Question $3.$

The figure $($not drawn to scale$)$ shows a state of stress in a xy frame of reference.

Given

direct stresses ${}_x=-5$MPa and ${}_y=15$MPa,

and shear stress ${}_{xy}=5$MPa,

calculate the principal stresses $,$ and the angle ${}_p$ at which they occur.

Enter your answers in the boxes below.

The answers are acceptable within a tolerance of $0\mathrm{.}1$MPa for the stresses and $0\mathrm{.}1$ for the angle.

${}_{\text{m}\text{a}\text{x}}$:

MPa $(2$ mark$)$

${}_{\text{m}\text{i}\text{n}}$:

MPa $(2$ mark$)$

${}_p$:

$(2$ mark$)$