Question

A cylindrical tank of radius r and wall thickness t has flat end closures. The tank is subjected to an internal pressure P. The longitudinal (${\sigma }_l$) and the circumferential (${\sigma }_h$) stresses respectively are given by:

• A. Pr/t, 0
• B. Pr/2t, Pr/t
• C. Pr/4t, Pr/3t
• D. Pr/6t, Pr/t

Answer 1

The correct option is B Pr/2t, Pr/t

Hoop or circumferential stress




$p\times l\times d={\sigma }_h\times 2l\times t$

${\sigma }_h=\frac{Pd}{2t}$

d = inner diameter
t = thickness
p = fluid pressure

$\cdot$ No shear exists on the section on which Hoop stress acts.

. $Hence,{\sigma }_h=\frac{pd}{2t}isaprincipalstress.$

$\cdot$ ${\sigma }_h$ is always tensile both in thick shells as well as in thin shells due to fluid pressure from inside. However for outside pressure ${\sigma }_h$ will be compressive.

Longitudnal Stress (${\sigma }_l$)



$\frac{\pi d^2}{4}\times p={\sigma }_l\times \pi (d+2\times \frac{t}{2})\times t$

$={\sigma }_l\times \pi (d+t)t$

Neglecting, $t^2$ term, as it is very small as compared to (d x t)

$\frac{\pi d^2}{4}\times p={\sigma }_l\times \pi dt$

${\sigma }_l=\frac{pd}{4t}$

As no shear, acts on section on which
${\sigma }_{l}isacting\Rightarrow {\sigma }_l=principalstress.$