----------- | -------------- | ------------------------------------- | ------------------------------ | | a0 | 0.13 | — | — | | a | 0.21 | Hot-finished HSS | Hot-finished HSS | | a | 0.21 | UC: h/b ≤ 1.2, tf ≤ 100mm (S235-S420) | — | | b | 0.34 | UC: h/b > 1.2 (S235-S420) | UC: h/b ≤ 1.2, tf ≤ 100mm | | c | 0.49 | tf > 100mm or S460+ | UC: h/b > 1.2 | | d | 0.76 | — | tf > 100mm or S460+ |

For standard UK UC sections (203×203 UC, 254×254 UC) in S275 or S355:

• h/b ≈ 1.0-1.05 → curve 'a' for y-y (α = 0.21), curve 'c' for z-z (α = 0.49 per UK NA NA.2.16)
• 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

Section properties: A = 58.8 cm², iz = 5.13 cm, iy = 8.73 cm, fy = 355 N/mm², curve a (y-y), curve c (z-z)

Column Buckling Capacity Table — 254×254 UC 73 in S355

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 (BS EN 1993-1-1 Table 5.2):

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 'a': α = 0.21
• Φ = 0.5[1 + 0.21(0.60 - 0.20) + 0.60²] = 0.72
• χy = 1/[0.72 + √(0.72² - 0.60²)] = 0.89

Nb,Rd,y = 0.89 × 5880 × 355 / 1.0 × 10⁻³ = 1858 kN

Minor axis buckling governs (z-z): Nb,Rd = 1085 kN > 800 kN — OK

Worked Example 2 — 254x254 UC 73, S275, 5.0m Effective Length

A second worked example demonstrating S275 grade steel for a typical multi-storey column. S275 is the most common structural steel grade for UK building columns, offering a good balance of strength and economy.

Given:

• Section: 254x254 UC 73, S275JR to EN 10025-2
• A = 92.9 cm^2 = 9,290 mm^2
• fy = 275 N/mm^2 (tf <= 16 mm), fu = 410 N/mm^2
• E = 210,000 N/mm^2
• Effective lengths: L_cr,y = 5.0 m, L_cr,z = 5.0 m (pinned-pinned, braced frame)
• N_Ed = 1,200 kN (total factored axial compression from all floors above)
• gamma_M0 = 1.00, gamma_M1 = 1.00 (UK NA)

Section properties (254x254 UC 73):

Step 1 — Section Classification (Clause 5.5):

epsilon = sqrt(235/fy) = sqrt(235/275) = sqrt(0.855) = 0.924

Web in pure compression: cw = 254.1 - 28.4 - 25.4 = 200.3 mm cw/tw = 200.3 / 8.6 = 23.3 Class 1 limit: 33epsilon = 330.924 = 30.5 — 23.3 < 30.5: Class 1 web.

Flange outstand in compression: c = (254.6 - 8.6 - 25.4) / 2 = 110.3 mm c/tf = 110.3 / 14.2 = 7.77 Class 1 limit: 9epsilon = 90.924 = 8.32 — 7.77 < 8.32: Class 1 flange.

Section is Class 1 in pure compression. Full gross area may be used for buckling resistance.

Step 2 — Non-Dimensional Slenderness:

Reference slenderness: lambda*1 = 93.9 * epsilon = 93.9 _ 0.924 = 86.8

Minor axis (z-z): lambda_bar_z = (5000/65.4) / 86.8 = 76.45 / 86.8 = 0.881 Major axis (y-y): lambda_bar_y = (5000/111) / 86.8 = 45.05 / 86.8 = 0.519

Step 3 — Buckling Curve Selection:

h/b = 254.1/254.6 = 0.998 <= 1.2, tf = 14.2 mm <= 100 mm, S275 (S235-S420 range):

• Major axis (y-y): curve 'a', alpha = 0.21
• Minor axis (z-z): curve 'c', alpha = 0.49 (UK NA NA.2.16)

Step 4 — Reduction Factor chi (z-z, curve c, alpha = 0.49):

Phiz = 0.5 * [1 + 0.49_(0.881 - 0.2) + 0.881^2] = 0.5 * [1 + 0.490.681 + 0.776] = 0.5 _ [1 + 0.334 + 0.776] = 0.5 _ 2.110 = 1.055

chi_z = 1 / (1.055 + sqrt(1.055^2 - 0.881^2)) = 1 / (1.055 + sqrt(1.113 - 0.776)) = 1 / (1.055 + sqrt(0.337)) = 1 / (1.055 + 0.581) = 1 / 1.636 = 0.611

Step 5 — Buckling Resistance (z-z governs):

N*b,Rd,z = 0.611 * 9,290 _ 275 / 1.00 = 0.611 * 2,554,750 = 1,561,000 N = 1,561 kN

Utilisation: N_Ed / N_b,Rd = 1,200 / 1,561 = 0.769 — Satisfactory.

Step 6 — Check Major Axis (y-y, curve a, alpha = 0.21):

Phiy = 0.5 * [1 + 0.21_(0.519 - 0.2) + 0.519^2] = 0.5 * [1 + 0.210.319 + 0.269] = 0.5 _ [1 + 0.067 + 0.269] = 0.5 _ 1.336 = 0.668

chi_y = 1 / (0.668 + sqrt(0.668^2 - 0.519^2)) = 1 / (0.668 + sqrt(0.446 - 0.269)) = 1 / (0.668 + sqrt(0.177)) = 1 / (0.668 + 0.421) = 1 / 1.089 = 0.918

N*b,Rd,y = 0.918 * 9,290 _ 275 / 1.00 = 2,345 kN

Minor axis buckling governs (z-z): N_b,Rd = 1,561 kN > 1,200 kN — OK at 77% utilisation.

Step 7 — Comparison S275 vs S355:

For the same section in S355 (fy = 355 MPa, lambda_1 = 76.4, lambda_bar_z = 1.00, chi_z = 0.52 per Worked Example 1):

The 12.7% increase in buckling resistance from S275 to S355 is less than the 29% increase in yield strength because the higher lambda_bar in S355 reduces chi_z. This is a key insight: higher grade steel provides proportionally less benefit for buckling-governed columns than for strength-governed members. For a column where lambda_bar > 0.5, the buckling reduction factor is in the descending portion of the buckling curve, and the gain from higher fy is partially offset by the lower chi.

Step 8 — Practical UK Column S275 Selection Guidance:

The 254x254 UC 73 in S275 is a common UK column section for multi-storey buildings with 6-8 storeys and typical bay sizes of 6-8 m. At 5.0 m effective length (corresponding to a 4.0-4.5 m actual floor-to-floor height with pinned ends), it can carry approximately 1,560 kN in pure compression. In practice, the column also carries bending moments from beam end reactions (nominally pinned but with some moment due to connection eccentricity) and must be checked for the combined axial + bending interaction per BS EN 1993-1-1 Clause 6.3.3.

For a quick sizing rule: a 254x254 UC 73 in S275 at L_cr = 5.0 m can support approximately 125 mm^2 of tributary floor area per kN of axial load. For a typical office ULS load of 12 kN/m^2 (1.35 x 5.5 dead + 1.5 x 2.5 live), each storey adds approximately 12 x tributary_area kN of column load. A 254x254 UC 73 can therefore support approximately 130 m^2 of floor area per storey x 6 storeys = 780 m^2 total with a design load of ~1,560 kN.

Buckling Length Recommendations for UK Practice

Flexural Buckling vs Other Modes

Check all three buckling modes:

1. Flexural buckling (Clause 6.3.1) — the primary check, covered above
2. Torsional buckling (Clause 6.3.1(4)) — short columns with low torsional stiffness
3. 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, BS 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

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Frequently Asked Questions

How is column buckling checked per EN 1993 with UK NA?

Column buckling resistance Nb,Rd = χ A fy / γM1 per BS 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) in S235-S420: buckling curve 'a' for major axis (y-y, α = 0.21), curve 'c' for minor axis (z-z, α = 0.49 per UK NA NA.2.16). For hot-finished HSS: curve 'a' for both axes. The more onerous curve 'c' for the minor axis is significant because most UC columns are controlled by minor axis buckling. Imperfection factors: α = 0.21 for curve 'a', 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. BS 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 BS 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 BS EN 1993-1-1:2005 Clause 6.3.1 and UK NA. This information does not constitute professional engineering advice.