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

Hoop or Circumference stressForce due to fluid pressure = Force due to Hoop stressForce which has a tendency to split the shell = resisting force due to stress 
Longitudinal stressForce due to fluid pressure = Force due to longitudinal stressThere is nothing like Longitudinal stress in sphere. There is only Hoop stress.So because of symmetry  
Maximum shear stress
Hoop or Circumferential strain
Longitudinal strainThere is nothing like Longitudinal strain in sphere. There is only Hoop strain.So because of symmetry 
Volumetric strain

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