Hyperboloid structure

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Shukhov Tower, as photographed by Alexander Rodchenko in 1926

Hyperboloid structures in architecture were first applied by Russian engineer Vladimir Grigorevich Shukhov (1853-1939). 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 paraboloid.

Partial view of the Olympiapark, Munich

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 non-Euclidean 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. The hyperbolic form of the tower is remarkably similar to that of the pseudosphere used to illustrate explanations of Lobachevskii's disproof of Euclid's parallel postulate. Shukhov built his first azhurnaia bashnia as a water tower 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 the Lipetsk region of Russia.

Unlike some of the other buildings pictured here, the Sydney Opera House does not use ruled surfaces, such as elliptic hyperboloids of one sheet or hyperbolic paraboloids. Rather, it uses elliptic hyperboloids of two sheets, which have positive Gaussian curvature, [link].

The Pengrowth Saddledome roof has the shape of hyperbolic paraboloid surface.

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.

References

A hyperboloid tower in the port of Kobe.

[The Origins of Modernism in Russian Architecture]
[Shukhov and Gaudi]
[Hyperboloid structures of Gaudi]
[Gaudi and Shukhov - DesignCommunity Forum]
[Special Structures]
[Shells: Hyperbolic paraboloids (hypar)]
Oscar Niemeyer [Brasília Cathedral]
Le Corbusier [Parliament Building, Chandigarh]
Le Corbusier, Iannis Xenakis [«Poème électronique» Hypar Philips Pavilion]
[Hyperboloid structures and music. Sydney Opera House.]
"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. [link]
[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, 264 p., University of Pennsylvania, 2000.

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Hyperboloid structure

See also

References