Types of Pressure Vessels Pressure vessels are mainly of two type:
Thin shells
If the thickness of the wall of the shell is less than 1/10 to 1/15 of its diameter, then shell is called thin shells.
Thick shellsIf the thickness of the wall of the shell is greater than 1/10 to 1/15 of its diameter, then shell is called shells.
where Nature of stress in thin cylindrical shell subjected to internal pressureHoop stress/circumferential stress will be tensile in nature.Longitudinal stress/axial stress will be tensile in natureRadial stress will be compressive in nature.Stresses in Thin Cylindrical Shell:
Circumferential Stress /Hoop Stress
Where, p = Intensity of internal pressure
d = Diameter of the shell
t = Thickness of shell
η = Efficiency of joint
Longitudinal Stress
Hoop Strain
Longitudinal Strain
Ratio of Hoop Strain to Longitudinal Strain
Volumetric Strain of cylinder
Hoop stress/longitudinal strain
Volumetric strain of sphere
Lame’s Theory
Lame’s theory is based on the following assumptions
Assumptions
Homogeneous material.Plane section of cylinder, perpendicular to longitudinal axis remains under plane and pressure. Hoop stress at any section 
Subjected to Internal Pressure (p)
At 
Subjected to External Pressure (p)
At 
Note: Radial and hoop stresses vary hyperbolically.