Question

If the thin cylindrical shell having diameter \( D \) and subjected to internal pressure \( p \), the ratio of longitudinal pressure to hoop stress is equal to

• A. 1
• B. \( \frac{1}{2} \)
• C. 2
• D. \( \frac{3}{4} \)

Hint:

For cylindrical shells under internal pressure, the hoop stress is always twice the longitudinal stress, so remember this key relationship when solving problems involving such shells.

Answer 1

The Correct Option is B

For a thin cylindrical shell under internal pressure, the longitudinal stress (\( \sigma_L \)) and the hoop stress (\( \sigma_H \)) are given by the formulas:
\[ \sigma_L = \frac{p D}{4t}, \quad \sigma_H = \frac{p D}{2t} \] Where \( p \) is the internal pressure, \( D \) is the diameter, and \( t \) is the wall thickness of the cylinder. The ratio of longitudinal pressure to hoop stress is: \[ \frac{\sigma_L}{\sigma_H} = \frac{\frac{p D}{4t}}{\frac{p D}{2t}} = \frac{1}{2} \] Thus, the correct answer is \( \frac{1}{2} \).