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Bridges are built using simpli ed engineering when components such as prestressed, precast concrete are selected from tables for short standard spans.
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Of course, the tables are produced by the most rigorous analysis methods. This type of simpli ed engineering is often used at the Type Study Phase of bridge design as a tool for comparison of structure types and costs. Simpli ed engineering, however, is not likely to be used in the nal design phase of a bridge. The standard code for bridges published by the American Association of State Highway and Transportation Of cials (AASHO) has, like the building codes, increased in complexity. One example of the increased complexity can be found in the change of the distribution factor for wheel loadings on interior bridge girders. The spacing factor of S/11 will soon be changed to a much more complex expression. Fortunately for the designer, computer programs can be used for the calculation. However, the feel for the number becomes lost, if not nonexistent.
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As present-day designers, we often are so immersed in our day-to-day operations that we seldom have the opportunity to formulate a rigorous design philosophy. We know how to perform our services, but do not always think much about the process. If asked, most of us would describe the methods we use in order to illustrate our philosophy. Most of us design structures from the top to the bottom for vertical loads rst. Then, after the horizontal and vertical members are selected, we determine which system to use to resist lateral forces. Although most engineers have three-dimensional design capability, we design buildings through analysis by separating orthogonal systems into components.
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In the 1960s, the computer became the modern tool for analysis, and many practical courses disappeared from the structural engineering curriculum. First, Surveying was eliminated. Then, Mechanical Drafting and Freehand Drawing were combined into Graphic Analysis. Some design and drafting courses were dropped from the curriculum in favor of basic computer programming. The Maxwell diagram, the string polygon, and Bow s notation are unknown to the younger generation of engineers. Yet, what simple but beautiful methods of analysis these were! Graphical analysis was so simple and logical that many truss manufacturers employed drafters to do this work. Pier Luigi Nervi remarked, I believe that graphical statics should play an important role in this last educational phase, since its procedures give a direct
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understanding much better than that afforded by analytical methods of force systems and their composition, decomposition, and equilibrium. 5 Nervi is well known for his ideas regarding mathematical analysis in building design. In the early 1950s, he wrote:
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It is highly regrettable that some of the highest qualities of the human mind, such as intuition and direct apprehension, have been banned from our schools and have been overwhelmed by abstract and impersonal mathematical formulas. We cannot forget that in the distant past intuition allowed the execution of works which cannot be analyzed today by the most modern theoretical methods, and before which we must bow in reverent and humble admiration. We cannot deny that the potentialities of mathematical methods are soon exhausted, even when their application is dif cult and complex. Special, skinresistant, and highly indeterminate structures cannot be analyzed by mathematical theories, although they are extremely ef cient from a technical, economical, and architectural viewpoint. Moreover, the most advanced chapters of theory of structures, which deal with the solution of statically indeterminate systems, can be used only to check the stability of a structure. They can be used only to analyze numerically a structure already designed, not only in its general outline, but in all its dimensional relations. The formative stage of a design, during which its main characteristics are de ned and its quality and faults are determined once and for all (just as the characteristics of an organism are clearly de ned in the embryo), cannot make use of structural theory and must resort to intuition and schematic simpli cations.5
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The essential part of the design of a building consists in conceiving and proportioning its structural system; in evaluating intuitively any dangerous thermal conditions and support settlements, in choosing materials and construction methods best adapted to the nal purpose of the work and to its environment; and, nally, in seeking economy. When all these essential problems have been solved and the structure is thus completely de ned, then and only then can we and should we apply the formulas of the mathematical theory of elasticity to specify with greater accuracy its resisting elements.
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