Documentation/Modules/Pipe Stress Analysis

Pipe Stress Analysis

Internal pressure and stress analysis

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
Sustained stress utilizationimplementedimplemented——
Occasional stress utilizationimplementedimplemented——
Peak stress utilizationimplementedimplemented——

Pipe Stress Analysis (pipes)

Purpose

Analyze cylindrical pipes under internal pressure, thermal expansion, and weight loads using ring–beam FEM. Computes hoop, longitudinal, and combined stresses with ASME B31.3 sustained, occasional, and peak stress screening.

Physics & theory

Thin-wall hoop stress from internal pressure: . Longitudinal stress from pressure end cap: . Thermal expansion strain generates stress if expansion is restrained by supports. Weight and sagging add bending in long horizontal spans.

ASME B31.3 categorizes stresses: sustained (pressure + weight), occasional (wind/seismic), and peak (thermal transients). Each has allowable limits based on yield and fatigue at discontinuities. Thick-wall pipes use Lamé solution when .

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

Ring–beam pipe FEM (solver): pipe meshed along length with circumferential ring stiffness for pressure. Thermal and weight loads superposed. Post-processing extracts stress components and B31.3 utilization categories.

Inputs

ParameterDescription
radius, thickness, lengthPipe geometry
pressureInternal design pressure
E, alpha, rhoMaterial properties
deltaTOperating minus install temperature
Support span, segmentsBoundary and mesh
Design codeASME B31.3 or Indicative

Outputs

  • Hoop, longitudinal, bending stresses
  • sustained/occasional/peak utilization
  • deflection
  • expansion thrust.

Design codes & checks

  • Indicative: Thin-wall pipe stress
  • US: ASME B31.3 §302.3 sustained, §302.3.6 occasional, peak/upset

Assumptions & limitations

  • Straight single pipe segment; no fittings, branches, or flanges modeled.
  • Linear elastic; no plastic shake-down analysis.
  • Stress intensification at welds requires user SIF factors for detailed work.
  • Minimum 8 segments required for adequate ring resolution.

Verification

References

  1. ASME B31.3:2022. Process Piping.
  2. Timoshenko, S. P., & Woinowsky-Krieger, S. Theory of Plates and Shells.
  3. Spuybroek, W. H. Flexibility Analysis of Piping Systems. Kluwer.
  4. ASME BPVC Section III (nuclear piping context, reference).
  5. Beer, F. P., et al. Mechanics of Materials, 8th ed. McGraw-Hill — foundational stress and deformation theory.
Maintainer note: Pressure + stress coupling with detailed solver internals.