Classification of pressure vessels: If the diameter D is 15 times the wall thickness t (i.e., D/t = 15), should the vessel be treated as a thick shell?

Introduction / Context:Pressure vessel analysis uses either thin-shell or thick-cylinder theory. Selecting the correct model is crucial because stress formulas and safety margins differ significantly between the two.

Given Data / Assumptions:

• Diameter-to-thickness ratio D/t = 15.
• Isotropic, elastic material; cylindrical vessel.
• Internal pressure acts; external pressure assumed negligible.

Concept / Approach:Rule of thumb: use thin-shell theory when t ≤ D/20 (equivalently D/t ≥ 20). If the wall is relatively thicker (D/t less than about 20), through-thickness stress variation is non-negligible and thick-cylinder (Lame) theory should be applied.

Step-by-Step Solution:

Verification / Alternative check:Check relative radial stress variation: in thick shells, sigma_r varies from −p at the inner surface to near zero at the outer surface, which thin formulas neglect; for D/t = 15 this variation is significant.

Why Other Options Are Wrong:Disagree contradicts the widely used D/t ≈ 20 threshold.Dependence on pressure magnitude or material brittleness does not change the geometric classification.Length-to-diameter ratio affects end conditions, not thin/thick wall selection.

Common Pitfalls:Applying thin-wall hoop stress sigma_h = p D / (2 t) when D/t is too small; ignoring radial stress in thick members.

Final Answer:

Agree