Thin cylindrical pressure vessels – Governing stress for design\n\nFor thin cylindrical shells under internal pressure, design is primarily based on which stress component?

Introduction / Context:
Thin-walled cylinders (t ≪ d) such as boilers and tanks are designed against tensile stresses caused by internal pressure. Two principal membrane stresses arise: hoop (circumferential) and longitudinal (axial).

Given Data / Assumptions:

• Uniform internal pressure p; diameter d; thickness t; thin-wall criterion satisfied.
• Membrane theory with negligible radial stress compared to tangential stresses.
• Isotropic, linear-elastic material.

Concept / Approach:
For a thin cylinder, hoop stress σ_h = p d / (2 t) and longitudinal stress σ_l = p d / (4 t). Hoop stress is twice the longitudinal stress; hence it governs the design for maximum tensile stress.

Step-by-Step Solution:
Derive σ_h by cutting the cylinder along a diametral plane: pressure force balanced by two hoop stress resultants → σ_h = p d / (2 t).Derive σ_l by cutting with a transverse plane through the heads: σ_l = p d / (4 t).Compare magnitudes: σ_h = 2 σ_l → hoop stress governs.

Verification / Alternative check:
Design codes limit circumferential stress more strictly; thickness sizing formulas are based on hoop stress with allowances for corrosion and joint efficiency.

Why Other Options Are Wrong:
(b) longitudinal stress is smaller; (c) and (d) use averages not employed in design; (e) radial stress in thin shells is small compared to tangential components.

Common Pitfalls:
Applying spherical vessel formulas; misusing diameter versus radius; forgetting joint efficiency in welded/riveted shells.

Final Answer:
hoop stress