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A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure.The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shellis
  • a)
    0.5
  • b)
    1.0
  • c)
    2.0
  • d)
    4.0
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A long thin walled cylindrical shell, closed at both the ends, is subj...
**Explanation:**

When a long thin-walled cylindrical shell is subjected to internal pressure, it experiences both hoop stress (circumferential stress) and longitudinal stress. The ratio of the hoop stress to the longitudinal stress can be determined using the equations for these stresses.

**Hoop Stress (Circumferential Stress):**

The hoop stress is the stress experienced by the material in the circumferential direction. It can be calculated using the following formula:

*Hoop Stress (σ_h) = (P * r) / t*

where:
σ_h = Hoop stress
P = Internal pressure
r = Radius of the cylindrical shell
t = Thickness of the cylindrical shell

**Longitudinal Stress:**

The longitudinal stress is the stress experienced by the material in the longitudinal direction. It can be calculated using the following formula:

*Longitudinal Stress (σ_l) = (P * r) / (2 * t)*

where:
σ_l = Longitudinal stress
P = Internal pressure
r = Radius of the cylindrical shell
t = Thickness of the cylindrical shell

**Ratio of Hoop Stress to Longitudinal Stress:**

To find the ratio of hoop stress to longitudinal stress, we can divide the equation for hoop stress by the equation for longitudinal stress:

*(σ_h / σ_l) = [(P * r) / t] / [(P * r) / (2 * t)]*

Simplifying the equation, we get:

*(σ_h / σ_l) = 2*

Therefore, the ratio of the hoop stress to the longitudinal stress developed in the shell is 2.

**Conclusion:**

The correct answer is option **C) 2.0**. The ratio of the hoop stress to the longitudinal stress in a long thin-walled cylindrical shell subjected to internal pressure is 2.
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A long thin walled cylindrical shell, closed at both the ends, is subj...
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