8b. Strain Transformation (SSES Ch. 8.5) • Strain Transformation • Principal Strain • Maximum Shear Strain |
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Strain Transformation at a point (in plane strain) is done in a similar manner as with the stresses. Simply substitute e_{x} for s_{x} and e_{y} for s_{y}. However, because of the way the math works out, substitute g/2 for t:
The principle of invariance works with normal strains: e_{x} + e_{y} = e_{x'} + e_{y} |
Principal Strains are the maximum and minimum normal strains that occur at a point as the coordinate system is rotated by a certain angle q_{p}. The principal strains are e_{I} and e_{II}, and occur along the x_{p}-y_{p} 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 q_{p}, 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. |
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