The figure $($not drawn to scale$)$ shows a state of stress in a xy frame of reference. We wish to calculate the state of stress in the rotated frame of reference $x^{\text{'}}{y}^{\text{'}}.$

Given

Angle of rotation $=22,$

direct stresses ${}_x=40$MPa and ${}_y=60$MPa,

shear stress ${}_{xy}=40$MPa,

calculate the state of stress in the rotated frame of reference.

Enter your answers in the boxes below.

The answers are acceptable within a tolerance of $1$MPa.

${}_{x^{\text{'}}}$:$,$MPa$(2$mark$)$

${}_{y^{\text{'}}}$:$,$MPa$(2$ mark $)$

${}_{x^{\text{'}}{y}^{\text{'}}}$:$,$MPa$(2$ mark $)$