The strain components $$ \epsilon_x $$, $$ \epsilon_y $$, and $$ \gamma_{xy} $$ are given for a point in a body subjected to plane strain. Determine the strain components $$ \epsilon_n $$, $$ \epsilon_t $$, and $$ \gamma_{nt} $$ 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 $$ \theta $$. Sketch the deformed shape of the element. $$ \epsilon_x = -1000 \mu \epsilon $$, $$ \epsilon_y = 470 \mu \epsilon $$, $$ \gamma_{xy} = 1100 \mu rad $$, and $$ \theta = 31^\circ $$.
Answer:
$$ \epsilon_n = $$
$$ \epsilon_t = $$
$$ \gamma_{nt} = $$