Consider the material element shown to the right.
This element is in a state of plane stress and has
normal stresses and shear stresses acting on it.
(a) Calculate $\sigma_x$, $\sigma_y$, and $\tau_{xy}$ when the
element is rotated counter-clockwise by
70°.
(b) Draw the stresses calculated in Part A on
the element rotated clockwise by 70°.
(c) Plot $\sigma_x$, $\sigma_y$, and $\tau_{xy}$ as a function of
the variable $\theta$ over the range $0 \le \theta \le 2\pi$.
Shown any work required, but feel free to
use software to produce these plots.
(d) Based on the results of Part C, identify the maximum and minimum values of $\sigma_x$, $\sigma_y$,
and $\tau_{xy}$ and the rotation angles they occur at.
(e) Confirm the results for maximum and minimum normal stresses in Part D with
calculations utilizing the equations for the principle stresses and the angles they occur at.
