HW: Plane Stress and Strain

#$1$:

Given ${}_x=80$MPa,${}_y=-80$MPa, and ${}_{xy}=0$

calculate

$(1){}_x,{}_y,$ and ${}_{xy}$

$(2){}_{x^{\text{'}}},{}_{y^{\text{'}}}$ and ${}_{x^{\text{'}}{y}^{\text{'}}}$ at $45$

#$2$:

Given ${}_x=80$MPa,${}_y=80$MPa, and ${}_{xy}=0$

calculate

$(1){}_x,{}_y,$ and ${}_{xy}$

$(2){}_{x^{\text{'}}},{}_{y^{\text{'}}},$ and ${}_{x^{\text{'}}{y}^{\text{'}}}$ at $45$

#$3$:

Compare results of $(1)$ and $(2)$

#$4$:

Given ${}_{x^{\text{'}}}=-5\mathrm{.}0{10}^{-3}{}_{y^{\text{'}}}=1\mathrm{.}0{10}^{-3},$ and ${}_{x^{\text{'}}{y}^{\text{'}}}=-10\mathrm{.}0{10}^{-3}$ at $30cw,$

Calculate ${}_x,{}_y,$ and ${}_{xy}$