Question

A thin-walled spherical pressure vessel has radius 500 mm and thickness 10 mm. Yield strength is 500 MPa. The internal pressure at which yielding occurs according to Tresca criterion is _________ MPa (rounded off to one decimal place).

Hint:

For thin spherical pressure vessels, the stress state is equal in all directions, so Tresca reduces to $\sigma_\theta = \sigma_y$.

Answer 1

Correct Answer: 19

For a thin spherical vessel, membrane (hoop) stress is: \[ \sigma_{\theta} = \frac{pr}{2t} \] Tresca criterion for yielding in biaxial tension: \[ \sigma_{\theta} = \sigma_y \] Substitute: \[ \frac{pr}{2t} = 500 \] Given:
$r = 500\ \text{mm}$
$t = 10\ \text{mm}$
\[ p = \frac{2t \cdot 500}{r} \] \[ p = \frac{20 \cdot 500}{500} = 20\ \text{MPa} \] \[ \boxed{20.0\ \text{MPa}} \]