Hyperboloid structure

"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."

"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."

"The theory of minimal surfaces and surfaces of constant mean curvature is a vigorously developing branch of mathematics which has a broad range of applications in physics, chemistry and biology where it investigates, for example, soap films and bubbles, bimaterial interfaces or capillaries. Over the past decades, it was also boosted by the anticipated nanotechnology applications. Applications of minimal surfaces have been extensively explored in the sculpture (see e.g. the works by ) and in architecture (s, the Shukhov radio tower ... works by etc.) The first mention of minimal surfaces goes back to Lagrange (1798), who considered the... variational problem..."

"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 Jürgen Linkwitz..."

"The structures of the great Russian engineer Vladimir Grigor'evič Šuchov (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 ..."

"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"

"Matthias Beckh analyzes these hyperbolic lattice towers... [and] demonstrates how... Shukhov was already parameterizing his structures as part of the design... Modern methods... provide... Beckh with the tools to place Shukhov's achievements in a historical context and validate their considerable contribution to the history of . He also...demonstrate[s] their relevance to modern structures. ...Beckh was part of the first research project into Shukhov's structures ...The research project ...included in-depth studies of building history ...and detailed investigations into the way the structures were built. Later investigations were intended to provide ...knowledge about the load assumptions... also... relevant to modern structures."

"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..."

"Even today, Shukhov's load-bearing system can be found in one form or another in architecture..."

"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."

"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."

"Shukhov's design process is reconstructed and the development of the water towers... illustrated."

"Until now, the form and geometry of the hyperbolic lattice structures have only been investigated to a limited extent."

"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."

"The chapter "Geometry and form of hyperbolic lattice structures"... deals with the form and geometry... A precise description of the mathematical principles of a one-sheeted hyperboloid precedes an explanation of the parametrisation..."

"[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..."

"An analysis of the design and construction of the NiGRES tower on the Oka... The initial ensemble of four electricity transmission masts represents the consummation of Shukhov's tower construction method. Only one... remains... today."

"The final chapter "Towers in comparison"... contains an extensive table and drawings of 18 towers."

"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."

"[A] series of kinetic structures which are capable of geometric transformations have been developed. ...[T]he most impressive ones are deployable bar structures with [a] single degree-of-freedom ...These structures ...may become stable and carry loads ...Therefore ...may offer viable solutions for architectural applications, especially for temporary buildings, emergency shelters, exhibition halls, outdoor recreation facilities or sporting fields ...[M]ost of them are composed of scissor like elements (SLEs) ...which is a complex structural system ...[P]resent solutions are insufficient to constitute real form flexibility, because they are limited to... forms such as singly-curved vaults and doubly-curved synclastic s."

"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."

"In 1829... Nikolai Ivanovich Lobachevsky published a disproof of Euclid's fifth or using the case of a doubly curved surface, thereby establishing non-Euclidean geometry."

"According to Elizabeth C. English, there was a direct connection between the mathematical discoveries of Lobachevsky and the structural explorations of"

"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 ..."

"Shukhov is credited with the construction of some 200 towers using this method ..."

"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."

"[T]he diagrid form could support both the gravity loads and the lateral loads without requiring additional means. In comparison, the new skyscraper types that were under development at this time used a steel frame to support the gravity loads... while the central core provided the stiffness required to resist wind loads. Where additional resistance was required, it was usually the core that carried the bracing."

"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."

"Russian engineers made many new and stimulating contributions to the design and construction of multiple-span lattice metal bridges, a great number of which were needed in railway work because of the multitude of large rivers in Russia. Ferro-concrete was first used in buildings there at the beginning of the twentieth century. Russian engineers... made their own contribution to the development of structural techniques in this area."

"The creative principles of innovative trends such as Rationalism and Constructivism were well understood by engineers and constructors bent on applying the latest technological achievements. Great engineers such as Shukhov, [Artur] Loleit and [Hermann] Krasin, were happy to work with innovative architects. They jointly explored new ways of developing architecture, and engineers became active members of Asnova and Osna. ...In the twenties... Soviet architecture set tasks for the building industry which prompted the employment of new materials and structural elements, and raised building standards. Engineering technology in the building industry achieved great successes during this period, such as the metal structures by Shukhov and Krasin, Loleit's work in the field of ferro-concrete, the elaboration of modern timber work by Karlson and the production of new hyperbolic paraboloid roofing by Markarova. The very latest structures and building materials, as well as modern production methods, were applied in the construction of engineering and industrial buildings such as Shukhov's radio tower in Moscow in 1922 and Krasin's viaduct at the Shatura power station in 1925."

"[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 first hyperboloid shaped cooling tower was introduced by the Dutch engineers and Gerard Kuypers and built in 1918 near having 35 meter height."

"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."

"The... structure is made of high-strength [cement,] Reinforced... Concrete... in the form of hyperbolic thin shell standing on diagonal, meridional, or vertical supporting columns and radial supports. The shell is sufficiently stiffened by upper and lower edge members."

"[T]o achieve sufficient resistance against instability, large cooling tower shells may be stiffened by additional internal or external rings which may also be used as repair or rehabilitation..."

"The hyperbolic form of thin-walled towers provides optimum conditions for good aerodynamics, strength, and stability."

"[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)."

"Determination [utilizing nonlinear static analysis] of the ultimate strength of the cooling towers... subjected to the severe quasistatic wind loads is one of the [research] objectives... for... structural engineers. Various nonlinear factors, such as the material nonlinearities in the concrete and reinforcing steel, tensile cracking, the bond effects between concrete and steel in the cracked concrete which is known as the tension stiffening, the large displacement effects, and so on; need to be taken into account..."

"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."