Question

For a thin spherical shell subjected to internal pressure, the ratio of volumetric strain to diametrical strain is.

• A. 5:4
• B. 3:2
• C. 2:1
• D. 3:1

Answer 1

Answer:

D. 3:1

For the thin spherical shell, the Hoop strain/longitudinal strain is,

$\epsilon_{L} = \epsilon_{h} = \frac{pd}{4tE} (1 - \mu)$

For the thin spherical shell, the Volumetric strain is,

$\epsilon_{V} = 3\epsilon_{h} = \frac{3pd}{4tE} (1 - \mu)$

The ratio of volumetric strain to diametrical strain is

$\frac{\epsilon_{V}}{\epsilon_{D}} =\frac {\epsilon_{V}}{\epsilon_{h}} =\frac 31$