From roofs to wings: Lightweight inflatable
structures are taking off
R.H. Luchsinger, C. Galliot
Empa - Center for Synergetic Structures, Überlandstrasse 129, CH-8600
Dübendorf, Switzerland. Web page: http://www.empa.ch/css
E-mail: rolf.luchsinger@empa.ch, cedric.galliot@empa.ch
Abstract
The load bearing capacity and the weight of a structure is the result of the applied
materials and the applied structural concept. A high live load to dead load ratio is the
result of a smart combination of materials and structure. In the Tensairity concept,
compressed air, fabrics, cables and struts are combined. This light-weight structure
has been successfully applied to roofs and bridges. In these applications, different
ways to couple the compression and tension element have been applied. Here, we
investigate the influence of this coupling on both the stiffness and the ultimate load
experimentally and with FEM. A major result is that the live load to dead load ratio
can be increased by a factor two with improved coupling of the compression and
tension element. In a new project Tensairity girders are investigated as the load
bearing structure of a high performance wing dedicated to harvest wind energy at
higher altitudes. With the proposed design a live load to dead load ratio of more than
270 is predicted using standard kite materials.
Keywords: Inflatable structure, Tensairity, Experimental tests, Finite Element
Analysis, Wing structure.
1
Introduction
The structural concept Tensairity is a synergetic combination of pneumatic fabric
structures with conventional structural elements such as cables and struts [1]. The
major focus of the Center for Synergetic Structures at Empa is to investigate the load
bearing behavior of Tensairity and to develop new applications for this lightweight
structure. In the last years several shapes of Tensairity structures have been studied
like plates and arches [2] but most of the efforts have been concentrated on straight
girders. In particular spindle shaped Tensairity girders have been investigated
experimentally, analytically and numerically with asymmetric [3] as well as
symmetric construction [4].
The studies have revealed the influence of the air pressure on the stiffness of the
structure. For the symmetric girder, results have also highlighted the subtle interplay
between the stiff chords and the soft inflated hull leading to a peculiar deformation
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of the system. The weak coupling between the tension and the compression chords
has been emphasized. In this paper the influence of an improved coupling between
the two struts is investigated experimentally and numerically for the same
symmetric spindle-shaped Tensairity girder. The original girder is thereafter
referenced as the o-spindle. Two modified Tensairity girders are studied that have
the same chord geometry as the o-spindle but have in addition an improved coupling
of the chords. The reinforcement of the c-spindle is a continuous fabric web while
for the d-spindle it is discrete and given by a number of cables. These three designs
have already been applied for the construction of roofs or bridges (Figure 1).
Figure 1. Tensairity girders (from left to right): 8 m span bridge
demonstrator (o-spindle), 10 m span ETH student project bridge (cspindle) and 28 m span roof over parking in Montreux (d-spindle).
In a second part the design of a Tensairity beam for a high performance kite is
presented. First investigations on the potential of Tensairity for kites have
highlighted many advantages like the aerodynamic and structural performance, the
low weight and the small storage volume [5]. In a new project, kites are developed
at the Center for Synergetic Structures for harvesting wind energy at higher altitude.
With the use of very light and strong materials the Tensairity technology can reveal
its full potential in this application.
2
Design of symmetrical spindle shaped Tensairity girders
The geometrical characteristics of the three Tensairity girders are shown in Figure 2.
They are identical in the front view, with a span of 5 m and a maximal distance
between the chords of 0.5 m at mid-span corresponding to a slenderness of 10. The
parabolic chords are made of aluminum with a total cross section of 40 x 15 mm2.
The end pieces connecting the upper and lower chords are made of steel. It is
important that the support of the girder is located exactly at the theoretical
intersection point of the lower and upper chord. The hulls including the web were
fabricated using a PVC coated polyester fabric material (VALMEX 7318). Great
care was taken that the fabric hull cannot move relative to the chords. To this end, a
keder was welded to the hull as shown in the Detail B of Figure 2. The two halves of
the chord are firmly clamped to the keder with a screw every 15 cm along the chord.
The force which pre-stresses the web of the c-spindle is given by the hoop stress and
depends on the air pressure, the radius of the hull segment and on the angle between
the hull and the web. This angle was varied along the span of the c-spindle in order
to obtain an equal pre-stress of the web. The pre-stress of the cables in the d-spindle
depends on the geometry of the hull and the air pressure. The same hull geometry
has been used for the c-spindle and d-spindle. Having a constant distance between
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the cables, the same pretension in all cables can be obtained. In total 23 stainless
steel wire ropes with 5 mm diameter each are used in the d–spindle.
Figure 2. Tensairity spindles design.
The total mass of the o-, c- and d-spindle is equal to 28.3 kg, 31.8 kg and 36.6 kg,
respectively. They all share the same chords, end pieces and connectors that
represent most of the system mass with 22.2 kg. As far as the hull is concerned, it
weighs 6.1 kg for the o-spindle and about 8 kg for the reinforced girders. The ospindle is the lightest structure while the fabric web of the c-spindle increases the
mass by about 12 %. The heaviest girder is the d-spindle. While the mass of all the
cables is about the same as the mass of the web, two bladders needed to obtain an
airtight structure as well as spacers and other small metallic parts needed for
positioning the cables increase the total mass of the d-spindle by 4.8 kg compared to
the c-spindle.
3
Testing and finite element analysis of the Tensairity girders
A dedicated test rig was set up to test the load bearing behavior of the Tensairity
girders (Figure 3). Two electromechanical drives with a maximal force of 20 kN
each activate a whippletree system which distributes the load into 32 evenly spaced
points. The simply supported girder is laterally supported in order to prevent out of
plane movements under loading. The applied load is measured with load cells
connecting the actuators with the whippletree system. Tests are displacement
controlled. Three load cycles are applied. Deformation data of the girder are taken
from the last cycle. The deformation of the girder is measured with a 3D digital
image correlation system (Limess Vic 3D). To this end, several markers were placed
along the chords of the test specimen to determine the deformation of the lower and
upper chord along the span (Figure 4). A theoretical accuracy of about 0.1 mm (1/30
of a pixel) can be obtained with this system in this setting. Depending on the light
conditions and the calibration a minimal accuracy of about 0.5 mm was obtained in
practice.
3
Figure 3. Test rig for homogeneous distributed load.
Figure 4. Test rig – position of the markers for 3D tracking of the
displacement of the compression and tension members.
Figure 5. Finite element models.
4
The Tensairity girders were modeled and analyzed with the finite element method
using ANSYS. The steel end parts and the aluminum chords are modeled by 3D
bricks and 2D shells, respectively. The membrane for the hull and the web are
modeled with 2D shell elements without bending stiffness. The cables are modeled
by 1D spar elements that have no bending stiffness and can only act under tension.
The meshes are presented in Figure 4. The material properties of the coated fabric
were obtained from in-house test procedures [6][7]. In addition a pressure-dependent
shear modulus was used as significant variations can be observed in inflatable
structures [8].
4
Comparison between the Tensairity girders
The measured and simulated displacement distributions along the span for the three
girders for the compression member and the tension member are given in Figure 6.
A distributed load of total 5000 N is applied. Obviously, the o-spindle deflects much
more than the c- and d-spindle. The displacement of the compression element adopts
an m-shape [4] with a maximal deflection at about 1.5 m from mid-span. This
behavior must be attributed to the arched shape of the compression element as it was
not found in the deflection behavior of an asymmetric o-spindle Tensairity girder
with a straight compression element [3]. Interestingly, the tension chord moves
against the direction of the applied load. This again can be attributed to the arched
shape of the compression chord. As the rise of the compression member becomes
smaller under the homogeneous loading, the ends connected with the tension
member are pushed slightly outwards. This spreading of the system tends to
straighten out the curved tension member leading to the observed displacement
against the direction of the applied load. The overall behavior with a different
displacement for the compression member and tension member indicates that the
coupling between the chords is rather weak for the o-spindle.
Figure 6. Deformation of the compression and tension members of
the spindles under a distributed load of 5 kN at 25 kPa.
The deflection of the compression member of the c-spindle also shows a slight mshape. However, the difference between the displacement at mid-span and the
maximal displacement is small and close to the accuracy of the optical system. With
a deflection of about 3 mm the c-spindle is much stiffer than the o-spindle. Both the
5
compression element and the tension element move in a very similar way in the
direction of the applied load with a slightly larger displacement at the compression
side where the load is being introduced. This proves that there is a much tighter
coupling between the chords in the c-spindle than in the o-spindle due to the fabric
web. In the case of the d-spindle, the maximal deflection is found at mid-span both
for the compression and the tension member which have an almost identical
displacement distribution. Again, as in the case for the c-spindle, a good coupling of
the compression and tension member is obtained by the connecting cables. The
deflection is about the same as for the c-spindle. Overall, it must be emphasized that
the correlation between the experimental results and the FEA predictions is very
good.
The experimental load-displacement behavior of all three girders is shown in Figure
7 for two different pressures. Due to the particular deformation distribution of the ospindle the average displacement of the compression element over the entire span is
shown on the x-axis in order to have a meaningful comparison. As already hinted in
Figure 6, the c- and d-spindle perform much better than the o-spindle both in terms
of stiffness and ultimate load. At 25 kPa for example the ultimate load is about a
factor of two higher compared to the o-spindle, while the stiffness increases by
about a factor of three due to the stronger coupling of the chords. Comparing the dspindle with the c-spindle, both the stiffness and the ultimate load are a bit higher for
the d-spindle. Due to the higher mass of the d-spindle, the ratio of live load to dead
load is about the same for the c-spindle and the d-spindle and in the order of 60 for
the given pressure of 25 kPa. This ratio almost reaches 100 for a pressure of 50 kPa
in some further tests. This is a dramatic improvement regarding the minute
modifications introduced in these girders in comparison to the original o-spindle
which reaches a live load to dead load ratio of only 54 for the same pressure.
Figure 7. Experimental load displacement behaviour of the spindles
under homogeneous distributed load for two hull pressures.
The Figure 7 also emphasizes the influence of the air pressure in the hull. As the
pressure increases the ultimate load increases for all three girders. For the o-spindle
it has been shown that this influence is not linear and levels off at higher pressures
[4]. For the c- and d-spindle however, the ultimate load is almost proportional to the
pressure. For those girders, the ultimate load is reached when the fabric web or the
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cables lose their pre-tension, which is indeed proportional to the pressure. Another
interesting result is that the stiffness of the c- and d-spindle remains almost constant
while the stiffness of the o-spindle significantly increases with the pressure.
Actually, as long as the fabric web or the cables are under tension they act similarly
to the web of a flanged beam whose flanges would be the chords. Therefore the
stiffness of such girders can be roughly estimated using an equivalent I-beam model.
These results will be discussed in more detail in an upcoming paper.
Based on the comparison between the three girders under homogeneous distributed
loading it appears that the c- and d-spindles are the most suitable Tensairity designs
for roof or bridge structures as they allow for optimizing the live load to dead load
ratio. The simpler design of the o-spindle makes it still very attractive for temporary
applications.
5
Lightweight wing structures for airborne wind energy
In order to satisfy the increasing demand for electric power as well as the CO2
emission reduction targets there is a growing need for sustainable energy production.
Among the various renewable technologies wind has seen a dramatic development
over the last twenty years. One major limitation of the wind turbines is however
their tower height which strongly limits their potential. Generally, the wind speed
increases with increasing altitude above ground. As the power density of the wind is
proportional to the cube of the wind speed, harvesting higher altitude wind could
significantly increase the energy production of the wind power systems. Today’s
largest capacity wind turbines (>7 MW) have a hub height of about 130 m and reach
a maximum height of about 200 m.
In order to reach higher altitude, wind airborne wind energy concepts have been
developed in the past decade [9]. One of these concepts is to use a kite or a tethered
wing connected to a winch on the ground. Electrical energy is produced by
transforming the linear aerodynamic lift force of the flying kite into a rotational
motion of the winch. A closed-loop process is achieved by flying so called pumping
cycles [10]. In the power phase, the kite flies crosswind generating high loads. The
tether pulls on the drum which starts to rotate. The kite rises and the generator
connected to the drum produces electrical power. Having reached a threshold
altitude, the kite is flown out of the wind and the retraction phase starts. The kite is
reeled in to a lower threshold altitude from where the power phase starts again.
For this application the weight of the kite is a crucial topic to keep the kite airborne
at low wind speed and to optimize the power production. Ideally, the mass per area
of the wing is below 1 kg/m2. In addition, the wing load needs to be at least in the
order of 50 kg/m2 in a kite power system which is equivalent to a live load to dead
load ratio of 50. Using the Tensairity technology for the main structural element it is
possible to design a lightweight wing that fulfills these requirements. In a previous
project for example [5], a Tensairity kite has been designed that has a live load to
dead load ratio of 40. The kite, presented in Figure 8, weighs 2.5 kg for an area of 11
m2 and can sustain a maximum of 1000 N of lift load.
The design of the Tensairity beam should match the particular constraints due to the
wing structure and the way it is attached. Contrary to roofs or bridges the beam is
7
not laterally supported and poorly constrained from the tether attachment. As a
result the beam should have a quite high lateral stiffness in order to avoid any large
out-of-plane deformations. Moreover if the wing has a constant cross section the
beam must be cylindrical. In that case it turned out that a web construction was not
as efficient as described in Sec. 4.
Figure 8. Tensairity kite.
Front view
Symmetry plane
Tether attachment point
Wing
Top view
Bottom view
Bottom
rods (blue)
Tethers
Cables
Beam position
in the wing
Cables
Top rod (red)
Cables
Figure 9. Design of the kite main beam (half view).
A new design has been proposed where two bended struts on the bottom side of the
beam allow for improving the lateral stiffness of the beam (Figure 8). They are used
as compression elements in the central part of the beam which is the mostly loaded.
In fact the aerodynamic load is not constant over the span but rather follows an
elliptical distribution. Another strut is located on top of the beam. It acts as a
8
compression element in the wing tips and also gives some stiffness to the beam in
the direction opposite to the loading. The struts are connected together with cables.
The beam is designed for a 4 m2 wing. It has a total span of 4.5 m, a diameter of 12
cm and the distance between the bridle attachment points is equal to 2.5 m. The
diameter is here limited by the thickness of the wing profile. The struts are carbon
composite pultruded tubes with a diameter of 6 mm on top and 8 mm at the bottom,
both with a wall thickness of 1 mm. Cables are made of Dyneema and have a
diameter of 4 mm. For the hull and the bladder, typical Nylon rip-stop and PU foil
are used. The total mass of the beam is estimated to 760 g.
An explicit quasi-static finite element analysis was performed with Abaqus. The hull
is modeled with 2D membrane elements while the struts and the cables are modeled
with 1D beam and 1D truss elements, respectively. The bladder is not modeled. The
final mesh is presented in Figure 10. For an elliptical load distribution as shown in
Figure 9 and a pressure of 30 kPa the maximum load is predicted to 2300 N.
However the beam starts already to rotate around its axis and to buckle sideways for
a total load of about 2050 N. This load is equivalent to a live load to dead load ratio
of more than 270.
The buckling load satisfies the target of loading of the wing which should support 50
kg/m2. The current wing has indeed a projected area of 4 m2 and therefore should
carry about 2000 N.
Figure 10. Kite main beam – finite element mesh and typical vertical
deformation under a total of 1400 N.
6
Conclusion
The role of a coupling between the compression and tension member in spindle
shaped Tensairity girders under homogeneous distributed bending loads has been
investigated. The coupling is accomplished either by a fabric web or by equidistant
cables. Although it does increase the mass by only 12 to 30% it significantly
increases the girder stiffness as well as its load bearing capacity. For example the
results reveal an increase in stiffness of a factor three and an increase in ultimate
load of a factor two at the given air pressure of 25 kPa. At a pressure of 50 kPa a
live load to dead load ratio of about 100 has even been obtained. Therefore the cand d-spindle are particularly suitable for demanding applications like roof and
bridge structures.
A Tensairity beam design has been presented for the structure of a high performance
wing dedicated to harvest high altitude wind energy. Using lightweight kite
materials and a novel Tensairity construction enabling higher lateral stiffness, a live
load to dead load ratio of more than 270 could be obtained for a pressure of 30 kPa.
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The study reveals that different Tensairity concepts can be optimal depending on the
structural problem to be solved.
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