Today, we will start here another important topic of strength of material i.e. thin cylindrical and spherical shells with the help of this post.

### Thin cylindrical and spherical shells

Thin cylindrical and spherical shells are also termed as pressure vessels 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.

Let us consider one cylindrical shell as displayed here in following figure. Fluid is stored here under pressure within the cylindrical shell. We will first find out here the condition to consider the shell as thin cylindrical or spherical shell.
d = Internal diameter of the shell
t = Wall thickness of the shell
l = Length of the cylinder
P = Internal pressure of the fluid stored inside the cylinder

### Condition for thin cylindrical or spherical shell

Wall thickness of thin cylinder < [(1/20) x Internal diameter]
t < d/20
t/d < 1/20
d/t > 20
This is the condition that we must have to note it to consider a cylindrical or spherical shell as thin cylindrical or spherical shell.

As we have recently discussed that pressure vessels are used to store the fluid under pressure. Therefore, there will be two cases of failure of cylindrical vessel as mentioned here.

### Case: 1

As 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.

### Case: 2

As fluid is stored under pressure inside the cylindrical shell, pressure will be acting at the both ends of the cylindrical wall. Pressure vessel will tend to burst as displayed here in following figure.
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We will now discuss another topic, thick cylinder lame's equation in the category of strength of material, in our next post.

### Reference:

Strength of material, By R. K. Bansal