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2 - Generalized stress

Published online by Cambridge University Press:  14 August 2009

John J. Gilman
Affiliation:
University of California, Los Angeles
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Summary

Stress is a generalization of the concept of pressure. The latter consists of a unit of force applied perpendicular to a vunit of area. However, in the case of stress, the force can be applied at any angle relative to the unit area. Thus, whereas pressure is a scalar that does not act in any special direction, two vectors are needed to define a general stress: one that indicates the direction of the force, and the other that gives the orientation of the area on which the force acts. Furthermore, in the case of solids, the orientation of the solid must be defined, except when the solid is isotropic. Stresses applied to surfaces (force per unit area) are called tractions. They can be resolved into two components: one parallel, and the other perpendicular to the unit surface areas on which they act. The orientation of the area is given by a unit vector lying perpendicular to it. For the force component that lies parallel to the unit surface area a shear traction is produced, and for the force component that lies perpendicular to the unit surface, a normal traction is produced.

Tractions tend to distort a solid material, either causing its volume to change, but not its shape, or causing its shape to change at constant volume (small changes), or both. That is, they create dilatational strain in the material, or shear strain, or both.

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Chapter
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Publisher: Cambridge University Press
Print publication year: 2003

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References

Nye, J. F. (1957). Physical Properties of Crystals. Oxford: Clarendon Press
Sines, G. (1969). Elasticity and Strength. Boston, MA: Allyn and Bacon
Timoshenko, S. P. (1983). History of the Strength of Materials. New York: McGraw-Hill, 1953. Republished by Dover Publications, New York
Voigt, W. (1910). Lehrbuch der Kristallphysik. Leipzig: Teubner

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  • Generalized stress
  • John J. Gilman, University of California, Los Angeles
  • Book: Electronic Basis of the Strength of Materials
  • Online publication: 14 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511541247.004
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  • Generalized stress
  • John J. Gilman, University of California, Los Angeles
  • Book: Electronic Basis of the Strength of Materials
  • Online publication: 14 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511541247.004
Available formats
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Save book to Google Drive

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  • Generalized stress
  • John J. Gilman, University of California, Los Angeles
  • Book: Electronic Basis of the Strength of Materials
  • Online publication: 14 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511541247.004
Available formats
×