Answer
$$F=94.9 \mathrm{kips}$$
Work Step by Step
$\begin{aligned} \delta_{y} &=-0.5 \times 10^{-3} \text {in. } \quad d=2.5 \mathrm{in.} \\ \varepsilon_{y} &=\frac{\varepsilon_{y}}{d}=-\frac{0.5 \times 10^{-3}}{2.5}=-0.2 \times 10^{-3} \\ v &=-\frac{\varepsilon_{y}}{\varepsilon_{x}}: \quad \varepsilon_{x}=\frac{-\varepsilon_{y}}{v}=\frac{0.2 \times 10^{-3}}{0.3}=0.66667 \times 10^{-3} \\ \sigma_{x} &=E \varepsilon_{x}=\left(29 \times 10^{6}\right)\left(0.66667 \times 10^{-3}\right)=19.3334 \times 10^{3} \mathrm{psi} \end{aligned}$
$A=\frac{\pi}{4} d^{2}=\frac{\pi}{4}(2.5)^{2}=4.9087 \mathrm{in}^{2}$
$F=\sigma_{x} A=\left(19.3334 \times 10^{3}\right)(4.9087)=94.902 \times 10^{3} \mathrm{lb}$
$F=94.9 \mathrm{kips}$
