# Thin-walled pressure vessel, hoop stress Question

1. Aug 14, 2016

### kidsasd987

2. Aug 16, 2016

### benny_91

I did not see a p*2pi*r^2 anywhere. Is this a case of a cylinder or a sphere?

3. Aug 17, 2016

### Staff: Mentor

They split the cylinder in half (including the air inside), and determine the forces on half the cylinder, either axially or in the hoop direction. Axially, the forces on the half-cylinder are $p\pi R^2$ and $2\pi R\sigma_{axial} t$, where $\sigma_{axial}$ is the axial stress in the shell. So, for equilibrium, $$2\pi R t\sigma_{axial}=p\pi R^2$$
Similarly, for the hoop direction, the forces on half the half-cylinder are $p(2R)L$ and $2Lt\sigma_{hoop}$. So, for equilibrium,
$$2Lt\sigma_{hoop}=p(2R)L$$