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):

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

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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