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States of Strain and Stress-Strain Relations

  • Anthony Bedford
  • Kenneth M. Liechti
Chapter

Abstract

The six components εx, εy, εz, γxy, γxz, and γyz of the state of strain at a point in terms of a given cartesian coordinate system were defined in Chapter 2. The definition of plane strain and the derivation of relations for the strain components εx, εy and γxy as functions of θ are presented which are entirely analogous to the corresponding results for plane stress. A description is given of the strain gauges commonly used for measuring normal strains. A set of three strain gauges measuring normal strains in three different directions near a given point are known as a strain-gauge rosette. The results can be used to determine the state of plane strain, including the shear strain, at the point. Determination of the maximum and minimum normal strains and the maximum magnitude of the shear strain is discussed. The application of Mohr’s circle to states of plane strain, altogether equivalent to the process for states of stress, is described. The stress-strain relations of a linear elastic material and the concept of isotropy are introduced. A relationship for the shear modulus in terms of the modulus of elasticity and Poisson’s ratio is derived. The bulk modulus of a material is defined and given as an expression in terms of the modulus of elasticity and Poisson’s ratio.

Keywords

Bulk modulus, Isotropic material Maximum strain Minimum strain Modulus of elasticity Mohr’s circle Normal strain Plane strain Poisson’s ratio Shear strain State of strain Strain Strain gauge Strain-gauge rosette Stress-strain relations 

Supplementary material

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Anthony Bedford
    • 1
  • Kenneth M. Liechti
    • 1
  1. 1.University of TexasAustinUSA

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