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Circumferential stress in a cylindrical steel boiler shell under internal pressure is 80MPa. Young’s modulus of elasticity and Poisson’s ratio are respectively 2 × 105 MPa and 0.28. The magnitude of circumferential strain in the boiler shell be
  • a)
    3.44 × 10−4
  • b)
    3.84 × 10−4
  • c)
    4 × 10−4
  • d)
    4.56 × 10−4
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Circumferential stress in a cylindrical steel boiler shell under inte...
Circumferential stress or Hoop stress,
Longitudinal stress,
Circumferential strain,
=
= 3.44 × 10−4
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Most Upvoted Answer
Circumferential stress in a cylindrical steel boiler shell under inte...
Circumferential stress in a cylindrical steel boiler shell under internal pressure is given as 80 MPa. We are required to find the magnitude of circumferential strain in the boiler shell.

The circumferential stress in a cylindrical shell under internal pressure can be calculated using the formula:

σc = pd/2t

Where:
σc is the circumferential stress
p is the internal pressure
d is the diameter of the boiler shell
t is the thickness of the boiler shell

Given that the circumferential stress is 80 MPa, we can rearrange the formula to solve for the thickness of the boiler shell:

t = pd/2σc

We also have the Young's modulus of elasticity (E) and Poisson's ratio (ν) for the steel material. The relationship between stress, strain, and these material properties is given by:

σ = Eε

Where:
σ is the stress
E is the Young's modulus of elasticity
ε is the strain

In this case, the circumferential strain (εc) is equal to the circumferential stress (σc) divided by the Young's modulus of elasticity (E):

εc = σc / E

Given that the Young's modulus of elasticity is 2 × 105 MPa, we can substitute the values and calculate the circumferential strain:

εc = 80 MPa / 2 × 105 MPa

Simplifying the expression:

εc = 0.0004

Therefore, the magnitude of the circumferential strain in the boiler shell is 4 × 10^-4, which corresponds to option A.
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Circumferential stress in a cylindrical steel boiler shell under internal pressure is 80MPa. Young’s modulus of elasticity and Poisson’s ratio are respectively 2 × 105 MPa and 0.28. The magnitude of circumferential strain in the boiler shell bea) 3.44 × 10−4b) 3.84 × 10−4c) 4 × 10−4d) 4.56 × 10−4Correct answer is option 'A'. Can you explain this answer?
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