Hyperboloid structure
Hyperboloid structures are architectural structures designed using a hyperboloid in one sheet. Often these are tall structures, such as towers, where the hyperboloid geometry's structural strength is used to support an object high above the ground. Hyperboloid geometry is often used for decorative effect as well as structural economy. The first hyperboloid structures were built by Russian engineer Vladimir Shukhov (1853–1939), [1] including the Shukhov Tower in Polibino, Dankovsky District, Lipetsk Oblast, Russia.
Properties
Hyperbolic structures have a negative
Hyperboloid structures are superior in stability against outside forces compared with "straight" buildings, but have shapes often creating large amounts of unusable volume (low space efficiency). Hence they are more commonly used in purpose-driven structures, such as water towers (to support a large mass), cooling towers, and aesthetic features.[3]
A hyperbolic structure is beneficial for cooling towers. At the bottom, the widening of the tower provides a large area for installation of fill to promote thin film evaporative cooling of the circulated water. As the water first evaporates and rises, the narrowing effect helps accelerate the laminar flow, and then as it widens out, contact between the heated air and atmospheric air supports turbulent mixing.[citation needed]
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 steel
Shukhov also turned his attention to the development of an efficient and easily constructed structural system (gridshell) for a tower carrying a large load at the top – the problem of the water tower. His solution was inspired by observing the action of a woven basket supporting 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 20 years, he designed and built nearly 200 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 in 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 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 1922.
Other architects
In the
A hyperboloid cooling tower by Frederik van Iterson and Gerard Kuypers was patented in the Netherlands on August 16, 1916.[7] The first Van Iterson cooling tower was built and put to use at the Dutch State Mine (DSM) Emma in 1918. A whole series of the same and later designs would follow.[8]
The Georgia Dome (1992) was the first Hypar-Tensegrity dome to be built.[9]
Gallery
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The hyperbolic paraboloid is adoubly ruled surface so it may be used to construct a saddle rooffrom straight beams.
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The Warszawa Ochota railway station has a hyperbolic paraboloid saddle roof. Warsaw, Poland, 1962.
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The Scotiabank Saddledome arena has a hyperbolic paraboloid saddle roof, Calgary, Canada, 1983.
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Stackable Pringles chips are hyperbolic paraboloids.
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Ultimaker 2, 2015
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The first 1918 Van Iterson cooling tower, 1984
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Five cooling towers in a row at DSM Emma, around 1930
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The Corporation Street Bridge is a horizontal doubly ruled hyperboloid structure, Manchester, England, 1999.
See also
- Geodesic dome
- Lattice mast
- List of thin shell structures
- Sam Scorer
- Tensile structure
- World's first hyperboloid structure
Notes
- ^ "Hyperboloid water tower". International Database and Gallery of Structures. Nicolas Janberg, ICS. 2007. Retrieved 2007-11-28.
- ISBN 9780442205256,
It is easier to build timber formwork for a concrete structure or to fabricate a steel structure if a surface is singly ruled, and even more so if it is doubly ruled.
- ISBN 978-0-262-68054-7. Retrieved 2009-08-09.
- ^ Burry, M.C., J.R. Burry, G.M. Dunlop and A. Maher (2001). "Drawing Together Euclidean and Topological Threads (pdf)" (PDF). Presented at SIRC 2001 – the Thirteenth Annual Colloquium of the Spatial Information Research Center. Dunedin, New Zealand: University of Otago. Archived from the original (PDF) on 2007-10-31. Retrieved 2007-11-28.
{{cite web}}
: CS1 maint: multiple names: authors list (link) - ^ "Fedala Reservoir". International Database and Gallery of Structures. Nicolas Janberg, ICS. 2007. Retrieved 2007-11-28.
- ^ "Zarzuela Hippodrome". International Database and Gallery of Structures. Nicolas Janberg, ICS. 2007. Retrieved 2007-11-28.
- ^ NL/GB Patent No. 108,863: "GB108863A Improved Construction of Cooling Towers of Reinforced Concrete". Espacenet, Patent search. Retrieved 2023-12-03.
- ^ "Koeltorens van de Staatsmijn Emma". Glück Auf (in Dutch). Retrieved 2023-12-03.
- ^ Castro, Gerardo and Matthys P. Levy (1992). "Analysis of the Georgia Dome Cable Roof". Proceedings of the Eighth Conference of Computing in Civil Engineering and Geographic Information Systems Symposium. Housing The Spectacle. Retrieved 2007-11-28.
References
- "The Nijni-Novgorod exhibition: Water tower, room under construction, springing of 91 feet span", "The Engineer", № 19.3.1897, pp. 292–294, London, 1897.
- ISBN 0-520-06929-3.
- 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.
- "Vladimir G. Suchov 1853–1939. Die Kunst der sparsamen Konstruktion.", Rainer Graefe, Jos Tomlow und andere, 192 pp., Deutsche Verlags-Anstalt, Stuttgart, 1990, ISBN 3-421-02984-9.
External links
- The research of the Shukhov's World's First Hyperboloid structure, Prof. Dr. Armin Grün
- International campaign to save the Shukhov Tower
- Anticlastic hyperboloid shells
- Shells: Hyperbolic paraboloids (hypar)
- Hyperbolic Paraboloids & Concrete Shells
- Special Structures
- Rainer Graefe: “Vladimir G. Šuchov 1853–1939 – Die Kunst der sparsamen Konstruktion.”, [1]