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April 10, 2026
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"Vaulted gridshell constructions... were formed with thin metal arches turned away from the frontal position at a particular angle. They thus worked as one continuous resilient truss. ...Each arch was made with rigid metal strips of equal length... during the assembling process, each piece was bent equally. ...It was the first time in the world’s building practice that double-curved spatial vaults were created with single type rod elements ..."
"Shukhov’s lattice-suspended and vaulted structures represented a carrying surface, which could be shaped in any form. ...The density of the grid made it possible to attach it to the shell without additional structures. ...[T]he grids were two to three times lighter than roofs with conventional frames..."
"The water tower was a unique structure of its time... According to Cooper, the idea... came directly from an imaginary hyperboloid geometry, invented by... Lobachevski in 1829..."
"Grigory Kovelman writes that Shukhov told him he had been thinking about the properties of hyperboloid structures for a long time, that he had studied hyperboloid forms at the Technical School, and that apparently the moment of enlightenment came about when he saw an up-ended wicker wastepaper basket with a focus on top of his desk. According to Shukhov, this was when he understood clearly how a hyperboloid structure with its curved surface [was] generated by straight rods..."
"The final chapter "Towers in comparison"... contains an extensive table and drawings of 18 towers."
"[T]his is the magical part... despite the surface being curved in two directions, it is made entirely of straight lines. Apart from the cost savings of avoiding curved beams or shuttering, they are far more resistant to buckling because the individual elements are straight..."
"The hyperboloid is the design standard for all nuclear cooling towers and some coal-fired power plants."
"When designing... cooling towers, engineers are faced with two problems: I. The structure must be able to withstand high winds and II. They should be built with as little material as possible... The hyperbolic form solves both..."
"The "idea of the " and the first... diagrid structure have been credited to... Shukhov. The design evolved as an efficient and easily constructed tower for carrying a large gravity load... a water tower. The "Shukhov Tower"... 1896, relies on the use of a diagonal lattice of steel angles, constrained laterally... by steel rings. ...The tower is hollow, requiring little resistance to wind loads ..."
"The main hazard for high-rise structures is the loads caused by wind gusts. The grid shell design... minimize[d] their influence. Open-work design... ensured... sufficient strength, high stability and low metal consumption. ...[C]onsumption of metal per unit height... was three times less than... the ..."
"Particular attention is paid to evaluation and analysis of Shukhov's tower calculations and the assumptions made for the structural model. His historical calculations are compared to the results of modern calculations."
"Even today, Shukhov's load-bearing system can be found in one form or another in architecture..."
"Shukhov's design process is reconstructed and the development of the water towers... illustrated."
"The structures of the great Russian engineer Vladimir Grigor'eviÄŤ Ĺ uchov (Shukhov) are among the world's most sophisticated and distinctive in the history of steel construction. These extremely stable structures, such as cable-stabilised arches, doubly curved grid-shells and above all lattice towers hold a great fascination... They result from the desire to achieve an engineering objective using as little material as possible. ...[T]hey are a testament to the extraordinary creativity and inventiveness of an extensively educated engineer ..."
"Construction history teaches us that excellent, huge structures like this one are invariably the result of a specific and singular solution, in which all aspects were reflected upon before or after early experiences in the building sequence. The author wants to compare the achievement of Segovia Aqueduct with more recent singular structures: the Oka electricity pylons (1929) by... Vladimir Gregoryevich Shukhov... and the roof of the 1972 Olympic Games in Munich, by a team directed by Gunter Behnish, , /, and JĂĽrgen Linkwitz..."
"Many engineering structures of today were anticipated in Shukhov's works. Some of his others have no modern equivalent or have remained unmatched in their visual impact and... technical efficiency. Among these are... the lattice towers... Countless towers with this new type of construction and geometries defined by just a few parameters were built [by him]... The fine-lined tower structures served as water towers, lighthouses, power transmission masts and fire brigade watchtowers—with some of them still in use today"
"The object of this book is gain deeper knowledge on the architectural history of hyperbolic structures. The focus of the investigation is the first hyperbolic lattice towers ever built, the work of... Shukhov."
"This form of construction, which had no predecessors... is notable for its strength and economy of materials. Added to this is the high visual impact..."
"This book presents the results of the first ever extensive analysis of the way these structures work."
"The of a one-sheeted hyperboloid is resolved into three different mesh variants to create open lattices and their structural behaviour investigated."
"A paper by Peter de Vries discussed the stiffness of simple hyperbolic lattice structures and highlighted a single connection between geometry and structural behaviour. The focus... is... on a simple form of hyperbolic lattice structure which always has the intermediate rings positioned at intersection points of the lattice members."
"[T]he form and structure of the Sukhov-built towers were developed not on geometrical or constructional criteria alone, their designs specifically took into account considerations."
"[T]he chapter "Structural analysis and calculation methods"... considers the principle means of transfer of vertical and horizontal loads and describes the interactions between geometry and structural behaviour. Then... an explanation of the theoretical principles of determining a lattice tower's ultimate load capacity."
"The chapter "Design and analysis of Sukhov's towers"... is devoted to consideration and analysis of Sukhov's structural calculations... Sukhov's design process is reconstructed based on... calculations of five different water towers. From... tables stored in the Moscow city archives, a summary... is produced to chart the development of the towers over more than three decades..."
"It is hoped that the examination of Sukhov's form of construction made public in this book will give an impetus to new applications in architecture."
"[A] new reconfigurable doubly-curved structure has been developed for a canopy roof."
"Due to... complexity... doubly-curved anticlastic surfaces such as hyperboloid and hyperbolic paraboloid (HP) have been rarely used for deployable structures. In fact, anticlastic structures can be easily constructed using simple straight bars rather than SLEs since their geometric forms can be generated by s..."
"[A]nticlastic structures are capable of resisting... various design loads through their curvatures and twists. Thus, their structural efficiency is more than ...others. ...[W]e have decided to use HP ...as a [deployable] canopy roof structure."
"Although the slender steel sections, when formed into the hyperbolic paraboloid shape, did undergo some bending, a diagrid shape emerges, using a combination of straight segments that are joined at their nodal points of intersection."
"The Shukhov towers tended to use much longer steel sections and overlap them at their crosspoints, rather than using the crosspoints as "nodes" in the fashion of later or spaceframe structures."
"The School of Engineering and Construction which came into being in Russia after the reforms of the 1860s, and in connection with large-scale railway construction towards the end of the nineteenth century, soon acquired a worldwide reputation. It produced distinguished theorists and practitioners who included Belelyubsky, Loleit, Proskuryakov, Shukhov and Yasinsky. The engineering work incorporated in the most diverse kinds of buildings in Russia during the last quarter-century before the Revolution show that this country not only kept pace with the more developed parts of Europe and the USA, but outstripped them in certain fields, in terms of engineering design, as well as the use of modern construction techniques and new materials. Thus Shukhov produced many original designs unparalleled in work done abroad. At the Nizhny-Novgorod Exhibition in 1896... several original designs by Shukhov appeared, the most important of which were latticed: suspended latticed roofs for exhibition halls with a circular, elliptical and rectangular ground plan, latticed roof vaults and hyperbolic latticed towers. This category of structure also included the dual curvature roof designed by Shukhov in 1897-98 to cover the workshop at the Vykhsusnk factory."
"Forms of spanning which have come into use in recent years were foreshadowed in various forms of latticed structures designed by Shukhov before the end of the last century—guyed structures, the spanning of dual curves by structures of standardized rods, the provision of curved 'hyperbolic' profiles by means of a straight component, using straight rods in Shukhov's case."
"[H]yperbolic s are associated with nuclear and thermal power plants... they are also used... in some large chemical and other industrial plants. [T]hey are high rise structures in the form of doubly curved thin walled shells of complex geometry..."
"The in-plane membrane actions primarily resist the applied forces and plays the secondary role in these special structures."
"The hyperbolic geometry has advantage of a negative which makes it superior in stability against external pressures..."
"The widened bottom of the tower accommodates large installation of fill to facilitate the evaporative cooling of the thin film of circulated water. Narrowing effect of the tower accelerates the of evaporation and diverging top promotes turbulent mixing which increases the contact between hot inside air and cooler outside air."
"[T]he first cooling tower shell [to be] analyzed by means of a shell bending theory [was in 1967]."
"[T]he most preferred method of the modeling and analysis of NDCT [natural draft cooling towers] is [the] (FEM)."
"Mahmoud and Gupta... concluded that the failure of the Port Gibson Tower [in] Mississippi was caused by the circumferential in the vicinity of the throat rather than the yielding of the reinforcement, which contradicts... previous researchers."
"Deformation response and ultimate strength of RC shell structures are governed predominantly by material response of concrete and reinforcing steel, tensile cracking of concrete, [and] bond between concrete and steel.... Softening response of concrete due to quasi-brittle cracking in tension also... influences the nonlinear response by inducing loss of strength and stiffness... Due to all [of] these, analysis requires attention for realistic modeling of the layer of shell concrete confined between the reinforcement layers. ...[O]ne of the most challenging areas... is the modeling techniques using the layered elements."
"Abu-Sitta and Davenport... investigated the effects of dynamic earthquake loading. ...[I]nduced dynamic stresses were related to equivalent membrane stresses from static loads, resulting in... a simplified earthquake analysis procedure."
"Asadzadeh et al... studied the structural response... under static wind and pseudo static seismic forces. ...[T]wo types of... column supports at the base of the towers had been considered... The structural response... under wind and earthquake was... completely different for the towers supported on different columns."
"Wind is the prime lateral load and its combination with self weight of the tower shell can cause the instability leading to catastrophic failure."
"After the sudden collapse of three immense cooling towers at Ferry-Bridge Power Station in England in 1965, experimental and theoretical investigations had been done in... the stability of hyperbolic shells to study the parameters increasing the wind resistance and buckling safety..."
"Shukhov's water tower['s]... double curved surface... was generated by a mesh of straight members overlapping in contrary directions... supported by horizontal rings. While... constructed from steel... Shukhov's 1896 patent application... initially mentions straight wooden beams as a material option. ...[T]he ...application describes ...being able to resist extreme forces while using very little material. As a result, Shukhov's... design was used extensively throughout Russia in the first half of the twentieth century."
"Noorzaei et al... analyzed the cooling tower–foundation–soil system under vertical and lateral load generated due to self-weight and wind loads. In this study, the unsymmetrical wind pressure distribution in terms of [were] given..."
"In recent years... numerical simulation... has been applied to describe the collapse of structures, e.g., the collapse of cooling towers under blasting demolition... and the collapse of the World Trade Center..."
"Due to the complexity of the building procedure, uncertainties in the material properties as well as differences between the theoretical and the real geometry... reliability analysis... seems... indispensible..."
"[T]here are... approaches that are closer to the field of the classical mechanics... so–called structural or discrete-continuous methods... The most straightforward example... is a modeled by the solid deformable rod... [T]he interatomic bonds are modeled as a deformable body or a construction. ...[T]hese approaches... can be implemented in standard computing packages based on the finite–element, boundary–element, or s. These methods can be considered as the bridges between the s of atomistic and continual models of the material."
"A groundbreaking advance on the way to efficient structures in steel construction was the principle of using tetrahedra as a basic module instead of rectangular geometries. The inventor is considered to be the all-round genius Alexander Graham Bell, who became famous for the invention of the telephone and who built kites that were big enough to lift people into the air. Another engineering genius was Vladimir Grgorevic Suchov, whose genius can definitely be compared to Gustav Eiffel. In 1919 he designed towers up to 350 m high on the principle of hyperbolic paraboloids. The lightness of his constructions is seldom achieved even today, in Moscow there is a television tower with a height of 160 m. His tent constructions with suspended steel grids can be seen as the forerunners of the Olympic roof in Munich or the new Center Pompidou Metz. In , Suchov realized the first double-curved lattice shells on the floor plan of rectangular halls as early as the 19th century. Most of the structures still in existence are massively endangered by corrosion and destruction; current rescue operations are trying to preserve this legacy."