Question

A thin cylindrical shell of internal diameter $D$ and thickness ${}^{\prime }{t}^{\prime }$ is subjected to internal pressure ${}^{\prime }{p}^{\prime }$. The change in diameter is given by

• A. $\frac{p{D}^2}{4tE}(2-\mu )$
• B. $\frac{p{D}^2}{4tE}(1-2\mu )$
• C. $\frac{p{D}^2}{2tE}(1-2\mu )$
• D. $\frac{p{D}^2}{2tE}(2-\mu )$

Answer 1

The correct option is A $\frac{p{D}^2}{4tE}(2-\mu )$

$\frac{\text{Change in diameter}}{\text{Original diameter}}=\frac{\Delta D}{D}$
$=\frac{1}{E}[{\sigma }_1-\mu {\sigma }_2]$
$=\frac{1}{E}[\frac{pD}{2t}-\frac{\mu pD}{4t}]=\frac{pD}{4tE}(2-\mu )$
$\therefore \Delta D=\frac{p{D}^2}{4tE}(2-\mu )$