Find out the intensity of the external pressure:
A thick cylinder of 0.5 m external diameter & 0.4 m internal diameter is subjected simultaneously to internal & external pressures. If the internal pressure is equal to 25 MN/m^{2} and the hoop stress at the inside of the cylinder is 45 MN/m^{2} (tensile), find out the intensity of the external pressure.
Solution
By using Lame's expression for hoop stress and radial stress, which are
σ_{h} = ( b /r^{2} )+ a
and
σ_{r } = b/r^{2} - a
For the internal surface, i.e. r = 0.2 m,
25= b/0.2^{2} + a
45 = b/0.2^{2} + a
On solving out , we get b = 1.4 and a = 10.
Therefore, the intensity of external pressure at r = 0.25 shall be
σ_{r } = (1.4 / 0.25^{2} )- 10 = 12.4 MN/m^{2}