Engineering

"Torroja was a specialist in stress analysis... and he wrote a... book on the mathematical theory of elasticity. This... led him to see a connection at Algeciras between the stresses in the shell and the reinforcement... but not to express those stresses in... visually evident ribs. We contrast... Nervi's Little Sports Palace... whereas Nervi sees shells as ribbed, Torroja sees them as ribless... since domes tend to spread, Nervi designed ribbed buttresses... whereas Torroja avoids buttresses by connecting vertical supporting columns with a... polygonal ring of horizontal ties... prestressed to counteract dead load and to lift the shell slightly off its scaffold... probably the first application of prestressing to a doubly curved shell. In the Nervi dome... the buttresses are supported below ground on a ring which carries the horizontal thrust and... transmits the vertical weight to the ground. ...[These] choices related to the [respective] local traditions in Italy and Spain."

"... all through school had a reputation of working alone and of doing his work in an unusual way. ...in 1950 he graduated with a degree in civil engineering. For his final-year design project, he chose to study thin shells... Following graduation... he helped [Pierre] Lardy with teaching, and also worked on the many cases of structural failure [both at his alma mater, the Federal Technical Institute]... When Isler left his position... he considered... [a] career as a painter, but challenged by shell design problems... while doing free-lance engineering work.. in late 1954, he designed a pneumatic form, thin shell factory for the Trösch Company. It was the first work in which he set the form completely on his own. In 1955, at an international congress in Amsterdam, he presented publicly for the first time his new designs..."

"The method of geometric modeling of multi-shell roofs depends mostly on the surface's properties forming the shell; their curvature, as well as continuity between them. ...s play a specific role, due to their characteristics. Catalan surfaces are s... They are oblique ruled surfaces which can be divided into two groups... second order—hyperbolic paraboloid... [and] of more than second order—s, cylindroids... The difference between hyperbolic paraboloid, conoid, and cylindroid results from different path of movement of a surface's ruling during formation. In all cases of Catalan surfaces' creation... each ruling is parallel to the fixed plane (not containing the surface's directrices)."

"[M]ost of Candela's structures are almost complete in themselves... the forms and proportions bear witness to his artistic sensibility. ...[B]alanced perfection ...makes a... structure into a work of art. ...[T]he whole must take precedence over any of its parts."

"Candela] is not just an engineer, or an architect, or a contractor and constructor, but all three... [W]hen he thinks out a new scheme, the method of construction and its economy is constantly in his mind. ...He prefers to obtain his economy by using his inventive skills as an engineer to reduce... material... [H]e recognizes the value of ... but he is also very conscious of its limitations. Especially is he skeptical about the value of the theory of elasticity as applied to concrete... of... calculations suggesting an accuracy which is purely fictitious... Designing... proceeds from a structural feeling acquired by experience and guided by rough calculations, a refinement of design... further analysis... and so on. ...[A] flair for making the right guess yields quicker and better results than a lot of mathematics... this is no reason for despising theoretical analysis... But one cannot design by theory..."

"Candela did not invent the concrete shell; nor is he the first to make use of the hyperbolic paraboloid... Other people... have contributed more to the theoretical analysis of shell structures. But nobody else can claim credit for such an exciting variety of shell structures... [H]e has concentrated his effort in one particular sphere: the construction of light concrete roofs."

"has designed some of the most striking thin shells in reinforced concrete of the second half of the twentieth century. He creates thin shells by hanging small membranes in tension and creating smooth curving surfaces that are then inverted and scaled up to create large-scale structures in compression. ...Within the constraint of economy, he discovered new forms from purely structural considerations and demonstrated the unlimited possibilities for thin compression shells to be found in hanging models."

"In the twentieth century, lightly reinforced brick shells were inspired by timbrel vaulting, a common building method in the Mediterranean. ... upon emigrating to the United States from in 1881, introduced the method with great success. His son, Rafael Guastavino, Jr. ...appears to be the first to have introduced steel reinforcing to thin brick shells. ...[T]wo patents... [1910, 1913] documented this system, which is a precursor to the thin shells of reinforced concrete developed widely in the ensuing decades."

"[T]he early work of Lambot... was one of the first applications of , but [was] also... a form of . His patent on wire-reinforced boats that was issued in 1847... This was the birth of reinforced concrete, but subsequent development differed from Lambot’s concept. The technology of the period could not accommodate the time and effort needed to make mesh of thousands of wires. Instead, large rods were used to make what is now called conventional reinforced concrete, and the concept of ferrocement was almost forgotten for 100 years."

"Thin shells — Three-dimensional spatial structures made up of one or more curved slabs or folded plates whose thicknesses are small compared to their other dimensions. Thin shells are characterized by their three-dimensional load-carrying behavior, which is determined by the geometry of their forms, by the manner in which they are supported, and by the nature of the applied load."

"The story of aerodynamics is itself dynamic, replete with smashing successes, abject failures, and intense human competitions that have had major social, economic, and political consequences. It is a story of human beings, some exceptional and some average, some admirable and some not so. Above all, it is the story of an intellectual quest to understand those laws of nature that have allowed the continuing development of aircraft that can fly faster, higher, and more efficiently than their predecessors."

"One can roll noncircular wheels over appropriate road surfaces. The most striking example of this is the fact that a can roll on a road that consists of linked catenaries (the catenaries are defined by y = - cosh x) ...(the ride is not smooth in the sense that the center does not move forward at a constant rate of rotation, but... the actual ride... feels quite smooth). This animation was inspired by an exhibit at San Francisco's ..."

"Concrete being such a fluid and dynamic material... finds its identity once it is contained. ...A few... who used the forming materials at hand [were]... Antoni Gaudi... ... ... Felix Candela... ... ... Miguel Fisac... Many of these early innovators pushed the computational envelope... Some, like Antoni Gaudi, looked to nature for inspiration. The question... Do we need to "reinvent forming" or just draw from nature, i.e., gravity—catenary action? as Gaudi did. Alan Chandler in fabric framework notes "...for Felix Candela and Christopher Alexander fabric acted as a permanent shutter (framework)..." Chandler speaks of the family of fabric construction that includes... s... Pneumatic structures... Hydrostatic structures and... Shell structures derived from membrane form-finding. When faced with extremely complicated and complex shapes Heinz Isler and Antoni Gaudi used fabric as a modeling tool. These visionaries recognized that hanging chains and fabrics, forming catenaries, are in pure tension and when inverted are in pure compression and very stable. Gaudi, whose ing preceded the works of Candela... looked to nature and natural forms—an approach today called biomimicry..."

"Certainly the most striking contemporary example of a similar form [ arch] is to be found in St. Louis' ... In its incredible scale and construction out of metal plates this structure also serves as a convenient reminder of the important developments of the production of iron and steel that took place during the Industrial Revolution and that have so significantly affected arches as well as all other types of structural forms for the past 150 years."

"The arch is one of those brilliant innovations... Spanning... with horizontal beams is a losing game. ...By converting all the stress that fractures the middle of... stone beams—technically tension—into compression on stone piers larger... spaces could be spanned. ...But shift the pressure even slightly off center, and the pillar is likely to collapse. ...In their early incarnations, the limitations of both arch and dome was the ability of craftsmen to shape the stones carefully enough to create blocks precisely in the wedge shapes needed for a particular arch. Despite their mathematical sophistication in most other respects, the architects of antiquity lacked a proper geometric solution to the ideal form of the arch. (It was not until 1675 that the English polymath Robert Hooke described mathematically the shape of an arch loaded in pure compression, that is, with no tension, by showing how it describes an upside-down version of the catenary curve of a hanging chain.) As a result, the only way they could design an arch, and its component stones, was completely by eye, and... such tolerances commanded high prices. Rome overcame this drawback with typical ingenuity, first replacing stones and mortar... and expensive stonecutters with relatively cheap bricklayers. Even more ingeniously, some anonymous Roman builder found how to combine the mortar—in Latin pulvis puteoli—with lime, sand, and gravel to make the first concrete. ...The concrete domes of Rome were not surpassed until the age of steel."

"I love the catenary because it tells the story of holding up the roof."

"A non-catenary curve might be perfectly doable, but it takes more material, it has bigger beam sections, and overall it is much more complicated to construct... Even if the cladding falls out, the interiors and everything else falls away and the whole thing turns to dust and rubble and sand, [the catenary] should still stand."

"The most difficult properties of the Catenary were revealed before the close of the seventeenth century. This curve is entitled to particular attention, not only because it throws light on the theory of arches, but because it applies directly to the construction of suspended bridges, which are now deservedly coming into repute."

"The Catenary has its name from Catena, a chain; being the curve which a regular and very flexible chain will assume, if suspended loosely from both ends. It seems to have been first noticed by the famous Galileo, who proposed it as the figure of an arch of equilibration, but unfortunately mistook it for a . In fact, the Catenary, near its vertex, differs insensibly from that curve, but afterwards deviates more considerably. ...the Parabola diverges faster from its axis than the Catenary. The error of Galileo in confounding those two curves was not perceived till , in 1669, ascertained, by actual experiment, that the Catenary is neither a Parabola nor an . It was in 1691, that the penetrating genius of James Bernoulli discovered the true nature of the catenarian curve. A similar investigation was soon produced by John Bernoulli, by Huygens, and by Leibnitz. This latter philosopher, whose powers of invention and stores of learning were alike transcendant, discovered the fine relation of the Catenary to the Logarithmic Curve."

"I will begin with the subject of your bridge... and it is with great pleasure that I learn... that the execution of the arch of experiment exceeds your expectations. ...You hesitate between the catenary and portion of a circle. I have lately received from Italy a treatise on the equilibrium of arches, by the Abbé Mascheroni. It appears to be a very scientifical work. I have not yet had time to engage in it; but I find that the conclusions of his demonstrations are, that every part of the catenary is in perfect equilibrium. ...I would propose that you make your middle rail an exact catenary, and the interior and exterior rails parallels to that. It is true, they will not be exact catenaries, but they will depart very little from it; much less than portions of circles will."

"The true Mathematical and Mechanical Form of all manner of Arches for building with the true butment necessary to each of them, a Problem which no Architectonick Writer hath ever yet attempted, much less perform'd. ...Ut pendet continaum flexile, sic stabit contiguum rigidum, which is the Linea Catenaria."

"As Hooke saw in 1675 with his ut pendet continuum flexile, sic stabit contiguum rigidum inversum, ...a hanging chain may be inverted to give a satisfactory arch to carry the same loads, but working in compression rather than tension. The compressive arch, however, if of vanishingly small thickness, would be in unstable equilibrium, and stability is conferred in practice by making the arch ring of finite depth. Now if purely compressive forces, without bending, are to be transmitted from one portion of the arch to the next (as purely tensile forces are transmitted in the chain), then the arch centre line can accept only a single type of loading. Thus a parabolic arch can carry only a uniformly distributed horizontal load (although the magnitude of the load is arbitrary). It is the depth in a real arch which enables the arch to carry wider ranges of loading; a large number of different idealized centre-line arches can be contained within a given practical profile. ...[T]his must be so, or no mediaeval bridge would have survived its decentering."

"The flexible chain, hanging under the action of applied force, will assume a certain shape, namely the catenary if the chain is subjected only to its own weight, or a if the load is uniformly distributed horizontally. Whatever the load, there will be a corresponding shape, and the structural action in all cases is the same; purely tensile forces are transmitted along the centre line of the chain."

"It was comparatively late that the theory of arches attracted the notice of mathematicians. Dr. Hooke gave the hint, that the figure of a perfectly flexible cord or chain, suspended from two points, was the proper form for an arch. Galileo considered the catenary as a parabolic curve, and John Bernouilli appears to have been the first who discovered its nature. Dr. Gregory (Phil. Trans. 1697) published an investigation of its properties, and observes that the inverted catenary is the best form for an arch on account of its lightness. This is true so long as it is not pressed by an extraneous weight. It is not, however, capable of bearing a load on any part, much less of being filled up on the spandrels, which must be the case in practice. Other considerations must be involved before it can be fitted to receive a roadway or other weight, either upon its crown or haunches."

"What has been objected by an anonymous author, in the Leipsic Acts of Feb. 1699, in his animadversions on my demonstrations concerning the catenary, is this: that I have undertaken to demonstrate, after my manner, a matter found out and published by others seven years ago. This is true, and I cannot find any thing in it that is blame worthy. Those great men Huygens, Leibnitz, and Bernouilli, have discovered and communicated many properties of the catenaria, but without demonstration. I have contrived demonstrations, which was the thing I undertook to do. But was this matter that is the nature and primary properties of the catenaria all found out and published by others? ...From all ages architects have made use of arches in public buildings, as well for strength as beauty. Yet what was the true geometrical figure of an arch was not known before my demonstrations came out."

"Corol. 6.—In a vertical plane, but in an inverted situation, the chain will preserve its figure without falling, and therefore will constitute a very thin arch or fornix: that is, infinitely small, rigid, polished spheres, disposed in an inverted curve of a catenaria, will form an arch no part of which will be thrust outwards or inwards by other parts, but, the lowest parts remaining firm, it will support itself by means of its figure... none but the catenaria is the figure of the true and legitimate arch or fornix. And when the arches of other figures is supported, it is because in their thickness some catenaria is included. ...From Corol. 5... it may be collected, by what force an arch or buttress presses a wall outwardly, to which it is applied. For this is the same with that part of the force sustaining the chain, which draws according to a horizontal direction. For the force which in the chain draws inwards, in an arch equal to the chain drives outwards. All other circumstances, concerning the strength of walls to which arches are applied, may be geometrically determined from this theory, which are the chief things in the construction of edifices."

"Within a shed erected on the construction site of the church of the Sagrada family... Gaudí... made an upside-down model using lightweight cables to represent the structural lines of the future church—a model based on the structural notion of the inverted catenary. ...Analogically represented by little pouches filled with lead pellets the action of the stresses has been done ...The resulting chain configurations are used to determine the geometrical shapes and structural profiles of columns, pillars, arches, and vaults. ...Vicens Vilarrubias i Valls took photos of the model ...Gaudí used these photos upside-down to draw over them the external and internal elevations, studies of details and sections of the building."

"The trolley-wire must... be suspended with only a very small sag, and to obtain this result without excessive tension in the wire the span must be relatively short, i.e. of the order of 10 ft. to 15 ft. It is obvious that for these short spans the method of construction adopted in tramway practice would be unsuitable, both from the mechanical as well as the electrical standpoint. However, by adopting the catenary system—that is, supporting the trolley-wire from another wire, suspended with considerable sag between supports of moderate span—we are able to obtain a level trolley-wire with a relatively small number of supporting structures. The wire from which the trolley-wire is supported is called the "catenary" or "messenger" wire, and by insulating this wire from the supporting structures there is no necessity for insulated hangers on the trolley-wire."

"The largest catenary structure of masonry is the Great Hall of the Palace of Taq Kisra, at Qesiphon, then the capital of Persia."

"In 1690... Jacob Bernoulli brought up the problem of the catenary in a memoir... in the '...Huygens' solution represents the past... a complex, though skillful, geometrical method. Leibniz, using his new [infinitesimal calculus] reaches a correct analytical formula...y/a = (b^\frac{x}{a} + b^\frac{-x}{a})/2 where a is [a] segment... and b... corresponds to... e... ...supplied two correct constructions ...presents valid statistical arguments and... new and important... equations of equilibrium in differential form. ...In 1697-1698, Jacob Bernoulli was the first to derive the general equations that not only solved the problem, but also permitted the treatment of the more general theme of the equilibrium of a flexible rope, subject to any distribution of tangential (f_t) and normal (f_n) forces. Bernoulli's equations are...\frac{dT}{ds} + f_t = 0, \qquad \frac{T}{r} + f_n= 0where T is the tension, s the curvilinear abscissa, and r the radius of curvature."

"Gaudí was drawn not just to the aesthetics of the catenary but also to what it represented mathematically. His use of catenaries made the structural mechanics of a building a principal feature of its design. Gaudí realized that the entire architecture of a building could be drafted using a model of hanging chains... when he was commissioned to design a church the Colònia Güell... he made an upside-down skeleton of the project. Instead of using metal chains, he used string weighed down by hundreds of sachets containing lead shot. The weight of each sachet on the string created a mesh of 'transformed' catenary curves. The arches of these transformed catenaries were the most stable curves to withstand a corresponding weight at the same position (such as the roof, or building materials)."

"One of the curious things about mathematics that clearly emerges... is that mathematics which is concerned with reasoning nevertheless creates processes which can be applied almost mechanically, that is, without reasoning. The thinking is, so to speak, mechanized and this mechanization enables us to solve complicated problems in no time. We think up processes so that we don't have to think."

"The overwhelming pressure of mechanization evident in the newspaper and the magazine, has led to the creation of vast monopolies of communication. Their entrenched positions involve a continuous, systematic, ruthless destruction of elements of permanence essential to cultural activity."

"It always demands a far greater degree of courage for an individual to oppose an organized movement than to let himself be carried along with the stream — individual courage, that is, a variety of courage that is dying out in these times of progressive organization and mechanization."

"Mediocrity serves it best because mechanization best serves the mediocre."

"Every machine is constructed for the purpose of performing certain mechanical operations, each of which supposes the existence of two other things besides the machine in question, namely, a moving power, and an object subject to the operation, which may be termed the work to be done. Machines, in fact, are interposed between the power and the work, for the purpose of adapting the one to the other."

"Paul wondered at what thorough believers in mechanization most Americans were, even when their lives had been badly damaged by mechanization."

"Coal being then the chief source of power, much industrial reconstruction depended on there being a plentiful and cheap supply. But the newly nationalized industry was not doing well. Productivity failed to increase in step with increases in mechanization. Men were leaving the mines in large numbers for more attractive opportunities in the factories. Among those who remained, absenteeism averaged 20 percent. Labor disputes were frequent despite improved conditions of employment. Some time earlier the National Coal Board had asked the Institute to make a comparative study of a high producing, high morale mine and a low producing, low morale, but otherwise equivalent mine."

"We conceive the prominent element in present-day industrial management to be: the mental attitude that consciously applies the transference of skill to all the activities of industry. Here emphasis is placed upon the word all, for the restricted application of this principle to machines and tools has been highly developed for a long period. But its conscious application in a broad way to the production departments, and particularly to the workmen, we believe has been made during the last quarter of a century."

"Transference of skill, when considered with reference to the industrial revolution and the introduction of machinery, might easily be interpreted to mean the transference of skill from the workman to the machine. What actually happened was that the machine brought to the aid of the workmen some of the vast forces of nature; and in addition it superseded the skill of the hand worker. That this was a distinct loss to the hand worker who was unable to adjust himself to the new conditions is incontestable in the face of economic history; and the sad record of the change is a solenm warning to present day managers to take every step possible to make the adjustment to new methods of management as easy and gradual as possible. The machine developed a new kind of skill on the part of the operator; but now it is a minute skill easily acquired and subject to sudden loss with the change in the design of the machine."

"Mechanisation leads to the decay of taste, the decay of taste leads to demand for machine-made articles and hence to more mechanisation, and so a vicious circle is established."

"The characteristic feature of our modern mechanical improvements, is the introduction of self-acting tool machinery. What every mechanical workman has now to do, and what every boy can do, is not to work himself, but to superintend the beautiful labor of the machine. The whole class of workmen that depend exclusively on their skill is now done away with."

"The mechanization of human labor was, in effect, the first step toward the humanization of the machine humanization in the sense of giving the automaton some of the mechanical equivalents of life-likeness."

"The incentive to mechanization lay in the greater profits that could be extracted through the multiplied and efficiency of the machine."

"Mechanization and regimentation are not new phenomena in history: what is new is the fact that these functions have been projected and embodied in organized form which dominate every aspect of our existence."

"Philosophy must re-emphasize man versus the collective body (with its envisaged collectivized mind), freedom versus the mechanization of inner and social life, common sense versus faith in science."

"The Mechanisation of Industry."

"There is considerable danger that psychoanalysis, as well as other forms of psychotherapy and adjustment psychology, will become new representations of the fragmentation of man, that they will exemplify the loss of the individual's vitality and significance, rather than the reverse, that the new techniques will assist in standardizing and giving cultural sanction to man's alienation from himself rather than solving it, that they will become expressions of the new mechanization of man."

"Advertising tends to make mechanized barbarians of us all."

"If the individual were no longer compelled to prove himself on the market, as a free economic subject, the disappearance of this kind of freedom would be one of the greatest achievements of civilization. The technological processes of mechanization and standardization might release individual energy into a yet uncharted realm of freedom beyond necessity. The very structure of human existence would be altered; the individual would be liberated from the work world's imposing upon him alien needs and alien possibilities. The individual would be free to exert autonomy over a life that would be his own."