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Documentation/Modules/3.4 Column Buckling

3.4 Column Buckling

Euler buckling and stability analysis

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

  • Does not replace a licensed professional engineer or official code compliance review.

Engineering checks

CheckINDUSEUISO
Buckling utilizationimplementedimplementedimplementedimplemented
Euler critical load checkimplementedimplementedimplementedimplemented

3.4 Column Buckling (columns) — beta

Purpose: Elastic column buckling — critical load, effective length, mode shapes.

Method: FEM eigenvalue hybrid — assembles elastic $K_E$ and geometric $K_G$ stiffness; Euler fallback for fast critical load:

P_{cr} = \frac{\pi^2 E I}{L_e^2}, \quad L_e = k L $$[^implemented-for-us-aisc-360-22-ch-e-eu-en-1993-1] Effective-length factor $k$ from end condition (pinned, fixed, fixed–pinned, etc.). **Inputs:** $L$, $P$, $I$, $A$, $E$, end condition. **Outputs:** $P_{cr}$, critical stress, slenderness, buckling mode shapes (1–3), deflected shape under load. **Design codes:** **Implemented** for US (AISC 360-22 Ch. E), EU (EN 1993-1-1 buckling), ISO 10721 — buckling utilization and Euler critical check. **UI:** Legacy `left`/`center`/`right` with `CalculatorGuidancePanel`; `useStandardCalculation` + region units. **Gaps:** Linear elastic buckling only; no inelastic column curves; area unit conversion noted as incomplete in page code. --- [^implemented-for-us-aisc-360-22-ch-e-eu-en-1993-1]: **Implemented** for US (AISC 360-22 Ch. E), EU (EN 1993-1-1 buckling), ISO 10721 — buckling utilization and Euler critical check.
Maintainer note: Buckling + FEM hybrid model, manageable migration surface.