This document summarizes information about thick and thin cylinders. It defines thick cylinders as those where the ratio of inner diameter to wall thickness is less than 20. For thin cylinders, the ratio must be less than 1/10. The key stresses in each cylinder type are described - thick cylinders experience varying tangential and radial stresses while thin cylinders have a constant circumferential stress. The document also presents Lame's equation, which is used to calculate thick cylinder wall thickness based on internal pressure and material properties.

1. SHANTILAL SHAH ENGINEERING
COLLEGE
BRANCH :- MECH(5th)
Subject :- Design of machine element
NAME ENROLLMENT NO
CHAVDA MAYUR 170433119006
DOSHI PARAS 170433119008
GUIDED BY :- B.D.UPADHYAY

2. TYPES OF CYLINDER
1 THICK CYLINDER
2 THIN CYCLINDER

3. THIN CYLINDER
• If the wall thickness of the cylinder is less than
1/20th of the internal diameter ‘di’,the variation
of the tangential stresses through the wall
thickness is small & the radial stresses may be
neglected. The solution can be then treated as
statically determinate & the vessel is said to be
thin pressure vessel. Thus a thin pressure
vessel is one whose thickness to inner radius
ratio is not greater than 1/10.

5. TYPES OF STRESS
• Circumferential or Hoop Stress :
• The stress which resists the failure of thin
cylinder along the circumference is called
circumferential stress or hoop stress.
• It is given by formula

6. • Longitudinal Stress :
• The stress which resists the failure of cylinder in
longitudinal direction is called longitudinal stress.
• It is given by formula
• From the two equations it is obvious that the
circumferential stress is TWICE the longitudinal
stress.

8. THICK CYLINDER
• A cylinder is said to be 'THICK' if the ratio of its
inner diameter to the thickness of wall is less
than 20. Examples are Hydraulic cylinders, high
pressure pipes and gun barrels.

9. TYPES OF STRESS
• Tangential stress.(Highest magnitude at
inner surface an gradually decreases
towards outer surface)
• Radial stress. (This is neglected in thin
cylinders)
• Axial or longitudinal stress.

10. LAMIS THEROME
• Lame's equation is used to find the thickness of the thick
cylinder subjected to internal pressure, It is given by,
• Where,
• t= thickness of thick cylinder
• Di= Internal diamter of thick cylinder,
• = Allowable tensile stress in the material of thick cylinder
• Pi= Internal pressure in the thick cylinder.
• Use of Lame's Equation : Lame's equation is based on
maximum principal stress theory of failure, as this theory
is more suitable for brittle materials, Lame's equation is
also applicable to brittle materials like Cast iron or Cast
Steel.

11. DIFFERENCE BETWEEN THICK & THHI
CYLINDER
Thick Cylinder Thin Cylinder
1.Circumferential stress
varies along the thickness of
the shell.
1. Circumferential stress ‘f’ is
constant throughout the
thickness of the shell.
2. Radial stress is no longer
negligible since a thick
cylinder is required to have a
heavy internal pressure
2.Radial stress ‘p’ is
negligible in comparison of ‘f’
and ‘f0

12. THANK YOU