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, Tees, and Angles under axial compression. The centroid shift generates additional moments (ΔM = N × e_N) in the 6.2.9 interaction check.

All five section paths (I, Channel, RHS, Tee, Angle) use the non-iterated ψ = 1 method per EN 1993-1-5 §4.3(3) default rule — slightly conservative versus the iterative alternative that accounts for centroid-shift-induced stress gradient on each subpanel.

Tees are a special case for axial: 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_plis preserved in those cases. Angles use the same per-leg outstand treatment with c = h − t − r; under bending, Tees and Angles revert to elastic W_el (only one leg/half is compressed per principal axis, so Class 4 does not apply). CHS Class 4 is not supported (shell buckling per EN 1993-1-6 not implemented).

Tension (6.2.3)

• N_t,Rd: Gross section yielding (A × f_y / γ_M0) — Class 4 reduction does not apply to tension
• N_u,Rd: Net section rupture (0.9 × A_net × f_u / γ_M2)
• Both checks reported under a single "Axial Resistance" result whose capacity field is the direction-governing value; intermediates expose both N_pl,Rd (tension) and N_c,Rd (compression) for inspection.

Compression (6.2.4 & 6.3.1)

• Section: N_c,Rd = A_eff × f_y / γ_M0 (A_eff = A for Class 1–3; Class 4 reduction per EN 1993-1-5 for I/Channel/RHS/Tee/Angle)
• Member: N_b,Rd = χ × A_eff × f_y / γ_M1 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) (a)–(g) for each section type, routed by fabrication: rolled I/H/Channel/Tee use the (a)/(b)/(c) rolled formulas; welded I/H/box use (d) η · Σ(h_wt_w) for load parallel to web and (e) A − Σ(h_wt_w) for load parallel to flanges; welded Tees use (c) t_w · (h − t_f/2).
• η factor: 1.2 (rolled with f_y ≤ 460 MPa) or 1.0 (welded sections and UK National Annex).
• Rolled I-shape and Channel minor-axis shear (load parallel to flanges) uses A_v = 2 · B · t_f (pure-flange convention) — the standard is silent for the rolled case. Welded sections in this configuration route to 6.2.6(3)(e).
• Non-square RHS: A_v swaps h↔b based on member orientation. Upright members use 6.2.6(3)(f1) A · h/(b + h) for the major-axis shear (which physically flows through the depth); members with the section rotated 90° (sideways) use 6.2.6(3)(f2) A · b/(b + h) for the same demand (shear now flows through the width).
• Shear-bending interaction (6.2.8): When V_Ed > 0.5V_pl,Rd, web contribution to moment is reduced via Eq 6.30. Applied to I, Channel, RHS (A_w = 2 · h_wt_w for both walls), and Tee (A_w = (D − t_f)·t_w stem). CHS and Angle excluded — shear is not web-decoupled.

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, section classification limits, and shear-area sub-formula routing per 6.2.6(3):

• 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: Rolled tees use EC3 6.2.6(3)(c): stem shear area = A − B × t_f + (t_w + 2r) × t_f / 2 (the I-section formula applied to half the I, with the (t_w + 2r) × t_f term halved). Welded tees use the welded variant of 6.2.6(3)(c): stem shear area = t_w × (h − t_f/2). Flange shear area = B × t_f for both. 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 casesfrom 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.