We were discussing the basic concept of spring in strength of material, Derivation of torsional equation, Theories of failure in machine design and difference between column and strut in our previous posts.
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.
Radial stress could be neglected when we deal with the thin cylinders.
Thick cylinder
Thick cylinders are basically those cylindrical vessels that contain fluid under pressure and ratio of wall thickness to the internal diameter of such cylindrical vessels will not be less than 1/20.
We can see the practical applications of thick cylinders in various areas such as domestic gas cylinders, oxygen gas cylinders used in medical field, barrel of a gun, water and gas pipelines, nozzle of a jet etc.
Condition for thick cylinder
Wall thickness of thick 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 cylinder as thick cylinder.
We will now discuss another topic, stresses in a thin cylinder subjected to internal pressure and thick cylinder lame's equation in the category of strength of material, in our next post.
You should also find out here some quite important posts as mentioned below
- Metal cutting tools: definition and classification
- Explain the geometry and nomenclature of a single point cutting tool
- Positive and negative effects of friction
- Classifications of friction
- Coulomb's law of dry friction
- Some guidelines for solving frictional problems
- Concept of rolling resistance or rolling friction
- Wedge friction and concept of self- locking
- Hook’s law
- Concept of eccentric loading
- Assumptions made in the Euler’s column theory
- Difference between long column and short column
- Euler’s formula and its limitations
Reference:
Strength of material, By R. K. Bansal
Image Courtesy: Google
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