Eurocode 3 (EN 1993-1-1)

The EC3 engine implements EN 1993-1-1:2005/A1:2014 - Design of Steel Structures, Part 1-1: General Rules and Rules for Buildings. It supports the default Recommended Values and the UK National Annex for partial factor overrides.

Open Eurocode 3 Calculator

Standard Reference

Supported Section Types

• I-Shapes (UKB, UKC, IPE, HEB, HEA - rolled and welded including plate girders)
• Channels (PFC - parallel flange channels)
• Tees (cut from UKB/UKC parents - beam tees and column tees)
• Rectangular Hollow Sections (SHS and RHS - hot-finished and cold-formed)
• Circular Hollow Sections (CHS)
• Angles (equal and unequal leg)

Checks Performed

Section Classification (Table 5.2)

Elements are classified as Class 1 (plastic), Class 2 (compact), Class 3 (semi-compact), or Class 4 (slender). Classification is action-specific: web limits depend on the applied axial force. The engine evaluates flanges and webs independently and takes the worst class.

Class 4 Effective Widths (EN 1993-1-5)

For Class 4 sections, effective widths are computed per EN 1993-1-5 using the Winter formula. Effective area (A_eff), effective section moduli (W_eff,y, W_eff,z), and centroid shifts (e_N,y, e_N,z) are computed for I-shapes, channels, RHS, and Tees (axial compression). The centroid shift generates additional moments (ΔM = N × e_N) in the 6.2.9 interaction check.

Tees are a special case: the standalone N_c,Rd path classifies the stem under uniform compression (k_σ = 0.43 outstand) and applies stem-outstand effective-width reduction independently of the load-state classifier. The load-state classifier (used for combined N+M) correctly returns Class 1 when the plastic NA sits in the flange and the stem is in tension, so tee bending W_pl is preserved in those cases. Angles and CHS still fall back to elastic section modulus (no Class 4 effective widths).

Tension (6.2.3)

• N_t,Rd: Gross section yielding (A × f_y / γ_M0)
• N_u,Rd: Net section rupture (0.9 × A_net × f_u / γ_M2)

Compression (6.2.4 & 6.3.1)

• Section: N_c,Rd = A × f_y / γ_M0 (A_eff for Class 4)
• Member: N_b,Rd = χ × A × f_y / γ_M1 (A_eff for Class 4) with buckling curves per Table 6.2
• Buckling curve selection based on section type, h/b ratio, steel grade, and flange thickness
• Flexural-torsional buckling for monosymmetric sections (tees) with β_y monosymmetry constant

Flexure (6.2.5 & 6.3.2)

• Section: M_c,Rd = W_pl × f_y / γ_M0 (Class 1/2) or W_el × f_y / γ_M0 (Class 3) or W_eff × f_y / γ_M0 (Class 4)
• LTB (6.3.2): M_b,Rd with χ_LT using the General Case or specific method per 6.3.2.3
• M_cr computed analytically including C₁ (moment distribution), C₂ (load height per NCCI SN003), and warping
• f-factor modification for rolled and welded I-shapes (6.3.2.3(2))
• Tees use the monosymmetric M_cr formula (with β_y) and I_w = 0, with buckling curve d. Angles use I_w = 0 and buckling curve d.

Shear (6.2.6)

• Shear area A_v computed per 6.2.6(3) for each section type
• η factor: 1.2 (default) or 1.0 (UK National Annex)
• Shear-bending interaction (6.2.8): When V_Ed > 0.5V_pl,Rd, web contribution to moment is reduced

Combined Actions

• 6.2.9: Bending and axial force - refined M_N,Rd reduction for Class 1/2, elastic stress check for Class 3/4 with centroid shift
• 6.3.3: Stability interaction (Equations 6.61/6.62) - compression + biaxial bending with buckling, using interaction factors from Annex B (Method 2)

Calculator Inputs

The standalone EC3 calculator accepts the following inputs. All values are in metric units.

Fabrication Type

Select the fabrication method - this affects buckling curves and section classification limits:

• Rolled - standard hot-rolled sections (IPE, HEB, HEA, UKB, UKC)
• Welded / Built-up - fabricated plate girders and welded sections
• Cold Formed - cold-formed hollow sections

Section Geometry

Select a shape group, then enter dimensions or pick from the built-in section library (European/UK shapes).

Material Properties

Partial Safety Factors (γ)

These can be adjusted to match national annex requirements:

Member Lengths & Bracing

A Continuously Restrained checkbox sets L_b = 0, bypassing the LTB check.

Design Actions

Partial Safety Factors

Partial factors can be adjusted in the calculator via the advanced settings panel.

Limitations & Notes

• Torsional-flexural buckling (compression): N_cr,TF per Clause 6.3.1.4 is computed for I-shapes (pure torsional), channels, and tees (coupled flexural-torsional). Angles are excluded (doubly-asymmetric - requires separate formulation not provided in EC3).
• CHS Class 4: Not supported. EN 1993-1-6 (shell buckling) is required for CHS with D/t exceeding Class 3 limits. The engine issues a warning if this limit is exceeded.
• Tee stem classification: Uses the plastic NA position computed from N_Ed and flange/stem areas. When the PNA lies in the flange, the stem is entirely in tension and classified Class 1. Otherwise, stress-dependent outstand limits from Table 5.2 Sheet 2 are applied (c/t ≤ 9ε/(α√α) for Class 1).
• C_m factors: Auto-calculated using the approximation 0.95 + 0.05α_h per Annex B, Table B.3. In the standalone calculator, C_my, C_mz, and C_mLT can be overridden manually. In the FEA tool they are computed automatically from the full moment diagram.
• Tee shear: Stem shear area = A − B × t_f + (t_w + 2r) × t_f / 2 per EC3 6.2.6(3)(d) for rolled tees (the I-section formula applied to half the I, with the (t_w + 2r) × t_f term halved); flange shear area = B × t_f. Major/minor shear demand is routed to the stem or flange based on the member's structural axis orientation (BT vs CT, with sideways rotation respected).
• M_cr methodology: Uses the analytical 3-factor formula (NCCI SN003 / Access Steel) rather than the exact eigenvalue solution. Some benchmark discrepancies (~1-2%) arise from this approximation.
• National Annex: Default values follow the EN 1993-1-1 Recommended Values used by most European countries. The UK National Annex (γ_M2 = 1.10, η = 1.0) is auto-applied when a UK section is selected from the library. Other national annexes can be matched by adjusting γ_M and η in the advanced settings.
• Torsion (6.2.7): Not an input in the standalone calculator. In the FEA tool, torsion is checked for closed hollow sections (RHS/CHS) only. Warping torsion for open sections (I-beams, channels, angles, tees) is not performed.

Verification

The engine is benchmarked against 126 independent test cases from SCI P364, the Designers' Guide to EN 1993-1-1, EUR 22898 EN, and Worked Examples in Eurocode 3 & 4, with an average difference of 0.43%. The higher average compared to other engines reflects differences in M_cr computation methodology (analytical vs. numerical), which are documented in individual benchmark notes.