STRENGTH OF MATERIALS FOR MECHANICAL ENGINEERS

1. BIBIN CHIDAMBARANATHAN
THIN CYLINDERS,
SPHERES AND THICK
CYLINDERS
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2. UNIT V
THIN CYLINDERS, SPHERES AND THICK
CYLINDERS
• Stresses in thin cylindrical shell due to internal pressure
• circumferential and longitudinal stresses
• deformation in thin and thick cylinders
• spherical shells subjected to internal pressure
• Deformation in spherical shells
• Lame’s theorem.
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3. Thin cylindrical shell
• Thin cylindrical shell is also termed as a
pressure vessel
• such vessels are usually used in various
engineering applications such as for storing the
fluid under pressure.
• Boilers, LPG cylinders, Air receiver tanks are
the best examples of thin cylindrical shells.
• A cylindrical or spherical shell will be
considered as thin cylindrical or spherical shell,
if the wall thickness of shell is very small as
compared to the internal diameter of the shell.
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4. Condition for thin cylindrical or spherical shell
• Wall thickness of a thin cylindrical and spherical shell will be equal or less than
the 1/20 of the internal diameter of shell.
• Wall thickness of thin cylinder < [(1/20) x Internal diameter]
• t < d/20
• t/d < 1/20
• d/t > 20
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5. Stresses in a thin cylindrical shell
• Let us consider one cylindrical
shell, subjected with internal fluid
pressure P.
• There will be two types of
stresses, which will be developed
in the wall of thin cylindrical shell
and these stresses are
• Circumferential stress or Hoop
stress
• Longitudinal stress
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6. Circumferential stress or Hoop stress
• Stress acting along the circumference of thin
cylinder will be termed as circumferential stress
or hoop stress.
• If fluid is stored under pressure inside the
cylindrical shell, pressure will be acting vertically
upward and downward over the cylindrical wall.
• Pressure vessel will tend to burst as displayed
here in following figure and stresses developed in
such failure of cylindrical shell will be termed as
circumferential stress or Hoop stress.
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7. Longitudinal stress
• Stress acting along the length of thin
cylinder will be termed as longitudinal
stress.
• If fluid is stored under pressure inside the
cylindrical shell, pressure force will be
acting along the length of the cylindrical
shell at its two ends.
• Cylindrical shell will tend to burst as
displayed here in following figure and
stresses developed in such failure of
cylindrical shell will be termed as
longitudinal stress.
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30. Thank You
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