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A thick cylinder of internal diameter 10 cm is subjected to an internal pressure of 50 N/mm2, then the thickness of the cylinder according to the maximum shear stress theory, if yield stress is 270 N/mm2 and factor of safety is 2, is _______mm
  • a)
    98.2
  • b)
    50
  • c)
    48.2
  • d)
    148.2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A thick cylinder of internal diameter 10 cm is subjected to an interna...
Inner radius, R1 = 50 mm
Let external radius is R2 mm
Radial pressure, p = 50 N/mm2
Principal stresses at inner surface of thick cylinder are
Maximum shear stress, τmax
Allowable normal stress, σa
Allowable shear stress.
Undefined control sequence \therefore
Thickness of cylinder,
t = R2 − R1 = 98.2 − 50 = 48.2mm
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Most Upvoted Answer
A thick cylinder of internal diameter 10 cm is subjected to an interna...
Given data:
Internal diameter of the cylinder (D) = 10 cm = 100 mm
Internal pressure (P) = 50 N/mm^2
Yield stress (σ_yield) = 270 N/mm^2
Factor of safety (FoS) = 2

To find:
Thickness of the cylinder according to the maximum shear stress theory.

Formula used:
According to the maximum shear stress theory, the maximum shear stress (τ_max) in a thick-walled cylinder is given by the formula:

τ_max = (P * r_i) / (2 * t)

Where:
P = Internal pressure
r_i = Internal radius
t = Thickness of the cylinder

Calculation:
1. Internal radius (r_i) = D/2 = 100/2 = 50 mm

2. Rearranging the formula to find the thickness (t):
t = (P * r_i) / (2 * τ_max)

3. Factor of safety (FoS) is given by the formula:
FoS = σ_yield / τ_max

Rearranging the formula to find the maximum shear stress (τ_max):
τ_max = σ_yield / FoS

4. Substituting the given values into the formula:
τ_max = 270 / 2 = 135 N/mm^2

5. Substituting the values of P and r_i into the formula for thickness (t):
t = (50 * 50) / (2 * 135) = 2500 / 270 ≈ 9.26 mm

Therefore, the thickness of the cylinder according to the maximum shear stress theory is approximately 9.26 mm.

Hence, the correct answer is option (C) 48.2 mm.
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A thick cylinder of internal diameter 10 cm is subjected to an internal pressure of 50 N/mm2, then the thickness of the cylinder according to the maximum shear stress theory, if yield stress is 270 N/mm2 and factor of safety is 2, is _______mma)98.2b)50c)48.2d)148.2Correct answer is option 'C'. Can you explain this answer?
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A thick cylinder of internal diameter 10 cm is subjected to an internal pressure of 50 N/mm2, then the thickness of the cylinder according to the maximum shear stress theory, if yield stress is 270 N/mm2 and factor of safety is 2, is _______mma)98.2b)50c)48.2d)148.2Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A thick cylinder of internal diameter 10 cm is subjected to an internal pressure of 50 N/mm2, then the thickness of the cylinder according to the maximum shear stress theory, if yield stress is 270 N/mm2 and factor of safety is 2, is _______mma)98.2b)50c)48.2d)148.2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thick cylinder of internal diameter 10 cm is subjected to an internal pressure of 50 N/mm2, then the thickness of the cylinder according to the maximum shear stress theory, if yield stress is 270 N/mm2 and factor of safety is 2, is _______mma)98.2b)50c)48.2d)148.2Correct answer is option 'C'. Can you explain this answer?.
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