Thin-shell structure

"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."

"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."

"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"

"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."

"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."

"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..."

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

"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..."