Documentation/Modules/Section Properties

Section Properties

I, Z, centroid, inertia calculations

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
Cross-sectional areaimplemented———
Second moment of areaimplemented———

Section Properties (sections)

Purpose

Calculate geometric section properties — area, centroid, second moments of area, section moduli, and radii of gyration — for standard and parametric cross-section shapes used in structural and machine design.

Physics & theory

Cross-section geometry determines resistance to axial load (), bending (), and torsion (). Centroid location defines neutral axis for bending. Parallel-axis theorem transfers inertia: . Section modulus links bending moment to extreme fiber stress .

Standard shapes (rectangle, circle, tube, I-beam built from rectangles) use closed-form formulas. Radii of gyration enter column buckling slenderness calculations.

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

Closed-form formulas for catalog shapes (engine). Composite sections built by summation with signed areas for voids. Outputs principal axes when asymmetric sections supported.

Inputs

ParameterDescription
Shape typeRectangle, circle, tube, I, T, etc.
DimensionsHeight, width, wall thickness, etc.
OrientationStrong/weak axis selection

Outputs

  • Area, centroid coordinates, $I_x
  • I_y
  • J$, section moduli, radii of gyration.

Design codes & checks

  • Indicative: Area and inertia calculations

Assumptions & limitations

  • Homogeneous solid sections; composite materials use Effective Width in Composites module.
  • Thin-walled open sections use approximate torsion constant.
  • No elastic-plastic section modulus ( ) for compact I-shapes per code — geometric only unless extended.

References

  1. Gere, J. M., & Goodno, B. J. Mechanics of Materials, 9th ed., Ch. 6.
  2. Roark, R. J., Young, W. C., & Budynas, R. G. Formulas for Stress and Strain.
  3. AISC. Steel Construction Manual, property tables.
  4. EN 10279:2007. Hot rolled steel channels (shape definitions).
  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: Geometric property equations with many shape variants.