Today we will see here the stresses in thin
cylindrical shells, subjected with internal pressure, with the help of this
post.
Before
going ahead, we will first remind here the fundamental of a thin cylindrical shell
Thin cylindrical shell is also termed as a pressure
vessel and 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.
Wall thickness of a thin cylindrical and spherical
shell will be equal or less than the 1/20 of the internal diameter of shell.
Stresses
in a thin cylindrical shell
Let us consider one cylindrical shell, as displayed
here, 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 as mentioned here.
Circumferential stress or Hoop stress
Longitudinal stress
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.
Circumferential stress or hoop stress developed in
the wall of cylindrical shell could be easily determined with the help of
following formula.
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.
Longitudinal stress developed in the wall of
cylindrical shell could be easily determined with the help of following formula.
Longitudinal stress = (1/2) x Circumferential stress
σL = 1/2 x [p x d]/2t
σL = p.d/4t
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box.
We will now derive the expression for circumferential
stress or Hoop stress developed in the wall of cylindrical shell, in the
category of strength of material, in our next post.
Reference:
Strength of material, By R. K. Bansal
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