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sci.thick-walled-cylinder-Lame Calculator
Calculates hoop and radial stress distributions in a thick-walled pressure vessel using Lamé's equations: σθ = (pi×ri² − po×ro²)/(ro²−ri²) + r_i²r_o²(pi−po)/((ro²−ri²)r²). Hoop stress is maximum at the inner wall and decreases radially — thick cylinder design must satisfy both yield and fracture mechanics criteria.
Inputs
Ri Mm
Distance from centre to edge of a circle. Radius = diameter / 2.
Ro Mm
Distance from centre to edge of a circle. Radius = diameter / 2.
Pi Mpa
Force per unit area (Pa). Atmospheric pressure at sea level: 101,325 Pa. Check whether gauge or absolute pressure is required.
Po Mpa
Force per unit area (Pa). Atmospheric pressure at sea level: 101,325 Pa. Check whether gauge or absolute pressure is required.
Results
hoop stress at inner wall σθ (MPa)
Internal force per unit area (Pa or MPa). Must stay below yield strength in service. Beyond yield: permanent deformation. Beyond tensile strength: fracture.
hoop stress at outer wall σθ (MPa)
Internal force per unit area (Pa or MPa). Must stay below yield strength in service. Beyond yield: permanent deformation. Beyond tensile strength: fracture.
radial stress at inner wall σr (MPa)
Internal force per unit area (Pa or MPa). Must stay below yield strength in service. Beyond yield: permanent deformation. Beyond tensile strength: fracture.
radial stress at outer wall σr (MPa)
Internal force per unit area (Pa or MPa). Must stay below yield strength in service. Beyond yield: permanent deformation. Beyond tensile strength: fracture.
σθ = A + B/r² | σr = A − B/r²
Reference formula or conversion factor shown for context.
wall ratio k = ro/ri
The proportional relationship between two quantities.