- Hyperboloid structure
**Hyperboloid structures**arearchitectural structure s designed withhyperboloid 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, but hyperboloid geometry is also often used for decorative effect as well as structural economy. The first hyperboloid structures were built by Russian engineerVladimir Shukhov (1853-1939). [*cite web | title = Hyperboloid water tower | date = 2007 | publisher = Nicolas Janburg, ICS | work = International Database and Gallery of Structures | url = http://en.structurae.de/structures/data/index.cfm?ID=s0037128 | accessdate = 2007-11-28*] The world's first hyperboloid tower is located inPolibino, Lipetsk Oblast , Russia.**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 surfacesNikolai Lobachevsky named "hyperbolic", Shukhov derived a family of equations that led to new structural and constructional systems, known as hyperboloids of revolution andhyperbolic paraboloid s. The steelgridshell s of the exhibition pavilions of the 1896 All-Russian Industrial and Handicrafts Exposition inNizhny Novgorod were the first publicly prominent examples of Shukhov's new system. Two pavilions of this type were built for the Nizhni Novgorod exposition, one oval in plan and one circular. The roofs of these pavilions were doubly-curvedgridshell s formed entirely of a lattice of straight angle-iron and flat iron bars. Shukhov himself called them "azhurnaia bashnia" ("lace tower", i.e.,lattice tower ). The patent of this system, for which Shukhov applied in 1895, was awarded in 1899.Shukhov also turned his attention to the development of an efficient and easily constructed structural system (

gridshell ) for atower carrying a large gravity load at the top - the problem of thewater 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. 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 12m to 68m.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 theEiffel 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 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, andShukhov Tower was completed by March 1922.**Other architects**Antoni Gaudi and Shukhov carried out experiments with hyperboloid structures practically simultaneously, but independently, in 1880-1895. Antoni Gaudi used structures in the form of hyperbolicparaboloid (hypar) and hyperboloid of revolution in theSagrada Família in 1910. [*cite web | title = Drawing Together Euclidean and Topological Threads (pdf) | last = Burry | first = M.C., J.R. Burry, G.M. Dunlop and A. Maher | work = Presented at SIRC 2001 - the Thirteenth Annual Colloquium of the Spatial Information Research Center | publisher = University of Otago | place = Dunedin, New Zealand | date = 2001 | url = http://www.business.otago.ac.nz/SIRC05/conferences/2001/05_burry.pdf | accessdate = 2007-11-28*] In the Sagrada Família, there are a few places on the nativityfacade - a design not equated with Gaudi's ruled-surface design, where the hyperboloid crops up. All around the scene with the pelican, there are numerous 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). The "bishop's mitre" spires are capped with hyperboloids.In the

Palau Güell , there is one set of interior columns along the main facade with hyperbolic capitals. The crown of the famous parabolic vault is a hyperboloid. The vault of one of the stables at theChurch of Colònia Güell is a hyperboloid. There is a unique column in thePark Güell that is a hyperboloid. The famous Spanish engineer and architectEduardo Torroja designed a thin-shell water tower in Fedala [*cite web | title = Fedala Reservoir | date = 2007 | publisher = Nicolas Janburg, ICS | work = International Database and Gallery of Structures | url = http://en.structurae.de/structures/data/index.cfm?ID=s0002124 | accessdate = 2007-11-28*] and the roof of hippodrome "Zarzuela" [*cite web | title = Zarzuela Hippodrome | date = 2007 | publisher = Nicolas Janburg, ICS | work = International Database and Gallery of Structures | url = http://en.structurae.de/structures/data/index.cfm?ID=s0000430 | accessdate = 2007-11-28*] in the form of hyperboloid of revolution.Le Corbusier andFélix Candela used hyperboloid structures (hypar ).A hyperboloid

cooling tower was patented by Frederik van Iterson and Petronelle Kuypers in 1929. [*[*]*http://v3.espacenet.com/textdoc?DB=EPODOC&IDX=GB320505&F=0 esp@cenet document view*]The

Georgia Dome was the first Hypar-Tensegrity dome to be built. [*cite web | title = Analysis of the Georgia Dome Cable Roof | last = Castro | first = Gerardo and Matthys P. Levy | work = Proceedings of the Eighth Conference of Computing in Civil Engineering and Georgraphic Information Systems Symposium | publisher = Housing The Spectacle | date = 1992 | url = http://www.columbia.edu/cu/gsapp/BT/DOMES/GEORGIA/g-anal.html | accessdate = 2007-11-28*]**ee also***

List of Hyperboloid structures

*Polibino, Lipetsk Oblast - The world's first Hyperboloid structure

*Tensile structure

*Thin-shell structure

*List of thin shell structures

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

* William Craft Brumfield, [*http://content.cdlib.org/view?docId=ft1g5004bj&chunk.id=d0e122 "The Origins of Modernism in Russian Architecture"*] , University of California Press, 1991, ISBN 0-520-06929-3.

* [*http://spec.lib.vt.edu/IAWA/inventories/English.html Elizabeth Cooper English*] : [*http://repository.upenn.edu/dissertations/AAI9989589/ “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.

* "Vladimir G. Suchov 1853-1939. Die Kunst der sparsamen Konstruktion.", Rainer Graefe, Jos Tomlow und andere, 192 S., Deutsche Verlags-Anstalt, Stuttgart, 1990, ISBN 3-421-02984-9.**External links*** [

*http://www.shukhov.org/news.html?n=34&id=1#news_34 International campaign to save the Shukhov Tower*]

* [*http://www.student.uwa.edu.au/~wongs30/shells__anticlastic_shells.htm Anticlastic hyperboloid shells*]

* [*http://nisee.berkeley.edu/elibrary/getpkg?id=GoddenE45-65 Shells: Hyperbolic paraboloids (hypar)*]

* [*http://www.recentpast.org/types/hyperpara/ Hyperbolic Paraboloids & Concrete Shells*]

* [*http://www.skyscrapercity.com/showthread.php?t=678936 Lattice shell structures*]

* [*http://web.eng.fiu.edu/~mirmiran/Papers/Special%20Structures%20Past%20Present%20and%20Future%20In%20Commemoration%20of%20the%20Sesquicentennial%20of%20ASCE.pdf Special Structures*]

* [*http://www.uibk.ac.at/baugeschichte/mitarbeiter/graefe.html Rainer Graefe*] : [*http://www.shukhov.ru/deutsch.html “Vladimir G. Šuchov 1853-1939 - Die Kunst der sparsamen Konstruktion.”*] , [*http://www.tec21.ch/pdf/tec21_4120041723.pdf*]**Gallery**

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