PhysSandbox
Classical MechanicsWaves & SoundElectricity & MagnetismOptics & LightGravity & OrbitsLabs
🌙Astronomy & The Sky🌡️Thermodynamics🌍Biophysics, Fluids & Geoscience📐Math Visualization🔧Engineering🧪Chemistry
ENRUESPTFRDE

Related simulators

Continue with similar topics in this category — or all 48 in Engineering.

View category →
NewSchool

Mohr Circle & Stress Transformation

Launch Simulator

Plane stress σx, σy, τxy: Mohr circle, transformed stresses on a rotated element, principal stresses, τmax, and θp.

NewUniversity / research

Hertzian Contact Stress

Launch Simulator

Sphere or cylinder on a flat: effective modulus, contact patch, peak pressure p0, elastic approach, and subsurface shear estimate.

NewSchool

Stress–Strain & Hooke’s Law

Launch Simulator

Qualitative σ–ε curve: elastic Hooke region, yield, strain hardening, necking, and fracture. Drag strain and tune E, σ_y, σ_u.

NewUniversity / research

Fracture Mechanics: Griffith / K_IC

Launch Simulator

Mode-I crack: K_I = Yσ√(πa), compare with K_IC, critical crack size, critical stress, and safe/unstable crack growth.

NewSchool

Bridge Builder

Launch Simulator

Place beams and joints. Apply load. See stress distribution.

NewSchool

RRT Path Planner (grid)

Launch Simulator

Same 40×28 wall map as A*: random samples, nearest-neighbor steer, goal bias, collision-checked edges; grow an RRT and compare summary stats with one-click Manhattan A* baseline.

PhysSandbox

Interactive physics, chemistry, and engineering simulators for students, teachers, and curious minds.

Physics

  • Classical Mechanics
  • Waves & Sound
  • Electricity & Magnetism

Science

  • Optics & Light
  • Gravity & Orbits
  • Astronomy & The Sky

More

  • Thermodynamics
  • Biophysics, Fluids & Geoscience
  • Math Visualization
  • Engineering
  • Chemistry

© 2026 PhysSandbox. Free interactive science simulators.

PrivacyTermsContact
Home/Engineering/Thin-Walled Pressure Vessel Stress

Thin-Walled Pressure Vessel Stress

Cylinder vs sphere membrane stresses: hoop σθ, longitudinal σz, von Mises stress, r/t thin-wall check, and yield safety factor.

This is a membrane-stress teaching model. Real vessel design also checks code allowables, joint efficiency, corrosion allowance, heads, openings, thermal stress, external pressure buckling, fatigue, and proof testing.

Vessel geometry

600 mm
8 mm

Pressure and material

2.5 MPa
250 MPa

Thin-wall formulas assume r/t is large, membrane stress dominates, and local nozzles, welds, heads, and buckling checks are outside the model.

Measured values

Hoop stress σθ187.5MPa
Longitudinal stress σz93.8MPa
von Mises stress162.4MPa
Safety factor1.54
Thin-wall ratio r/t75.0
Yield pressure estimate3.33MPa

Live graphs

About this model

Thin-walled pressure-vessel theory treats wall stresses as membrane stresses when the radius-to-thickness ratio is large. For a closed cylindrical vessel the hoop stress is σθ = pr/t and the longitudinal stress is σz = pr/(2t); for a sphere both principal membrane stresses are pr/(2t). This simulator compares cylinder and sphere behavior, computes the von Mises equivalent stress, estimates a yield safety factor, and warns when r/t is too small for the thin-wall assumption. It is a teaching model only: real vessel design also considers design codes, joint efficiency, corrosion allowance, heads and nozzles, local discontinuity stresses, thermal gradients, external pressure buckling, fatigue, proof testing, and inspection.

Who it's for: Mechanics of materials, pressure-vessel design introductions, process equipment, HVAC, piping, and mechanical engineering courses.

Key terms

  • Thin-walled pressure vessel
  • Hoop stress
  • Longitudinal stress
  • Membrane stress
  • Safety factor

How it works

Thin-wall pressure vessel stress calculator: compare cylindrical and spherical membrane stresses, hoop stress, longitudinal stress, von Mises stress, and yield safety factor.

Key equations

Cylinder: σθ = pr/t, σz = pr/(2t)
Sphere: σθ = σφ = pr/(2t); σvm = sqrt(σθ² − σθσz + σz²)

Frequently asked questions

Why is hoop stress twice the longitudinal stress in a cylinder?
A longitudinal split is resisted by wall area 2tL, giving σθ = pr/t. An end-cap force is resisted by the circumferential wall area 2πrt, giving σz = pr/(2t).
When do thin-wall formulas stop being accurate?
A common rule of thumb is r/t ≥ 10. Below that, stress varies noticeably through the wall and thick-cylinder Lamé equations are more appropriate.