Plane Strain and Coordinate Transformations Plane Strain, Transforms 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 Plane State of Strain  Some common engineering problems such as a dam subjected to water loading, a tunnel under external pressure, a pipe under internal pressure, and a cylindrical roller bearing compressed by force in a diametral plane, have significant strain only in a plane; that is, the strain in one direction is much less than the strain in the two other orthogonal directions. If small enough, the smallest strain can be ignored and the part is said to experience plane strain. Assume that the negligible strain is oriented in the z-direction. To reduce the 3D strain matrix to the 2D plane stress matrix, remove all components with z subscripts to get, where exy = eyx by definition. The sign convention here is consistent with the sign convention used in plane stress analysis. Coordinate Transformation The transformation of strains with respect to the {x,y,z} coordinates to the strains with respect to {x',y',z'} is performed via the equations, The rotation between the two coordinate sets is shown here, where q is defined positive in the counterclockwise direction.
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