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If a thick cylindrical shell is subjected to internal pressure. then hoop stress, radial stress and longitudinal stess at point in the thickness will be
- a)Tensile, compressive and compressive respectively
- b)All compressive
- c)All tensile
- d)Tensile, compressive and tensile respectively
Correct answer is option 'D'. Can you explain this answer?
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If a thick cylindrical shell is subjected to internal pressure. then h...
Hoop Stress, Radial Stress, and Longitudinal Stress in a Thick Cylindrical Shell
When a thick cylindrical shell is subjected to internal pressure, the stresses that develop in the shell can be analyzed using the theory of elasticity. The three main stresses that develop in the shell are hoop stress, radial stress, and longitudinal stress.
Hoop Stress
Hoop stress is the stress that develops in the circumferential direction of the shell. It is caused by the internal pressure trying to expand the shell in the radial direction. The hoop stress is given by the formula:
σh = pd/2t
where σh is the hoop stress, p is the internal pressure, d is the diameter of the shell, and t is the thickness of the shell.
Since the hoop stress is proportional to the internal pressure and inversely proportional to the thickness of the shell, it is a tensile stress.
Radial Stress
Radial stress is the stress that develops in the radial direction of the shell. It is caused by the internal pressure trying to compress the shell in the radial direction. The radial stress is given by the formula:
σr = pd/4t
where σr is the radial stress.
Since the radial stress is proportional to the internal pressure and inversely proportional to the thickness of the shell, it is a compressive stress.
Longitudinal Stress
Longitudinal stress is the stress that develops in the axial direction of the shell. It is caused by the internal pressure trying to elongate the shell in the axial direction. The longitudinal stress is given by the formula:
σl = pd/4t
where σl is the longitudinal stress.
Since the longitudinal stress is proportional to the internal pressure and inversely proportional to the thickness of the shell, it is a tensile stress.
Conclusion
Therefore, the correct answer is option D. The hoop stress is tensile, the radial stress is compressive, and the longitudinal stress is tensile.
When a thick cylindrical shell is subjected to internal pressure, the stresses that develop in the shell can be analyzed using the theory of elasticity. The three main stresses that develop in the shell are hoop stress, radial stress, and longitudinal stress.
Hoop Stress
Hoop stress is the stress that develops in the circumferential direction of the shell. It is caused by the internal pressure trying to expand the shell in the radial direction. The hoop stress is given by the formula:
σh = pd/2t
where σh is the hoop stress, p is the internal pressure, d is the diameter of the shell, and t is the thickness of the shell.
Since the hoop stress is proportional to the internal pressure and inversely proportional to the thickness of the shell, it is a tensile stress.
Radial Stress
Radial stress is the stress that develops in the radial direction of the shell. It is caused by the internal pressure trying to compress the shell in the radial direction. The radial stress is given by the formula:
σr = pd/4t
where σr is the radial stress.
Since the radial stress is proportional to the internal pressure and inversely proportional to the thickness of the shell, it is a compressive stress.
Longitudinal Stress
Longitudinal stress is the stress that develops in the axial direction of the shell. It is caused by the internal pressure trying to elongate the shell in the axial direction. The longitudinal stress is given by the formula:
σl = pd/4t
where σl is the longitudinal stress.
Since the longitudinal stress is proportional to the internal pressure and inversely proportional to the thickness of the shell, it is a tensile stress.
Conclusion
Therefore, the correct answer is option D. The hoop stress is tensile, the radial stress is compressive, and the longitudinal stress is tensile.
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If a thick cylindrical shell is subjected to internal pressure. then hoop stress, radial stress and longitudinal stess at point in the thickness will bea)Tensile, compressive and compressive respectivelyb)All compressivec)All tensiled)Tensile, compressive and tensile respectivelyCorrect answer is option 'D'. Can you explain this answer?
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