Tensile Structures

Tensile structures innovative envelopes

ECOSTRUCTURES Prof: Peter Land Ricardo Urech Spring 2015

Ricardo Urech Garcia de la Vega 1

Outline

0. introduction 1. main concept a. double curvature b. tension

2. history a. domes b. cable suspended bridges c. tents

3. mathematics a. synclastic surfaces b. anticlastic surfaces

4. physics a. cables b. joints c. support elements d. membranes

5. case studies a. Frei Otto b. Fazlur Khan c. Bodo Rasch

6. innovation in tensile structures

7. conclusion

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Outline

0. introduction 1. main concept a. double curvature b. tension

2. history a. domes b. cable suspended bridges c. tents

3. mathematics a. synclastic surfaces b. anticlastic surfaces

4. physics a. cables b. joints c. support elements d. membranes

5. case studies a. Frei Otto b. Fazlur Khan c. Bodo Rasch


7. conclusion

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8. bibliography

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0. introduction The present paper summarizes the research I’ve done on tensile structures, and specifically membrane structures. The review will include a brief concept introduction, and some historic references that need to be mentioned; also some mathematical concepts are worth mentioning and the physical arrangement of these structures. Finally, we will see some examples of these structures by masters of the technology and we will take a look into the future of these fantastic architecture. It is worth to say that this material has been developed and adopted by the same few people in the most important examples. I’ve become familiar with engineers and architects like Fazlur R. Khan, Horst Berger, David Geiger, Paul Weidlinger or Frei Otto, a generation that has become the masters and pioneers in the use of tensile structures. 1. main concepts: terminology Tensile structures are possible because of two ideas, one physical and the other mathematical: tension and double curvature. For the tensile structures to stand, a unique equilibrium between shape and stress exists. This is the only way that membranes are able to bear the weight of snow and wind forces.

Figure 1. Double curvature surface.

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Figure 2. Tension

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Double curvature surfaces are surfaces that curve in two directions. They have two main curves with which these surfaces can be generated. Tension is an axial stress pulling to the ends of a rope or a cable. It is the opposite stress to compression. Tensile members can be as thin as their tensile capacity allows because they don’t suffer from buckling, like compressed members do. 2. history Some of the concepts that tensile structures use are not new. Humans have known them for centuries and used them in previous developments. For example: first wooden dwellings shaped like domes, cable bridges in China or tents used by many different cultures in the world. a.domes Some of the first dwellings that humans erected were erected following the rules of domes. For example, in Terra Amata, near Nize in France, there are remainders of these type of dwellings. These people stuck tree saplings in the ground forming an oval floor plan. Then they bent the saplings until they touched a ridge beam and laced to each other to form arches. This structure was the thatched with palm or grass. The saplings were held to the ground with rocks.

Figure 3. Sketch of dwelling in Terra Amata

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Later on, Heinz Isler designed his super-thin concrete domes. These were designed using the inverted catenary. This is important because the catenary is the form a cable assumes under its own weight, it is the optimal form to carry tension loads. So Isler’s domes are like inverted membranes that hang from four points. He was a pioneer using this kind of form finding with wet cloths. Therefore the entire shell is under compression, avoiding cracks. For example the indoor tennis sports center in Heimberg is a 3-inch thick shell spanning 80 feet!

Figure 4. Heinz Isler’s concrete shell

Figure 5. Interior of tennis courts.

b. suspended bridges Suspended bridges relay on the possiblity of cables to span long distances with little material. We can trace the origin of cable suspended bridges in Asia. They use the principle of load distribution. The beautiful Kuanksien Anlan bridge is made of bamboo cables. It was constructed more than 2000 years ago. The bridge is closed two months every year due to reparation work as bamboo, even though it is a strong material, needs careful maintenance. The ropes were made of bamboo and hemps, fibrous materials.

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Fi ure 6. Load distribution in cable.

Figure 7. Kuanksien Anlan bridge.

Later on, wrought iron chains were used in bridges until the adoption of high strength steel cables. This made possible larger spans with lesser material. Steel is an alloy of iron and carbon with very interesting mechanical properties, it is because of the existence of this material that we can build most of the structures of the world. Althoug Brooklyn bridge is not the first example, it is indeed one of the first bridges and a great example of cable bridges of the XX century.

Figure 7. Brooklyn bridge.

c. tents This is the most evident precedent of what we know today as tensile structures. Humankind has had needs for portable housing due to many different reasons. Military

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armies since the Roman Empire used textile tents in their campaigns all over Europe. Even today, tents are laid out on missions around the globe. Also, nomadic cultures such as the Bedouins, Moors, Berbers of Mongols developed tent structures which they could load onto their camels and horses and erect anywhere in matter of minutes.

Figure 8. Catherine de Medici signs peace outside her tent.

Figure 9. Tents provide shade in ho t desert climates.

To erect tents, the fabric was put under stress to keep it from flapping in the wind. Introducing internal stress is part of the assembly and erection proc ess. 3. mathematics In order to understand the forms that tensile structures adapt when subjected to stress we must immerse ourselves into the world of mathematics (for a least a moment). The inherent geometrical quality that enables the existence of tensile structures is the double curvature. Without double curvature fabric and membranes would swing and flap under wind forces and other stresses. The double curvature can be represented in one number, the Gaussian curvature, which is the product of the main curvatures. The sign of the Gaussian curvature can be used to characterize the surface.

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•

If both principal curvatures are the same sign: κ 1κ 2 > 0, then the Gaussian curvature is positive and the surface is said to have an elliptic point. At such points the surface will be dome like, locally lying on one side of its tangent plane. All sectional curvatures will have the same sign.

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If the principal curvatures have different signs: κ 1κ 2 < 0, then the Gaussian curvature is negative and the surface is said to have a hyperbolic point. At such points the surface will be saddle shaped. For two directions the sectional curvatures will be zero giving the asymptotic directions.

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If one of the principal curvature is zero: κ 1κ 2 = 0, the Gaussian curvature is zero and the surface is said to have a parabolic point.

This abstract concept can be understood fairly easily with diagrams.

Figure 10. Example of three surfaces with different Gaussian curvature.

a. synclastic surfaces Synclastic surfaces have positive Gaussian curvature. A typical example would be a dome. But, regarding membrane structures, synclastics are usually pneumatic domes. Air pressure inside puts stress into the membrane the stretches until it reaches its final form.

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For example, David Geiger’s US pavilion for Expo ’70 in Osaka was an airsupported membrane roof. As we can see, the whole space is pressurized, this air-pressure pushes the membrane outwards. To help shape the membrane, steel cables are attached to the fabric forming a diagrid. Fabric was made of fiberglass coated with Teflon fluorocarbon resin.

Figure 11. Interior of the US pavilion with structure of the fabric

Figure 12. Aerial view. Diagrid structure.

b. anticlastic surfaces Anticlastic surfaces are mainly hyperboloids and paraboloids. In tensile structures the most common geometries are related to the paraboloid, commonly known as saddle surface. The saddle surface is the easiest double curvature surface to build. The archetypical method is called the drying clothesline problem, starting from the 4-point structure. Two posts are stuck in the ground with a clothesline hanging in between. Another cable is attached to the ground perpendicularly to the first rope passing over and tensioning it. This process is repeated in both directions to increase the stiffness of the cable net.

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Figure 13. Drying clothesline problem illustration.

There are many examples of this 4 point surface in tensile structures. Most famous where designed by Frei Otto, one of the pioneers in the developing of this technology. The image in the left shows the music pavilion of the Bundesgarten in Kassel, Germany, erected in 1955. Note that the masts are inclined to ease construction and their stress. The right one shows an exhibition pavilion also designed by Otto in Leonberg, Germany, in 1988.

Figure 14. Music pavilion in Kassel.

Figure 15. Exhibition pavilion in Leonberg.

Frei Otto studied these surfaces with great attention. He figured out that saddle surfaces can be combined in many ways which provide great flexibility and almost infinite possibilities. Some of his sketches show this concern. Ridge and valley surfaces are arranged this way.

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Figure 16. Hand drawings from Frei Otto collection. Different combinations of saddle surfaces.

A very particular and interesting way to combine saddle surfaces is radially. It is very typical to use fabric structures in stadiums and other constructions that usually have a centralized shape. This common arrangement can be seen in the King Fahd International

Figure 17. King Fahd International Stadium in Riyadh.

Figure 18. Radial configuration o saddle surfaces.

Stadium designed by Ian Fraser, John Roberts & partners. However, structural engineer

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was Horst Berger, very well known for other fabric structures such as the Denver International Airport or the San Diego Convention Center. Saddle surfaces are the most common anticlastic surfaces, however, there is another family of surfaces related to polar geometry (surfaces of revolution). These are the tents, also very common in fabric structures. A very popular example of tents is he Hajj Terminal of h King Abdul Aziz International Airport in Jeddah. This will be studied in depth later.

Figure 19. Radial tent

Figure 20. Hajj Terminal in Jeddah by SOM.

4. physics The other main concept discussed above of the tensile structures is the prestress level it is submitted to. So now it is time to look into the materials and thei r properties. a. cables One of the main elements of the tensile structures are cables, they need to be carefully calculated and placed because they are the main carriers of the load. Cables are usually made of non-carbon steel alloys. They consist of strands twisted together. These strands are also made of multiple wires twisted in the same direction or the opposite. The twisting is made because when it is under high stress the strinds tend to bond together and push each other to the center. Ecostructures

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Figure 22. Different designs of clams for anchoring to a rigid structure.

These cables and their efficiency carrying ax ial loads made possible the existence of tensile structures. b. joints A critical aspect of tensile structures is the joint between cables and supporting elements. These are specially designed or the high stresses they suffer. There are many different terminations, but must common are clams between cables, or clam with loop with a thimble inside to help the cable not to break. Also here are swaged unions and eye splices but they are rarer.

Ecostructures Figure 22. Different designs of clams for anchoring to a rigid structure.

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c. rigid elements The main structure of a tensile structure carries the stresses down to the ground. Different elements conform the rigid system, such as masts, poles, beams or buttresses. And also, we have man y different choices of materials to conform the rigid structure. steel

The rigid elements in tensile structures must be strong, light, reliable, readily available, but also easy to fabricate, transport and erect. Structural steel satisfies these requirements excellently. Although, it needs protection against corrosion, either by painting, or by galvanizing. With this material we can make steel masts or trussed arches, and can satisfy infinite configurations. The ASU Skysong campus shows the two configurations. It was designed by FTL engineers in collaboration with Pei Cobb Freed & Partners.

Figure 23. ASU Skysong Campus.

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Figure 24. Curved triangulated beam.

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precast concrete

Prefabricated concrete can also be used for the rigid structure of a tensile structure. Pros are that it is -reproof and also weather self-protecting. It is available anywhere, and it is fairly inexpensive. At the AELTC indoor practice facility the fabric membrane hangs from precast concrete

Figure 25. This glowing effect is thanks to the translucency of the fabric envelope. AELTC indoor practice.

arches connected to piers which are cast in place. Designed by Ian C. King Associates and assisted by Horst Berger Associates. glue laminated wood

Laminated wood is suitable for use in arches, frames or columns. But, this material is vulnerable to fire; nonetheless, fire protection measures can be achieved easily enough and at a reasonable cost. Glulam arches support the fabric membrane Figure 26. Bullocks deparment store in San Jose, California.

at the Bullocks department store in San José,

California. Structural engineer was Horst Berger. c. membrane fabric

Membranes can be engineered to pass or reect light, heat, sound, or moisture, in whatever combination of directions one chooses. Three are the main factors of a fabric

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membrane: structural strenght, behavior during construction and use; and surface properties. There are two main materials in this field: polyester fabric with PVC coating, which is less expensive and can last 15 to 20 years; or Teflon-coated fiberglass, which has a higher performance. It is the primary material in tensile architecture. It is chemically inert and requires moisture protection. But, it is noncombustible, easy to keep clean, highly reflective and highly translucent.

Figure 27. Amphitheater in Grand Canyon designed by Structureflex. Fabric was made of polyester with a PVC coating.

Figure 28. The fabric in Riyadh King Fahd stadium was a Teflon-coated fiberglass.

ETFE

ETFE is also a very innovative material. Totally inert, it can be formed in cushions or in two-skin unique shapes. It is a great insulator, and also totally inert, and easy to clean. It has been widely used in pneumatic domes, but also with a structural steel frame filled

Figure 29. ETFE pneumatic dome in BC place in Vancouver designed by David Geiger.

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Figure 30. Interior of BC place. Sausage-like cushions.

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with cushions as in the Beijing Watercube. 5. case studies a. Frei Otto. German pavilion expo Montreal ‘67. Canada.

One of the earliest examples of tensile structures, the german pavilion was a cable net tent structure supported by steel masts. A curvacelously swinging roofscape was spread widely over a sculptured ground platform and differently raised exhibition terraces. The net was made of steel ropes 1/2’’ thick with a mesh width of 20’’ and it covered an area of 86,000 sqft. A membrane of PVC-coated Polyester fabric was suspended under the net for weather protection.

The pavilion was built according to Frei Otto’s and Rolf Gutbrod’s competition design in 1967. º Figure 31. Exterior of the cable net tents.

Figure 33. Plan.

Figure 32. Interior of german pavilion in Expo ’67 in Montreal.

Figure 34. Roof plan.

Figure 35. Section.

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The erection procedure followed a detailed sequence which before was elaborated carefully in the trial run with the Vaihingen test structure of the later IL institute building. First, all masts were put in position and stabilized with auxiliary guying cables. The cable net sections (each delivered in 30ft wide rolls) were assembled on round around the masts and hoisted up to the mast tops while further net sections for adjacent areas were added. After the completion of the cable net it was attached to the exterior anchor points and to the interior low points. The initial prestressing was achieved by jacking up the masts to their definite height. The final prestressing was brought in by tensioning the edge cables in two cycles around the perimeter outline. The roof membrane was assembled in parts on ground, including the clear eye parts, drawn up piece by piece, attached pointwise under the cable net and finally prestressed.

Figure 36. Steel fixture of the fabric to the cable net

Figure 37. Steel fixture of the fabric to the cable net

b. SOM. Hajj terminal of the King Abdul Aziz international airport. Jeddah. Saudi Arabia.

The firm was approached to design a terminal for the pilgrims that travel to Makkah every year via King Abdul-Aziz International Airport in Jeddah. They had some special

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requirements: tight schedule, grand open space for 500,000 pilgrims, only open one month a year... And also the site had its complications: very high temperatures, ultraviolet rays and a corrosive-marine environment.

Figure 38. Model of the Hajj terminal.

Figure 39. Environmental diagram.

The idea of creating a large enclosed artificial space was out of the question, and so creating large concrete lattice structures. A new structural concept was needed to provide shade and ventilation for 43 million square feet. To be able to erect the membrane, a second ring was designed to fit with a previously lifted ring.

Figure 40. Sketch of the rising of a tent.

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Figure 41. Sea of tents, note the person down to the left to get an idea of the scale of the pr oject.

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c. Bodo Rasch. Umbrellas of the Holy Mosque. Medina. Saudi Arabia.

The commission to design a convertible shade roof for two large courtyards of the Holy Mosque of the Prophet in Medina presented an unusual architectural and technical challenge. At this location, where tens of thousands of believers gather every day, the climatic conditions had to be improved without destroying the character of the open quadrangles and their familiar environment. The solution consisted of twelve convertible

Figure 42. Umbrellas shut down every evening when shading is not necessary anymore.

Figure 43. Umbrellas displayed to shade when hot temperatures.

parasols, 50x54 ft large and with a height of 45 ft at the eaves in their opened condition, which fit in perfectly with the proportions of the courtyards. With a span of 75 ft, measured diagonally across the corners, they are the largest ones built of this kind. The six parasols with their funnel-shaped membranes create the effect of translucent vaults, spanning between the columns and the arched arcades surrounding the courts, and produce a large free space. Their timeless form with its carefully designed ornaments match harmoniously with the traditional architecture.

The components of the parasol structure, mast column, arms and struts, are a welded construction of a high-strength fine grain steel. For good precision of the movements the bearing bores of the critical hinges were made by a (computer-controlled) NC-milling

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machine. This manufacturing precision of the movable parts together with the placement of the hydraulics pumping in a central plant makes an almost noiseless working of the p arasols possible.

Figure 44. Section showing the mechanism that allows the movement.

Figure 45. The masts allow the space to flow without distraction.

The parasol has altogether 20 arms: four long diagonal arms with two short passive arms each connected to them, eight middle arms, of which four are shorter and four longer. The parasol is opened and closed by a hydraulic cylinder on the column axis, whose upper end is pin-connected with all the active arms. In the closed condition the hydraulic cylinder has driven out completely at the top; to open the parasol it drives down, whereby the struts,

Figure 46. Diagram illustrating summer behavior of the place.

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Figure 47. Diagram illustrating umbrellas reflecting sun light.

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which are pinned above the capital, push the parasol arms, which are connected at the upper end of the hydraulic cylinder, to the outside, prestressing the parasol membrane. The electronic controls and hydraulic pump are housed in a central controls room in the basement and connected with the 12 parasols via high pressure pipes under the marble floor of the courtyards. Opening and closing times of the parasols are computed electronically for every day according to the position of the sun, dependent on the seasons, and allowing for weather conditions, outside temperature, wind and cloud cover and the results fed into the parasol controls. To make the climatic conditions in the courtyards more comfortable during the summer months, when the air temperatures in the shade can exceed 45°C, the parasols' controls are coupled with the bulding's air-conditioning system. Air outlets in the base and the capital of the parasol column distribute cool air noiselessly in a wide area, so that the entire quadrangle is cooled evenly and effectively. Wind stress is a huge problem for tensile structures. Wind tunnel tests for the specific situation in the courtyards served as a basis for the design of the structural elements of the parasols, which were designed for the opened and closed condition using a wind speed of 100 mph. An anemometer connected with the central controls prevents the opening and closing at wind speeds above 20 mph.

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a. AWM carpark in Munich, 1999

This facility was designed by Kurt Ackermann and Partners, and is a very particular mixture of concepts, its tents employ tensegrity ideas with tensile elements. Its very elegant structure employs the least material possible.

Figure 48. Interior of the car park.

Figure 49. Exterior view of the structure.

The protected parking facilities for the city's 150 refuse vehicles form one section of a three-part complex erected for the municipal Office for Waste Management. The roof over the vehicle port is a point-supported membrane structure in translucent PTFE-coated glass fiber fabric. The parking areas are laid out on two levels, consisting of an open concrete upper deck erected within a solid tank structure sunk into the ground. The deck also accommodates changing rooms and showers for 500 refuse workers. More than 85000 ft² in area, the tent roof is supported by a grid of 88 steel columns laid out at 30 x 36 ft centers. The membrane itself consists of 36 ft precut strips welded together on site.

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Figure 50. Detail of the compression strud with the structure of the tent.

The inner columns are protected against ramming by concrete plinths and have flexible seatings at the base. Horizontal loads are transmitted via raking peripheral columns to the lower-floor structure. Each of the 70 bays of the membrane is tensioned by a central

Figure 51. Detail view of an outside column.

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Figure 52. Detail view of the anchor on top of the column.

Figure 53. Braces connect the main column with another that is leaning and anchored to the ground to help carry to the ground the high h orizontal stresses.

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steel suspended column on the underside. The roof is drained by a vacuum system within the main steel columns. The lightweight membrane construction was facilitated by the fact that it contains no members subject to bending. It was designed as a structurally continuous area, with thin steel cables on top of the skin articulating the individual ba ys. b. new roof for the AWM carpark in Munich, Taiyo engineering, 2012

An application that is gaining a lot of popularity is the integration of membranes with photovoltaic systems. Large envelopes that are exposed to daylight many hours a day are a perfect target to put PV panels and generate free electricity for an ever growing power demand.

Figure 54. Interior view of the new carport in Munich

This is what Taiyo Europe achieved with their design for the AWM carpak in Munich. It is a ETFE structure with integrated Flexible Photovoltaic (FPV) panels. The 80,000 square feet roof covers a vast commercial transport hub in Munich, Germany. In total the long span roof houses 3080 FPV modules generating upwards of 141kW/hr. The FPV panels are contained in a three layer ETFE cushion system, in total 220 ETFE cushions form the blanket like roof.

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Figure 55. Interior view. Trusses hang between steel columns. Between them the cushions span helped by a structure that also adapts some tensegrity concepts.

The roof structure is made up of a three layer ETFE cushion system:

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Inner layer: 250 micron film printed with negative dot pattern in silver color.

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Middle layer: transparent 100 micron film fitted with integrated flexible photovoltaic system.

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Outer layer: transparent 250 micron film

Figure 56. Accessibility was an important concern, as this structure was built after a failure of the previous one because of high snow loads.

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Figure 57. The integration of ETFE with PV layers not only is efficient but also appealing in terms of aesthetics.

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c. umbrellas in market square in Avenches The original project, to develop a pergola for a restaurant in the marketplace of the Swiss town of Avenches, was expanded at the suggestion of the architects into a flexible covering for the entire square. This was ultimately commissioned by the local authority. Each of the lightweight sunshades can be inserted in one of the 16 hinged mountings, set upright and cranked taut. The cushion-like roof volumes consist of two membranes sloping in opposite directions. The watertight junctions and the drainage of the modules called for intensive development work. They are fitted with a zip on all four edges. Rainwater flows from the upper membrane of one sunshade into the lower membrane of the adjoining element and from there into the column and on to drainpipes beneath the square.

Figure 58. The umbrellas can be laid out in very different situations creating unique environments when the requirements of the weather or the program change.

Figure 59. When the maximum coverage is needed te umbrellas are squared and zipped altogether.

A medieval well discovered during foundation work – now covered with glass and illuminated – forms a central feature of the market place design.

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Figure 59. Detailed section of an umbrella


Figure 60. Zipped junction.

Figure 60. Drawings showing the anchorage of the structure to the ground.

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Figure 61. Axonometric.

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d. new applications heat responsive structures

Graduate students Felecia Davis and Delia Dumitrescu recently presented their research on interactive, knitted tension structures that respond to heat or electrical current. Using a tubular knitting machine, with electronic circuits running throughout the fabrics tested, Davis and Dumitrescu, tested and created four tubular fabric structures that change surface appearance when stimulated in response to current or heat. One prototype opens up regular “pores” when heated to high temperature; another changes opacity depending on an electrical current.

Figure 62. This prototypes make use of electric current to change their properties, like opacity or porosity.

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7. conclusion To conclude I’d like to make some comments about what I believe is the strongest in tensile structures and how do I see this structures in the future. First, I believe that working mainly in tension, the y are the most efficient structures to enclose spaces. Where climate conditions are fa vorable, tensile structures are one of the, if not the, best solution to cover large spaces such as stadiums, auditoriums or other spaces where program is basically a gathering with no very specific functions. However, Denver Airport proves that membranes can enclose also c omplex spaces. Anyway, I understand that membranes are not the best solution in cooler climates where thin fabric wouldn’t be the best insulation. Let’s see if flexible graphene p roves itself to be the solution. Second, it is aesthetically appealing. These structures are pu re, are true, are graceful. Combined with illumination a beautiful glow appears. They are light, and portable, if different elastic membranes appear they can be transformable. Flexibility matters, and in the XXI century more than ever before. Finally, because they are easy. They are relatively easy to construct. Specialized skill is not needed to erect them, and with computers helping out with the form finding, and precise digitalized cutters cutting the pattern, we will be able to experiment with form in ways we haven’t even imagined yet.

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