UK Column Design — EN 1993-1-1 & UK NA Guide
This reference covers column design for UK steel design per EN 1993-1-1:2005 Clause 6.3.1 and UK NA. Steel column design in UK practice centres on flexural buckling resistance using the European buckling curves, with cross-section classification determining whether local buckling reduces the effective area.
Design requirements, worked examples, and practical design guidance are provided for common design office applications.
Code Reference: EN 1993-1-1:2005 Clause 6.3.1 and UK NA
Flexural Buckling Resistance (EN 1993-1-1 Clause 6.3.1)
[ N*{b,Rd} = \frac{\chi A f_y}{\gamma*{M1}} ]
Where:
- (\chi) = reduction factor for flexural buckling (function of slenderness (\bar{\lambda}) and buckling curve)
- (A) = gross cross-sectional area (Class 1-3), effective area Aeff (Class 4)
- (f_y) = yield strength
- (\gamma_{M1} = 1.00) (UK NA)
Non-dimensional slenderness:
[ \bar{\lambda} = \sqrt{\frac{A fy}{N{cr}}} = \frac{L_{cr}}{i} \frac{1}{\lambda_1} ]
Where:
- (N*{cr} = \pi^2 E I / L*{cr}^2) — elastic critical buckling load
- (\lambda_1 = \pi \sqrt{E / f_y} = 93.9 \varepsilon)
- (\varepsilon = \sqrt{235 / f_y})
Buckling Curves for UK UC Sections (EN 1993-1-1 Table 6.2)
| Buckling Curve | Imperfection α | UC Sections — Major Axis (y-y) | UC Sections — Minor Axis (z-z) |
|---|---|---|---|
| a0 | 0.13 | — | — |
| a | 0.21 | Hot-finished HSS | Hot-finished HSS |
| b | 0.34 | UC: h/b ≤ 1.2, tf ≤ 100mm | — |
| c | 0.49 | UC: h/b > 1.2 | UC: h/b ≤ 1.2, tf ≤ 100mm |
| d | 0.76 | tf > 100mm | tf > 100mm |
For standard UK UC sections (203×203 UC, 254×254 UC):
- h/b ≈ 1.0-1.05 → curve 'b' for y-y, curve 'c' for z-z
- These curves directly affect the χ factor and hence column capacity
Buckling Reduction Factor χ
[ \chi = \frac{1}{\Phi + \sqrt{\Phi^2 - \bar{\lambda}^2}} \leq 1.0 ]
Where (\Phi = 0.5 [1 + \alpha (\bar{\lambda} - 0.2) + \bar{\lambda}^2])
Column Buckling Capacity Table — 203×203 UC 46 in S355
| Effective Length Lcr (m) | λ¯ (z-z) | χz | Nb,Rd,z (kN) | λ¯ (y-y) | χy | Nb,Rd,y (kN) |
|---|---|---|---|---|---|---|
| 2.0 | 0.47 | 0.91 | 1765 | 0.80 | 0.73 | 1416 |
| 3.0 | 0.70 | 0.83 | 1610 | 1.19 | 0.52 | 1009 |
| 4.0 | 0.94 | 0.66 | 1280 | 1.59 | 0.34 | 660 |
| 5.0 | 1.17 | 0.49 | 950 | 1.99 | 0.23 | 446 |
| 6.0 | 1.41 | 0.36 | 698 | 2.39 | 0.17 | 330 |
Section properties: A = 58.8 cm², iz = 5.13 cm, iy = 8.73 cm, fy = 355 N/mm², curve b (y-y), curve c (z-z)
Column Buckling Capacity Table — 254×254 UC 73 in S355
| Effective Length Lcr (m) | Nb,Rd,z (kN) | Nb,Rd,y (kN) | Critical Axis |
|---|---|---|---|
| 2.0 | 2472 | 1973 | y-y |
| 3.0 | 2177 | 1570 | y-y |
| 4.0 | 1760 | 1175 | y-y |
| 5.0 | 1335 | 871 | y-y |
Section properties: A = 92.9 cm², iz = 6.54 cm, iy = 11.1 cm, fy = 355 N/mm²
Cross-Section Classification for Columns
For columns under axial compression, stricter web limits apply (EN 1993-1-1 Table 5.2):
| Class | Web slenderness limit (S355, ε = 0.81) | Meaning |
|---|---|---|
| 1 | c/t ≤ 33ε = 26.8 | Full plastic resistance |
| 2 | c/t ≤ 38ε = 30.8 | Plastic but limited rotation |
| 3 | c/t ≤ 42ε = 34.1 | Elastic resistance only |
Most UC sections (web c/t ≈ 17-25 for 203 UC, 15-22 for 254 UC) are Class 1 or Class 2 in pure compression.
Worked Example — 203×203 UC 46, S355, 4.0m Effective Length
Given:
- Section: 203×203 UC 46, fy = 355 N/mm²
- A = 58.8 cm² = 5880 mm²
- Lcr = 4.0 m (pinned-pinned about both axes)
- NEd = 800 kN (compression)
Section classification:
- Web: c/t = 19.7, limit for Class 1 = 33ε = 26.8 → Class 1
- Flange: c/t = 7.1, limit for Class 1 = 9ε = 7.3 → Class 1
Minor axis (z-z) buckling:
- iz = 5.13 cm, Lcr = 4000 mm
- λ¯z = (4000/51.3) / (93.9 × 0.81) = 1.02
- Curve 'c': α = 0.49
- Φ = 0.5[1 + 0.49(1.02 - 0.2) + 1.02²] = 1.22
- χz = 1/[1.22 + √(1.22² - 1.02²)] = 0.52
Buckling resistance: Nb,Rd,z = 0.52 × 5880 × 355 / 1.0 × 10⁻³ = 1085 kN UT = 800/1085 = 0.74 — Satisfactory
Major axis (y-y) buckling:
- iy = 8.73 cm
- λ¯y = (4000/87.3) / (93.9 × 0.81) = 0.60
- Curve 'b': α = 0.34
- Φ = 0.5[1 + 0.34(0.60 - 0.20) + 0.60²] = 0.75
- χy = 1/[0.75 + √(0.75² - 0.60²)] = 0.88
Nb,Rd,y = 0.88 × 5880 × 355 / 1.0 × 10⁻³ = 1837 kN
Minor axis buckling governs (z-z): Nb,Rd = 1085 kN > 800 kN — OK
Buckling Length Recommendations for UK Practice
| Condition | Major Axis (y-y) | Minor Axis (z-z) |
|---|---|---|
| Pinned both ends | 1.0 L | 1.0 L |
| Fixed both ends | 0.7 L | 0.7 L |
| Fixed-pinned | 0.85 L | 0.85 L |
| Portal frame (unbraced) | 1.0-2.0 L | 1.0 L |
| Braced frame (beam-to-column) | 0.85 L | 1.0 L |
Flexural Buckling vs Other Modes
Check all three buckling modes:
- Flexural buckling (Clause 6.3.1) — the primary check, covered above
- Torsional buckling (Clause 6.3.1(4)) — short columns with low torsional stiffness
- Flexural-torsional buckling (Clause 6.3.1(4)) — asymmetric sections (angles, channels, tees)
For typical UC sections, torsional and flexural-torsional buckling are not critical. For asymmetric sections, EN 1993-1-1 Clause 6.3.1.4 provides specific rules.
Design Resources
- UK Beam Design — Companion beam design guide
- UK Steel Properties — S275/S355 material data
- UK Base Plate — Column base plate design
- UK Connection Design — Column splices and connections
- UK Steel Beam Sizes — Full section table
- UK UB/UC Sections — Section property data
- All UK References
Frequently Asked Questions
How is column buckling checked per EN 1993 with UK NA?
Column buckling resistance Nb,Rd = χ A fy / γM1 per EN 1993-1-1 Clause 6.3.1. UK NA specifies γM1 = 1.00 and uses buckling curves a0, a, b, c, d based on section type and axis. The reduction factor χ depends on non-dimensional slenderness λ¯ and the imperfection factor α associated with each buckling curve. For λ¯ < 0.2, χ = 1.0 (no buckling reduction).
What buckling curves apply to UK UC sections?
For UK UC sections (h/b ≤ 1.2, tf ≤ 100mm): buckling curve 'b' for major axis (y-y), curve 'c' for minor axis (z-z). For stronger axes: curve 'a' for hot-finished HSS. The more onerous curve 'c' for the minor axis is significant because most UC columns are controlled by minor axis buckling. Imperfection factors: α = 0.34 for curve 'b', α = 0.49 for curve 'c'.
When does column section classification govern design?
Class 4 sections (slender) require effective area Aeff for buckling calculations, which reduces capacity. Most hot-rolled UK UC sections in S275/S355 are Class 1 or Class 2 for axial compression. However, sections with very thin flanges (e.g., specialist lightweight sections) or higher steel grades (S460+) may become Class 3 or 4. EN 1993-1-5 gives effective width rules for Class 4 sections.
How does moment interaction affect column design?
Columns with coexistent bending and axial force require interaction checks per EN 1993-1-1 Clause 6.3.3. The combined check uses: [ \frac{N*{Ed}}{N*{Rk}/\gamma*{M1}} + k*{yy} \frac{M*{y,Ed}}{M*{y,Rk}/\gamma*{M1}} + k*{yz} \frac{M*{z,Ed}}{M*{z,Rk}/\gamma_{M1}} \leq 1.0 ] Interaction factors kyy and kyz depend on section type, buckling curve, and the shape of the moment diagram (Method 2 from Annex B is commonly used in UK practice).
What effective lengths are used for column buckling in UK frames?
For braced frames, effective length is typically 0.85-1.0L for major axis (depending on end restraint from beams) and 1.0L for minor axis (often unbraced between floor levels). For unbraced (sway) frames, effective lengths can be 1.2-2.0L. The UK NA does not modify the effective length rules, but SCI publication P364 provides comprehensive guidance for frame stability design.
Reference only. Verify all values against the current edition of EN 1993-1-1:2005 Clause 6.3.1 and UK NA. This information does not constitute professional engineering advice.