Answer
$$E=28.973 \times 10^{3} \mathrm{psi}$$
$$v=0.44444$$
$$\sigma=10.0291 \times 10^{3} \mathrm{psi}$$
Work Step by Step
$A=\frac{\pi}{4} d^{2}=\frac{\pi}{4}\left(\frac{5}{8}\right)^{2}=0.306796 \mathrm{in}^{2}$
$P=800 \mathrm{lb}$
$\sigma_{y}=\frac{P}{A}=\frac{800}{0.306796}=2.6076 \times 10^{3} \mathrm{psi}$
$\varepsilon_{y}=\frac{\delta_{y}}{L}=\frac{0.45}{5.0}=0.090$
$\varepsilon_{x}=\frac{\delta_{x}}{d}=\frac{-0.025}{0.625}=-0.040$
$E=\frac{\delta_{y}}{\varepsilon_{y}}=\frac{2.6076 \times 10^{3}}{0.090}=28.973 \times 10^{3} \mathrm{psi}$
$v=-\frac{\varepsilon_{x}}{\varepsilon_{y}}=\frac{-0.040}{0.090}=0.44444$
$\sigma=\frac{E}{2(1+v)}=\frac{28.973 \times 10^{3}}{(2)(1+0.44444)}=10.0291 \times 10^{3} \mathrm{psi}$
