Definition of thin shell in pressure vessel design Evaluate the statement: “A pressure vessel is called a thin shell when it is made of thin sheets.”

Introduction / Context:The classification of pressure vessels as thin or thick shells determines the stress formulas used in design. It is based on geometry, not merely on how the vessel is fabricated.

Given Data / Assumptions:

• Cylindrical shell of diameter d and wall thickness t.
• Internal pressure p, elastic material.

Concept / Approach:A shell is considered thin when the wall thickness is small compared to its radius/diameter, so that stress through the thickness is nearly uniform and radial stress is negligible. A common criterion is t/d ≤ 1/20 (or t/r ≤ 1/10).

Step-by-Step Reasoning:Check the geometric ratio t/d.If t/d ≤ about 1/20, thin-shell (use membrane formulas).If thicker, use Lame’s thick-cylinder theory with radial stress variation.

Verification / Alternative check:Thin-shell formulas give hoop stress σ_h = p d / (2 t) and longitudinal stress σ_l = p d / (4 t), which assume negligible radial stress compared to σ_h and σ_l.

Why Other Options Are Wrong:Fabrication by “thin sheets” is not the deciding factor; operating pressure and diameter alone do not define thinness without t/d.

Common Pitfalls:Equating “sheet metal” with thin-shell theory; ignoring diameter’s role in t/d.

Final Answer:Disagree