Thin cylinder criterion: A cylindrical shell may be treated as “thin” if the ratio of wall thickness t to diameter D is less than which limit?

Introduction / Context:
Formulas for thin-walled pressure vessels assume a uniform membrane stress through the thickness and neglect radial stress variation. A practical geometric limit separates “thin” from “thick.”

Given Data / Assumptions:

• Cylindrical shell with diameter D and thickness t.
• Membrane theory valid when t/D is small.
• Elastic, isotropic material; moderate internal pressure.

Concept / Approach:
For thin cylinders, hoop and longitudinal stresses are evaluated using σ_hoop = p * D / (2 * t) and σ_long = p * D / (4 * t). These rely on negligible radial stress gradient. A commonly adopted limit is t/D < 1/20 (or equivalently D/t > 20).

Step-by-Step Solution:
Check criterion: if t/D < 1/20, thin-wall equations apply.For t/D ≥ 1/20, switch to thick-cylinder (Lame) theory.

Verification / Alternative check:
Codes and textbooks often use 1/20 to 1/10 as transition ranges; 1/20 is the conventional conservative threshold for thin shells.

Why Other Options Are Wrong:
1/10 or 1/15: too thick for thin-wall assumptions.1/25: more restrictive than needed (still acceptable but not the standard conventional cutoff).1/5: far too thick for thin-wall theory.

Common Pitfalls:
Applying thin-wall formulas outside their validity range, leading to unsafe stress estimates.

Final Answer:
1/20.