What is the introduction of tensile structure?

Structure whose members are only in tension

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In structural engineering, a tensile structure is a construction of elements carrying only tension and no compression or bending. The term tensile should not be confused with tensegrity, which is a structural form with both tension and compression elements. Tensile structures are the most common type of thin-shell structures.

Most tensile structures are supported by some form of compression or bending elements, such as masts (as in The O2, formerly the Millennium Dome), compression rings or beams.

A tensile membrane structure is most often used as a roof, as they can economically and attractively span large distances. Tensile membrane structures may also be used as complete buildings, with a few common applications being sports facilities, warehousing and storage buildings, and exhibition venues.

History

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This form of construction has only become more rigorously analyzed and widespread in large structures in the latter part of the twentieth century. Tensile structures have long been used in tents, where the guy ropes and tent poles provide pre-tension to the fabric and allow it to withstand loads.

Russian engineer Vladimir Shukhov was one of the first to develop practical calculations of stresses and deformations of tensile structures, shells and membranes. Shukhov designed eight tensile structures and thin-shell structures exhibition pavilions for the Nizhny Novgorod Fair of , covering the area of 27,000 square meters. A more recent large-scale use of a membrane-covered tensile structure is the Sidney Myer Music Bowl, constructed in .

Antonio Gaudi used the concept in reverse to create a compression-only structure for the Colonia Guell Church. He created a hanging tensile model of the church to calculate the compression forces and to experimentally determine the column and vault geometries.

The concept was later championed by German architect and engineer Frei Otto, whose first use of the idea was in the construction of the West German pavilion at Expo 67 in Montreal. Otto next used the idea for the roof of the Olympic Stadium for the Summer Olympics in Munich.

Since the s, tensile structures have been promoted by designers and engineers such as Ove Arup, Buro Happold, Frei Otto, Mahmoud Bodo Rasch, Eero Saarinen, Horst Berger, Matthew Nowicki, Jörg Schlaich, and David Geiger.

Steady technological progress has increased the popularity of fabric-roofed structures. The low weight of the materials makes construction easier and cheaper than standard designs, especially when vast open spaces have to be covered.

Types of structure with significant tension members

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Linear structures

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Three-dimensional structures

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• Bicycle wheel (can be used as a roof in a horizontal orientation)
• 3D cable trusses
• Tensegrity structures

Surface-stressed structures

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• Prestressed membranes
• Pneumatically stressed membranes
• Gridshell
• Fabric structure

Cable and membrane structures

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The world's first steel membrane roof and lattice steel shell in the Shukhov Rotunda, Russia,

Membrane materials

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Common materials for doubly curved fabric structures are PTFE-coated fiberglass and PVC-coated polyester. These are woven materials with different strengths in different directions. The warp fibers (those fibers which are originally straight&#;equivalent to the starting fibers on a loom) can carry greater load than the weft or fill fibers, which are woven between the warp fibers.

Other structures make use of ETFE film, either as single layer or in cushion form (which can be inflated, to provide good insulation properties or for aesthetic effect&#;as on the Allianz Arena in Munich). ETFE cushions can also be etched with patterns in order to let different levels of light through when inflated to different levels.

In daylight, fabric membrane translucency offers soft diffused naturally lit spaces, while at night, artificial lighting can be used to create an ambient exterior luminescence. They are most often supported by a structural frame as they cannot derive their strength from double curvature.[1]

Simple suspended bridge working entirely in tension

Cables

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Cables can be of mild steel, high strength steel (drawn carbon steel), stainless steel, polyester or aramid fibres. Structural cables are made of a series of small strands twisted or bound together to form a much larger cable. Steel cables are either spiral strand, where circular rods are twisted together and "glued" using a polymer, or locked coil strand, where individual interlocking steel strands form the cable (often with a spiral strand core).

Spiral strand is slightly weaker than locked coil strand. Steel spiral strand cables have a Young's modulus, E of 150±10 kN/mm2 (or 150±10 GPa) and come in sizes from 3 to 90 mm diameter.[citation needed] Spiral strand suffers from construction stretch, where the strands compact when the cable is loaded. This is normally removed by pre-stretching the cable and cycling the load up and down to 45% of the ultimate tensile load.

Locked coil strand typically has a Young's Modulus of 160±10 kN/mm2 and comes in sizes from 20 mm to 160 mm diameter.

The properties of the individual strands of different materials are shown in the table below, where UTS is ultimate tensile strength, or the breaking load:

Cable material E (GPa) UTS (MPa) Strain at 50% of UTS Solid steel bar 210 400&#;800 0.24% Steel strand 170 &#; 1% Wire rope 112 &#; 1.5% Polyester fibre 7.5 910 6% Aramid fibre 112 2.5%

Structural forms

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Air-supported structures are a form of tensile structures where the fabric envelope is supported by pressurised air only.

The majority of fabric structures derive their strength from their doubly curved shape. By forcing the fabric to take on double-curvature the fabric gains sufficient stiffness to withstand the loads it is subjected to (for example wind and snow loads). In order to induce an adequately doubly curved form it is most often necessary to pretension or prestress the fabric or its supporting structure.

The behaviour of structures which depend upon prestress to attain their strength is non-linear, so anything other than a very simple cable has, until the s, been very difficult to design. The most common way to design doubly curved fabric structures was to construct scale models of the final buildings in order to understand their behaviour and to conduct form-finding exercises. Such scale models often employed stocking material or tights, or soap film, as they behave in a very similar way to structural fabrics (they cannot carry shear).

Soap films have uniform stress in every direction and require a closed boundary to form. They naturally form a minimal surface&#;the form with minimal area and embodying minimal energy. They are however very difficult to measure. For a large film, its weight can seriously affect its form.

For a membrane with curvature in two directions, the basic equation of equilibrium is:

w = t 1 R 1 + t 2 R 2 {\displaystyle w={\frac {t_{1}}{R_{1}}}+{\frac {t_{2}}{R_{2}}}}

where:

• R1 and R2 are the principal radii of curvature for soap films or the directions of the warp and weft for fabrics
• t1 and t2 are the tensions in the relevant directions
• w is the load per square metre

Lines of principal curvature have no twist and intersect other lines of principal curvature at right angles.

A geodesic or geodetic line is usually the shortest line between two points on the surface. These lines are typically used when defining the cutting pattern seam-lines. This is due to their relative straightness after the planar cloths have been generated, resulting in lower cloth wastage and closer alignment with the fabric weave.

In a pre-stressed but unloaded surface w = 0, so t 1 R 1 = &#; t 2 R 2 {\displaystyle {\frac {t_{1}}{R_{1}}}=-{\frac {t_{2}}{R_{2}}}} .

In a soap film surface tensions are uniform in both directions, so R1 = &#;R2.

It is now possible to use powerful non-linear numerical analysis programs (or finite element analysis) to formfind and design fabric and cable structures. The programs must allow for large deflections.

The final shape, or form, of a fabric structure depends upon:

• shape, or pattern, of the fabric
• the geometry of the supporting structure (such as masts, cables, ringbeams etc.)
• the pretension applied to the fabric or its supporting structure

It is important that the final form will not allow ponding of water, as this can deform the membrane and lead to local failure or progressive failure of the entire structure.

Snow loading can be a serious problem for membrane structure, as the snow often will not flow off the structure as water will. For example, this has in the past caused the (temporary) collapse of the Hubert H. Humphrey Metrodome, an air-inflated structure in Minneapolis, Minnesota. Some structures prone to ponding use heating to melt snow which settles on them.

Saddle Shape

There are many different doubly curved forms, many of which have special mathematical properties. The most basic doubly curved from is the saddle shape, which can be a hyperbolic paraboloid (not all saddle shapes are hyperbolic paraboloids). This is a double ruled surface and is often used in both in lightweight shell structures (see hyperboloid structures). True ruled surfaces are rarely found in tensile structures. Other forms are anticlastic saddles, various radial, conical tent forms and any combination of them.

Pretension

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Pretension is tension artificially induced in the structural elements in addition to any self-weight or imposed loads they may carry. It is used to ensure that the normally very flexible structural elements remain stiff under all possible loads.[2][3]

A day to day example of pretension is a shelving unit supported by wires running from floor to ceiling. The wires hold the shelves in place because they are tensioned &#; if the wires were slack the system would not work.

Pretension can be applied to a membrane by stretching it from its edges or by pretensioning cables which support it and hence changing its shape. The level of pretension applied determines the shape of a membrane structure.

Alternative form-finding approach

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The alternative approximated approach to the form-finding problem solution is based on the total energy balance of a grid-nodal system. Due to its physical meaning this approach is called the stretched grid method (SGM).

Simple mathematics of cables

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Transversely and uniformly loaded cable

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A uniformly loaded cable spanning between two supports forms a curve intermediate between a catenary curve and a parabola. The simplifying assumption can be made that it approximates a circular arc (of radius R).

By equilibrium:

The horizontal and vertical reactions :

H = w S 2 8 d {\displaystyle H={\frac {wS^{2}}{8d}}}

V = w S 2 {\displaystyle V={\frac {wS}{2}}}

By geometry:

The length of the cable:

L = 2 R arcsin &#; S 2 R {\displaystyle L=2R\arcsin {\frac {S}{2R}}}

The tension in the cable:

T = H 2 + V 2 {\displaystyle T={\sqrt {H^{2}+V^{2}}}}

By substitution:

T = ( w S 2 8 d ) 2 + ( w S 2 ) 2 {\displaystyle T={\sqrt {\left({\frac {wS^{2}}{8d}}\right)^{2}+\left({\frac {wS}{2}}\right)^{2}}}}

The tension is also equal to:

T = w R {\displaystyle T=wR}

The extension of the cable upon being loaded is (from Hooke's Law, where the axial stiffness, k, is equal to k = E A L {\displaystyle k={\frac {EA}{L}}} ):

e = T L E A {\displaystyle e={\frac {TL}{EA}}}

where E is the Young's modulus of the cable and A is its cross-sectional area.

If an initial pretension, T 0 {\displaystyle T_{0}} is added to the cable, the extension becomes:

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e = L &#; L 0 = L 0 ( T &#; T 0 ) E A {\displaystyle e=L-L_{0}={\frac {L_{0}(T-T_{0})}{EA}}}

Combining the above equations gives:

L 0 ( T &#; T 0 ) E A + L 0 = 2 T arcsin &#; ( w S 2 T ) w {\displaystyle {\frac {L_{0}(T-T_{0})}{EA}}+L_{0}={\frac {2T\arcsin \left({\frac {wS}{2T}}\right)}{w}}}

By plotting the left hand side of this equation against T, and plotting the right hand side on the same axes, also against T, the intersection will give the actual equilibrium tension in the cable for a given loading w and a given pretension T 0 {\displaystyle T_{0}} .

Cable with central point load

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A similar solution to that above can be derived where:

By equilibrium:

W = 4 T d L {\displaystyle W={\frac {4Td}{L}}}

d = W L 4 T {\displaystyle d={\frac {WL}{4T}}}

By geometry:

L = S 2 + 4 d 2 = S 2 + 4 ( W L 4 T ) 2 {\displaystyle L={\sqrt {S^{2}+4d^{2}}}={\sqrt {S^{2}+4\left({\frac {WL}{4T}}\right)^{2}}}}

This gives the following relationship:

L 0 + L 0 ( T &#; T 0 ) E A = S 2 + 4 ( W ( L 0 + L 0 ( T &#; T 0 ) E A ) 4 T ) 2 {\displaystyle L_{0}+{\frac {L_{0}(T-T_{0})}{EA}}={\sqrt {S^{2}+4\left({\frac {W(L_{0}+{\frac {L_{0}(T-T_{0})}{EA}})}{4T}}\right)^{2}}}}

As before, plotting the left hand side and right hand side of the equation against the tension, T, will give the equilibrium tension for a given pretension, T 0 {\displaystyle T_{0}} and load, W.

Tensioned cable oscillations

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The fundamental natural frequency, f1 of tensioned cables is given by:

f 1 = ( T m ) 2 L {\displaystyle f_{1}={\frac {\sqrt {\left({\frac {T}{m}}\right)}}{2L}}}

where T = tension in newtons, m = mass in kilograms and L = span length.

Notable structures

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Rotunda by Vladimir Shukhov Nizhny Novgorod Rotunda and rectangular pavilion by Vladimir Shukhov in Nizhny Novgorod

Gallery of well-known tensile structures

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Classification numbers

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The Construction Specifications Institute (CSI) and Construction Specifications Canada (CSC), MasterFormat Edition, Division 05 and 13:

• 05 16 00 &#; Structural Cabling
• 05 19 00 - Tension Rod and Cable Truss Assemblies
• 13 31 00 &#; Fabric Structures
• 13 31 23 &#; Tensioned Fabric Structures
• 13 31 33 &#; Framed Fabric Structures

CSI/CSC MasterFormat Edition:

• &#; Cable-Supported Structures
• &#; Fabric Structures

See also

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References

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Further reading

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Historically inspired by some of the first man-made shelters&#;such as the black tents first developed using camel leather by the nomads of the Sahara Desert, Saudi Arabia, and Iran, as well as the structures used by Native American tribes&#;tensile structures offer a range of positive benefits compared to other structural models.

Tensile structure is the term usually used to refer to the construction of roofs using a membrane held in place on steel cables. Their main characteristics are the way in which they work under stress tensile, their ease of pre-fabrication, their ability to cover large spans, and their malleability. This structural system calls for a small amount of material thanks to the use of thin canvases, which when stretched using steel cables, create surfaces capable of overcoming the forces imposed upon them.

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Predominantly used in coverings of sports centers, of arenas, and industrial and agroindustrial constructions, tensile structures are based on the old systems used during the Roman Empire. However, from the Roman period until the mid-20th century, due to the low demand, usability, and lack of manufacturers of cables, canvasses, and connections capable of resisting the forces generated, there were few technological advances. It was only after the Industrial Revolution and the triggering of the era of Fordism that new developments were able to meet the intrinsic needs of this construction system. The low cost of mass production and the demand for systems capable of adapting to the most varied terrains with large spans, such as circus tents for example, encouraged the development of the technique.

The instability caused in previous models by the application of interlaced cables and very light covers, resulting in structural deficiencies, was solved during the middle of the last century. This was done thanks to a system of steel cables and fiber membranes with a high degree of strength, together with layers of waterproof coatings, giving protection against ultraviolet rays, fungus, fire, and allowing greater or less translucency and reflectivity.

Such progress was only possible thanks to the physical-structural studies initiated by German architect and engineer Frei Otto, who since the s conducted the first scientific studies and the first works of roofing using tensioned steel cables combined with membranes.

As a student, Otto visited the office of Fred Severud, where he saw the Raleigh Arena in North Carolina and was impressed by the bold aesthetics and propitious comfort of the project. Back in Germany, he began to explore small-scale physical models, empirically generating several surfaces, by means of chains, pulled cables, and elastic membranes.

Convinced by the usefulness of tensioned roofs, he developed the first large-scale project using the system, which later enabled projects including Olympic stadiums, clubs, zoo, and pavilions. In he founded the Center for the Development of Light Construction in Berlin. Seven years later, in he created the Institute of Light Structures in Berlin at the University of Stuttgart, Germany.

Author of notable projects passed by experiments and technical refinement, such as the German Pavilion for the Expo in Montreal and the Munich Olympic Stadium in , the architect is renowned for his intense research work and was honored with the RIBA Royal Gold Medal in and the Pritzker Prize. Frei Otto is still responsible for the first comprehensive book on tensile structures&#;"Das Hangende Dach" ()&#;and intensified the idea of reinventing material rationality, prefabrication, flexibility and luminosity over internal space, and even sustainability, when the term was not yet used in architecture.

There are three different main classifications in the field of tensile construction systems: membrane tensioned structures, mesh tensioned, and pneumatic structures. The first relates to structures in which a membrane is held by cables, allowing the distribution of the tensile stresses through its own form. The second case corresponds to structures in which a mesh of cables carries the intrinsic forces, transmitting them to separate elements, for example, sheets of glass or wood. In the third case, a protective membrane is supported by means of air pressure.

Structurally, the system is formalized by combining three elements: membranes, rigid structures such as pole and masts, and cables.

The membranes of PVC-coated polyester fibers have greater ease in factory production and installation; lower cost; and medium durability&#;around 10 years. 

PTFE-coated glass fiber membranes have superior durability&#;around 30 years; and greater resistance to the elements (sun, rain, and winds); however, they require skilled labor.

In this system, there are two types of support: direct and indirect. The direct supports are those in which the construction is arranged directly on the rest of the building structure, while the second case is arranged from a raised point such as a mast. 

The cables, which are responsible for the distribution of the tensile stresses and the hardening of the canvasses, are classified in one of two ways according to the action which they perform: load-bearing and stabilizing. Both types of cable cross orthogonally, ensuring strength in two directions and avoiding deformations. The load-bearing cables are those that directly receive the external loads, fixed at the highest points. On the other hand, the stabilizing cables are responsible for strengthening the load-bearing cables and cross the load-bearing cables orthogonally. It is possible to avoid attaching the stabilizing cables to the ground by using a peripheral fixation cable.  

Further, some nomenclatures for different cables are generated according to their position: a ridge-line cable refers to the uppermost cable; while valley cables are fixed below all other cables; radial cables are stabilizer cables in the form of a ring. Ridge-line cables support gravitational loads while valley cables support wind loads.

Here are some projects already published on Archdaily using tensile structures:

References

ARCOLINI, Tatiana; BARRADAS, Paula. Coberturas tensionadas são soluções eficientes e econômicas. Available at: <https://www.aecweb.com.br/cont/m/rev/coberturas-tensionadas-sao-solucoes-eficientes-e-economicas__10_0>. Acessed on 24 Dec .
Tensoestruturas: Cabos e Membranas. Available at: http://wwwo.metalica.com.br/tensoestruturas-cabos-e-membranas. Acessed on: 24 Dec .
Tensoestruturas: Cobertura de Estruturas de Membrana Tensionada. Available at: <http://wwwo.metalica.com.br/tensoestrutura-cobertura-de-estruturas-de-membrana-tensionada>. Acessed on 24 Dec .

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