---
title: Member Buckling Verification
description: Run EN 1993-1-1 §6.3 flexural and lateral-torsional buckling on columns and beams using effective lengths from the 3D model.
category: Eurocode
---

## 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:

```
N_b,Rd = (χ · A · f_y) / γ_M0    (Class 1, 2, 3)
N_b,Rd = (χ · A_eff · f_y) / γ_M0  (Class 4)
```

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

```
λ̅ = √(A · f_y / N_cr)
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 |

```
<div class="screenshot-placeholder">
  📸 Screenshot: The buckling panel showing χ values for both axes and the imperfection factor α.
  TODO: replace with actual screenshot
</div>
```

## Lateral-torsional buckling

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

```
M_b,Rd = χ_LT · W_y · f_y / γ_M0
```

The slenderness for LTB uses the elastic critical moment M_cr:

```
M_cr = C1 · π² · E · I_z / L² · √(1 + (π² · E · I_w / L² / G · I_t))
```

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**: L_eff = 0.5 L
- **Fixed–pinned**: L_eff = 0.7 L
- **Pinned–pinned**: L_eff = 1.0 L
- **Continuous**: L_eff = 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:

```
N_Ed / (χ_y N_Rk / γ_M1) + k_yy · M_y,Ed / (W_y · f_y / γ_M1) ≤ 1.0
N_Ed / (χ_z N_Rk / γ_M1) + k_zy · M_y,Ed / (W_y · f_y / γ_M1) ≤ 1.0
```

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

```
<div class="screenshot-placeholder">
  📸 Screenshot: The combined loading panel showing the interaction check and k-factors.
  TODO: replace with actual screenshot
</div>
```

## 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 L_eff
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.