Documentation/Modules/Area Properties

Area Properties

Centroid, inertia and moduli for common profile shapes

Standards catalog

Validation: indicative · Method band: formula

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
Section areaimplemented———
Principal inertiaimplemented———

Area Properties (profiles)

Purpose

Compute cross-sectional area properties for arbitrary 2D profiles defined by SVG outlines or parametric shapes using finite-element mesh integration. Supports custom extrusions and imported geometry with visual preview.

Physics & theory

For arbitrary simply-connected regions, area , centroid coordinates , and second moments are evaluated numerically over a triangular mesh of the outline. Green's theorem converts boundary integrals to mesh summation.

Principal axes and angles derive from the inertia tensor. Minimum wall thickness and bounding box support manufacturing and buckling screens. Mesh quality affects accuracy — finer meshes reduce discretization error on curved boundaries.

Material and section data underpin all stress and deflection calculations in PhyCalcPro. Consistent unit conversion to SI base quantities occurs at the solver boundary via the shared units layer. Temperature-dependent properties should be evaluated when operating temperature differs significantly from room temperature.

Cross-section properties assume homogeneous isotropic material unless the Composites module is used for laminated sections.

Governing equations

Numerical method

2D FEM mesh integration (femSolver, femPost): SVG path or polygon tessellated into triangles. Properties integrated per element; results compared to analytical benchmarks for standard shapes. SVG outline preview in results picker.

Inputs

ParameterDescription
Profile outlineSVG path or parametric shape
Mesh densityTessellation fineness
Hole cutouts (optional)Subtracted regions

Outputs

  • Area, centroid, $I_x
  • I_y
- I_{xy}$, principal inertias and angle, section moduli, bounding box, mesh preview.

Design codes & checks

  • Indicative: Section area and principal inertia

Assumptions & limitations

  • Single material homogeneous section; no composite layup.
  • 2D plane section only; no thin-walled shear center for open profiles unless extended.
  • Mesh-dependent accuracy on sharp corners.
  • SVG import requires closed, non-self-intersecting paths.

References

  1. Cook, R. D., et al. Concepts and Applications of FEA, 4th ed.
  2. Roark, R. J., Young, W. C., & Budynas, R. G. Formulas for Stress and Strain.
  3. Gere, J. M., & Goodno, B. J. Mechanics of Materials, 9th ed.
  4. ISO 10303 (STEP) — CAD exchange context for profile import.
  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: Cross-section property FEA with SVG outline previews in results picker.