EN 1993-1-1 Column Buckling Capacity — Verification Benchmark

Complete hand calculation of a UC 152x152x30 column buckling capacity against the Steel Calculator WASM engine, matched to EN 1993-1-1:2005 Clause 6.3.1.

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Chartered Engineer (CEng) or Professional Engineer (PE/SE) before use in any project.

Problem Statement

Member: UC 152x152x30, steel grade S275 (fy = 275 MPa, fu = 430 MPa) Length: L = 4.0 m, pinned-pinned about both axes (effective length factor k = 1.0) Objective: Determine the design buckling resistance Nb,Rd about the weak (z-z) axis per EN 1993-1-1

Section Properties — UC 152x152x30

Hand Calculation — EN 1993-1-1, Clause 6.3.1

Step 1: Material Parameters

Per EN 1993-1-1 Clause 3.2.6:

epsilon = sqrt(235 / fy) = sqrt(235 / 275) = sqrt(0.8545) = 0.9244

lambda_1 = 93.9 * epsilon = 93.9 * 0.9244 = 86.80

Step 2: Effective Length and Slenderness

Lcr = k * L = 1.0 * 4.0 m = 4,000 mm

lambda_bar = (Lcr / iz) / lambda_1
           = (4,000 / 38.3) / 86.80
           = 104.44 / 86.80
           = 1.203

Step 3: Buckling Curve Selection — EN 1993-1-1 Table 6.2

For hot-rolled H-section UC 152x152x30:

• h/b = 1.03 <= 1.2
• tf = 9.4 mm <= 100 mm
• Buckling about z-z axis (minor axis)

Per Table 6.2: Buckling curve c, imperfection factor alpha = 0.49.

Step 4: Reduction Factor chi — EN 1993-1-1 Clause 6.3.1.2

Phi = 0.5 * [1 + alpha * (lambda_bar - 0.2) + lambda_bar^2]
    = 0.5 * [1 + 0.49 * (1.203 - 0.2) + (1.203)^2]
    = 0.5 * [1 + 0.49 * 1.003 + 1.447]
    = 0.5 * [1 + 0.4915 + 1.4472]
    = 0.5 * 2.9387
    = 1.4694

chi = 1 / (Phi + sqrt(Phi^2 - lambda_bar^2))
    = 1 / (1.4694 + sqrt(1.4694^2 - 1.203^2))
    = 1 / (1.4694 + sqrt(2.1591 - 1.4472))
    = 1 / (1.4694 + sqrt(0.7119))
    = 1 / (1.4694 + 0.8437)
    = 1 / 2.3131
    = 0.4323

Check: chi <= 1.0 ✓. The reduction accounts for the member imperfection and residual stress captured by the Ayrton-Perry formulation underlying the European buckling curves.

Step 5: Design Buckling Resistance

Per EN 1993-1-1 Clause 6.3.1.1(3):

Nb,Rd = chi * A * fy / gamma_M1
      = 0.4323 * 3,830 * 275 / 1.00
      = 0.4323 * 1,053,250
      = 455,400 N
      = 455.4 kN

Step 6: Cross-Section Check — Clause 6.3.1.1(1)

Per Clause 6.3.1.1(1), the design buckling resistance of a compression member:

N_Ed / Nb,Rd <= 1.0

For an applied axial load N_Ed = 300 kN:
Utilization = 300 / 455.4 = 0.659  →  PASS at 65.9%

WASM Output Comparison

The Steel Calculator WASM engine (EN 1993 region), run with identical inputs:

All 10 quantities match within 0.00%. The EN 1993 buckling calculation is exact — there are no rounding-sensitive intermediate values in this example.

Sensitivity Check — What If the Axial Load Exceeds Capacity?

The WASM engine correctly identifies overloaded members. For N_Ed = 500 kN:

Code References — EN 1993-1-1:2005

How to Reproduce

1. Navigate to the Steel Calculator Column Capacity tool
2. Select EN 1993-1-1 as the design code
3. Enter: UC 152x152x30, S275, L=4.0m, k=1.0 for weak axis
4. Enter axial load N_Ed = 300 kN
5. Click Calculate — the WASM engine produces the output shown above

The WASM engine also handles the full Eurocode capacity check including cross-section classification to EN 1993-1-1 Clause 5.5, not just buckling alone.

Why Verification Matters

Structural engineering software must produce correct results. Every calculation engine powering Steel Calculator is verified against published textbook examples, SCI (Steel Construction Institute) design guides for Eurocode 3, and independent hand calculations. These verification pages are public, reproducible evidence of accuracy for all supported design codes.

See also: AISC Beam Verification, AS 4100 Bolt Verification, CSA Weld Verification, AISC Base Plate Verification.

Last verified: 2026-05-08. WASM version: core-wasm-v2 stage-4-member-design. Tolerance standard: all quantities within 1.0% of hand calculation or textbook published value. EN 1993 gamma_M values per UK National Annex.

Disclaimer: This content is for educational purposes only. Results must be verified by a licensed professional engineer. Steel Calculator provides preliminary design tools — NOT a substitute for professional engineering judgment.