“Lightweight concrete obtained with special admixtures producing bubbles throughout the mass shows lower resistance, which makes it less suitable for structural purposes; its practical application is limited to smaller structural elements adequately reinforced in which thermal insulation is required.”

— Eduardo Torroja

p, 125
Philosophy of Structures (1958)

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Eduardo Torroja 29

Spanish architect 1899–1961

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“Concrete presents, besides a coefficient of thermal expansion, a coefficient of hygroscopic dilation which is more appreciable. While concrete is kept wet… it expands; and as it dries, it contracts, in inverse proportion to the hygroscopic degree of the ambient air. …The shrinkage …will vary with the porosity of the concrete and with the thickness used in the structural member. …Shrinkage is much greater in structures consisting of thin elements subjected to intemperateness of dry climate, and disappears or becomes negligible in underground structures”

Eduardo Torroja (1899–1961) Spanish architect

e.g., foundations
Philosophy of Structures (1958)

“Study after study shows that the very best designers produce structures that are faster, smaller, simpler, clearer, and produced with less effort. The differences between the great and the average approach an order of magnitude.”

Fred Brooks No Silver Bullet

Page 202.
No Silver Bullet (1986)

“Equilibrium requires that the whole of the structure, the form of its elements, and the means of interconnection be so combined that at the supports there will automatically be produced passive forces or reactions that are able to balance the forces acting upon the structures, including the force of its own weight.”

Eduardo Torroja (1899–1961) Spanish architect

p, 125
Philosophy of Structures (1958)

“The third and intermediate kind of instruction, which connects the first two… relates to the application of scientific principles to practical purposes. It qualifies the student to plan a structure or a machine for a given purpose, without the necessity of copying some existing example, and to adapt his designs to situations to which no existing example affords a parallel. It enables him to compute the theoretical limit of the strength or stability of a structure, or the efficiency of a machine of a particular kind—to ascertain how far an actual structure or machine fails to attain that limit—to discover the cause of such shortcomings—and to devise improvements for obviating such causes; and it enables him to judge how far an established practical rule is founded on reason, how far on mere custom, and how far on error.”

William John Macquorn Rankine (1820–1872) civil engineer

p, 125
"On the Harmony of Theory and Practice in Mechanics" (Jan. 3, 1856)

“One should become so familiar with the structure as to have the feeling of being, in full vitality and sentiment, part of it and of all its elements. …it is necessary to achieve a sincere Einfühlung [empathy] of the process of resistence… through the deformation that is always essentially united with the process of stressing. …[T]he comprehension of a structure requires intuitive knowledge of the ethology of its resistance and of its constituent materials.”

Eduardo Torroja (1899–1961) Spanish architect

Philosophy of Structures (1958)

“Adobe (sun-dried clay bricks) is a material usable in regions where sandy clays suitable for fabrication are found. Adobe masonry, is, however, useful only for walls and structural elements subjected to lower values of tension and compression, and is, therefore, of little interest as a structural material.”

Eduardo Torroja (1899–1961) Spanish architect

p, 125
Philosophy of Structures (1958)

“Clay masonry, like concrete, is a "plastic" material that permits the pouring in situ of large monoliths of any shape or form, with certain limitations and by using special methods. Its economical possibilities when used in walls of popular housing, its excellent heat and sound insulation, as well as its aesthetic possibilities, should not be underestimated. Its resistance and durability can be substantially improved by using modern techniques and methods, for example, admixture of small amounts of Portland cement in accordance with granulometric investigation, petrographic composition, and rheological behaviour of all constituents.”

Eduardo Torroja (1899–1961) Spanish architect

Philosophy of Structures (1958)

“[T]here are three different but interconnected conceptions to be considered in every structure, and in every structural element involved: equilibrium, resistance, and stability.”

Eduardo Torroja (1899–1961) Spanish architect

p, 125
Philosophy of Structures (1958)

“The process of formulating and structuring a system are important and creative, since they provide and organize the information, which each system. "establishes the number of objectives and the balance between them which will be optimized". Furthermore, they help identify and define the system parts. Furthermore, they help identify and define the system parts which make up its "diverse, specialized structures and subfunctions.”

Harold Chestnut (1917–2001) American engineer

Source: Systems Engineering Tools, (1965), Systems Engineering Methods (1967), p. 70; First sentences of Ch. 3. Formulating and Structuring the System
In this text Harold Chestnut is here citing:
C. West Churchman, Russell L. Ackoff, and E. Leonard Arnoff (1957) Introduction to Operations Research. Wiley. New York, and
J. Morley English (1964) "Understanding the Engineering Design Process." The Journal of Industrial Engineering, Nov-Dec. 1964 Vol 15 (6). p. 291-296

“The real significance of the Russell paradox, from the standpoint of the modal-logic picture, is this: it shows that no concrete structure can be a standard model for the naive conception of the totality of all sets; for any concrete structure has a possible extension that contains more 'sets.'”

Hilary Putnam (1926–2016) American philosopher

"Mathematics without foundations"
Source: Philosophical Papers Volume 1: Mathematics, Matter, and Method (1975, 1979)
Context: (If we identify sets with the points that represent them in the various possible concrete structures, we might say: it is not possible for all possible sets to exist in any one world!) Yet set theory does not become impossible. Rather, set theory becomes the study of what must hold in, e.g. any standard model for Zermelo set theory.

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Eduardo Torroja 29

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