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. \( \frac{(m - 1)}{(2m - 1)} \)
• B. \( \frac{(m - 1)}{(m - 1)} \)
• C. \( \frac{(m - 2)}{(3m - 4)} \)
• D. \( \frac{(m - 2)}{(5m - 4)} \)

Hint:

- The volumetric strain is three times the longitudinal strain.

Answer 1

The Correct Option is C

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).