find out the intensity of the external pressurea

Question

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/m² and the hoop stress at the inside of the cylinder is 45 MN/m² (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 /r²  )+ a

and

σ_r  =   b/r²  - a

For the internal surface, i.e. r = 0.2 m,

25=      b/0.2² + a

45 =     b/0.2² + 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 / 0.25² )- 10 = 12.4 MN/m²