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If the resultant forces are resolved in the three co-ordinate directions and divided by the area of the face of the cube we have the general state of 3-dimensional stress as shown.
Stresses acting normal to the facesare denoted by σ and those acting parallel to the faces are shear stresses denoted by τ.
The second subscript refers to the direction in which the stress acts (e.g. τyx acts on the y face in the x direction). The normal stresses areusually abbreviated to σx, σy and σz.
Using Laplace transfom, the following differential equation d y dy dt reduces to the algebraic equation of the form Resolve y(s) into partial fractions
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