Member Buckling Verification

Run EN 1993-1-1 §6.3 flexural and lateral-torsional buckling on columns and beams using effective lengths from the 3D model.

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Member Buckling Verification

Member buckling is the most common failure mode for steel columns and beams. FrameAI calculates flexural buckling (about both axes) and lateral-torsional buckling per EN 1993-1-1 §6.3.

Flexural buckling

The design buckling resistance of a member in compression:

Nb,Rd = (χ · A · fy) / γM0 (Class 1, 2, 3) Nb,Rd = (χ · Aeff · fy) / γM0 (Class 4)

where the reduction factor χ depends on the non-dimensional slenderness:

λ̅ = √(A · fy / Ncr) α = imperfection factor (0.21 for curve a, 0.34 for curve c) φ = 0.5 [1 + α(λ̅ - 0.2) + λ̅²] χ = min(1, 1 / (φ + √(φ² - λ̅²)))

FrameAI selects the buckling curve based on the section type:

Section Buckling curve (about y-y) Buckling curve (about z-z)
Hot-rolled I/H a b
Welded I/H b c
Cold-formed c c

📸 Screenshot: The buckling panel showing χ values for both axes and the imperfection factor α. TODO: replace with actual screenshot

Lateral-torsional buckling

For beams subjected to bending about the strong axis, FrameAI calculates the LTB resistance:

Mb,Rd = χLT · Wy · fy / γM0

The slenderness for LTB uses the elastic critical moment Mcr:

Mcr = C1 · π² · E · Iz / L² · √(1 + (π² · E · Iw / L² / G · It))

C1 depends on the loading and end moment diagram (from Annex Annex BB of EN 1993-1-1).

Effective lengths

FrameAI derives effective lengths from the 3D model geometry and connection stiffness assumptions:

**Fixed–fixed**: Leff = 0.5 L

**Fixed–pinned**: Leff = 0.7 L
**Pinned–pinned**: Leff = 1.0 L
**Continuous**: Leff = 0.9 L (frame action)

You can override the effective length factor from the member detail panel.
Interaction formula

For combined axial compression and bending (M + N), EN 1993-1-1 §6.3.3 uses:

NEd / (χy NRk / γM1) + kyy · My,Ed / (Wy · fy / γM1) ≤ 1.0 NEd / (χz NRk / γM1) + kzy · My,Ed / (Wy · fy / γM1) ≤ 1.0

The k-factors (kyy, kzy) are calculated per Annex A (method 1) or Annex B (method 2), whichever gives the higher utilisation.

📸 Screenshot: The combined loading panel showing the interaction check and k-factors. TODO: replace with actual screenshot

Reviewing results

Members with ξ > 1.0 (FAIL) should be reviewed. Common fixes:

1. **Increase section size** — a larger I/H has more buckling resistance
2. **Add lateral restraints** — intermediate bracing reduces Leff
3. **Change end conditions** — a fixed base provides more stiffness than pinned
4. **Reduce slenderness** — shorter effective length reduces λ̅

All overrides and their justifications are recorded in the job audit log.

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