Engineering

"All building naturally divides into two classes, the architecture of the beam and that of the arch, which have been called trabeated and arcuated—according to the means which it uses for covering openings and spaces—the first being that which covers them by beams or s, the second that which uses arches. The logical development of the two classes leads in the one to flat ceilings and straight roofs, in the other to vaults and s."

"French architects and engineers in the 16th, 17th, and 18th centuries occupied themselves a good deal with roofs with curved ribs, and two systems of constructing the rib were worked out. In the most modern of them, that invented by Colonel Emy, the ribs were constructed of a series of thicknesses of bent timber, one on the back of another, and held together by bolts. In the older system that of Philibert de l'Orme, the ribs were also built up, but the pieces composing them are placed side by side, and either form a polygon approaching a semicircle or are cut to bring them to a curve.&bnsp;thumb|Bourse de commerce (dome of the Paris Corn Market)In fact, the ribs are very much such as... used for the great dome of the Paris Corn Market. There is, however, a great difference between a dome—the strongest of all forms—and one permitting the introduction of as many rings of ties as may be desired; and a roof over an ordinary oblong space, where no such binding together is admissible, and where straight rafters may have to be used, which loads the rib at certain points only. In the latter case, a good many precautions have, generally speaking, to be taken to prevent the rib from being unequally loaded, and so either spreading or losing its shape in some other way. The rib made of unbent timber, side by side, on De l'Orme's plan, is admitted to be stronger than the one made of bent timbers laid one on the back of the other; but both have been largely used, and good examples of both may be met with, even if we confine ourselves to English ones alone, and leave the French ones unnoticed. thumb|Chatsworth - Great Conservatory in the 19th centuryA very fine roof with ribs, one on which the load (though light) is borne without a rafter solely by the rib, is the one erected over the great conservatory built by His Grace the Duke of Devonshire, at Chatsworth. ...It consists of a wide and lofty central portion, with a kind of broad aisle at the sides, roofed at a lower level. The central roof here is of the section of a pointed arch and hipped at both ends, and is entirely covered with glass. It is carried by timber ribs, and the glazing is on the ridge and furrow principle. The low aisle referred to forms to some extent an abutment for the ribs, and the ridge-and-furrow glazing helps, no doubt, to fortify them, but still the greater part of the strength is derived from the ribs themselves."

"Shell structures have been constructed since ancient times. The Pantheon in Rome and the in Istanbul are well-known examples. After the Roman times the traditions of domes continued up to the 17th century. Since then they seemed forgotten. Stimulated by the newly developed reinforced concrete and the demand to cover long-spans economically and column free the shell made a comeback in the early 20th century. and Ulrich Finsterwalder designed in 1925 the first thin concrete shell of the modern era, the Zeiss planetarium in Germany. The modern era of shell construction is recognised by the trend towards greater spans and thinner shells. Guided by well-known engineers as , Eduardo Torroja, Anton Tedesko, Nicolas Esquillan, and a blooming period of widespread shell construction took place between 1950 and 1970. Shell construction suddenly vanished at the end of the 1970s, mainly caused by the high costs [relative] to other structural systems. Moreover, inflexible usability and uncertainties in the structural behaviour of shells and difficulty of proper analysis methods did not help[,] neither did the stylistic identification with the 1950s and 1960s. Today the great era of thin shells is over, however, nowadays natural free-form shapes and blobs attract more and more attention. In addition, recent developments in concrete technology have led to ultra high performance fibre reinforced concrete with revolutionary performance in tension and compression. Eventually this may lead to a revival of the thin concrete shell."

"Galankin... writes that Shukhov used to make calculations in a unique way... so laconic... that other specialists found them difficult to understand. In spite their brevity... if Shukhov was asked about load, rod stress, rod profile and section, rivet quantity, material weight, temperature impact or any other specifications, he always had an answer, because his concise calculations covered all these aspects, but nothing that was irrelevant..."

"In 2010, the journal Detail published an analysis of Shukhov’s constructions, calling his approach to design 'an early example of ’..."

"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..."

"Suspension lattice structures... were based on tension, the most advantageous type of stress for metal constructions... designed according to Shukhov’s elaborate investigations of material properties. ...They were called ‘roofs without trusses’... and the clear, extremely simple suspension structure system and the easy-to-perform node conjunction made on-site construction fast and straightforward."

"According to the formula, the minimal covering weight could be achieved only if the construction had no s and if the distance between es was equal to the distance between the missing purlins. The answer to this riddle was the spatial lattice structure, where trusses and purlins were the same, and the distances between trusses and purlins were equal. In 1895 Shukhov obtained a patent for the invention. The new structures were first presented to the general public at the All-Russian Industrial Art Exhibition in Nizhniy Novgorod in 1896... where Shukhov designed a number of objects using three types of lattice structure: suspension, vaulted and rigid spatial shell."

"One of Shukhov’s most significant architectural inventions was the thin metal lattice (or ' shell') structure. This was developed after intense research into the most rational type of rafters which weighed and cost the least and which could be assembled quickly. Shukhov suggested a formula to define the proportional relationships between structural elements, which at first sight seemed senseless:α = e = c'where a- length of panels, e - minimal distance between frames, and с - distance between two purlins, dependent on the actual situation"

"Looking back to the past century, there were various visionary designers such as Isler, Otto, Candela and Shukhov using design methods comparable to today’s computational design, operating in a pre-computational parametric set-up. They applied mathematical algorithms and principles observed in nature to develop pioneering buildings... as milestones of architectural production. Vladimir Shukhov... was one of the first to embrace such an innovative approach."

"Now what got me into shells... was a building in South America... and it absolutely enchanted me. It was in ... a baseball stadium... doubly curved... I saw this thing, and all I'd ever known... the buildings that were being built in those days were boxes, very uninspired things, and here I see this picture, this gorgeous shell... and it just enchanted me. I thought, "My God, what a beautiful structure, but how on earth does it stand up? How did the guy do it?" ..[T]hat is what really made me decide, "I've got to get the answer to this. How is this done?" [T]hat's what set me off on years and years of searching before I finally found a way to do it. ...[W]hen I finally did a building... I searched around into the theory of shells until I understood the theory... [T]hen I started looking for ways of solving these things, and I found out that they did not exist in the... architectural structural engineering profession... [F]ortunately at that time... we had here a very huge aerospace industry, and I had friends at Lockheed... I got in touch with a guy at Lockheed... and they had ways of solving very difficult problems because they were building the rockets... and so I found this way of doing it... [I]t was a very tedious, complex way of doing it, but you would get an actual, true answer... [I]t was done... the same way that it's done today with computers... But you could do it my way... You took two guys... I was one of them... they go through it step by step, and then [periodically]... compare the answer... to make sure that they don't go off. ...You could get an answer. You don't get it down to the forth of fifth decimal... The smallest I could get, chunks of the shell to work with, would be about [a theoretical] 2 feet square... Today, with a computer, you can get down to 2/10 of an inch... But it was such a tedious, horrible way of working that I never used the system again. By then I learned enough that I knew ways of short-cutting that were not as accurate... but that were close enough... [B]y this time I had developed a pretty good feel... and so I'd cut shells in pieces in my mind, put them back together again, and put them in equilibrium... From this, I finally found my way of doing things. ...As far as I know, nobody had ever done it that way... They'd done aerospace stuff this way... but there they'd put ten guys on it, not two. ...Several times I did things that I thought were the first, but I just said that "It's not universally used, or known..." or something like that. ...You're doing something that you're not really aware of yourself, which is, you're developing a very sophisticated, intuitive way of working with these things, where you can just... take them and you can say it doesn't look right... which was the way architecture was done all through the Middle Ages... in fact, in Antiquity... they didn't have engineers, all they had were architects."

"The first shell I did was in Honalulu, and there I worked with an architect, that I had worked with at the Navy yard, named Pete Wimberly... Wimberly's architectural firm went on to be one of the biggest in the world. ...Pete and I were good friends, and when I went to Honolulu I'd stay in his house, and we'd start barnstorming at night. ...A lot of our stuff was just crazy talk, but a lot of it was freeing ourselves of inhibitions that later on we remembered... Pete had a very good intuitive sense for structure. He could... guess a structure that would make sense. ...[T]he first shell I did was a bowling alley near Pearl Harbor... a single curvature shell, cylindrical shapes... a span of about 93 feet... I could not find any way that... other shells were engineered. If you tried... you'd always get some kind of double-talk... [T]he world didn't have translations of everything then, like it has now. If a guy did something behind the it stayed... [T]he way I finally did it, I figured out that it must behave an awful lot like a... simple beam, even though it was a... curved structure, and so largely I figured it that way and it worked fine, and it's still up, and it was quite thin, it was 2 1/2 inches thick. In that day that was pretty daring..."

"The greatest of them all, in my opinion was Nervi. ...First of all, he did a tremendous volume of work. Now Torroja, from Spain, was very good, but the bulk of his work was quite small. ...Candela came along and... was very experimental and very creative, but he stuck almost entirely with the hyperbolic paraboloid form of the shells. ...[H]e did... a lot of great buildings, but they were... limited in that they were all this one type... Nervi stuck with all kinds of different stuff: precast... and Nervi had a laboratory in ... where he made experimental models. ...Torroja had a lab too and... finally became... just a professor... [so he] didn't do a great deal of volume. ...Nervi kept on doing these things his whole life... working with models, and working with whatever theory he could learn... [T]he great Lamella roof hangar he built before the war, that the Germans finally blew up when they had to retreat from Italy, was a magnificent... and a huge structure... [T]he other two... Torroja and Candela, were excellent engineers. Candela became a friend of mine later on... but they never had the tremendous variety and the huge buildings that Nervi did... Nervi's the guy that I really admire... most..."

"[W]e will mainly be dealing with uniform shells. The shells are uniform in the sense that the material properties do not vary through the thickness. (RC) is... regarded as sufficiently uniform... [since] the difference in between steel and concrete is not large..."

"[T]he ratio [of] radii of curvature to thickness of the shell, \frac{R}{t}... greater than 20 can be characterized as thin shells... an egg shell has a ratio of around 55..."

"[D]evelopment of the theory employs (elastic material), equilibrium and compatibility. Hooke’s law relates strains with stresses, equilibrium relates stress resultants with external loading and compatibility relates strains with deformation/displacements. These three sets of equations together with appropriate boundary conditions make up the mathematical aspect of the problem."

"Concrete shells can be built by the assembly of several cast units, or cast in one piece (monolithic). Monolithic concrete shells are structurally stronger..."

"[U]sing concrete shells as roofing provides the possibility of constructing spacious columnless buildings... has enhanced this possibility."

"[C]losed surfaces are more rigid than open surfaces. ...Therefore to achieve ...rigidity the openings [are] compensated."

"A shell can be defined as a body that is bounded by two surfaces parallel to its middle surface, and is deformed in any arbitrary manner. This is true for shells of a constant thickness... considered in this study. ...One particular way of classifying shell surfaces is according to their Gaussian curvature. \kappa_g = \kappa_1 \cdot \kappa_2 = \frac{1}{r_1} \cdot \frac{1}{r_2}Another way of describing shell surfaces is according to how the surfaces are generated. Using this method, in 1980 classified shell surfaces into Geometric, Structural and Sculptural surfaces. Geometric shells are well defined mathematically and... easily calculated analytically. These type of shells were quite significant in the development of shell structures [when] computer[s]... were not available. ...geometrically shell surfaces can be classified as cylindrical... spherical... conical... paraboloidal... etc."

"Compared to structural elements such as beams, slab and walls, the structural behaviour of shells in not easy to predict. Hence evaluating the accuracy of the results obtained from FEA of shell structures is a challenging task. Having the knowledge and understanding of the analytical solution method can provide the basis for this verification and... give ...much needed insight into the structural behaviour of shells. ...for some of the most commonly constructed concrete shell structures, a complete analytical solution procedure is available. The two types of concrete shell structures considered in this paper are axisymmetric shells and cylindrical shell roofs. ...[A]xissymetrical shells include structures such as containment buildings, tanks and silos. ...[C]ylindrical shell roofs are often preferred structural elements for large span concrete roof structures."

"Concrete shell structures, often referred to as ’thin shells’ are suitable structural elements for building spacious infrastructures. ...Loads acting on the surface of shell structures are mainly carried by the so called membrane action. This is a general state of stress [which] consists of the in-plane normal and resultants only. In comparison, other structural forms such as beams and plates carry loads acting on their surfaces by action, which can be said [to be] structurally less efficient. Usually the in-plane stresses in shells are low such that with a relatively small thickness it is possible to span over large distances."

"Experimental and numerical observations identically showed that heat transfer capacity of the cooling tower proportionally increased with wind velocity up to 3 m/s, and then decreased for higher wind velocity..."

"[A c]ooling tower is normally designed for stagnant ambient air condition, but experimental observation showed that cooling efficiency... might decrease to 75 percent in the range of moderate to high wind velocity..."

"[I]n 1967, closed-form expressions [were] derived by Gould and Lee... for determining the resultant stresses in the shell and corresponding deformations under static seismic design load."

"The meridional directed forces developed in [a] tower shell due to the self-weight... may cause local (diamond-shaped) buckling or axisymmetric circular buckling... Overall buckling of the tower shell may [be] caused by combination[s] of wind load and self-weight..."

"The NDCT [natural draft cooling tower] shell structures are submitted to environmental loads such as wind, earthquake and thermal gradients that are in nature. The dead loads, settlement, and construction load are... common... and various accidental loads, e.g., explosion [are]... experience[d]... in their lifetime."

"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."

"[T]he first cooling tower shell [to be] analyzed by means of a shell bending theory [was in 1967]. ...Because of the complex geometry of the cooling towers and also the classical methods of analysis of shell structures, the most preferred method of the modeling and analysis of NDCT [natural draft cooling towers] is [the] (FEM)."

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

"The... structure is made of high-strength Reinforced Cement Concrete (RCC) 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."

"The hyperbolic 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..."

"A collander... contains holes for draining food, but these holes do not stop it from being a shell. A sieve... is made from a large number of initially straight wires which are woven into a flat sheet and then bent into a hemisphere. It is also a shell, a gridshell. ...The spider web is essentially flat and made up of straight elements and when the wind blows, it bows outward like a sail and becomes curved. ...We call this a 'form-active' structure. This feature is characteristic of tension structures. The sieve may be in tension, compression, or a mixture of the two, but appears rigid. It does not significantly adjust its shape to the applied loading and, therefore, we call this a 'form-passive' structure. Where it is in compression, deflections lead to a structure becoming less able to carry the load, possibly leading to buckling. Columns carry loads via axial forces, but bending stiffness is required to stop buckling, and so it is with shells, although with shells buckling is resisted by a combination of bending and in-plane action."

"Today, most engineers fear shells and domes: they are mysterious and difficult to assess and master. ...Historic arches, shells and vaults are too easily seen as risks instead of opportunities. Under the motto of 'safety', these structures are destroyed and replaced by common beam-column systems. This is regrettable: their great historic and aesthetical value is lost forever. A better understanding and assessment of their structural behaviour holds the key to their conservation. ...[S]hells and arches are highly efficient structures."

"The shell designer seeks forms to carry the applied loads in axial compression with minimal bending forces. The earliest example of structural form finding for an arch was published by the English engineer and scientist, Robert Hooke... 1676... As hangs the flexible line, so but inverted will stand the rigid arch. ...'Hooke's law of inversion', can be extended... and considered for shell structures of various geometries. In the context of shell structures, the term funicular means 'tension-only' or 'compression-only' for a given loading, typically considered... Unlike the case of the hanging cable with a single funicular form... hanging membranes have multiple possible forms. ...[T]he three dimensional shell can carry a wide range of different loadings through membrane behaviour without introducing bending. ...[A] three-dimensional model of intersecting chains could be... used to design a design a discrete shell, in which elements are connected at nodes, or the model could be used to help define a continuous surface. If hanging from a circular support, the model-builder could create a network of meridional chains and hoop chains. By adjusting the length of each chain, various tension-only solutions can be found... Once inverted, this geometry would represent a compression-only form. Such... would quickly illustrate that many different shell geometries can function in compression due to self-weight."

"Shells play a special, singular role for engineers. Their shape directly derives from their flow of forces, and defines their load-bearing behaviour and lightness, saving material by creating local employment, their social aspect. This is especially true for thin concrete shells with their characteristic curvatures: single curvature (cylindrical and conical), synclastic (dome-like), anticlastic (saddle-like) of free (experimental). If well formed, there are no bending but membrane forces only (axial compression and tension)..."

"[A] list of factors combined to make thin shell concrete a less desirable solution for long spans by the 1970s. ...material efficiency could no longer off set the labor premiums demanded by complex formworks ...shapes were more difficult to create when an insulating layer was required ...A third challenge posed to compressive structures ...was the rapid development of s. ’s experiments with tensile membranes were mature enough in 1972 that they were used on Munich’s Olympic Stadium."

"[T]he infill fields of a Gothic cathedral’s ing behave as masonry shells, and by the 1860s masonry s of great beauty were developed by in both Spain and the United States. Gustavino’s work and graphic design methods... influence[d] Antonio Gaudí... whose work has been shaped by an interest in force-derived architectural form. While early engineers such as Guastavino pushed unreinforced masonry’s limits in thin shell construction, it was the introduction of steel reinforcement, initially in concrete, that sparked the Twentieth century’s interest in thin shell construction. Early [twentieth century] shell-builders were often engineers, and were engaged to design economical long-span structures... as aircraft hangars, train sheds and factories."

"History shows that not all thin shell concrete buildings are funicular—other families... chosen for pragmatic reasons such as their constructability, or because they were geometrically simple enough [that] through calculation... bending... was [found to be] within... tolerances... for the material."

"I have selected the use of hanging models to simulate compressive forces. This is one of the longest-used form finding techniques. It has its roots in physical models, but in recent years it has also given rise to a range of digital tools that are fairly accessible to an uninitiated designer... Hanging models... can be used to simulate... funicular structures. ...derived from the Latin word for “rope”... a structure takes its shape in response to the magnitude and location of forces acting upon it. For example, a rope suspended from two level points will form a “V” when a single point load is added at midpoint, but will form a catenary when under an evenly-distributed load. While a suspended rope is a purely tensile system, if inverted and made rigid that same form converts into a system that is in pure compression. This was first postulated (and wonderfully expressed) by the English scientist Robert Hooke... The value of a structure that is purely in compression is that it experiences no due to structural loads. With no bending present materials can be used very efficiently, allowing for the use of extremely thin elements... materials that are strong in compression... as tiles or masonry, can... be employed."

"The most prominent designer to eschew s is the Swiss engineer . In 1954... Isler hit on the idea that a “bubble” (in this case a pillow) takes the optimal shape for its edge boundaries. Isler began to construct models by inflating surfaces or by hanging and then hardening them."

"[T]he second wave of shell building (1940-1960s)... focused almost exclusively on s... [to] include s and hyperbolic paraboloids. ...[T]hey were definable through mathematical formulas, which allowed the designer to understand the forces... Ruled surfaces are... more constructible, because they can be created out of linear elements, such as... boards and pipes..."

"Dieste’s hypar masonry roofs are inexpensive, utilitarian statements about space enclosure..."

"By their very nature all funicular structures, including thin shell, use... less material... By designing only for pure tension or compression these structures experience very little force. These pure forces require less material to resist..."

"Forces present in the structure, shape thin shell concrete. Areas of uniform load present smooth, catenary curvatures, while areas of concentrated force express themselves as sharp bends or spikes in the surface form."

"By the 1970s the use of thin shell concrete had all but disappeared... This change was due to a combination of [economic] factors... This disappearance was also caused by the design challenges [of] thin shell concrete. Shell structures, because of their thinness, must be shaped to conform to the forces present in the structure. Until recently this shell form-finding could only be done... with specialized computer expertise, or through... physical model testing and measurement. ...In recent years ...simple computational models ...have been adopted ...to explore rapid form-finding in ...early design phase."

"The German engineering firm of ['s]... design of the concrete dome for ’s Century [or Centennial] Hall in Breslau... in 1913... became the first modern building whose clear span exceeded Rome’s Pantheon. Other notable structures of this early phase are the elegant works of Eduardo Torroja in Spain, including the Algecira market hall (1934), and Freyssinet’s economical segmented system for an aircraft hangar at Orly (1921)."

"In the early twentieth century was a new building technology. Its novelty inspired experimentation, both from architects, such as Le Corbusier, and from engineers, who dreamed up different applications for the new ferroconcrete. One application for reinforced concrete that developed rapidly was its use in thin shells. These shells spanned great distances or stretched out in dramatic s, their thinness seemingly impossible for the distance they extended. This technology quickly grew ever more common, especially in long-span utilitarian settings, where thin shell concrete was able to cover large areas economically."

"[T]wo primary research questions can be formulated: [1] What is for a shell of hemispherical geometry, with given material properties, given support conditions, and subjected to a given load, the knock-down factor which indicates the difference between the linear critical buckling load and the actual critical buckling load taking into account imperfections and geometrical and physical nonlinearities? ...[2] Can high strength fibre reinforced concrete add to the trend towards greater spans and thinner shells with possibilities for even more slender structures? To obtain an answer to the research questions a series of analyses (linear elastic, stability, geometrically nonlinear and geometrically and phy sically nonlinear) is performed on a given hemispherical shell: the Zeiss planetarium shell."

"In case of a failure, the shell may fail due to large deformations (buckling) or due to material nonlinearity (cracking and crushing) or by a combination of both (so-called inelastic or plastic buckling). ... Opposite to columns and plates, shells experience a sudden decrease in load carrying capacity after the bifurcation point (which can be obtained by a simple linear buckling analysis). ...compound buckling ...refers to several buckling modes associated with the same critical load. In the postbuckling range the modes... start to interact resulting in a significantly reduced load carrying capacity. As discovered by Koiter... geometrical imperfections in the shell cause the bifurcation point never to be reached and lead to... buckling at a considerably lower load. The size of the imperfections determines the limit load at which the shell fails. In case of plastic buckling, the fall-back is further intensified by material nonlinearity."