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Heyman J. Elements of the Theory of Structures

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Heyman J. Elements of the Theory of Structures
Cambridge University Press, 1996. — 137 p.
The theory of structures is one of the oldest branches of engineering. There was early interest in large, indeed ostentatious, buildings, and the design of such buildings needed more than peasant tradition; they were intended to be, and were, spectacular feats, and they required professional advice from acknowledged masters. Names of their designers are known through two or three millenia, and building manuals have survived through the same period. (Man showed also an early interest in waging war, and military engineering
is another ancient profession; civil engineers are non-military engineers.) As might be expected from an ancient discipline, the theory of structures
is an especially simple branch of solid mechanics. Only three equations can be written; once they are down on paper, the engineer can in principle solve the whole range of structural problems. Sometimes the equations can be examined individually; sometimes a simple tool, virtual work, can be used to combine them to yield surprising results. In every case, however, it is only the three master equations which come into play. Equations of statics will ensure that a structure is in equilibrium. Geometrical equations will ensure that all parts of a structure fit together before and after deformation, and that the structure rests securely on its foundations. Finally, the properties of the material used to build the structure will enter the equations relating the strain in a member to the applied stress.
These equations were, effectively, known by 1826 (Navier), or more certainly by 1864 (Barre de Saint-Venant). Of course, although the equations
are essentially simple, individual pieces of mathematics may become difficult. By the end of the nineteenth century, indeed, many problems had been formulated completely, but the equations were so complex that they could not usually be solved in closed form, and numerical computation was impossibly heavy. This situation gave an exhilarating spur in the twentieth century to the development of highly ingenious approximate methods of solution, and also to a fundamental reappraisal of the whole basis of the theory of structures. These developments have now been almost completely arrested by the advent of the electronic computer; the Victorian equations, insoluble a century ago, can now be made to yield answers. That the equations may not be a good reflexion of reality, so that their solutions do not actually give the required information, is only slowly being realized.
This book is concerned with the basic equations and the way in which they should be used. The equations themselves have an intrinsic interest, as
does their application to a whole range of structural problems. The later chapters of this book give a tiny sample, from the almost infinite number
of topics in the theory of structures, for which the results are important, or startling, or simply amusing.
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