HYPERBOLOID STRUCTURE

'Hyperboloid structures' are architectural structures designed with hyperboloid geometry. Often these are tall structures such as towers where the hyperboloid geometry's structural strength is used to support an object high off the ground, however hyperboloid geometry is also often used for decorative effect as well as structural economy. The first hyperboloid structures were built by Russian engineer Vladimir Shukhov (1853-1939).
==Work of Shukhov==
In the 1880s, Shukhov began to work on the problem of the design of roof systems to use a minimum of materials, time and labor. His calculations were most likely derived from mathematician Pafnuty Chebyshev’s work on the theory of best approximations of functions. Shukhov’s mathematical explorations of efficient roof structures led to his invention of a new system that was innovative both structurally and spatially. By applying his analytical skills to the doubly-curved surfaces Nikolai Lobachevsky named "hyperbolic," Shukhov derived a family of equations that led to new structural and constructional systems, known as hyperboloids of revolution and hyperbolic paraboloids.
The hyperboloid roofs of the exhibition pavilions of the 1896 All-Russian Industrial and Handicrafts Exposition in Nizhny Novgorod were the first publicly prominent examples of Shukhov’s new system. The roofs of these pavilions were doubly-curved surfaces formed entirely of a lattice of straight angle-iron and flat iron bars. Shukhov himself called them “metal lace.” The patent of this system, for which Shukhov applied in 1895, was awarded in 1899.
Two pavilions of this type were built for the Nizhni-Novgorod exposition, one oval in plan and one circular.
Shukhov also turned his attention to the development of an efficient and easily constructed structural system for a tower carrying a large gravity load at the top - the problem of the water tower. His solution was inspired by observing the action of a woven basket holding up a heavy weight. Again, it took the form of a doubly-curved surface constructed of a light network of straight iron bars and angle-iron.
Shukhov's patent for an ''azhurnaia bashnia'' ("lace tower," i.e., lattice tower) was submitted in 1896 and awarded in 1899. Shukhov built his first example as a water tower (hyperbolic shell) for the 1896 All-Russian Exposition.
Over the next twenty years, he designed and built close to two hundred of these towers, no two exactly alike, most with heights in the range of 15m to 40m. The world's first hyperboloid tower is located in Polibino of Lipetsk Oblast, Russia.
At least as early as 1911, Shukhov began experimenting with the concept of forming a tower out of stacked sections of hyperboloids. Stacking the sections permitted the form of the tower to taper more at the top, with a less pronounced “waist” between the shape-defining rings at bottom and top. Increasing the number of sections would increase the tapering of the overall form, to the point that it began to resemble a cone.
By 1918 Shukhov had developed this concept into the design of a nine-section stacked hyperboloid radio transmission tower for Moscow. Shukhov designed a 350m tower, which would have surpassed the Eiffel tower in height by 50m, while using less than a quarter of the amount of material. His design, as well as the full set of supporting calculations analyzing the hyperbolic geometry and sizing the network of members, was completed by February of 1919; however, the 2200 tons of steel required to build the tower to 350m were not available. In July 1919, Lenin decreed that the tower should be built to a height of 150m, and the necessary steel was to be made available from the army’s supplies. Construction of the smaller tower with six stacked hyperboloids began within a few months, and Shukhov Tower was completed by March of 1922.

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Other architects

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Other architects

Antoni Gaudi and Shukhov carried out experiments with hyperboloid structures practically simultaneously in 1880-1895. They did those experiments independently from each other. Antoni Gaudi used structures in the form of hyperbolic paraboloid (hypar) and hyperboloid of revolution in the Sagrada Família in 1910.^[1] In the Palau Güell, there is one set of interior columns along the main facade with hyperbolic capitals. Also, it appears that the crown of the famous parabolic vault is a hyperboloid. The vault of one of the stables at the Church of Colònia Güell appears to be a hyperboloid. There is one unique column of sorts in the Park Güell that is a hyperboloid. Also, in the Sagrada Família, there are a few places on the nativity facade - a design not equated with Gaudi's ruled-surface design, where the hyperboloid crops up. All around the scene with the pelican, there are numberous examples (including the basket held by one of the figures). There is a hyperboloid adding structural stability to the cypress tree (by connecting it to the bridge). And finally, the "bishop's mitre" spires are capped with hyperboloids.
The famous Spanish engineer and architect Eduardo Torroja designed thin-shell water tower in Fedala^[2] and the roof of hippodrome "Zarzuela"^[3] in the form of hyperboloid of revolution.
Le Corbusier and Félix Candela used hyperboloid structures (hypar).
The Georgia Dome is the first Hypar-Tensegrity dome to be built. ^[4]

See also

★ List of Hyperboloid structures

★ The world's first Hyperboloid structure

★ Tensile structure

★ Thin-shell structure

★ Cooling tower

References

1. [1]
2. water tower in Fedala
3. hippodrome "Zarzuela"
4. [2]

External links

★ Anticlastic hyperboloid shells

★ Shells: Hyperbolic paraboloids (hypar)

★ Hyperbolic Paraboloids & Concrete Shells

★ Analyses hyperboloidal Shells

★ Special Structures

★ "The Nijni-Novgorod exhibition: Water tower, room under construction, springing of 91 feet span", "The Engineer", № 19.3.1897, P.292-294, London, 1897.

★ Rainer Graefe: “Vladimir G. Šuchov 1853-1939 - Die Kunst der sparsamen Konstruktion.”, S.192, Stuttgart, DVA, 1990. [3]

★ The Origins of Modernism in Russian Architecture

★ Elizabeth Cooper English: “Arkhitektura i mnimosti”: The origins of Soviet avant-garde rationalist architecture in the Russian mystical-philosophical and mathematical intellectual tradition”, a dissertation in architecture, 264p., University of Pennsylvania, 2000.

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