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Shukhov hyperboloid of rotation





Almost 94 years ago, broadcasts began from one of the engineering masterpieces of the time - a radio tower built in Moscow according to the design of Vladimir Grigorievich Shukhov. A talented engineer, by that time already an academician, who had erected many complex structures throughout the country, Vladimir Grigorievich embodied a remarkable idea in his tower - he carried out the supporting structure in the form of a hyperboloid of rotation. High strength, wind resistance, low cost of production and ease of construction, coupled with the visual lightness and elegance of the tower, rightly made it one of the symbols of engineering and architectural craftsmanship. And although Shukhov designed and built many more complex and sophisticated objects, it was the tower that became its most famous creation.







Engineer by vocation



The tower on Shabolovka is not the first hyperboloid structure erected by Vladimir Grigorievich. Back in January 1896, he filed an application for a patent for the construction of such structures. This brilliant in its simplicity and efficiency idea was born to him thanks to the analysis of ... woven peasant baskets. And for the first time it was embodied in metal at the Nizhny Novgorod Industrial Art Exhibition of 1896, where Shukhov erected a water tower with a height of 25 m. The tank contained 10 thousand buckets of water, and a viewing platform on top led by a spiral staircase.

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This water tower has survived to the present day. It is a one-cavity hyperboloid of revolution, created from 80 straight steel profiled beams. To increase the strength, eight steel rings were added, tightening the structure.







It is worth noting that at this exhibition the hyperboloid tower was not the only unique building of Shukhov. According to his projects in Nizhny Novgorod for the first time in the world steel mesh hanging arches were built, forming exhibition pavilions, including the so-called Shukhov rotunda .











After the exhibition, Shukhov created a lot of open metal vaults for various objects. One of the most striking examples are the arches of the Kiev railway station and GUM in Moscow.



















Hyperboloid and hanging mesh constructions were embodied on hundreds of objects: in factories, in water towers, in public buildings. And near Kherson the 80-meter lighthouse was erected.







Shukhov designed more “traditional” objects - bridges, workshops, cranes, barges, oil refineries, industrial boilers, tanks, pipelines and much more. He paid great attention to the technological effectiveness of his designs, convenience of mass production and unification.



The contribution of Vladimir Grigorievich to the industrialization of the Russian Empire and the Soviet Union is invaluable. With his participation such industrial giants as Magnitka, Chelyabinsk Tractor Plant, Beloretsky, Vyksa, Izhevsk and Nizhny Tagil plants, Azovstal, Caucasian oil pipelines, supplying the country with a strategically important resource, were built. Years later, all these enterprises will allow our country to stand in the most severe war.



Birth tower



In 1919, Vladimir G. Shukhov created a project of a 350-meter hyperboloid radio tower - it was she who was supposed to rise today at Shabolovka.







At one time, Eifel became famous throughout the world, erecting a 324-meter tower in the center of Paris. But the project V. Shukhov would eclipse the construction of the Frenchman for a variety of parameters. The creation of the Eiffel Tower required 7.3 thousand tons of metal, and the mass of the hyperboloid tower would have been only 2.2 thousand tons, while it would have been 26 meters higher.







Alas, this unique project was not implemented. It was 1919, civil war and devastation reigned in the country.







The metal was in great shortage, and Shukhov was refused to erect a tower. Then the tireless engineer created a new project - about 150 m high and weighing 240 tons. It was approved by Lenin, construction work began.



Resolution of the Workers 'and Peasants' Defense Council.



  1. To ensure reliable and constant communication of the center of the Republic with Western states and the outskirts of the Republic, the People's Commissariat Pocht and Telegraphs are instructed to install a radio station equipped with instruments and machines with the most advanced and powerful enough to perform this task in an extremely urgent manner.
  2. All government agencies and organizations are invited to provide the People’s Commissariat of Posts and Telegraphs in the performance of this task with the most active and energetic assistance in the supply of all necessary materials for transport. road, water and animal and to attract to this work skilled and unskilled workers, providing them with food and shelter.
  3. Workers on installation of a radio station shall be considered mobilized on the spot and therefore not subject to appeal / regardless of age / until the radio station is completed.
  4. All workers qualified and unqualified, working on the installation of a radio station, shall issue a Red Army ration until the radio station is completed.
  5. To monitor the implementation of this task in the shortest possible time and the correctness of the work to be done, establish a special commission from Composhtel’s decree and representatives from V.C.N. State control and from the Radio section of the Proletarian Production Union of People’s Communications; commission members to establish special remuneration within the limits of the norms provided for by the decisions of S.N.K. about concurrently.


Chairman of the Council of Defense V. Ulyanov / Lenin /

Moscow Kremlin,

July 30th, 1919


The Shukhov radio tower consists of six tiers (the height of each is 25 m). Each tier is a hyperboloid of rotation - a three-dimensional structure made of straight steel beams, the ends of which are fastened with steel rings.



The first tier rests on a concrete foundation with a diameter of 40 m and a depth of 3 m. The tower was erected without the use of scaffolding or cranes — each subsequent tier was assembled inside the tower, and with the help of blocks and winches it went up. That is, the tower grew telescopically.















The supply of construction metal was carried out by Lenin’s personal order, but interruptions still occurred. And the quality of the metal was also not always satisfactory. When lifting the fourth tier, the steel cable broke, and the fallen structure damaged the already erected tiers. This incident almost cost the life of Shukhov himself, since the commission of the Cheka initially regarded it as sabotage.







Fortunately, the real reason for the break was confirmed - metal fatigue, so construction was resumed.







Here is a quote from Shukhov’s workbook dated February 28, 1919, which describes the method for calculating the radius of the support rings of each hyperboloid layer:



“The outer contour of the tower contour. Basic size. Cone with variable r incident on a constant increment; in our case, r, 2r, 3r, 4r ... or even r, r + f, r + 2f, r + 3f, etc. and a variable increment with a continuous increase in slope from the vertical α. Those. the inclination increment is expressed by the formula α * n * (n - 1) / 2, where n is the number of the tower floor, counting from the top. Thus, the following series is obtained: 1) f, 2) 2f + α, 3) 3f + 3α, 4) 4f + 6α, 5) 5f + 10α, 6) 6f + 15α, 7) 7f + 21α, 8) 8f + 28α, etc., and the sizes of r, f and α are specified. In this case, r = 2.75 m, f = 2.75 m = r, α = 0.25 m, and therefore the radii are 2.75, 5.75, 9, 12.5, 16.25, 20.25 (slopes 3 → 3.25 → 3 5 → 3.75 → 4) ".




Based on these data, the radius of the support ring of the tier n is expressed by the formula:



R = 2.75 * n + 0.25 * n * (n - 1) / 2.



And since the height of each section is 25 m, the distance from the top of the tower to the support ring of section n is H = 25 * n. Then the above formula can be expressed as:



R = H * H / 5000 + H * 21/200



Although it should be noted that the actual dimensions of the support rings coincide with the estimated only at the four lower tiers. That is, Shukhov made changes to the project already at the construction stage. Also, the results of modern measurements show that the nodes connecting the beams of different tiers do not at all coincide with the drawings of 1919. That is, we can assume that after the start of construction, Vladimir Grigorievich continued to improve the design of the tower, making many changes compared to the original project.



In 1922, the construction of the tower was completed, and regular broadcasting began on March 19. In March 1939, the Shukhov Tower became the main source and symbol of television broadcasting in the USSR, retaining this role until the Ostankino television tower was commissioned.



The brainchild of Shukhov soon became famous throughout the country, and then mesh steel shells began to be massively applied throughout the world. Over the past almost 100 years, several high-rise hyperboloid towers have been built around the world, including a 600-meter TV tower in China . By the way, it was the Shukhov Tower that inspired Alexei Tolstoy to write the science fiction novel “The Hyperboloid of Engineer Garin ”.











The hyperboloid design turned out to be very economical from the point of view of metal intensity, but at the same time quite strong. And its openwork makes it possible to effectively resist the wind load, the main enemy of high-rise structures. The structural elements are easy to manufacture, therefore, their cost is low. The construction does not require the use of complex or time-consuming technologies, since the joints were made using the riveting method. The stability of the tower is ensured not only by the interposition of the beams that make up the hyperboloids, but also by a certain percentage of the mobility of riveted joints, unlike welded or bolted joints.







Although the Shukhov Tower is 2 times lower than the Eiffel Tower, it is still interesting to make a superficial comparison of these projects. The metal consumption has already been mentioned above: at a comparable height, the Shukhov design requires 3 times less metal. In addition, the tower on Shabolovka more technological in terms of the diversity of the range of parts and connecting nodes.



Here is a copy of the 1919 drawing:







The tower consists of straight beams and ring supports, simple and inexpensive to manufacture. Node connections also have a simple configuration. Despite the fact that the actual configurations of the nodes do not coincide with the project, they remain just as simple and technologically advanced.











But the drawings of the Eiffel Tower, its compounds and some elements:



























As they say, feel the difference. In contrast to the Parisian "competitor", even the original 350-meter version of the Shukhov Tower would require a much smaller range of parts and would be much cheaper to build.



Someone might argue that the Eiffel Tower has a higher wind resistance. Indeed, in the entire history of observations, the maximum deviation of the top of the symbol of Paris from the action of the wind reached 12 cm . It is curious that the massive metal structure is much more affected ... sunlight. On a bright summer day, when the luminary heats up one of the sides of the Eiffel Tower, its top may deviate by 18 cm due to the uneven thermal expansion of the elements.



It should be noted that at the time of the construction of the Shukhov radio tower, the method for calculating the strength of hyperboloid structures was far from perfect. In subsequent decades, it continued to develop and deepen, but the tower at Shabolovka was built on the basis of calculations characteristic of its time. In particular, simplified load distribution models were used; a number of characteristic features, such as torsion of the support rings, beam twist and longitudinal deformations, were not taken into account. Various empirical and semi-empirical formulas and coefficients were used, and the lack of accuracy of calculations was compensated by the tabulation of excessive strength. Nevertheless, studies of the strength of the Shukhov Tower, carried out in subsequent decades, in which more advanced and accurate methods of calculation were used, showed results close to those of Shukhov himself.



Two cases speak about the stability of the construction of the Shukhov Tower. After its construction, the steel cable that connected the tower to one of the winches on the ground was not dismantled. In the 1930s, a mail plane touched this cable with a wing and fell nearby. The winch was torn down from the foundation, and the tower was hit hard. However, inspection of the structure showed that the hyperboloid came out of this scrape without any damage or deformation.



The second case is connected with another tower of Shukhov - a hyperboloid pillar of the transmission line with a height of 128 m, installed on the bank of the Oka. In fact, there were two supports, but one of them was destroyed in 2005 by vandals - for the sake of metal.







A few years later, a third of the beams were cut from the lower tier of the second tower. In this form, the tower stood for several years, carrying several tons of cables and being subjected to the pressure of water and ice during floods. Subsequently, the lost structural elements were restored, and the tower still stands today. What can we say about the wind resistance of the Moscow radio tower.







Unfortunately, for 94 years, the Shukhov tower in Shabolovka was covered with anti-corrosion paint only three times. That is, she spent most of the time without any protection. The steel structure rusted and collapsed, metal fatigue accumulated. Recently, supporting structures have been installed inside the tower to remove some of the load. At the same Eiffel Tower, about 3% of elements are annually replaced with similar ones manufactured using the same technologies as during construction. And the Shukhov Tower has been standing for almost a century without any care. Fortunately, its destruction can be stopped by retaining this unique monument of domestic engineering.

Source: https://habr.com/ru/post/391819/



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