Question 2.17: Solve Example 2.16 if the rotation of xyz reference is 30° c...
Solve Example 2.16 if the rotation of xyz reference is 30° clockwise.
Direction cosine matrix for transformation (Fig. 2.27)
\left[C\right]=\begin{vmatrix} {0.866} & {-0.5} & {0} \\ {0.5} & {0.866} & {0} \\ {0} & {0} & {1} \end{vmatrix}Using Eq. (2.10d)
\left[\tau _{n s}\right]=\left[C\right]\times \left[\tau _{i j }\right]\times \left[C\right]^{T}
or, \left[\tau _{n s}\right]=\begin{vmatrix} {0.866} & {-0.5} & {0} \\ {0.5} & {0.866} & {0} \\ {0} & {0} & {1} \end{vmatrix}\begin{vmatrix} {80 } & {-60} & {0} \\ {-60 } & {-40} & {0} \\ {0} & {0} & {40} \end{vmatrix}\begin{vmatrix} {0.866} & {0.5} & {0} \\ {-0.5} & {0.866} & {0} \\ {0} & {0} & {1} \end{vmatrix}
=\begin{vmatrix} {101.96} & {21.96} & {0} \\ {21.96} & {-61.96} & {0} \\ {0} & {0} & {40} \end{vmatrix} MPa
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