$1.[2$op$].$ A structure consisting of a steel shaft attached to a wall and a bracket is loaded by forces $F_1$ and $F_2.$ A strain gage rosette is bonded $($Point $\text{'}A\text{'})$ the shaft, see Fig. below. Analysis of the readings from the strain gages $($not considered here$)$ reveals the principal strains; ${}_{1p}=270$ and ${}_{2p}=40.$ The state of principal strain is illustrated in a Fig. below. $($Notice that ${}_z=0$ and the principal strain directions and principals stress directions coincide$).$

With $E=200$GPa and

$u=0\mathrm{.}3($steel$),$ determine the principal stresses, ${}_{1p}$ and ${}_{2P}$