Hoop and radial Stresses

The general expressions for the hoop and radial stress are the following:

\[ \small\sigma_{hoop}(r)=P_{int}\frac{r_{int}^2}{r_{ext}^2-r_{int}^2}[1+\frac{r_{ext}^2}{r^2}]-P_{ext}\frac{r_{ext}^2}{r_{ext}^2-r_{int}^2}[1+\frac{r_{ext}^2}{r^2}] \]

\[ \small\sigma_{radial}(r)=P_{int}\frac{r_{int}^2}{r_{ext}^2-r_{int}^2}[1-\frac{r_{ext}^2}{r^2}]-P_{ext}\frac{r_{ext}^2}{r_{ext}^2-r_{int}^2}[1-\frac{r_{ext}^2}{r^2}] \]

Note

Hoop and radial stresses are evaluated using both inner and outer radii and the maximum amplitude stresses are returned.