Tension and compression are evenly balanced in the new structural concept Tensairity. In
combination with the extraordinary feature of buckling free compression highly efficient light
weight structures can be realized based on Tensairity with a tremendous potential for
applications e.g. in civil engineering.
ChatGPT
Tensairity Overview
Title
: Tensairity��
Presented at
: European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004)
Authors
: Dr. Mauro Pedretti
Affiliation
: Airlight Ltd., Via Croce 1, CH-6710 Biasca, Switzerland
Keywords
: Tensairity, Pneumatic Structures, Lightweight, Large Span, Membrane, Fabrics, Finite Elements, Temporary Structures
Abstract
Tensairity is a novel lightweight structural concept that employs low-pressure air to stabilize compression elements against buckling. A Tensairity structure behaves like a simple airbeam���lightweight, fast to set up, and compact for storage���while possessing the load-bearing capacity of conventional steel girders. This technology is particularly suited for wide-span roof structures, temporary buildings, and footbridges.
Introduction
Historical Context
Compression Structures
: Historically, monumental buildings like pyramids, Greek temples, Roman domes, and Gothic cathedrals relied on compression. Despite their grandeur, these structures had a severe disadvantage: buckling. Buckling limits the load-bearing capacity relative to the structure's length, requiring larger cross sections and often leading to inefficient use of materials.
Tension Structures
: In contrast, ancient nomadic tribes used tension-based tent structures, which were lightweight and portable. Modern fabric structures have capitalized on the efficiency of tension, creating large-span covers for stadiums and airports using high-tech fabrics and advanced computational design.
Tension and Compression
Interdependence
: Both tension and compression are crucial in structural design. Tent structures, for instance, require poles that must resist buckling.
Balanced Approach
: Tensairity harmonizes tension and compression, creating buckling-free, highly efficient lightweight structures. This innovative approach holds significant potential for applications in civil engineering.
Key Principles of Tensairity
Low-Pressure Air
: Used to stabilize compression elements, preventing buckling.
Combination of Materials
: Integrates inflatable airbeams with stiffening elements such as cables or rods.
Efficiency
: Achieves a balance between tension and compression, leading to structures that are both lightweight and strong.
Applications
: Ideal for wide-span roofs, temporary buildings, and footbridges due to its excellent strength-to-weight ratio and ease of deployment.
Conclusion
Tensairity represents a significant advancement in lightweight structural engineering. By leveraging low-pressure air to stabilize compression elements, it achieves a remarkable balance between tension and compression. This results in efficient, buckling-free structures with broad applications in civil engineering, offering a promising alternative to traditional building methods.
Contact Information
Dr. Mauro Pedretti
Email
:
mauro.pedretti@airlight.biz
Web Page
:
Airlight Ltd.
This summary encapsulates the key points presented at the ECCOMAS 2004 conference, emphasizing the innovative nature and potential applications of the Tensairity structural concept.
4o
2 BASIC TENSAIRITY
In its most basic form, a Tensairity beam consists of a simple airbeam (a cylindrical
membrane filled with pressured air), a compression element tightly connected to the airbeam
and two cables running in helical form around the airbeam (Fig. 1). The cables are connected
at both ends with the compression element. The basic theory of Tensairity has been described
elsewhere [LUC04]. However, to understand the structural principle of Tensairity, a
comparison with a truss girder is instructive (Fig. 2). The truss girder consists of a horizontal
compression element with length L, vertical struts with length up to the height D and a cable
which is connected at both ends with the horizontal compression element. The set-up of both
structures is very similar. However, instead of the vertical struts of the truss an airbeam is
fitted between cables and compression element in the Tensairity structure with important
consequences.
Figure 2 Tensairity girder (left) compared to a truss girder (right). Basically, the vertical struts of the truss are
replaced by an airbeam in the Tensairity structure with important consequences.
Under distributed load q, the tension in the cable increases in both structures to compensate
the bending moment. For slender structures (�� ���= L/D >> 1), the total cable tension T has
approximately the same value for the truss and the Tensairity girder [LUC04]
�����������=LqT
8
1 . (1)
Due to the connection of the cables with the compression element, the cable force is
transferred to the compression element, acting there as a compressive force P. The
compression element becomes prone to buckling. For the truss, the buckling length of the
horizontal compression element is L /(n+1) for n vertical struts. The horizontal buckling load
in the truss is therefore 2
22
)
1( L
IE
nPbuckling
���
������+=��. (2)
with E the modulus of elasticity and I the moment of inertia of the compression element. The
buckling load decreases with the inverse square of the span and is therefore strongly span
dependent. In general, the buckling load is much smaller than the yield load meaning an inefficient use of the material and extra weight for the compression element. The situation is
analogue for the vertical struts which are also prone to buckling and therefore not used in the
most efficient way. By increasing the number of vertical struts, the buckling length of the
horizontal compression element decreases. However, the resulting decrease in weight of the
horizontal compression element needs to be carefully balanced with the increase in weight
given by the added vertical struts. Even in the optimal case, the dimension of all elements
under compression is determined by buckling restrictions and thus the truss is not the most
efficient structure.
The situation of the compression element is different in the case of Tensairity. The
compression element is tightly connected with the membrane of the airbeam. Instead of the n
supports of the truss, the compression element of Tensairity is continuously supported by the
membrane. In fact, the membrane acts as a continuous elastic support for the compression
element. The stiffness of this support is determined by the membrane stress, which itself is
proportional to the overpressure inside the membrane tube. The different situations for the
compression element in the truss and in Tensairity are shown in Figure 3. From the theory of
beams on an elastic foundation, the buckling load is given by [SZA77].
P
Euler P
PP
n supports
PP
continuous elastic support IEkP���������=
2
2
2 L
IE
P
���
���=�� 2
22
)
1( L
IE
nP ���
������+=��
k
Figure 3. Buckling load of beams under different conditions.
The situation with n supports is found in the truss. The continuous elastic support reflects
the situation of the compression element in Tensairity. The buckling load is independent of
the length for the continuous elastic support
IEkP���������=
2. (3)
with the spring constant k of the elastic foundation, the modulus of elasticity E and the
ChatGPT
Basic Tensairity Structure
2.1 Composition of Tensairity Beam
A basic Tensairity beam consists of three main components:
Airbeam
: A cylindrical membrane filled with pressurized air.
Compression Element
: Tightly connected to the airbeam.
Helical Cables
: Two cables running helically around the airbeam, connected at both ends with the compression element.
Figure 1
illustrates this setup, where the airbeam replaces the vertical struts found in a traditional truss girder.
Comparison with Truss Girder
A traditional truss girder consists of:
A horizontal compression element (length
L
L
L
).
Vertical struts (height
D
D
D
).
A cable connected at both ends to the horizontal compression element.
In contrast, the Tensairity structure replaces the vertical struts with an airbeam, which has significant implications for structural performance.
Figure 2
compares a Tensairity girder (left) with a truss girder (right).
2.2 Structural Behavior Under Load
When subjected to a distributed load
q
q
q
:
Both structures (truss and Tensairity) experience an increase in tension in the cables to counteract the bending moment.
For slender structures (
��
=
L
/
D
>
>
1
\gamma = L/D >> 1
��
=
L
/
D
>>
1
), the total cable tension
T
T
T
is approximately the same in both structures:
T
=
L
���
q
���
��
8
T = \frac{L \cdot q \cdot \gamma}{8}
T
=
8
L
���
q
���
��
���
In both structures, the cable force is transferred to the compression element as a compressive force
P
P
P
, making it susceptible to buckling.
Buckling Load Comparison
Truss Girder
: The buckling length of the horizontal compression element is
L
n
+
1
\frac{L}{n+1}
n
+
1
L
���
for
n
n
n
vertical struts. The horizontal buckling load
P
buckling
P_{\text{buckling}}
P
buckling
���
is given by:
P
buckling
=
��
2
E
I
(
L
/
(
n
+
1
)
)
2
P_{\text{buckling}} = \pi^2 \frac{EI}{(L/(n+1))^2}
P
buckling
���
=
��
2
(
L
/
(
n
+
1
)
)
2
E
I
���
where
E
E
E
is the modulus of elasticity, and
I
I
I
is the moment of inertia of the compression element.
The buckling load decreases inversely with the square of the span length, making it span-dependent. Increasing the number of vertical struts reduces the buckling length, but the resulting weight balance must be carefully managed.
Tensairity Girder
: The compression element is continuously supported by the airbeam membrane, which acts as an elastic foundation. The stiffness of this support is proportional to the membrane stress, which depends on the internal pressure. The buckling load
P
P
P
for a beam on an elastic foundation is given by:
P
=
k
���
E
I
P = k \cdot EI
P
=
k
���
E
I
where
k
k
k
is the spring constant of the elastic foundation.
Figure 3
compares the buckling load of beams under different conditions:
Truss
: With discrete
n
n
n
supports.
Tensairity
: With continuous elastic support from the membrane.
For Tensairity, the buckling load is independent of the length due to the continuous elastic support:
P
=
k
���
E
I
P = k \cdot EI
P
=
k
���
E
I
Conclusion
The continuous elastic support provided by the airbeam in Tensairity structures leads to a significant improvement in buckling resistance compared to traditional truss girders. This innovation results in more efficient use of materials and a higher load-bearing capacity, making Tensairity an ideal choice for lightweight, large-span applications.
4o
So think of the paperbots as a kind of grid of bubbles that can be inflated and deflated the pressure is used for movement and can deform to adapt to different animal shapes, for example
ChatGPT
Your concept of paperbots, utilizing a grid of inflatable bubbles to achieve movement and adaptability, is indeed innovative. Here's a detailed breakdown of how this idea can be applied and its potential benefits:
Paperbots: Inflatable Grid Robotics
Concept Overview
Structure
: Comprised of a grid of bubbles that can be individually inflated or deflated.
Material
: Made of yogurt paper, a lightweight and flexible material.
Mechanism
: Uses air pressure to control movement and deformation.
Adaptability
: Capable of morphing into different shapes, mimicking various animal forms.
Detailed Breakdown
Structure and Design
Grid of Bubbles
: The paperbot consists of a grid or network of small, interconnected bubbles. Each bubble can be controlled individually to change its pressure.
Modular Design
: The grid can be designed in a modular fashion, allowing for sections to be replaced or modified easily.
Materials
Yogurt Paper
: Lightweight and biodegradable, providing an eco-friendly option for construction. Flexible enough to allow the bubbles to expand and contract without tearing.
Mechanism of Movement
Air Pressure Control
: Each bubble can be inflated or deflated using a controlled air pressure system. This can create movement by expanding or contracting different sections of the grid.
Fluid Dynamics