$($a$)$

A cylindrical component is subjected to a tensile stress of $100$ MPa in the axial direction $({}_1),$ a compressive stress of $50$ MPa in the radial direction $({}_2),$ and no stress in the hoop direction $)=(0.$ Calculate the von Mises stress acting on the component.

$($b$)$

A $7075$ T$6$ aluminum component has a plane stress element shown below, which is found to have the following stresses:

${}_x=10$ksi,${}_y=25$ksi, and ${}_{xy}=15$ksicw.

What is the factor of safety using von Mises theory?

Note: shear in the counter clockwise direction $($ccw$)$ is positive. Shear in the clockwise direction $($cw$)$ is negative.