Question:
A thin cylindrical shell of diameter \( d \) and thickness \( t \) is subjected to an internal pressure \( p \). The ratio of longitudinal strain to volumetric strain is
A thin cylindrical shell of diameter \( d \) and thickness \( t \) is subjected to an internal pressure \( p \). The ratio of longitudinal strain to volumetric strain is
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- The volumetric strain is three times the longitudinal strain.
Updated On: Feb 27, 2025
- \( \frac{(m - 1)}{(2m - 1)} \)
- \( \frac{(m - 1)}{(m - 1)} \)
- \( \frac{(m - 2)}{(3m - 4)} \)
- \( \frac{(m - 2)}{(5m - 4)} \)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding strain components.
- Longitudinal strain:
\[
\epsilon_L = \frac{p d}{4 t E} (1 - 2\nu)
\]
- Volumetric strain:
\[
\epsilon_V = 3 \epsilon_L
\]
Step 2: Taking the ratio.
\[
\frac{\epsilon_L}{\epsilon_V} = \frac{(m - 2)}{(3m - 4)}
\]
Step 3: Selecting the correct option.
Since the correct ratio is \( \frac{(m - 2)}{(3m - 4)} \), the correct answer is (C).
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