PRESSURE VESSELS (THIN & THICK WALL)

Thin-wall (D/t > 20) cylindrical vessels under internal pressure see hoop stress σ_h = P·r/t and longitudinal stress σ_L = P·r/(2t); hoop is twice longitudinal. For thick walls, Lamé equations give radial and tangential stress varying through wall thickness. ASME BPVC Section VIII Division 1 prescribes minimum thickness with allowable stress S, joint efficiency E, and corrosion allowance: t = P·R / (S·E - 0.6·P) for cylindrical shells.

• σ_h = P·r / t (thin)
• σ_L = P·r / (2t) (thin)
• σ_t,r = (Pi·ri² - Po·ro²) / (ro² - ri²) ± (Pi - Po)·ri²·ro² / [r²(ro²-ri²)] (Lamé)
• t_min = P·R / (S·E - 0.6·P) (ASME UG-27)

References & StandardsASME BPVC Section VIII Div 1, ASME B31.3

Size pressure vessels, pipe walls, hydraulic cylinders. Choose thin-wall formula for D/t > 20 (most piping); use Lamé for thick wall (gun barrels, high-pressure dies). For ASME-coded equipment, design to VIII-1 with appropriate weld joint efficiency (E=1.0 for full radiography, 0.7 for spot, 0.6 for none). Always include corrosion allowance (often 1/16" or 3 mm) and verify external pressure (buckling) separately.