Pressure vessel classification: a cylindrical shell is classed as a “thick” shell when the ratio of its internal diameter to wall thickness (D/t) is approximately below which value?

Introduction / Context:Pressure vessel analysis distinguishes between thin and thick cylinders because stress distributions differ significantly. Thin-shell formulas assume negligible radial stress variation, while thick-shell theory (e.g., Lame’s equations) accounts for radial gradients and is needed when walls are relatively thick.

Given Data / Assumptions:

• Internal pressure service with cylindrical geometry.
• D denotes internal diameter; t denotes wall thickness.
• Standard engineering thresholds used for preliminary classification.

Concept / Approach:A common rule places thin-shell validity when t ≤ D/20 (i.e., D/t ≥ 20). As the wall becomes thicker (smaller D/t), thin-shell assumptions break down and thick-shell analysis is required. Some practices use a stricter threshold near D/t ≈ 10 for conservative classification of “thick” shells.

Step-by-Step Solution:

Verification / Alternative check:Design texts show thin-shell hoop stress σ_h = P D /(2 t) applies well when t ≤ D/20; for thicker walls, Lame’s solution is recommended.

Why Other Options Are Wrong:

• “D/t greater than 10 or 20” indicate thin walls; thick-shell classification applies to smaller D/t, not larger.
• “D/t less than about 20” is broader and includes some thin-shell range; the more accepted “thick” cutoff is nearer 10.

Common Pitfalls:Using thin-shell equations outside their range; forgetting joint efficiency and corrosion allowance implications; ignoring external pressure buckling checks.

Final Answer:D/t less than about 10