Question: The general from for a three-dimensional stress field is given by Where the diagonal terms represent tensile or compressive stresses and the off-diagonal terms represent

The general from for a three-dimensional stress field is given by

Where the diagonal terms represent tensile or compressive stresses and the off-diagonal terms represent shear stresses. A stress field (in MPa) is given by

To solve for the principal stresses, it is necessary to construct the following matrix (again in MPa):

?₁, ?₂, and ?₃, can be solved from the equation

?₃, - 1?² + 11? ? 111 = 0?

?Where

1, 11, and 111 are known as the stress invariants. Find ?₁, ?₂, and ?₃, using a root-finding technique.

Orr Ory Oxz Oxy dyy Oy:

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