Thin cylinders & spheres - Introduction & differences 

 

a)      Pressure vessels are closed structures containing liquids or gases under pressure. These are special case of plane stress i.e. 

b)      When pressure vessels have walls that are thin in comparison to their overall dimensions, they are included within a more general category known as shell structures.

c)      Pressure vessels are considered to be thin-walled when the ratio of radius r to wall thickness t is greater than 10

 

Cylindrical

Spherical

Hoop or Circumference stress

Force due to fluid pressure = Force due to Hoop stress

Force which has a tendency to split the shell = resisting force due to stress

 

Longitudinal stress

Force due to fluid pressure = Force due to longitudinal stress

There is nothing like Longitudinal stress in sphere. There is only Hoop stress.

So because of symmetry 

 

Maximum shear stress

Hoop or Circumferential strain

Longitudinal strain

There is nothing like Longitudinal strain in sphere. There is only Hoop strain.

So because of symmetry 

Volumetric strain