Design Problem

Problem: Verify a 254 x 254 UC 73 in S355 steel acting as an internal column in a multi-storey braced frame. The column is simply connected (pinned base, pinned top). Storey height = 5.0 m. The column forms part of a sway-frame where sway effects are resisted by a concrete core (braced in both directions per EN 1993-1-1 Clause 5.2.1).

Loading:

Design parameters per UK NA:

Section Properties — 254 x 254 UC 73

From SCI P363 (Blue Book):

Property Symbol Value Units
Depth of section h 254.1 mm
Flange width b 254.6 mm
Web thickness tw 8.6 mm
Flange thickness tf 14.2 mm
Root radius r 12.7 mm
Area A 93.1 cm2
Iy Iy 11,400 cm4
Iz Iz 3,910 cm4
iy iy 11.1 cm
iz iz 6.48 cm
h/b ratio h/b 1.00 —

Step 1: Cross-Section Classification — Clause 5.5

Flange classification (outstand in compression):

c = (b - tw - 2r) / 2 = (254.6 - 8.6 - 25.4) / 2 = 110.3 mm c / tf = 110.3 / 14.2 = 7.77 epsilon = sqrt(235 / 355) = 0.814

Class 1 limit for flange in compression: 9·epsilon = 9 x 0.814 = 7.32 Class 2 limit: 10·epsilon = 10 x 0.814 = 8.14

7.77 > 7.32 but 7.77 < 8.14 => Flange is Class 2

Web classification (pure compression):

c = d = h - 2tf - 2r = 254.1 - 28.4 - 25.4 = 200.3 mm (approximately) c / tw = 200.3 / 8.6 = 23.3

Class 1 limit for web in compression: 33·epsilon = 33 x 0.814 = 26.9 23.3 < 26.9 => Web is Class 1

Overall classification: Class 2 (governed by flange).

Step 2: Cross-Section Compression Resistance — Clause 6.2.4

For Class 2 section, use the plastic resistance with no local buckling reduction:

Nc,Rd = A x fy / gamma_M0 = 9,310 x 355 / 1.00 = 3,305 kN

Gross utilisation (ignoring buckling): NEd / Nc,Rd = 1,755 / 3,305 = 0.531

Step 3: Flexural Buckling Resistance — Clause 6.3.1

Effective length (pinned-pinned):

Lcr,y = k_y x L = 1.0 x 5,000 = 5,000 mm (buckling about y-y axis) Lcr,z = k_z x L = 1.0 x 5,000 = 5,000 mm (buckling about z-z axis, weaker)

Non-dimensional slenderness:

lambda_y = Lcr,y / iy = 5,000 / 111 = 45.0 lambda_1 = 93.9·epsilon = 93.9 x 0.814 = 76.4 lambda_bar_y = lambda_y / lambda_1 = 45.0 / 76.4 = 0.589

lambda_z = Lcr,z / iz = 5,000 / 64.8 = 77.2 lambda_bar_z = lambda_z / lambda_1 = 77.2 / 76.4 = 1.010 (governing)

The z-z axis governs — buckling is about the weaker axis.

Step 4: Buckling Curve Selection — UK NA Table 6.2

Buckling about y-y axis:

h/b = 254.1 / 254.6 = 1.00 <= 1.2, tf = 14.2 mm <= 100 mm => Buckling curve b (UK NA Table 6.2) alpha_y = 0.34 (imperfection factor for curve b)

Buckling about z-z axis:

h/b = 1.00 <= 1.2, tf = 14.2 <= 100 mm => Buckling curve c (UK NA Table 6.2 — minor axis) alpha_z = 0.49 (imperfection factor for curve c)

Step 5: Reduction Factor chi — Clause 6.3.1.2

Buckling about y-y axis (curve b):

Phi_y = 0.5 x [1 + alpha_y x (lambda_bar_y - 0.2) + lambda_bar_y2] Phi_y = 0.5 x [1 + 0.34 x (0.589 - 0.2) + 0.5892] = 0.5 x [1 + 0.132 + 0.347] = 0.740

chi_y = 1 / (Phi_y + sqrt(Phi_y2 - lambda_bar_y2)) chi_y = 1 / (0.740 + sqrt(0.7402 - 0.5892)) = 1 / (0.740 + 0.448) = 0.842

Buckling about z-z axis (curve c) — governing:

Phi_z = 0.5 x [1 + alpha_z x (lambda_bar_z - 0.2) + lambda_bar_z2] Phi_z = 0.5 x [1 + 0.49 x (1.010 - 0.2) + 1.0102] = 0.5 x [1 + 0.397 + 1.020] = 1.209

chi_z = 1 / (Phi_z + sqrt(Phi_z2 - lambda_bar_z2)) chi_z = 1 / (1.209 + sqrt(1.2092 - 1.0102)) = 1 / (1.209 + 0.663) = 0.534

Step 6: Buckling Resistance

Governing buckling resistance (z-z axis):

Nb,Rd = chi_z x A x fy / gamma_M1 Nb,Rd = 0.534 x 9,310 x 355 / 1.00 = 1,765 kN

Utilisation:

NEd / Nb,Rd = 1,755 / 1,765 = 0.994 (99.4 %)

The 254 x 254 UC 73 is very tightly utilised. In practice, a designer would likely select the next size up (254 x 254 UC 89) to provide a margin of safety, or verify that the effective length assumptions are conservative.

Step 7: Alternative — 254 x 254 UC 89

Let us verify the next UC section for comparison:

Property UC 73 UC 89
Area 93.1 cm2 113 cm2
iz 6.48 cm 6.55 cm
lambda_bar_z 1.010 0.998
chi_z (curve c) 0.534 0.545
Nb,Rd 1,765 kN 2,187 kN
Utilisation 99.4 % 80.2 %

The UC 89 provides a much more comfortable 80 % utilisation with minimal weight penalty (89 versus 73 kg/m).

UK Buckling Curve Selection Rules — Summary

Per UK NA to BS EN 1993-1-1, Table 6.2:

Section type Limits Buckling about y-y Buckling about z-z
UC (h/b <= 1.2, tf <= 100 mm) S235-S460 b c
UB (h/b > 1.2, tf <= 100 mm) S235-S355 b c
UB (h/b > 1.2, tf <= 100 mm) S420-S460 a b
RHS hot-finished All a a
CHS hot-finished All a a
Welded box sections tf <= 40 mm c c

Key UK NA differences from EN 1993-1-1 recommended values:

Frequently Asked Questions

Why does the UK NA use curve c for minor-axis UC buckling?

Extensive UK research (SCI Report RT953 and University of Sheffield full-scale testing) demonstrated that residual stress patterns in domestically produced UC sections reduce the minor-axis buckling capacity compared to the EN 1993-1-1 default curve b. The UK NA conservatively adopts curve c to reflect UK production practices. For UK-designed buildings, curve c must be used unless project-specific testing justifies otherwise.

How does effective length factor k differ between braced and unbraced frames?

For braced frames (Clause 5.2.1), k <= 1.0 for columns that do not contribute to sway stability. Pinned-pinned columns use k = 1.0; fixed-fixed columns use k = 0.5 (theoretical) or 0.7 (practical, allowing for imperfect fixity by a factor of 1.4). For sway frames (Clause 5.2.2), k > 1.0 is typical — the SCI P362 stability guidance provides charts. The UK NA recommends using second-order analysis for k > 1.5 to avoid conservatism in the effective length method.

What is the minimum UC size for a given UK storey height?

For pinned-pinned UC columns in typical multi-storey braced frames: 152UC for heights to 3.0 m, 203UC for 3-4 m, 254UC for 4-6 m, 305UC for 6-8 m. These are approximate and depend on loading. Deep columns (356UC) are used when high axial loads exceed 2,500 kN or when 152/203UC slenderness exceeds limits. UK practice favours UC sections over fabricated box or compound sections wherever possible.

When does torsional or torsional-flexural buckling govern?

For doubly-symmetric hot-rolled UC and UB sections, flexural buckling (Clause 6.3.1) almost always governs. Torsional or torsional-flexural buckling (Clause 6.3.1.4) governs only for: (1) open sections such as angles, tees, and channels; (2) cruciform sections; (3) sections where the shear centre and centroid do not coincide. For UK UC sections, buckling is always flexural about the minor axis.

Related Pages

Educational reference only. All design values are per BS EN 1993-1-1:2005 + UK National Annex and BS EN 10025-2:2019. Verify all values against the current editions of the standards and the applicable UK National Annex for your project jurisdiction. Designs must be independently verified by a Chartered Structural Engineer registered with the Institution of Structural Engineers (IStructE) or the Institution of Civil Engineers (ICE). Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent professional verification.