Thin Cylinders

By Mallesham Devasane|Updated : December 30th, 2016

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 shells
If 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 pressure
  1. Hoop stress/circumferential stress will be tensile in nature.
  2. Longitudinal stress/axial stress will be tensile in nature
  3. Radial 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
s11   Stresses in Thin Spherical Shell:
  • Hoop stress/longitudinal stress
  • Hoop stress/longitudinal strain


  • Volumetric strain of sphere


Lame’s Theory
Lame’s theory is based on the following assumptions
  1. Homogeneous material.
  2. Plane section of cylinder, perpendicular to longitudinal axis remains under plane and pressure. Hoop stress at any section image014 Radial pressure image015

Subjected to Internal Pressure (p)

  • At image016
  • At image017
Subjected to External Pressure (p)
  • At image018
  • At image019
Note: Radial and hoop stresses vary hyperbolically.

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Mallesham DevasaneMallesham DevasaneMember since Oct 2015
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Masthan Wali
Thanks sir
Pavan Kamble

Pavan KambleJun 12, 2016

Thanx sir...
Yuvaraj Yuvaraj
Easy to understand
nani babu

nani babuJun 28, 2016

Thanku sit
Akarsh Kumar

Akarsh KumarJun 30, 2016

Sir,  do we have to mug up all these formulas
Dinu Hate

Dinu HateJul 11, 2016

Thank you soo much sir☺

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