Question

Find the strain components $\epsilon_n, \epsilon_t$, and $\gamma_{n t}$ at the point if the $n t$-axes are rotated with respect to the $x y$-axes by the amount and in the direction indicated by the angle $\theta$ shown in figure.

Solution

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Given values:

\begin{align*} \epsilon_x&=-800\text{ \muin./in.}\\ \epsilon_y&=640\text{ \muin./in.}\\ \gamma_{xy}&=-960\text{ \murad}\\ \theta_n&=42\degree\\ \theta_t&=\theta_n+90\degree=132\degree \end{align*}

The sketch:

We have to determine:

\begin{align*} \epsilon_{n}=?\\ \epsilon_{t}=?\\ \gamma_{nt}=? \end{align*}