Difficulty: Easy
Correct Answer: less than
Explanation:
Introduction:
Design formulas for thin pressure vessels assume membrane action with negligible through-thickness stress gradient. The classification relies on the ratio t/D (thickness to diameter).
Given Data / Assumptions:
Concept / Approach:
When t/D is small, hoop and longitudinal stresses vary little across the wall, so thin-shell formulas are valid. Many textbooks adopt thresholds such as t/D ≤ 1/10 (or more conservatively ≤ 1/20); the key idea is "less than" a small fraction of diameter.
Step-by-Step Solution:
Verification / Alternative check:
For very small t/D, radial stress is negligible compared to hoop/longitudinal membrane stresses, validating thin-shell equations like σ_hoop = pD/(2t).
Why Other Options Are Wrong:
Common Pitfalls:
Confusing different conservative thresholds (1/10 vs 1/20). The safer interpretation is that t/D must be less than a small fraction of diameter for thin-shell theory to hold.
Final Answer:
Discussion & Comments