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Documentation/Modules/3.1 Beam Analysis

3.1 Beam Analysis

Deflection, bending moment, shear force

Standards catalog

Validation: beta · 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.

Limitations

  • 2D beam model; LTB uses simplified unbraced length = span unless overridden.
  • Shear check uses rectangular-web estimate from I and c.

Engineering checks

CheckINDUSEUISO
Bending stress utilizationimplementedimplementedimplementedimplemented
Shear utilizationimplementedimplementedimplemented—
Deflection / serviceability limitimplementedimplementedimplementedimplemented
Lateral-torsional bucklingimplementedimplementedimplemented—

3.1 Beam Analysis (beams) — beta

Purpose: 2D Euler–Bernoulli beam analysis — deflection, moment, shear, bending stress for common supports and arbitrary point/UDL/moment loads.

Method: FEM — 2-node Hermite beam elements; mesh-refinable (meshSegments). Not a full 3D or Timoshenko model.

Key relations:

  • Element stiffness from $EI/L^3$; curvature–moment:
M = EI\,\kappa $$[^aisc-360-22-ch-f-flexure-serviceability-en-1993-] - **Bending stress:**

\sigma = M,c/I

- Deflection from solved nodal rotations/displacements **Inputs:** span $L$, $E$, $I$, distance to extreme fiber $c$, support type (simply supported, cantilever, fixed–fixed), load list, material preset, mesh density. **Outputs:** $V(x)$, $M(x)$, $w(x)$, $\sigma(x)$; peaks; interactive load diagram; `calculationSpec` with flexure and deflection checks. **Design codes:** AISC 360-22 (Ch. F flexure, serviceability), EN 1993-1-1 (Cl. 6.2.5). **Implemented:** bending stress, deflection. **Planned:** shear (Ch. G / Cl. 6.2.6), lateral–torsional buckling. **UI:** Modern `inputs`/`results`; `useDesignCodeUnits`; local project save. Featured module. **Gaps:** No shear check in solver spec; no LTB; legacy `useCalculationPipeline` instead of `useStandardCalculation`; high refactor risk (core FEM). --- [^aisc-360-22-ch-f-flexure-serviceability-en-1993-]: AISC 360-22 (Ch. F flexure, serviceability), EN 1993-1-1 (Cl. 6.2.5). **Implemented:** bending stress, deflection. **Planned:** shear (Ch. G / Cl. 6.2.6), lateral–torsional buckling.
Maintainer note: Core FEM workflow with broad usage and legacy interfaces.