Pressure vessels – definition of a thick shell A pressure vessel is said to be a thick shell when which geometric condition holds true?

Introduction / Context:
In strength of materials and machine design, pressure vessels are classified as thin or thick shells to choose appropriate stress formulas. Thin-shell (membrane) theory assumes nearly uniform stress across thickness, while thick-shell theory (Lame’s equations) accounts for radial stress variation. Correct classification hinges on the ratio of wall thickness to diameter.

Given Data / Assumptions:

• D = internal (or mean) diameter of the cylindrical or spherical vessel.
• t = wall thickness of the vessel.
• Elastic, isotropic material; small deformations.
• Classification threshold used in standard design practice.

Concept / Approach:
When the wall is relatively thin compared to diameter, stress variation through the wall is small and thin-cylinder formulas apply. As thickness increases, the radial stress and hoop stress vary significantly across the wall, requiring thick-cylinder theory.

Step-by-Step Solution:
Classification criterion widely used: thin shell if t / D ≤ 1/20 to 1/10 (engineering practice uses conservative bounds).If the wall is relatively thick, i.e., t / D > 1/10, thin-shell assumptions break down.Therefore, a pressure vessel is treated as a thick shell when t / D is greater than 1/10.

Verification / Alternative check:
Another common rule uses t / r (r = radius). If t / r > 0.05, thick formulas (Lame’s) are needed. Since D = 2 r, t / D > 0.1 corresponds to t / r > 0.2, a conservative threshold; both indicate the necessity of thick-wall analysis.

Why Other Options Are Wrong:
“Manufactured from thick sheets” and “internal pressure very high” do not, by themselves, dictate stress distribution; geometry governs theory choice. “t / D less than 1/10” indicates thin shell, not thick. A specific value like 1/20 is a thin-wall guideline, not thick.

Common Pitfalls:
Confusing service pressure with geometry; using thin-wall hoop stress (σ_hoop = p D / (2 t)) for thick shells, leading to unsafe designs.

Final Answer:
t / D is greater than 1/10