Documentation/Modules/Pressure Vessels

Pressure Vessels

Thin and thick wall vessel design

Standards catalog

Validation: indicative · Method band: fem

Open calculator

Indicative method: Indicative closed-form or numerical model

Assumptions

  • Linear elastic material behavior unless noted otherwise.
  • User is responsible for load combinations and load factors per the selected design code.
  • Design standard (US/EU/ISO) sets unit defaults and screening check labels — not a full code worksheet.

Limitations

  • Professional screening / indicative workspace — does not replace a licensed PE or official code compliance review.
  • Where specialized evaluators are not implemented, checks map solver outputs to catalog templates for orientation only.

Engineering checks

CheckINDUSEUISO
Hoop stress utilizationimplemented———
Required thickness marginimplemented———

Pressure Vessels (vessels)

Purpose

Design and analyze cylindrical and spherical pressure vessel shells for internal pressure using thin-wall and thick-wall (Lamé) theory with ASME VIII-1 UG-27 and EN 13445 screening checks.

Physics & theory

Thin cylindrical shells (): hoop stress governs; longitudinal . Spherical shells: . Required thickness per ASME UG-27 with joint efficiency and allowable stress .

Thick-wall cylinders use Lamé stresses varying through wall thickness. Heads (elliptical, hemispherical, flat) have separate formulas for discontinuity stresses at shell–head junction — simplified screening may treat head as equivalent sphere segment.

Pressure systems combine membrane stress from internal pressure with bending from weight, thermal expansion, and external loads. ASME codes distinguish sustained, occasional, and peak stress categories with different allowable limits reflecting primary vs secondary stress character.

Thin-wall theory applies when wall thickness is small compared to radius; thick-wall Lamé solutions are required for heavy-wall vessels and high-pressure cylinders.

Governing equations

Numerical method

Thin/thick-wall closed-form with optional FEM mesh for nozzle or head transitions (engine, mesh). Required thickness and hoop utilization computed per selected code. Joint efficiency and corrosion allowance user-specified.

Inputs

ParameterDescription
radius, thicknessShell geometry
pressureInternal design pressure
Material allowable , yieldCode allowable
Joint efficiency Seam weld factor
Corrosion allowanceAdded to required
Head typeCylinder, sphere, elliptical

Outputs

  • Hoop/longitudinal stress, required thickness, utilization, thick vs thin-wall flag.

Design codes & checks

  • Indicative: Hoop stress and required thickness screening
  • US: ASME VIII-1 UG-27
  • EU: EN 13445-3 design rules

Assumptions & limitations

  • No detailed nozzle reinforcement per UG-37 unless extended.
  • Wind/seismic external loads not combined unless user superposes.
  • Fatigue evaluation per VIII-2 not included.
  • MDMT and impact testing requirements not evaluated.

References

  1. ASME BPVC Section VIII, Division 1 (2023). UG-27.
  2. EN 13445-3:2021. Unfired pressure vessels — Design.
  3. Harvey, J. F. Theory and Design of Pressure Vessels, 2nd ed.
  4. Bednar, H. H. Pressure Vessel Design Handbook, 3rd ed.
  5. PhyCalcPro verification benchmarks in src/data/verification/ where available for this module.
  6. Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.
Maintainer note: Thin/thick-wall logic; clear fit for shared dimension checks.