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33-431: A gridshell is a structure which derives its strength from its double curvature (in a similar way that a fabric structure derives strength from double curvature), but is constructed of a grid or lattice. The grid can be made of any material, but is most often wood (similar to garden trellis) or steel. Gridshells were pioneered in the 1896 by Russian engineer Vladimir Shukhov in constructions of exhibition pavilions of

66-473: A loom (frame) while the horizontal weft (also called the woof ) is drawn through (inserted over and under) the warp thread. In the terminology of weaving, each warp thread is called a warp end (synonymous terms are fill yarn and filling yarn ); a pick is a single weft thread that crosses the warp thread. In the 18th century, the Industrial Revolution facilitated the industrialisation of

99-524: A spiral warp , in which the warp is made up of a single, very long yarn wound in a spiral pattern around a pair of sticks or beams. The warp must be strong to be held under high tension during the weaving process, unlike the weft which carries almost no tension. This requires the yarn used for warp ends, or individual warp threads, to be made of spun and plied fibre . Traditionally natural fibres such as wool , linen , alpaca , and silk were used. However, improvements in spinning technology during

132-447: A circular arc (of radius R ). By equilibrium : The horizontal and vertical reactions : By geometry : 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 (from Hooke's Law , where the axial stiffness, k, is equal to k = E A L {\displaystyle k={\frac {EA}{L}}} ): where E

165-409: A fabric structure depends upon: 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

198-414: 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/mm (or 150±10 GPa ) and come in sizes from 3 to 90 mm diameter. Spiral strand suffers from construction stretch, where the strands compact when

231-416: A structural frame as they cannot derive their strength from double curvature. 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

264-408: 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,

297-421: 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 is tension artificially induced in the structural elements in addition to any self-weight or imposed loads they may carry. It

330-573: 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 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

363-403: 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. This form of construction has only become more rigorously analyzed and widespread in large structures in the latter part of

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396-458: 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: Combining the above equations gives: 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

429-430: Is the set of yarns or other things stretched in place on a loom before the weft is introduced during the weaving process. It is regarded as the longitudinal set in a finished fabric with two or more sets of elements. The term is also used for a set of yarns established before the interworking of weft yarns by some other method, such as finger manipulation, yielding wrapped or twined structures. Very simple looms use

462-523: Is used to ensure that the normally very flexible structural elements remain stiff under all possible loads. 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

495-587: The All-Russia industrial and art exhibition 1896 in Nizhny Novgorod . Large span timber gridshells are commonly constructed by initially laying out the main lath members flat in a regular square or rectangular lattice, and subsequently deforming this into the desired doubly curved form. This can be achieved by pushing the members up from the ground, as in the Mannheim Multihalle. More recent projects such as

528-525: 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. 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

561-582: The Industrial Revolution created cotton yarn of sufficient strength to be used in mechanized weaving. Later, synthetic fibres such as nylon or rayon were employed. While most weaving is weft-faced, warp-faced textiles are created using densely arranged warp threads. In these the design is in the warp, requiring all colors to be decided upon and placed during the first part of the weaving process, which cannot be changed. Such limitations of color placement create weavings defined by length-wise stripes and vertical designs. Many South American cultures, including

594-624: The Nizhny 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 the Sidney Myer Music Bowl , constructed in 1958. 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

627-600: The Savill Garden gridshell were constructed by laying the laths on top of a sizeable temporary scaffolding structure which is removed in phases to let the laths settle into the desired curvature. Tensile structure Most tensile structures are supported by some form of compression or bending elements, such as masts (as in The O 2 , formerly the Millennium Dome ), compression rings or beams. A tensile membrane structure

660-465: The actual equilibrium tension in the cable for a given loading w and a given pretension T 0 {\displaystyle T_{0}} . A similar solution to that above can be derived where: By equilibrium: Warp (weaving) In the manufacture of cloth , warp and weft are the two basic components in weaving to transform thread and yarn into textile fabrics. The vertical warp yarns are held stationary in tension on

693-411: The ancient Incas and Aymaras, employed backstrap weaving , which uses the weight of the weaver's body to control the tension of the loom. Because the weft does not have to be stretched on a loom the way the warp is, it can generally be less strong. It is usually made of spun fibre, originally wool , flax and cotton, today often of synthetic fibre such as nylon or rayon. The weft is threaded through

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726-505: The basic dichotomy of the world we live in, as in, up/down, in/out, black/white, Sun/Moon, yin/yang, etc. The expression is also used similarly for the underlying structure upon which something is built. The terms "warp" and "woof" are also found in some English translations of the Bible in the discussion of mildews found in cloth materials in Leviticus 13:48-59. In computing, a warp is a term for

759-481: The basic equation of equilibrium is: where: 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

792-460: The breaking load: 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

825-419: 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/mm 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

858-831: 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 1972 Summer Olympics in Munich . Since the 1960s, 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

891-595: 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 R 1 = − R 2 . 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

924-457: 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 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

957-548: The production of textile fabrics with the "picking stick" and the " flying shuttle ", which latter was invented by John Kay , in 1733. The mechanised power loom was patented by Edmund Cartwright in 1785, which allowed sixty picks per minute. The word weft derives from the Old English word wefan , to weave. Warp means "that across which the woof is thrown". (Old English wearp , from weorpan , to throw, cf. German werfen , Dutch werpen ). The warp

990-448: 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 the stretched grid method (SGM). 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

1023-737: 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

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1056-439: 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

1089-470: The warp using a " shuttle ", air jets or "rapier grippers". Handlooms were the original weaver's tool, with the shuttle being threaded through alternately raised warps by hand. The expression "warp and weft" (also "warp and woof" and "woof and warp") is used metaphorically the way "fabric" is; e.g., "the warp and woof of a student's life" equates to "the fabric of a student's life". Warp and weft are sometimes used even more generally in literature to describe

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