EN 1993 Column Design — Compression per Eurocode 3 Clause 6.3.1
Complete guide to steel column flexural buckling design per EN 1993-1-1:2005 Clause 6.3.1. Buckling curves a0, a, b, c, d, non-dimensional slenderness λ̄, χ reduction factor, member buckling resistance Nb,Rd. Worked example with HEA 300 column in S355 steel.
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Design Procedure — Clause 6.3.1.1
The design buckling resistance of a compression member is:
N_b,Rd = χ × A × f_y / γ_M1
For Class 1, 2, and 3 sections, use the gross cross-sectional area A. For Class 4 sections, use A_eff.
γ_M1 = 1.00 per EN 1993-1-1 Clause 6.1.
The reduction factor χ is obtained from the non-dimensional slenderness:
λ̄ = √(A × f_y / N_cr)
Where N_cr is the elastic critical force for the relevant buckling mode:
N_cr = π² × E × I / L_cr²
Buckling Curves — Table 6.1 and 6.2
Imperfection Factor α
| Buckling Curve | α (imperfection factor) |
|---|---|
| a0 | 0.13 |
| a | 0.21 |
| b | 0.34 |
| c | 0.49 |
| d | 0.76 |
Curve Selection for Rolled Sections
Per EN 1993-1-1 Table 6.2:
| Section Type | Axis | Curve (S235-S355) | Curve (S460) |
|---|---|---|---|
| I-sections (h/b ≤ 1.2, t_f ≤ 100 mm) | y-y | b | a0 |
| I-sections (h/b ≤ 1.2, t_f ≤ 100 mm) | z-z | c | a0 |
| I-sections (h/b > 1.2, t_f ≤ 40 mm) | y-y | b | b |
| I-sections (h/b > 1.2, t_f ≤ 40 mm) | z-z | c | c |
| I-sections (t_f > 40 mm to 100 mm) | y-y | c | c |
| I-sections (t_f > 40 mm to 100 mm) | z-z | d | d |
| Hollow sections (hot-finished) | — | a | a0 |
| Hollow sections (cold-formed) | — | c | c |
For HEA 300 (h/b = 290/300 = 0.97 ≤ 1.2, t_f = 14 mm ≤ 40 mm):
- Major axis (y-y): curve b (α = 0.34)
- Minor axis (z-z): curve c (α = 0.49)
Reduction Factor χ — Clause 6.3.1.2
χ = 1 / (Φ + √(Φ² - λ̄²)) but χ ≤ 1.0
Where:
Φ = 0.5 × [1 + α × (λ̄ - 0.2) + λ̄²]
The 0.2 term defines a plateau where λ̄ ≤ 0.2 and no buckling reduction is needed (χ = 1.0).
Worked Example — HEA 300 Column in S355
| Property | Value |
|---|---|
| Section | HEA 300 |
| Steel | S355 (fy = 355 MPa) |
| A | 11250 mm² |
| I_y | 18260 × 10⁴ mm⁴ |
| I_z | 6310 × 10⁴ mm⁴ |
| L | 4.0 m |
| End conditions | Pinned (K = 1.0) |
Major Axis (y-y)
| Parameter | Value |
|---|---|
| L_cr,y | 4.0 m |
| N_cr,y | π² × 210000 × 182.6×10⁶ / 4000² = 23,650 kN |
| λ̄_y | √(11250 × 355 / 23,650,000) = 0.41 |
| Curve | b (α = 0.34) |
| Φ_y | 0.5 × [1 + 0.34×(0.41-0.2) + 0.41²] = 0.57 |
| χ_y | 1 / (0.57 + √(0.57² - 0.41²)) = 0.95 |
| N_b,Rd,y | 0.95 × 11250 × 355 / 1.00 = 3795 kN |
Minor Axis (z-z)
| Parameter | Value |
|---|---|
| L_cr,z | 4.0 m |
| N_cr,z | π² × 210000 × 63.1×10⁶ / 4000² = 8170 kN |
| λ̄_z | √(11250 × 355 / 8,170,000) = 0.70 |
| Curve | c (α = 0.49) |
| Φ_z | 0.5 × [1 + 0.49×(0.70-0.2) + 0.70²] = 0.82 |
| χ_z | 1 / (0.82 + √(0.82² - 0.70²)) = 0.77 |
| N_b,Rd,z | 0.77 × 11250 × 355 / 1.00 = 3075 kN |
Governing: minor axis, N_b,Rd = 3075 kN (77% of squash load)
Buckling Lengths — Typical Values
| End Condition | K (effective length factor) |
|---|---|
| Both ends pinned | 1.0 |
| Both ends fixed | 0.5 |
| One end fixed, one end pinned | 0.7 |
| One end fixed, one end free | 2.0 |
| Propped cantilever | 1.0 (lateral restraint at tip) |
See the effective length factor guide for alignment chart calculations per EN 1993-1-1 Annex E.
Column Buckling Curves Summary Chart
For a given λ̄, the reduction factor χ for each curve:
| λ̄ | Curve a0 | Curve a | Curve b | Curve c | Curve d |
|---|---|---|---|---|---|
| 0.2 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
| 0.5 | 0.964 | 0.943 | 0.908 | 0.867 | 0.808 |
| 1.0 | 0.721 | 0.661 | 0.588 | 0.518 | 0.438 |
| 1.5 | 0.469 | 0.419 | 0.367 | 0.322 | 0.270 |
| 2.0 | 0.310 | 0.278 | 0.244 | 0.215 | 0.182 |
The difference between curves is most significant in the intermediate slenderness range (λ̄ = 0.5-1.5).
Frequently Asked Questions
What buckling curve should I use for an HEA column in S355 steel?
For HEA sections, h/b ≤ 1.2 for most sizes. Per EN 1993-1-1 Table 6.2, use curve b (α = 0.34) for major axis buckling and curve c (α = 0.49) for minor axis buckling when S235-S355 steel.
When can column buckling be neglected per EN 1993-1-1?
Column buckling may be neglected per Clause 6.3.1.2 when the non-dimensional slenderness λ̄ ≤ 0.2, or when N_Ed / N_cr ≤ 0.04. In these cases, the reduction factor χ = 1.0 and only cross-section compression resistance needs to be checked.
Related Pages
- Column K-Factor — Effective length per Annex E
- EN 1993 Beam Design — Flexural design guide
- Compact Section Limits — Class 1-4 per Table 5.2
- Combined Loading — Axial + bending interaction
- All European References
Educational reference only. Design per EN 1993-1-1:2005 + A1:2014 Clause 6.3.1. Buckling curves per Table 6.1 and 6.2. Verify actual column end conditions determine effective length. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent verification.
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