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**Unformatted text preview: **Problem 1. (i) Write the three linear equations you will use to determine the corresponding principal direction. (ii) Solve the above equations to determine the principal direction. If there are multiple principal directions for σ n =2, then show them in a parametric for Solution ( - )-- ( - ) ( - ) = 4 2 20 2 4 2 000 2 2 nxnynz 000 The first two equations are the same:-= → = 2nx 2ny 0 nx ny The last equation does not yield any useful information. Hence n z is arbitrary, say n z = α . Then the direction cosines of the principal stress direction take the form: +∝ , , 12 21 1 α where -∞≤ ≤+∞ α Some examples of the principal stress directions (eigen vectors) α n x n y n z-∞-1 1 1 ½ 2/3 2/3 1/3 +∞ +1...

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