Eurocode 3 (EN 1993-1-1)

This page covers design checks to EN 1993-1-1:2005+A1:2014 for I/H sections, channels, tees, angles, RHS/SHS and CHS. The National Annex can be CEN recommended values or the UK National Annex; Automatic uses the UK National Annex for UK library sections and CEN otherwise.

Open Eurocode 3 Calculator

Standard Reference

Supported Section Types

• I-Shapes (UKB, UKC, IPE, HEB, HEA - rolled and welded including plate girders)
• Channels (PFC/UPN/UAP where available from the section library or imported section data)
• 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

The design-check table shows the check and clause used for each member result. Summary by clause group:

• Section classification (5.5 / Table 5.2): I/H, channel, and RHS/SHS classes are evaluated from signed N, My, and Mz at every analysis section along the member. Internal-part Class 3 limits use psi from gross elastic plate-edge stresses; force-envelope maxima are not combined into a synthetic stress state.
• Class 4 effective sections (EN 1993-1-5): I/H, RHS/SHS, and supported channel component checks use pure-compression Aeff or pure-bending Weff. Where a Class 4 member carries axial force with bending, or bending about both axes, effective properties for that combined loading are not calculated: the 6.2.9 and 6.3.3 interaction checks are not made and are listed under Additional verification required. I/H, channel and RHS/SHS members show a gross-section bound row (6.2.9.3 Eq 6.44): over 100% fails for certain, under 100% does not clear the section. Tee/angle compression uses Aeff; Class 4 tee/angle bending is not checked. CHS Class 4 shell resistance requires separate verification under EN 1993-1-6.
• Section resistance (6.2.3-6.2.10 / EN 1993-1-5 Cl 5): Tension, compression, bending, shear, shear-bending, and N+M section checks use the reported clause row. Slender I/channel web shear buckling needs confirmed support end-post details at each applicable end; unknown or absent required support stiffeners produce an INCOMPLETE shear-buckling row without a numerical resistance.
• Member buckling (6.3.1 / 6.3.1.4): Flexural buckling is checked for supported sections. Torsional or flexural-torsional compression buckling is checked for I/H sections, channels, tees and angles. Equal angles use the coupled quadratic; unequal angles use the lowest positive root of the general cubic, with EC3 curve b and the applicable effective area.
• LTB (6.3.2.1(3) / 6.3.2.2 / 6.3.2.3): LTB resistance uses the general or modified I/H reduction method according to the section family. C1 comes from the moment diagram (SN003 cases); other diagrams on equal-flange I/H and channel spans between fork supports, loaded at the shear centre, use a general quarter-point C1, otherwise C1 = 1.
• Combined stability and torsion (6.3.3 / 6.2.6(4) / 6.2.7): Clause 6.3.3 Annex B member interaction is reported for supported doubly symmetric sections. For channels, tees, angles and unequal-flange I-sections under compression with bending, no numerical 6.3.3 or alternative member interaction is reported; section and individual buckling checks remain available. Treat this as a design-scope limitation when interpreting the reported checks. Closed-hollow-section torsion rows are reported where applicable.

Calculator Inputs

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

Fabrication Type

The fabrication selector affects buckling curves, section classification limits and the shear-area path under 6.2.6. The options depend on the shape:

• I/H, channels and tees: Hot Rolled or Welded / Built-up
• RHS / SHS: Hot Finished, Cold Formed or Welded Box. For a welded box with b/t < 30 and h/t < 30, a box weld throat selector (a ≤ 0.5t or a > 0.5t) chooses between buckling curves b and c; left unspecified, curve c is assumed.
• CHS: Hot Finished or Cold Formed
• Angles: no selector (buckling curve b is used)

Section Geometry

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

Material Properties

Member Lengths & Bracing

Continuous Restraint means the top flange is continuously restrained, for example by a concrete slab or welded metal deck. Sagging (negative M_y,Ed) compresses the restrained top flange, so χ_LT = 1.0 without M_cr (Clause 6.3.2.1(2)). Hogging (positive M_y,Ed) compresses the bottom flange and no credit is taken for the top-flange restraint: LTB is checked as for an unrestrained member over L_b = KLT × L, with the C₁, M_cr, k_c,LT, load-height and cantilever rules, and reported as a separate check. Clause 6.3.3 is evaluated at the sagging maxima with χ_LT = 1.0 and at the hogging maxima with the hogging χ_LT, and the governing result is reported. Enter KLT = 0 if the bottom flange is also braced. The Clause 6.3.1.4 torsional buckling length is independent of this setting and still applies where that mode is checked. For single angles the setting restrains the whole member.

Load height is available for I-shapes, channels, and tees. For a tee with top-flange loading and active LTB, supply M_cr; otherwise the required LTB check returns OUT_OF_SCOPE and prevents an overall member PASS. With continuous restraint this applies only to hogging moment, unless KLT = 0.

In the FEA Design tab the Cantilever control has three settings: Auto (default) follows the model and shows what it detected, for example "Auto (detected: cantilever, held at Node A)"; Span and Cantilever override the detection. Active cantilever LTB requires a supplied elastic-buckling M_cr for the actual loading and restraints, because C₁ alone does not establish fixed-free restraints; without it the LTB check is INCOMPLETE. Table 6.6 covers segments between fork supports, so a cantilever uses k_c = 1.0 unless a k_c,LT is entered. In the standalone calculator, tick Cantilever: the LTB loading case, C₁ and load height are then not used, M_cr is required, and C_my/C_mz default to 0.9.

Design Actions

Partial Safety Factors

The National Annex selector (Automatic, CEN recommended, UK NA) prefills the factors below, which remain editable. Each factor must be between 1.0 and 2.0 and a blank entry uses the annex value.

Limitations & Notes

• Design stiffness: Resistance and stability checks use E = 210,000 MPa and G = 81,000 MPa under Clause 3.2.6. Material stiffness entered for structural analysis does not change these design values.
• Slender I/channel web shear buckling: Where the web exceeds 72ε/η and the member carries major-axis shear, EN 1993-1-5 Clause 5 requires transverse support stiffeners, and the end-post condition is entered for each end (the held end only for a cantilever). Select non-rigid to use the non-rigid Table 5.1 column, or rigid only for an end post checked separately to Clause 9.3.1; where the ends differ, the weaker column is used. Until each end is confirmed, or where no support stiffener is provided, shear buckling is INCOMPLETE with no numerical resistance. Intermediate web stiffeners and their panel geometry are not modelled.
• Class 3/4 classification along the member: For I/H, channel, and RHS/SHS members, signed concurrent N, M_y, and M_z are evaluated along the member. Internal-part Class 3 limits use ψ from gross elastic plate-edge stresses.
• I/H, channel, and RHS/SHS Class 4 combined actions: Pure-compression A_eff and pure-bending W_eff remain available for independent component checks. If the member is Class 4 and any point along the member has concurrent axial-flexural or biaxial demand, no effective section is available for that combined state: the 6.2.9 and 6.3.3 checks are not made and are listed under Additional verification required. Gross or pure-action effective properties are not substituted. A fail-only screen on the gross section (Eq 6.44 with gross A and W_el) can show a failure but never clears the section.
• Custom-section axes: EC3 results use Eurocode notation: y-y is the major axis and z-z is the minor axis. Check that the moments of inertia and elastic and plastic section moduli match the section preview. Incorrect axis assignments affect bending, buckling and LTB resistance.
• Net section: Tension rupture under 6.2.3 uses the entered A_net. Bolt-hole and staggered-path geometry are not inferred.
• Torsional-flexural buckling (compression): Clause 6.3.1.4 torsional or flexural-torsional buckling is checked for I/H sections, channels, tees, and angles. Equal angles use the coupled quadratic; unequal angles use the lowest positive root of the general cubic. Angle resistance uses curve b and the compression effective area for Class 4 sections. Elastic properties use the gross section and the thin-wall shear centre at the leg mid-line intersection.
• Channel, tee, and angle compression with bending: Clause 6.3.3(1) is limited to doubly symmetric sections, so no member compression-and-bending stability interaction is evaluated for these shapes. Section resistance and individual buckling checks are still reported, and the member status covers only those checks. Arrange a separate member stability assessment where needed.
• Unequal-flange I-sections: Automatic major-axis LTB resistance is unavailable; provide continuous restraint (top flange in sagging, or both flanges with KLT = 0) or a justified elastic critical moment M_cr. Neither option supplies the missing Clause 6.3.3 compression-bending stability assessment for this singly symmetric section. Class 4 effective properties and some high-shear and plastic combined-action checks also remain unavailable. Review any checks that are not reported and complete them separately.
• Tee/angle Class 4 bending: Axial compression may use the EN 1993-1-5 effective area. Effective bending properties are not implemented, so any bending demand makes the check INCOMPLETE and the member reads PASS (partial) at best. Numeric bending resistance, LTB, and dependent interaction results are not reported, and gross elastic section moduli are not substituted; they are used only in a separate upper-bound check that can reject the member but never pass it.
• CHS Class 4: Shell-sensitive compression, bending and stability resistance is unavailable without EN 1993-1-6 shell buckling; these checks return OUT_OF_SCOPE. Gross-yield and net-rupture tension checks under 6.2.3 remain available with valid strength and net-area inputs.
• High shear with bending (6.2.8): Applied when V_Ed > 0.5V_pl,Rd for I/H, channel, tee, RHS/SHS and CHS sections (CHS conservatively reduce the whole section). For angles, shear stresses are included in the Clause 6.2.1(5) von Mises check instead.
• Web yield strength: Where the section catalogue gives a separate web yield strength, web classification and web shear buckling use it; section resistances use f_y.
• Angle shear resistance: EN 1993-1-1 gives no shear area for angles; each leg is taken to carry shear along its own length only (an equal angle gives A/√2).
• Tee stem classification: Tee classification follows the active stress state and Table 5.2 Sheet 2 limits for the reported stress state.
• C_m factors: Clause 6.3.3 uses independent member compression and moment maxima; moment-gradient factors are computed from the moment diagram where available and applied once, or can be overridden in the standalone calculator. Section Clause 6.2.9 still uses coincident actions.
• Sway buckling mode (linear analysis): Set the buckling mode per axis. Sway uses C_my/C_mz = 0.9 (Table B.3 note) and needs sway-mode buckling lengths (5.2.2(8)); non-sway uses the moment diagram; unspecified uses the larger of the two. Cantilevers always use 0.9. P-Delta results already include sway, so the diagram value is used. C_mLT always follows the moment diagram.
• Tee shear: Tee shear follows the relevant EC3 6.2.6 path for rolled or welded tees, with shear routed to the active stem or flange direction based on member orientation.
• M_cr methodology: Uses a supplied M_cr when present; otherwise M_cr is calculated analytically. Results can differ from a numerical eigenvalue buckling analysis.
• LTB loading case: The FEA Design tab takes C₁ from SN003b Table 3.1 for a signed linear end-moment diagram. For an equal-flange (doubly symmetric) I-section, select a full-span UDL or midspan point load only when fork supports, free warping, and the displayed moment diagram match that case. Any other diagram on an equal-flange I-section or channel, between fork supports with load at the shear centre and K_LT = 1, uses the general expression of López, Yong and Serna (2006) from the signed moments M₁ to M₅ at the segment ends and quarter points: C₁ = 1/√A₁ with A₁ = (M_max² + 5M₂² + 10M₃² + 5M₄²) / (21M_max²). The result is divided by 1.06, so it stays at or below SN003b Table 3.1 and the exact elastic buckling value for end moments combined with a uniform or midspan point load, and is kept between 1.0 and 2.57. This route uses k_c = 1.0 (no Table 6.6 case), except where the UK NA 2.18 value 1/√C₁ applies. Remaining diagrams (other sections, K_LT ≠ 1, or too few moment values along the member) use the conservative uniform-moment value C₁ = 1.0 unless a C₁ or buckling-analysis M_cr is supplied; top-flange loading on an unmatched diagram needs M_cr. The standalone calculator accepts a peak moment, so select its loading case explicitly. A UDL or midspan point-load case selected for any other section is not used, and the results say so. Cantilevers follow the Cantilever control described above.
• Local transverse forces and reactions: EN 1993-1-5 local transverse force (patch loading, web bearing and web buckling), end-post and transverse-stiffener checks are not performed, including at FEA reactions, point loads and connections. Check support bearing and concentrated load introduction separately.
• National Annex: Automatic (default), CEN recommended or UK NA. Automatic uses the UK NA for United Kingdom library sections and CEN otherwise. γ_M0, γ_M1, γ_M2 and η are prefilled from the annex and remain editable. For another country's annex, choose CEN and enter its partial factors; other non-numeric choices (such as LTB curves) follow CEN, and the report states this.
• UK NA rules: γ_M2 = 1.10, η = 1.0, Table NA.1 LTB curves and parameters (NA 2.17) and k_c = 1/√C₁ in the f modification (NA 2.18).
• Torsion (6.2.6(4)): Not an input in the standalone calculator. In the FEA tool, closed hollow sections (RHS/SHS/CHS) use a torsional shear stress check when a torsional section modulus is supplied or derivable. Shear with torsion uses Equation 6.28; RHS checks each shear axis and CHS checks the concurrent resultant. Warping resistance for applied open-section torsion is not calculated and requires separate verification.
• Serviceability and special design states: The EC3 member check does not cover serviceability limits, vibration, fatigue, fire, corrosion/durability, connection detailing or execution. Analysis displacements are reported separately.

Verification

The public verification pages contain 95 published comparisons from SCI P364, the Designers' Guide, EUR 22898 EN and published EC3/EC4 worked examples, with an average numerical difference of 0.44%. Classification outcomes do not contribute to the numerical mean. SCI Examples 4/12 compare resistance and interaction using the published SN002/P362 buckling parameters.