Membrane structures: understanding their forms. - Research-Unit

Membrane structures: understanding their forms.
Prof. Dr. Eng. M. Mollaert
Department of Architecture
Vrije Universiteit Brussel.
1 Introduction.
The oldest tents were made out of skins or woven fabrics. The fabric only resists
tensioning and has almost no compression or bending stiffness.
The material is flexible and can be folded or rolled up into a small parcel.
Nomad shelters in the Tundra and in Iran [1]
Transport of temporary shelters [2]
Also ropes and cables are flexible. If a rope hangs freely under its dead weight it takes the
form of a catenary curve. The higher the curvature, the lower is the horizontal
component of the reaction forces.
The form changes for different point loads.
A fabric that hangs freely under its dead weight also changes its shape if it is loaded, it
could even reverse its form.
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Hanging ropes, juwels and textiles [3]
Tension implies an optimal use of the material, since the whole section is uniformly
stressed. Moreover there is no buckling problem, like it is the case for compression.
The form finding of fabric structures tries to take full advantage of the tensile strength
of the material, while preventing negative stresses to occur.
To withstand upward and downward loads, a cable has to be stabilised and
pretensioned: compression in this case means a reduction of the initial pretension.
Flexible ropes, cables pretensioned with bars and turnbuckles [4]
The same approach has to be considered for fabric roofs: due to their low dead weight,
both upward and downward wind loads become important. The membrane needs to be
pretensioned.
Balloons resist external loads by means of an inner pressure.
In circus tents internal poles and ropes are used to introduce the pretension in the
membrane and to reduce deformations due to wind load.
Introducing pretension: inner pressure, poles, tensioning ropes [5]
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To obtain a stable surface without an inner pressure, both an inward and an outward
curvature need to be realised in each point of the surface.
2 Basic form 1: the hypar or saddle shape.
The first basic form is the saddle shape. It has a double curvature: the hanging curve can
bear the downward load, the downward curve can bear the upward wind load.
The saddle shape fixed between boundary points, open-air theatre by Bodo Rasch [6]
The boundaries could be sloped arches (even forming a circle in plan view) or placed
vertical.
The saddle shape fixed between arches [7]
The double curved membrane could be tensioned into a 3D curved ring or between two
parallel circles (polygons).
Net tensioned in a 3D boundary and between 2 parallel circles [8]
3 Combining saddle shapes.
Individual saddles could be placed in a grid, in this case they act as structurally independent
units.
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Repetition of identical saddles: Yulara Resort and Olympic Games 2000 in Australia [9]
In the next canopies small slightly curved saddles are jointed in a larger net: they act all
together.
Large saddle shapes built up from smaller parts: at the World Expo in Sevilla ‘96 and in Palma de Mallorca [10]
4 Other possibilities with saddle shapes.
The next example is the roof above the architecture office of Willy Van Der Meeren built
in 1969. It was the first membrane roof, as far as I know, built in Belgium. Along its
boundary it has several high and low points.
Smooth surface in an irregular boundary [11]
The following structure built by Tensoforma has 4 high and 4 low boundary points. It is a
seasonal structure, the membrane is taken away during the winter.
Supporting structure with and without the fabric roof [12]
Membrane structures: understanding their forms.
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5 Basic form 2: the conical shape.
Another basic form is the conical one with an internal point out of the plane of the
perimeter support. Again this shape has a double curvature. This time the horizontal rings
bear the load from inside to outside and radial lines bear the load from outside to inside.
The high point can be supported by inner or outer compression elements.
The conical form can be placed in the upright position. In the umbrellas of the World Expo
in Lisbon ‘98 an inner frame takes the pretension.
Different supports for the conical shape, built structures by Canobbio [13]
Frei Otto designed the following foldable umbrellas.
Umbrellas for the Bundesgartenschau [14]
Conical shapes are characterised by large radial stresses near to the center, while there is
less and less material to withstand the pretension and to transfer the forces to the supporting
element.
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In the Diplomatic Club of Ryadh (by Frei Otto) additional compression elements solve the
problem. Steel cones reinforce the high points of the awnings for the Olympic Games 2000.
Radial arches support the high points in the Schlumberger factory in Paris (by Renzo
Piano).
Reinforced high points [15]
6 Combining conical shapes.
Several forms can be combined: they either touch at fixed boundary elements
(Yokohama Show '89, Kurokawa, Hamautsu) - remaining structural independent - or
they act as a unity.
Combining conical shapes [16]
The Palenque built in the Expo in Sevilla ‘96 (by IPL) consists of double modules
supported by external compression elements and longitudinal cables. Along the boundary
cable trusses ensure the pretension.
Combining forms with 2 high points [17]
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The roof of the Florida Festival Hall (by Berger) consists of four high point membranes
with a square base: one larger and three smaller ones are arranged around one common
corner point. This corner point is a low point. The roof is tensioned in between these
internal points and a concrete ring beam. Around the roof the ground is sloped and covered
with grass, which integrates the construction naturally in the landscape.
Combining high point roofs, the common corner point is pulled down [18]
7 Surfaces with conical regions.
Several high and low points could be used in the same roof.
Alternating high and low points in one surface [19]
The canopy built in the Markies building in Brussels is an example of conical forms jointed
together into one structure. Along its boundary it is fixed with cables to the second floor of
the building. Cables fixed at the sixth floor pull up the high points. The structure takes full
advantages of the heavy surrounding building.
High points pulled up by cables [20]
The high points of the covering of the stand of Lord's cricket ground (by Hopkins) are
alternately supported by masts and cables. Transverse pretension is introduced by
compression elements connected to the masts.
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High points supported by masts or cables, the transverse force is taken internally [21]
The following open-air theatre at Bad Hersfeld (by Stromeyer) is a foldable roof: by
means of cables, the corner points and top points can be pulled to the same position. This
technique is still used for swimming pools and coverings for cultural events.
Foldable roof, tensioned by internal high points [22]
The overall shape of the roof can be synclastic (principle curvatures have the same
direction) if the roof is supported by arches like the skating rink in Paris (by Blasco).
Foldable membrane tensioned in a synclastic steel structure [23]
The roof over the swimming pool in Sevilla is supported by a scissors system (by Escrig).
The supporting system can itself be folded together. The scissors are placed both in the xand y-direction and form arches when unfolded. Diagonal elements are added to stiffen the
unfolded shape.
Foldable membrane in a foldable synclastic dome [24]
Membrane structures: understanding their forms.
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The playground of the Colombo Shopping Centre in Lisbon is covered with a membrane
roof. It contains 9 high points either supported by ‘A frames’ or by masts. A closer look to
the cutting patterns shows that the roof has been considered as an assembly of saddle
shapes rather than an assembly of conical units.
Saddle shapes tensioned between high points [25]
8 Arch supported shapes.
The following basic unit is supported by an arch. The built roof is constructed for the
Olympic Games 2000 in Sydney.
Membrane tensioned by a compression arch [26]
Also the Diadema for the Expo in Sevilla ‘96 (by IPL) can be considered to be supported
by an arch. Due to the fact that this is a high structure, special wind tunnel tests have been
performed to be sure to dimension this structure properly.
Boundary and internal arch [27]
In the Milan Fairgrounds cover the main arch is supported by a hanging cable. The hanging
cable supports a row of high points in the Misano cover.
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A similar cable supports a standing arch or high points with an arched profile [28]
9 Combining arch supported shapes.
The Zenith in Paris and in Montpellier (by Chaix, Morel) are covered by square modules
each one tensioned by a diagonal arch.
Arches placed along the diagonal of each square membrane unit [29]
10 More possibilities for arch supported shapes.
Arches could be placed parallel.
Parallel arches (Sydney) [30]
The Fina Service Station in Wanlin was designed by Samyn & Partners.
Parallel arches, longitudinal forces are taken internally [31]
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The equilibrium calculations were performed with EASY. The structure stands upon 6
concrete columns. They hold 3 planar arches in the transverse direction. Compression
elements transmit the compression from one end to the other. The curvature for the upward
wind (which could be high for an open structure) is quite small and for that reason cable
trusses were added under the roof. They only act for upward wind.
Continuous arches hang on high poles in the Bigo in Genua (by Renzo Piano). The
anchoring occurs at both sides of the arches by cables connected to the appropriate weights
in the water. Special attention has been paid to the possibility to adjust and refine the
pretension.
Steel arches hang on high masts [32]
The structure in Venafro designed by Samyn & Partners and IPL is supported by
triangulated arches.
Sloped arches [33]
Their slope slightly increases towards the end creating a radial and more appropriate
reaction to the tension forces. The building is in fact a second skin for the office buildings
inside but is the only protection for the research installations. The boundary cables form 3D
curves.
Arches can be placed one against the other like in the Momi tent. The arches are reinforced
by fine bars and cables to create a very light structure.
Tensegrity compression elements to make the arches stiffer [34]
Membrane structures: understanding their forms.
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A structure could be tensioned by complete rings, like the EDF Tower in Bouchain or the
sculpture by Aleksandra Kasuba.
Complete rings introduce pretension [35]
A square membrane could be tensioned by 4 arches along its sides, which creates the
possibility to place several units one beside the other.
Arches on the four sides of the square membrane unit [36]
Much lower arches are used in the Parasol Dome. To ensure form stability extra cables pull
the midpoint of each module downwards to the corner points.
In the Nihon University the supporting arches are placed on the midpoints of the larger
arches and create triangular units.
The membrane could be hold by diagonal arches supported by floating masts like in the
HST Station in Nantes.
Systems with arches [37]
11 Wave forms.
Another type of structure is the wave form, based on a two-dimensional system with a load
bearing cable, a tensioning cable and connecting cable elements. If the load bearing cables
and tensioning cables are placed in parallel planes a wave form is obtained.
Membrane structures: understanding their forms.
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Typical wave form [38]
For the structure used in the World Expo in Brisbane ‘88 (by IPL) a similar principle was
arranged radially. Extra cables pull the structure downward to withstand the large wind
loads on this high construction.
Wave in a radial pattern [39]
The Akita Sky Dome is supported by a double arch in one direction and a single arch in the
other. Between the double arches a cable tensions the membrane covering downward
creating a wave in the membrane.
Wave form supported by stiff arches [40]
12 Tensegrity.
The possibility to support structures by means of floating masts has already been
mentioned. Sculptures have been made which consists of bars and cable elements in such a
way that an endpoint of a bar only touches cable elements. They are called tensegrity
structures.
Membrane structures: understanding their forms.
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Tensegrity sculpture by Snelson and structural models [41]
Membrane elements can be combined with this type of structure.
Tensegrity awnings: Hemweg Amsterdam (by Octatube) and L'Arche de La Defense (by von Spreckelsen, Rice) [42]
The Georgia Dome with a span of 200m is completely supported by floating masts. In the
middle they are aligned, up to the boundary they form ellipses. The mast tops are hold in
position by the membrane covering, the base points are supported by two upward and
outward cable elements (to the tops of the masts on the next ring) and two inward cable
elements (forming a horizontal hoop).
Tensegrity system and Georgia Dome [43]
Membrane structures: understanding their forms.
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13 Design rules.
It is sometimes mentioned that membrane structures (tensile architecture) allow creating
free forms. But because membrane roofs are pretensioned specific rules should be
respected.
Membrane structures are more flexible than we generally accept for steel or concrete
frames. They need curvature to bring the deformations up to an acceptable level. It is not
the best solution to add cables afterwards to prevent the inversion of the form.
The less the curvature, the larger the risk for inversion [44]
Too much curvature could give rise to high buildings, which implies very important wind
loads and requires reinforcements for the structure. A good compromise is necessary.
Also the boundary cables should have enough curvature.
Curvature in the boundary cables of the Aviary in Stuttgart (by Auer, Weber) and the awning in Zeebrugge (by Tentech) [45]
High and low points need special attention. The structure could be reinforced or the
membrane could be replaced by cables in a radial pattern or forming a loop.
Solutions for low or high internal points [46]
Complex shapes can have locations where one or two principle curvatures become zero.
Large deformations could occur in such area. If it is functionally possible the
corresponding area can be left open.
Membrane structures: understanding their forms.
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Dancing springs (by Frei Otto) [47]
The coated fabric itself is a very light material but one always has to verify the layout of the
boundaries to make sure that the foundations become not the very heavy part of the so
called lightweight structure.
The Curtain Valley by Christo spans 100m [48]
Since every detail is visible all connections should be conceived properly and be well
dimensioned.
If the rules to create beauty are respected in every detail membranes provide good solutions
to cover both small entities and large free spans.
Small and large: on an old Chinese drawing and Gerry Weber Stadium [49]
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References for the illustrations.
[1]
[2]
Behling S. and S., Sol Power, Prestel-Verlag, 1996.
first picture: Prussin L., African Nomadic Architecture, Smithsonian, 1995,
second picture: Shelter, Shelter publications, Ten Speed Press, 1973.
[3]
fifth photo: IL 30, Sun & Shade, Institute of Lightweight Structures, University of Stuttgart. 1984.
[4]
first photo: Canobbio Documentation.
[5]
second photo: Canobbio Documentation,
third photo: Hebbelinck S., Onder gefragmenteerd zeil, Internal report V.U.B. 1998.
[6]
first picture: Canobbio Documentation,
second picture: Engel H., Structure Systems. Deutsche Verlags-Anstalt Stuttgart. 1977.
[7, 38]
Engel H., Structure Systems. Deutsche Verlags-Anstalt Stuttgart. 1977.
[8, 14, 23] Drew Ph., Frei Otto Form and Structure. Crosby Lockwood Staples London 1976.
[9]
first photo: SarnaTent Documentation.
[10] first photo: Verseidag Indutex Documentation,
second photo: Rasch B., Bradatsch J., Retractable Roof to Open-Air Theatre in Wiltz, Detail, 6/1994.
[11] De Kooning M., Willy Van Der Meeren, Laat-XXe-Eeuws Genootschap.
[13] first picture: Engel H., Structure Systems. Deutsche Verlags-Anstalt Stuttgart. 1977,
second picture: : Canobbio Documentation, drawings: Carl Nolte Documentation.
[16]
[17]
[19]
Membrane Design in Japan (1967-1990), Shinkenchiku-sha Co, 1990.
first photo: Verseidag Indutex Documentation.
first picture: Engel H., Structure Systems. Deutsche Verlags-Anstalt Stuttgart. 1977,
second photo: Drew Ph., Frei Otto Form and Structure. Crosby Lockwood Staples London 1976.
[21, 27]
Verseidag Indutex Documentation.
[22] Kugel, F., Wie von Geisterhand. Deutsche Bauzeitung. 9/1993, 102-108.
[26] first picture: Engel H., Structure Systems. Deutsche Verlags-Anstalt Stuttgart. 1977.
[28, 32]
Canobbio Documentation.
[29] Doriez M., Blin P., Architecture Textile. A Tempera Editions. 1990.
[32] second Photo: Samyn and Partners
[34] Pawley M., Future Systems: the story of tomorrow, Phaidon 1993
[35] first photo: Doriez M., Blin P., Architecture Textile. A Tempera Editions. 1990.
[36] Tensoforma Documentation.
[37] first and second foto: Ishii K., Membrane structures in Japan, SPS Publishing Company, Tokyo, 1995,
third photo: Doriez M., Blin P., Architecture Textile. A Tempera Editions. 1990.
[39] Carl Nolte Documentation.
[40] Ishii K., Membrane structures in Japan, SPS Publishing Company, Tokyo, 1995.
[41] second picture: Mimram M., Sructures et formes, Dunod Presse Ponts et chaussées.
[42] first and second photo: Eekhout M., Architecture in space structures. 010 Publishers Rotterdam,
third and fourth photo: Hoechst Documentation
[43] photo: Birdair Tensioned Structures.
[46] first and third photo: Drew Ph., Frei Otto Form and Structure. Crosby Lockwood Staples London 1976.
[47] Drew Ph., Frei Otto Form and Structure. Crosby Lockwood Staples London 1976.
[48] Christo, The Curtain Valley
[49] first photo: Rudofsky B., Architecture without Architects, Museum of Modern Art, New York, 1964.
Further references.
Gründig L. and Moncrieff E., Form Finding of Textile Structures. Studiedag Textielstrukturen, 25/05/1993, Vrije
Universiteit Brussel.
Kronenburg R., Portable Architecture, Architectural Press, 1996.
Aldo Capasso, Massimo Majowiecki, Vincenzo Pinto, La tensostrutture a membrana per l’architettura. Maggioli
Editore. 1993.
Lyonnet, Les structures textiles tendues. 1993.
Membrane structures: understanding their forms.
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