UK Column Design Example — EN 1993-1-1 Worked Example

This worked example demonstrates column design to EN 1993-1-1:2005 with UK NA. A 254×254 UC 89 column supports a 3.5 m storey in a braced steel frame with pinned base and continuous at first floor level.

Design Data

Section Properties — 254×254 UC 89

Section Classification (EN 1993-1-1 Table 5.2)

For S355: ε = √(235/355) = 0.81

Flange in compression (Class 1 limit = 9ε): c/t_f = (256.3/2 - 10.5/2 - 10.2) / 17.3 = 6.9 ≤ 9 × 0.81 = 7.3 → Class 1

Web in compression (Class 1 limit = 33ε): c/t_w = (260.3 - 2×17.3 - 2×10.2) / 10.5 = 19.6 ≤ 33 × 0.81 = 26.8 → Class 1

Entire section is Class 1 under uniform compression.

Section Compression Capacity (EN 1993-1-1 Clause 6.2.4)

[ N*{\text{c,Rd}} = \frac{A f_y}{\gamma*{M0}} = \frac{11400 \times 345}{1.00} \times 10^{-3} = 3933 \text{ kN} ]

Note: fy = 345 MPa because flange thickness 17.3 mm falls in the 16 < t ≤ 40 mm bracket.

N_Ed / N_c,Rd = 1200 / 3933 = 0.31 → Satisfactory

Buckling Resistance — y-y Axis (EN 1993-1-1 Clause 6.3.1)

Non-dimensional slenderness: [ \bar{\lambda}y = \frac{L{\text{cr}}}{i_y \lambda_1} \quad \text{where} \quad \lambda_1 = 93.9\varepsilon = 93.9 \times 0.81 = 76.1 ] [ \bar{\lambda}_y = \frac{3500}{112 \times 76.1} = 0.41 ]

For rolled UC section (h/b = 260.3/256.3 = 1.02 ≤ 1.2, t_f ≤ 100 mm): Buckling curve: b for y-y axis (α = 0.34)

[ \phiy = 0.5[1 + 0.34(0.41 - 0.2) + 0.41^2] = 0.62 ] [ \chi_y = \frac{1}{0.62 + \sqrt{0.62^2 - 0.41^2}} = 0.93 ] [ N{\text{b,y,Rd}} = 0.93 \times 3933 = 3658 \text{ kN} ]

Buckling Resistance — z-z Axis (EN 1993-1-1 Clause 6.3.1)

[ \bar{\lambda}_z = \frac{3500}{65.4 \times 76.1} = 0.70 ]

Buckling curve: c for z-z axis (α = 0.49)

[ \phiz = 0.5[1 + 0.49(0.70 - 0.2) + 0.70^2] = 0.87 ] [ \chi_z = \frac{1}{0.87 + \sqrt{0.87^2 - 0.70^2}} = 0.79 ] [ N{\text{b,z,Rd}} = 0.79 \times 3933 = 3107 \text{ kN} ]

Unity Check

The z-z axis governs (lower buckling resistance): [ \frac{N*{\text{Ed}}}{N*{\text{b,Rd}}} = \frac{1200}{3107} = 0.39 \leq 1.0 \quad \text{→ Satisfactory} ]

The 254×254 UC 89 in S355 is adequate at 39% utilisation. A smaller section (254×254 UC 73) would likely suffice.

Alternative Section Sizing

The UC 73 works at 48% utilisation, offering 18% weight saving but the UC 89 provides additional robustness margin.

Design Resources

• UK Column Design — Design methodology
• UK Column Buckling — Buckling curves
• UK Column K-Factor — Effective length
• UK Combined Loading — Axial + bending
• All UK References

Frequently Asked Questions

What are the steps for column design per EN 1993-1-1 with UK NA?

Column design proceeds in seven steps: (1) determine design loads N_Ed, (2) select trial section, (3) classify section per Table 5.2, (4) calculate section compression capacity N_c,Rd, (5) determine effective length and non-dimensional slenderness, (6) select buckling curve per Table 6.2, (7) check buckling resistance N_b,Rd for both axes. The weakest axis (typically z-z for UC sections) governs.

How is effective length determined for UK steel columns?

Effective length L_cr = K × L_system where K depends on end restraint. Per EN 1993-1-1 Annex E: K = 0.5 for fixed-fixed, 0.7 for fixed-pinned, 1.0 for pinned-pinned, 2.0 for cantilever. In UK braced frames, columns are typically modelled as pinned-pinned (K=1.0) for the strong direction and continuous (K=0.85-1.0) for the weak direction when rotationally restrained at floor levels.

What buckling curve should be used for UK UC sections?

For rolled UC sections (h/b ≤ 1.2, t_f ≤ 100 mm): buckling curve b (α = 0.34) for y-y axis, curve c (α = 0.49) for z-z axis. The z-z axis almost always governs for UC sections due to the lower radius of gyration and higher imperfection factor. For welded box sections, curve c applies for both axes.

How does yield strength reduction with thickness affect column capacity?

For the 254×254 UC 89 with t_f = 17.3 mm, the 16 < t ≤ 40 bracket applies, reducing fy from 355 to 345 MPa (3% reduction). Only the lightest UC sections (t_f ≤ 16 mm) can use the full 355 MPa. This reduction must be applied per EN 1993-1-1 Table 3.1 for all member design.

Column Buckling Theory

Euler Buckling

The Euler buckling load represents the theoretical critical load for an ideal elastic column:

Pcr = π²EI / (KL)²

Where:

• E = modulus of elasticity (200 GPa for steel)
• I = moment of inertia about the buckling axis
• K = effective length factor
• L = unbraced length

Real Column Behavior

Real columns deviate from Euler theory due to:

• Initial out-of-straightness (typically L/1000)
• Residual stresses from manufacturing (hot-rolling or welding)
• Eccentricity of applied load
• Inelastic material behavior

These effects are accounted for through column strength curves that reduce the theoretical Euler capacity based on slenderness ratio (KL/r) and section type.

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Frequently Asked Questions

What is the recommended design procedure for this structural element?

The standard design procedure follows: (1) establish design criteria including applicable code, material grade, and loading; (2) determine loads and applicable load combinations; (3) analyze the structure for internal forces; (4) check member strength for all applicable limit states; (5) verify serviceability requirements; and (6) detail connections. Computer analysis is recommended for complex structures, but hand calculations should be used for verification of critical elements.

How do different design codes compare for this calculation?

AISC 360 (US), EN 1993 (Eurocode), AS 4100 (Australia), and CSA S16 (Canada) follow similar limit states design philosophy but differ in specific resistance factors, slenderness limits, and partial safety factors. Generally, EN 1993 uses partial factors on both load and resistance sides (γM0 = 1.0, γM1 = 1.0, γM2 = 1.25), while AISC 360 uses a single resistance factor (φ). Engineers should verify which code is adopted in their jurisdiction.

Reference only. Verify all values against the current edition of EN 1993-1-1:2005, UK National Annex, and BS EN 1090-2. This information does not constitute professional engineering advice.