Problem $7\mathrm{.}5-1$

A rectangular steel plate with thickness $t=\frac{5}{8}$ in is subjected to uniform normal stresses ${}_x$ and ${}_y.$ Strain gages A and $B,$ oriented in the $x$ and $y$ directions, respectively, are attached to the plate. The gage readings give normal strains ${}_x=0\mathrm{.}00065($elongation$)$ and ${}_y=0\mathrm{.}00040($elongation$).$ Knowing that $E=30106$ psi and $v=0\mathrm{.}3,$ determine the stresses ${}_x$ and ${}_y$ and the change in thickness $t$ of the plate.