Question

The circumferential strain in case of a thin cylindrical shell, when subjected to internal pressure ($p$), is equal to:

• A. $\frac{pd}{2tE} (1 - \nu)$
• B. $\frac{pd}{2tE} \left(1 - \frac{1}{2}\nu \right)$
• C. $\frac{pd}{4tE} (1 - \nu)$
• D. $\frac{3pd}{4tE} (1 - \nu)$

Hint:

For thin cylindrical shells: - Use $\epsilon_c = \frac{pd}{2tE} \left(1 - \frac{1}{2}\nu \right)$ to determine circumferential strain under internal pressure.

Answer 1

The Correct Option is B

The circumferential (hoop) strain for a thin cylindrical shell subjected to internal pressure ($p$) is derived from the relationship between stress, strain, and material properties. For thin-walled cylinders, the relationship includes Young's modulus ($E$) and Poisson's ratio ($\nu$), and the expression is:
\[\epsilon_c = \frac{pd}{2tE} \left(1 - \frac{1}{2}\nu \right).\]
Here:
$E$: Young's Modulus,
$\nu$: Poisson's ratio,
$p$: Internal pressure,
$t$: Thickness of the shell.
This formula accounts for both the direct and lateral strain effects due to the applied pressure.