Eduardo Torroja: Structure

“Mathematics is merely a convenient tool by which the designer determines the physical proportions and details of a planned structure in order to transform his ideas… to the actuality of a finished structure.”

“The equilibrium… in order to become static—should be steady, permanent, lasting. …This type of equilibrium… is… independent of any scale. A reduced model will show the same effects as the proper structure. Experiments on models are simple and… instrumental for understanding such structural problems.”

“[E]very structure has a resistant function to fulfill… to ensure …the static equilibrium of the structure for a long period of time.”

“[M]ost of our structures in the past consisted of individual members having relatively small transverse dimensions as compared with their length, and in such members stress analysis is much more simple. …[M]any modern structures consist of frameworks of this type, and frequently the word "structure" refers specifically to assemblies consisting of linear elements.”

“[E]xperimental investigation of stresses in a plane structure is of great interest and merit as applied to shells with single curvature (barrel shells, pipes) and to shells with double curvature (domes, etc.). In these structures similar states of stress are produced and can be determined at any point as acting in a plane tangential to the center layer of the shell.”

“In general, these phenomena are very easy to perceive and understand, but difficult to calculate. The danger of failure increases rapidly with decreasing depth or thickness of the structural member…”

“Stone can effectively resist compression but is relatively weak in tension. Because of its mass and weight it may be used advantageously in structural types that can be made stable by the proper weight (dead load, gravity) and are but slightly exposed to lateral forces.”

“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”

“The technical literature on structural engineering abounds with theoretical works of a mathematical nature, but few publications are concerned with the various kinds of structures or the fundamental reasons for their existence.”

“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.”

“The material in all elementary parts of a structure must have the properties of resistence to all internal forces produced by general loading conditions and by the action of any exterior force.”

“Before a man can successfully plan a structure… he must study, from every possible angle, the ultimate purpose of his building. Attention must be directed to the basic structural concept before the mathematical process of calculation is undertaken.”

“Long before… our techniques of today, men could conceive and build structures adapted to the requirements of resistance… because he had observed… the branches of a tree bending under the weight of fruits and the tensioned cords of strings in which children have rocked from time immemorial…”

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

“Structural design is… very much concerned with art, common sense, sentiment, aptitude, and enjoyment of the task of creating opportune outlines to which scientific calculations will add finishing touches, substantiating that the structure is sound and strong…”

“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.”

“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.”

“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.”