 | This article includes a list ofgeneral references, butit lacks sufficient correspondinginline citations. Please help toimprove this article byintroducing more precise citations.(September 2011) (Learn how and when to remove this message) |
Instructural engineering, atensile structure is aconstruction of elements carrying onlytension and nocompression orbending. The termtensile should not be confused withtensegrity, which is a structural form with both tension and compression elements. Tensile structures are the most common type ofthin-shell structures.
Most tensile structures are supported by some form of compression or bending elements, such as masts (as inThe O2, formerly theMillennium Dome), compression rings or beams.
Atensile membrane structure is most often used as aroof, 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.
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 intents, where theguy ropes and tent poles provide pre-tension to the fabric and allow it to withstand loads.
Russian engineerVladimir 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 andthin-shell structures exhibition pavilions for theNizhny Novgorod Fair of 1896, covering the area of 27,000 square meters. A more recent large-scale use of a membrane-covered tensile structure is theSidney Myer Music Bowl, constructed in 1958.
Antonio Gaudi used the concept in reverse to create a compression-only structure for theColonia 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 byGerman architect and engineerFrei Otto, whose first use of the idea was in the construction of theWest German pavilion at Expo 67 in Montreal. Otto next used the idea for the roof of the Olympic Stadium for the1972 Summer Olympics inMunich.
Since the 1960s,tensile structures have been promoted bydesigners andengineers such asOve Arup,Buro Happold,Frei Otto,Mahmoud Bodo Rasch,Eero Saarinen,Horst Berger,Matthew Nowicki,Jörg Schlaich, andDavid 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.
Common materials for doubly curved fabric structures arePTFE-coatedfiberglass andPVC-coatedpolyester. These are woven materials with different strengths in different directions. Thewarp fibers (those fibers which are originally straight—equivalent to the starting fibers on a loom) can carry greater load than theweft or fill fibers, which are woven between the warp fibers.
Other structures make use ofETFE film, either as single layer or in cushion form (which can be inflated, to provide good insulation properties or for aesthetic effect—as on theAllianz Arena inMunich). 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]
Cables can be ofmild steel,high strength steel (drawn carbon steel),stainless steel,polyester oraramid 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 aYoung's modulus,E of 150±10 kN/mm2 (or 150±10GPa) 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 isultimate 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 | 1550–1770 | 1% |
| Wire rope | 112 | 1550–1770 | 1.5% |
| Polyester fibre | 7.5 | 910 | 6% |
| Aramid fibre | 112 | 2800 | 2.5% |
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 sufficientstiffness to withstand the loads it is subjected to (for examplewind andsnow loads). In order to induce an adequately doubly curved form it is most often necessary topretension 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 1990s, 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:
where:
Lines ofprincipal curvature have no twist and intersect other lines of principal curvature at right angles.
Ageodesic orgeodetic 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 surfacew = 0, so.
In a soap film surface tensions are uniform in both directions, soR1 = −R2.
It is now possible to use powerfulnon-linearnumerical analysis programs (orfinite 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:
It is important that the final form will not allowponding 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 theHubert H. Humphrey Metrodome, an air-inflated structure inMinneapolis, Minnesota. Some structures prone toponding use heating to melt snow which settles on them.
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 ahyperbolic paraboloid (not all saddle shapes are hyperbolic paraboloids). This is a doubleruled surface and is often used in both in lightweight shell structures (seehyperboloid structures). True ruled surfaces are rarely found in tensile structures. Other forms areanticlastic saddles, various radial, conical tent forms and any combination of them.
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.
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 thestretched grid method (SGM).
A uniformly loaded cable spanning between two supports forms a curve intermediate between acatenary curve and aparabola. The simplifying assumption can be made that it approximates a circular arc (of radiusR).
Byequilibrium:
The horizontal and vertical reactions :
Bygeometry:
The length of the cable:
The tension in the cable:
By substitution:
The tension is also equal to:
The extension of the cable upon being loaded is (fromHooke's Law, where the axial stiffness,k, is equal to):
whereE is theYoung's modulus of the cable andA is its cross-sectionalarea.
If an initial pretension, is added to the cable, the extension becomes:
Combining the above equations gives:
By plotting the left hand side of this equation againstT, and plotting the right hand side on the same axes, also againstT, the intersection will give the actual equilibrium tension in the cable for a given loadingw and a given pretension.
A similar solution to that above can be derived where:
By equilibrium:
By geometry:
This gives the following relationship:
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, and load,W.
The fundamentalnatural frequency,f1 of tensioned cables is given by:
whereT = tension innewtons,m =mass in kilograms andL = span length.
TheConstruction Specifications Institute (CSI) and Construction Specifications Canada (CSC),MasterFormat 2018 Edition, Division 05 and 13:
CSI/CSCMasterFormat 1995 Edition:
{{citation}}: CS1 maint: DOI inactive as of November 2024 (link)
