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 |
|
|