Question

A thick cylinder of internal and external radii 300 mm and 500 mm respectively is subjected to a gradually increasing internal pressure P. Determine the value of P when:

(a) the material of the cylinder first commences to yield;

(b) yielding has progressed to mid-depth of the cylinder wall;

(c) the cylinder material suffers complete “collapse”.

Take uY = 600 MN/m’.

Answer 1

By Lame's theorem hoop system,

When the material starts yielding,

$\delta_{\theta} =\dfrac{ (\rho_{i}×r_{i})}{(r_{0} ^ 2 - r_{i} ^ 2) }(\dfrac{(r_{o} ^ 2)}{(r ^ 2)} + 1)$

r_i = internal radius = 300mm = 0.3m

r_o = external radius = 500mm = 0.5m

where, r = mean radius = $(300+500)/2$ = 400mm

$600 =\dfrac{ \rho_{i}×0.3}{0.5^ 2 -0.3 ^ 2}× \dfrac{(0.5^ 2)}{(0.4^ 2)} + 1$

$\rho_i =124.9\ Pa$