Question

A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1% with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is

• A. 0
• B. 1
• C. 1.08
• D. 2.02

Answer 1

The correct option is D 2.02

$Hoopstress=\frac{pd}{4t}$

where, p= Internal pressure;
d = Diameter of shell;
t = Thickness of shell

Now
${\sigma }^{\prime }=\frac{p{d}^{\prime }}{4t^{\prime }};d^{\prime }=1.01dand{t}^{\prime }=0.99t$

$\therefore {\sigma }^{\prime }=\frac{p\times 1.01d}{4\times 0.99t}=1.0202\sigma$

% change
$=\frac{{\sigma }^{\prime }-\sigma }{\sigma }\times 100$

$=\frac{(1.0202-1)\sigma }{\sigma }\times 100=2.02\%$