The engineering design of large structures often involves a two-stage process: first, the internal force field acting on the structural material must be defined, and second, the response of the material to that force field must be determined. The first stage involves an analysis of the stresses acting within the structural elements; the second involves a knowledge of the properties of the structural material. The linear relationship between stress and strain in an idealized material forms the basis of the mathematical theory of elasticity, which has in turn been applied widely in practice to actual materials to estimate stress or strain in the structural elements under a specified working load condition. These stresses are restricted to be less than the specified working or allowable stress that is chosen as some fraction of the yield strength of the material. A safe design thus is evolved, not due to the adequacy of the structural analysis and the understanding of the properties of the material, but by reliance upon the experience of decades or centuries.
An actual structure is a very complex body with an extremely complicated state of stress. Many secondary stresses arise owing to fabrication, erection, and localization. The combination of unknown initial stress, secondary stresses, and stress concentration and redistribution due to discontinuities of the structure defy an idealized calculation based on the theory of elasticity. The theory of plasticity represents a necessary extension of the theory of...
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