Question 5.7: Calculate the tensile stresses (circumferential and longitud......

Does thin-walled theory apply? Is the thickness t ≤ $0.1r_i$ ?

We can use thin-walled theory.
The circumferential, or hoop stress, is calculated:

$\sigma_{\theta \theta}=\frac{p r_{\mathrm{i}}}{t}=\frac{(300  \mathrm{psi})(9  \mathrm{in})}{0.25  \mathrm{in}}=10.8  \mathrm{ksi}$.

The longitudinal stress due to the internal pressure may be combined with the normal stress due to the axial load by straightforward superposition, as these stresses are due to forces in the same direction and act normal to areas with the same orientation:

Note: the area on which P acts can also be calculated as $\pi r_o^2-\pi r_i^2$; this gives essentially the same results for thin circular sections.