8b. Strain Transformation  (SSES Ch. 8.5) • Strain Transformation • Principal Strain • Maximum Shear Strain Back | Index | Next

 Strain Transformation Strain Transformation at a point (in plane strain) is done in a similar manner as with the stresses. Simply substitute ex for sx and ey for sy. However, because of the way the math works out, substitute g/2 for t: The principle of invariance works with normal strains: ex + ey = ex' + ey

 Principal Strains Principal Strains are the maximum and minimum normal strains that occur at a point as the coordinate system is rotated by a certain angle qp. The principal strains are eI and eII, and occur along the xp-yp axes. These directions are NOT necessarily the same as those for the Principal Stresses for the associated stress-state. The Principal Strains for a given strain state are given by: The principal strains occur when the element has been rotated by an angle of qp, where: As with the angles for principal stresses, there are two solutions, 90° apart. KEY POINT: When the Normal Strains are Principal Strains the Shear Strain is Zero.

 Maximum (In-Plane) Shear Strain The Maximum (In-Plane) Shear Strain occurs when the Principal Strain element is rotated 45° and is given by: The angle at which the Maximum Shear Strain occurs is given by: Again, there are two solutions, 90° apart. KEY POINT: When the Shear Strain is Maximum, the Normal Strains are equal to each other and are the average of the Principal Strains.

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Updated: 05/23/09 DJD