Stress from Pressure
Thin-Walled Vessel Analysis
Thin-Walled Vessel Stress Calculator
Hoop Stress (Circumferential)
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Longitudinal Stress (Axial)
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Maximum Shear Stress
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Valid for: Thin-walled vessels where t/r < 0.1 (wall thickness to radius ratio less than 10%). For thicker vessels, use thick-wall analysis (Lamé equations).
Thin-Walled Vessel Stress Equations
Cylindrical Vessel (Hoop Stress)
σ_θ = P × r / t
P = Internal pressure (Pa)
r = Inner radius (m)
t = Wall thickness (m)
This is the dominant stress; acts circumferentially around the vessel
r = Inner radius (m)
t = Wall thickness (m)
This is the dominant stress; acts circumferentially around the vessel
Cylindrical Vessel (Longitudinal Stress)
σ_z = P × r / (2t)
Acts along the axis of the cylinder
Equals half the hoop stress for cylindrical vessels
Longitudinal stress is contained by end caps/closures
Equals half the hoop stress for cylindrical vessels
Longitudinal stress is contained by end caps/closures
Spherical Vessel (Membrane Stress)
σ = P × r / (2t)
For spherical pressure vessels, stress is uniform in all directions
Spheres are more efficient at containing pressure than cylinders
No distinction between hoop and longitudinal stress
Spheres are more efficient at containing pressure than cylinders
No distinction between hoop and longitudinal stress
Maximum Shear Stress (Cylinder)
τ_max = (σ_θ - σ_z) / 2 = P × r / (4t)
Critical for ductile failure analysis
Use for von Mises or Tresca failure criteria
Use for von Mises or Tresca failure criteria
Thin-Walled Criterion
t / r < 0.1
For equations to be valid, wall thickness to radius ratio should be less than 10%
If t/r ≥ 0.1, use thick-wall analysis (Lamé equations)
Use r for inner radius; for diameter, divide by 2
If t/r ≥ 0.1, use thick-wall analysis (Lamé equations)
Use r for inner radius; for diameter, divide by 2