Question

A cylindrical shell of $100cm$ diameter made of mild steel plate is to be subjected to an internal pressure of $10kg/c{m}^2$. If the material yields at a stress of $200kg/c{m}^2$, assuming factor of safety as $4$ and using maximum principal stress theory, the requisite thickness of the plate will be

• A. $8mm$
• B. $10mm$
• C. $12mm$
• D. $15mm$

Answer 1

The correct option is B $10mm$

For a cylindrical shell, principal stress is given by
${\sigma }_1=\frac{pd}{2t}$
Given $d=100cm,p=10kg/c{m}^2$
Yield stress ${\sigma }_y=200kg/c{m}^2$
Now, according to maximum principal stress theory,
${\sigma }_1\le \left(\frac{{\sigma }_y}{FoS}\right)$
$\therefore \frac{pd}{2t}\le \frac{200}{4}$
$\Rightarrow \frac{10\times 100}{2\times t}\le 50$
$\Rightarrow t\ge 10cm=100mm$