Question

A thin cylinder of thickness ${}^{\prime }{t}^{\prime }$, width ${}^{\prime }{b}^{\prime }$ and internal radius ${}^{\prime }{r}^{\prime }$ is subjected to a pressure ${}^{\prime }{p}^{\prime }$ on the entire internal surface. What is the change in radius of the cylinder? ($\mu$ is the Poisson's ratio and $E$ is the modulus of elasticity) ?

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

Answer 1

The correct option is C $\frac{p{r}^2(2-\mu )}{2Et}$

$Hoopstress,{\sigma }_{\theta }=\frac{pr}{t}$
$Longitudinalstress,{\sigma }_z=\frac{pr}{2t}$
Strain in circumferetial direction,
${\epsilon }_{\theta }=\frac{1}{E}({\sigma }_{\theta }-\mu {\sigma }_z)=\frac{pr}{2tE}(2-\mu )$
Change in radius $={\epsilon }_{\theta }\times r$
$=\frac{p{r}^2(2-\mu )}{2Et}$