Question $2$

$[12]$

Figure $2$ shows a strain gauge rosette with readings ${}_1=100({10}^{-6}),{}_2=-200({10}^{-6})$ and ${}_3=200({10}^{-6}).$ Determine the angin A which is the axis of the principle stresses.

Figure $2$

$\frac{{}_{x^{\text{'}}{y}^{\text{'}}}}{2}=-\frac{{}_x-{}_y}{2}sin2+\frac{{}_{xy}}{2}cos2$