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The maximum shear stress is induced in a thin-walled cylindrical shell having an internal diameter 'D' and thickness‟t‟ when subject to an internal pressure 'p' is equal to
- a)pD/t
- b)pD/2t
- c)pD/4t
- d)pD/8t
Correct answer is option 'D'. Can you explain this answer?
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The maximum shear stress is induced in a thin-walled cylindrical shell...
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Explanation:
When a thin-walled cylindrical shell is subjected to an internal pressure p, the maximum shear stress induced in the shell can be calculated using the following formula:
τmax = pD/4t
where τmax is the maximum shear stress, p is the internal pressure, D is the internal diameter of the cylinder, and t is the thickness of the cylinder.
To understand why this formula works, we need to consider the forces acting on the cylindrical shell. When the shell is subjected to an internal pressure, the force acting on the inside of the shell is balanced by an equal and opposite force acting on the outside of the shell. These forces create a shear stress in the material of the shell, which is maximum at the surface of the cylinder.
To calculate the maximum shear stress, we need to divide the force acting on the surface of the cylinder by the area of the surface. The force acting on the surface of the cylinder can be calculated using the following formula:
F = pπD^2/4
where F is the force acting on the surface of the cylinder, p is the internal pressure, and D is the internal diameter of the cylinder.
The area of the surface of the cylinder can be calculated using the following formula:
A = πDt
where A is the area of the surface of the cylinder, D is the internal diameter of the cylinder, and t is the thickness of the cylinder.
Dividing the force by the area gives us the maximum shear stress:
τmax = F/A = pD/4t
Therefore, the maximum shear stress induced in a thin-walled cylindrical shell having an internal diameter D and thickness t when subject to an internal pressure p is equal to pD/4t.
When a thin-walled cylindrical shell is subjected to an internal pressure p, the maximum shear stress induced in the shell can be calculated using the following formula:
τmax = pD/4t
where τmax is the maximum shear stress, p is the internal pressure, D is the internal diameter of the cylinder, and t is the thickness of the cylinder.
To understand why this formula works, we need to consider the forces acting on the cylindrical shell. When the shell is subjected to an internal pressure, the force acting on the inside of the shell is balanced by an equal and opposite force acting on the outside of the shell. These forces create a shear stress in the material of the shell, which is maximum at the surface of the cylinder.
To calculate the maximum shear stress, we need to divide the force acting on the surface of the cylinder by the area of the surface. The force acting on the surface of the cylinder can be calculated using the following formula:
F = pπD^2/4
where F is the force acting on the surface of the cylinder, p is the internal pressure, and D is the internal diameter of the cylinder.
The area of the surface of the cylinder can be calculated using the following formula:
A = πDt
where A is the area of the surface of the cylinder, D is the internal diameter of the cylinder, and t is the thickness of the cylinder.
Dividing the force by the area gives us the maximum shear stress:
τmax = F/A = pD/4t
Therefore, the maximum shear stress induced in a thin-walled cylindrical shell having an internal diameter D and thickness t when subject to an internal pressure p is equal to pD/4t.
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The maximum shear stress is induced in a thin-walled cylindrical shell having an internal diameter 'D' and thickness‟t‟ when subject to an internal pressure 'p' is equal toa)pD/tb)pD/2tc)pD/4td)pD/8tCorrect answer is option 'D'. Can you explain this answer?
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