Principal Strain for the Case of Plane Strain Principal Strain (2D) Formula Home Mechanics of Matl. Stress Strain Plane Strain Principal Strain Mohr's Circle Mohr's Circle Usage Mohr's Circle Examples Hooke's Law Applications Pressure Vessels Rosette Strain Gages Failure Criteria Calculators Stress Transform Strain Transform Principal Stress Principal Strain Elastic Constants Resources Bibliography  Login   Home Membership Magazines Forum Search Member Calculators  Materials  Design  Processes  Units  Formulas  Math Principal Directions, Principal Strain The normal strains (ex' and ey') and the shear strain (ex'y') vary smoothly with respect to the rotation angle q, in accordance with the transformation equations given above. There exist a couple of particular angles where the strains take on special values. First, there exists an angle qp where the shear strain ex'y' vanishes. That angle is given by, This angle defines the principal directions. The associated principal strains are given by, The transformation to the principal directions with their principal strains can be illustrated as: Maximum Shear Strain Direction Another important angle, qs, is where the maximum shear strain occurs and is given by, The maximum shear strain is found to be one-half the difference between the two principal strains, The transformation to the maximum shear strain direction can be illustrated as: Home  Membership  About Us  Privacy  Disclaimer  Contact  Advertise Copyright © 2019 eFunda, Inc.