Question

A thin-walled long cylindrical tank of inside radius r is subjected simultaneously to internal gas pressure p and axial compressive force F at its ends. In order to produce 'pure shear' state of stress in the wall of the cylinder, F should be equal to

• A. $\pi P{r}^2$
• B. $2\pi P{r}^2$
• C. $3\pi P{r}^2$
• D. $4\pi P{r}^2$

Answer 1

The correct option is C $3\pi P{r}^2$

Inside radius = r
Internal gas pressure = p

In order to produce 'pure shear' state of stress in the wall of cylinder, tensile hoop stress must be equal to compressive longitudinal stress.

Hoop stress,
${\sigma }_h=\frac{pr}{t}\left(tensile\right)$

${\sigma }_l=\{\frac{F}{2\pi rt}-\frac{pr}{2t}\}compressive$

${\sigma }_h={\sigma }_l$

$\frac{pr}{t}=\frac{F}{2\pi rt}-\frac{pr}{2t}$

$\frac{F}{2\pi rt}=\frac{3}{2}\frac{pr}{t}$

$F=3\pi p{r}^2$