EN 1993 (Eurocode 3): Design of Steel Structures
EN 1993, commonly known as Eurocode 3, is the European standard for the design of steel structures. Published by CEN (European Committee for Standardization), it is used across all EU/EEA member states, the UK (as BS EN 1993), and many countries worldwide that have adopted or adapted the Eurocode system. Unlike AISC 360 or AS 4100, Eurocode 3 is split into multiple parts covering different aspects of steel design. This page covers the standard's structure, partial safety factors, the National Annex system, and links to every calculator on this site that implements EN 1993 provisions.
Overview of EN 1993 (Eurocode 3)
The Eurocode system follows a consistent limit state design philosophy across all structural materials. For steel structures, the fundamental verification is:
E_d <= R_d
where E_d is the design value of the effect of actions (from EN 1990/EN 1991 load combinations) and R_d is the design resistance. The design resistance is obtained by dividing the characteristic resistance by a partial safety factor:
R_d = R_k / gamma_M
This is conceptually the inverse of the phi-factor approach used in AISC, AS 4100, and CSA S16. Where those standards multiply the nominal capacity by a factor less than 1.0, the Eurocodes divide by a factor greater than 1.0. The net effect on reliability is comparable.
The Eurocode ecosystem
EN 1993 does not stand alone. A complete Eurocode-based steel design requires:
- EN 1990 (Basis of Design) -- Defines partial factors for actions, combination rules, and reliability classes
- EN 1991 (Actions on Structures) -- Loading (dead, live, wind, snow, thermal, accidental)
- EN 1992 (Concrete) -- Referenced for composite design and anchor design
- EN 1993 (Steel) -- The subject of this page, multiple parts
- EN 1994 (Composite) -- Composite steel-concrete design
- EN 1998 (Seismic) -- Earthquake-resistant design
Units
All Eurocodes use SI units: forces in kN, moments in kN.m, stresses in MPa (N/mm^2), dimensions in mm. All calculators on this site output in these units when EN 1993 is selected.
Key Parts of EN 1993
EN 1993 is divided into six main parts, each addressing a specific aspect of steel design. The most commonly used parts for building structures are 1-1 and 1-8.
EN 1993-1-1: General Rules and Rules for Buildings
The core part covering member design. Key clauses:
Cl. 5 -- Structural Analysis Defines methods of global analysis (elastic, plastic, advanced), imperfections (equivalent horizontal forces, member bow imperfections), and second-order effects. Frame classification as sway or non-sway depends on alpha_cr >= 10 for elastic analysis or >= 15 for plastic analysis.
Cl. 5.5 -- Classification of Cross-Sections Cross-sections are classified as Class 1 (plastic), Class 2 (compact), Class 3 (semi-compact), or Class 4 (slender) based on the width-to-thickness ratios of compressed plate elements. The class depends on both the geometry and the stress distribution:
| Class | Behavior | Design Approach |
|---|---|---|
| 1 (Plastic) | Can form plastic hinge with rotation capacity | Plastic moment M_pl, plastic analysis permitted |
| 2 (Compact) | Can reach plastic moment but limited rotation | Plastic moment M_pl, elastic analysis only |
| 3 (Semi-compact) | Can reach yield in extreme fiber | Elastic moment M_el = f_y * W_el |
| 4 (Slender) | Local buckling before yield | Effective section properties per EN 1993-1-5 |
Cl. 6.1 -- General (Resistance) All resistance calculations use the partial factor gamma_M appropriate to the limit state. For cross-section checks, gamma_M0 = 1.00. For member instability checks, gamma_M1 = 1.00 (recommended; National Annex may modify).
Cl. 6.2 -- Cross-Section Resistance Covers axial tension (6.2.3), axial compression (6.2.4), bending (6.2.5), shear (6.2.6), and combinations. For combined bending and axial force, interaction formulae depend on the cross-section class.
Cl. 6.3 -- Buckling Resistance of Members The critical section for column and beam design:
- Cl. 6.3.1 -- Compression members: N*b,Rd = chi * A _ f_y / gamma_M1, where chi is the buckling reduction factor from the Perry-Robertson formulation. Five buckling curves (a0, a, b, c, d) are specified in Table 6.2, selected based on section type, axis of buckling, and fabrication method (hot-rolled vs welded).
- Cl. 6.3.2 -- Lateral-torsional buckling: Mb,Rd = chi_LT * Wy * f_y / gamma_M1. Two methods are provided: the general case (Cl. 6.3.2.2) and the method for rolled or equivalent welded sections (Cl. 6.3.2.3) which gives higher capacities. The LTB curves are selected from Table 6.4.
- Cl. 6.3.3 -- Combined bending and compression: Interaction formulae using k_yy, k_yz, k_zy, k_zz factors from Annex A (exact) or Annex B (simplified). Two equations must be satisfied simultaneously.
EN 1993-1-8: Design of Joints
The connection design part, equivalent to AISC Chapter J. Key clauses:
Cl. 2.2 -- Applied forces and moments Connections must be designed for the internal forces and moments from global analysis. The distribution of forces within a connection depends on whether the connection is classified as rigid, semi-rigid, or pinned.
Cl. 3 -- Connections Made with Bolts, Rivets, or Pins
- Table 3.1 -- Nominal values of f_ub and f_yb: Bolt property classes 4.6, 4.8, 5.6, 5.8, 6.8, 8.8, and 10.9. The first number times 100 gives f_ub in MPa (e.g., 8.8 -> f_ub = 800 MPa); the product of both numbers times 10 gives f_yb.
- Cl. 3.6 -- Shear resistance: Fv,Rd = alpha_v * fub * A / gamma_M2. For 4.6, 5.6, 8.8: alpha_v = 0.6; for 4.8, 5.8, 6.8, 10.9: alpha_v = 0.5 (shear plane through threaded portion).
- Cl. 3.6.1 -- Tension resistance: Ft,Rd = k_2 * fub * A_s / gamma_M2, where k_2 = 0.9 for standard bolts.
- Cl. 3.6.1 -- Combined shear and tension: F_v,Ed / F_v,Rd + F_t,Ed / (1.4 * F_t,Rd) <= 1.0.
- Cl. 3.6.1 -- Bearing resistance: Fb,Rd = k_1 * alphab * f*u * d _ t / gamma_M2, where alpha_b depends on end distance, bolt spacing, and strength ratio.
- Cl. 3.9 -- Slip-resistant connections: F*s,Rd = k_s * n _ mu * F_p,C / gamma_M3 (or gamma_M3,ser for serviceability). mu is the slip factor (0.20 to 0.50 depending on surface treatment per Table 3.7).
- Cl. 3.10 -- Block tearing: Combines net tension area rupture with gross shear area yielding.
Cl. 4 -- Welded Connections
- Cl. 4.5 -- Design resistance of fillet welds: Two methods -- the simplified method (Cl. 4.5.3.2) and the directional method (Cl. 4.5.3.3). The simplified method: Fw,Rd = f_vw,d * a _ L_w, where f_vw,d = f_u / (sqrt(3) _ betaw * gamma_M2). The correlation factor beta_w depends on steel grade (Table 4.1).
- Cl. 4.7 -- Design resistance of butt welds: Full penetration butt welds are designed as parent metal. Partial penetration welds use the fillet weld rules with an effective throat equal to the penetration depth minus 2 mm (for single-V) or 3 mm.
Cl. 5 & 6 -- Joint Classification and Modelling Classifies joints as simple (pinned), semi-rigid, or rigid based on initial rotational stiffness. The component method (Cl. 6) provides a systematic approach to calculate the stiffness and resistance of end-plate, angle cleat, and fin plate connections.
EN 1993-1-3: Cold-Formed Steel
Covers cold-formed thin-gauge members and sheeting. Uses effective width concepts from EN 1993-1-5 but with additional provisions for distortional buckling and edge stiffeners.
EN 1993-1-5: Plated Structural Elements
Critical for plate girder design. Covers shear buckling (Cl. 5), local plate buckling (Cl. 4), and interaction between axial force, bending, and shear (Cl. 7). Provides effective width formulations for Class 4 sections.
EN 1993-1-9: Fatigue
Fatigue design using detail categories and S-N curves. Each welded detail is assigned a category (e.g., 160, 125, 90, 71) representing the stress range in MPa at 2 million cycles. Required for crane runway beams, bridges, and structures subject to cyclic loading.
EN 1993-1-10: Material Toughness and Through-Thickness Properties
Selection of steel grades based on fracture toughness requirements. Table 2.1 provides maximum permissible thicknesses based on Charpy impact test results, reference temperature, and stress level.
Partial Safety Factors (Gamma_M)
EN 1993 uses partial safety factors applied to resistance (dividing the characteristic strength). The following table shows the recommended values from EN 1993. National Annexes may modify these values.
| Partial Factor | Recommended Value | Application | Clause |
|---|---|---|---|
| gamma_M0 | 1.00 | Cross-section resistance (tension, compression, bending, shear) | EN 1993-1-1 Cl. 6.1 |
| gamma_M1 | 1.00 | Member instability (buckling, LTB) | EN 1993-1-1 Cl. 6.1 |
| gamma_M2 | 1.25 | Cross-section resistance at bolt/weld holes (net section), bolt and weld capacity | EN 1993-1-1 Cl. 6.1, EN 1993-1-8 |
| gamma_M3 | 1.25 | Slip resistance at ULS | EN 1993-1-8 Cl. 3.9 |
| gamma_M3,ser | 1.10 | Slip resistance at SLS | EN 1993-1-8 Cl. 3.9 |
| gamma_c | 1.50 | Concrete in compression (EN 1992-1-1) | EN 1992-1-1 Table 2.1N |
| gamma_Ms (tension) | 1.20 | Anchor steel failure in tension | EN 1992-4 |
| gamma_Ms (shear) | 1.25 | Anchor steel failure in shear | EN 1992-4 |
Important -- National Annex values: Several countries modify the recommended values. Notable examples:
| Country | gamma_M0 | gamma_M1 | gamma_M2 |
|---|---|---|---|
| Recommended (CEN) | 1.00 | 1.00 | 1.25 |
| UK (BS EN) | 1.00 | 1.00 | 1.25 |
| Germany (DIN EN) | 1.00 | 1.10 | 1.25 |
| France (NF EN) | 1.00 | 1.00 | 1.25 |
| Spain (UNE EN) | 1.05 | 1.05 | 1.25 |
| Italy (UNI EN) | 1.05 | 1.05 | 1.25 |
Our calculators use the CEN recommended values (gamma_M0 = 1.00, gamma_M1 = 1.00, gamma_M2 = 1.25). If your National Annex specifies different values, adjust accordingly.
Comparison with phi factors: The Eurocode gamma approach is the inverse of the phi approach. For example, gamma_M2 = 1.25 for bolt resistance is equivalent to a phi factor of 1/1.25 = 0.80, which is close to (but not identical to) AISC's phi = 0.75 for bolts. The nominal strength formulations also differ, so comparing only the factors is misleading.
National Annexes
The National Annex (NA) is a critical concept unique to the Eurocode system. Each CEN member country publishes a National Annex for each Eurocode part, which:
- Sets Nationally Determined Parameters (NDPs) -- Values where the Eurocode provides a recommended value but permits national choice (e.g., partial factors, imperfection amplitudes, buckling curve parameters).
- Specifies the method where the Eurocode offers alternatives (e.g., Annex A vs Annex B interaction factors for EN 1993-1-1 Cl. 6.3.3).
- Provides supplementary information -- Additional guidance, worked examples, or restrictions.
The National Annex does not alter the Eurocode text itself. It only fills in the designated boxes. This means the same EN 1993 document is used everywhere, but the numerical parameters may differ between countries.
Practical consequence: When verifying a calculation against EN 1993, always confirm which National Annex applies. A beam designed to the UK NA may have different interaction factors than the same beam designed to the German NA, even though both use EN 1993-1-1 Cl. 6.3.3.
Common National Annex differences
- Buckling curves: Most countries follow the recommended curves, but some specify different imperfection factors for certain section types.
- Interaction method: The UK NA specifies Annex B (simplified) as the default for Cl. 6.3.3. Germany permits both Annex A and Annex B. France defaults to Annex A (more economical for many cases).
- LTB method: Some NAs restrict the use of Cl. 6.3.2.3 (rolled section method) or modify the f-factor.
- Bolt hole deductions: In some NAs, deduction for bolt holes in the compression flange is not required if the holes are filled with bolts.
Cross-References to Other Standards
| EN 1993 Concept | AISC 360 Equivalent | AS 4100 Equivalent | CSA S16 Equivalent |
|---|---|---|---|
| gamma_M (partial factor) | phi (resistance factor) | phi (capacity factor) | phi (resistance factor) |
| EN 1990 load combos | ASCE 7 load combos | AS/NZS 1170 combos | NBCC load combos |
| EN 1993-1-8 (Joints) | Chapter J (Connections) | Section 9 (Connections) | Clause 13 (Connections) |
| Cl. 6.3.2 (LTB) | Chapter F (Flexure) | Section 5 (Bending) | Clause 13.5-13.6 |
| Cl. 6.3.1 (Buckling) | Chapter E (Compression) | Section 6 (Compression) | Clause 13.3 |
| Class 1-4 classification | Compact/Noncompact/Slender | Compact/Noncompact/Slender | Class 1-4 classification |
| chi (buckling reduction) | Phi_c*F_cr (critical stress) | alpha_c (slenderness factor) | (built into C_r formula) |
| beta_w (correlation factor) | -- (direct F_EXX approach) | -- (f_uw approach) | -- (X_u approach) |
| Component method (Cl. 6) | -- (no equivalent) | -- (no equivalent) | -- (no equivalent) |
Note on section classification: EN 1993 and CSA S16 both use a 4-class system (Class 1 through 4). AISC 360 and AS 4100 use compact/noncompact/slender (3 categories). The Class 1 vs Class 2 distinction matters for plastic analysis but not for elastic design.
Available Calculators
Every calculator below implements EN 1993 provisions with full clause-by-clause derivation output. Select EN 1993 as the design code in the calculator interface. CEN recommended partial factors are used by default.
Connection design
- Bolted Connection Calculator -- Bolt shear (Cl. 3.6), bearing (Cl. 3.6), tension, combined shear-tension interaction (Cl. 3.6.1), and block tearing (Cl. 3.10). Supports property classes 4.6 through 10.9.
- Welded Connection Calculator -- Fillet weld capacity per Cl. 4.5 using the directional method, with beta_w correlation factor per Table 4.1.
- Base Plate & Anchors Calculator -- Concrete bearing per EN 1992-1-1, T-stub model for plate bending, and anchor bolt design per EN 1992-4.
- Gusset Plate Calculator -- Whitmore section, block tearing, and plate buckling checks.
- Splice Connection Calculator -- Bolted and welded splice design per EN 1993-1-8.
Member design
- Beam Capacity Calculator -- Cross-section resistance (Cl. 6.2.5), lateral-torsional buckling (Cl. 6.3.2) with LTB curve selection, and shear (Cl. 6.2.6) for IPE, HEA, HEB, UB, and welded sections.
- Column Capacity Calculator -- Flexural buckling (Cl. 6.3.1) with buckling curve selection (a0, a, b, c, d) per Table 6.2.
- Beam Deflection Calculator -- Serviceability checks against National Annex deflection limits.
Utilities
- Load Combinations (EN 1990) -- ULS and SLS combinations per EN 1990 with psi factors.
- Steel Grades Reference -- f_y and f_u for S235, S275, S355, S420, S450, and S460 per EN 10025.
- Weld Electrode Reference -- Matching electrodes and beta_w correlation factors by steel grade.
- Section Properties (IPE/HEA/HEB) -- Comparison of European section series.
Frequently Asked Questions
Which National Annex does the calculator use? The calculator uses CEN recommended values (gamma_M0 = 1.00, gamma_M1 = 1.00, gamma_M2 = 1.25). If your National Annex specifies different partial factors, you must adjust the results manually or apply the NA factor ratio.
How does the Eurocode handle bolt grades differently from AISC? Eurocode uses property class notation (4.6, 8.8, 10.9) where the numbers encode the ultimate and yield strengths. AISC uses ASTM designations (A325, A490). The physical bolts may be identical (e.g., ASTM A325 is essentially equivalent to class 8.8) but the design equations differ in form.
What is the correlation factor beta_w for welds? beta_w accounts for the difference between weld metal and parent metal strength. It varies by steel grade: 0.80 for S235, 0.85 for S275, 0.90 for S355, 1.00 for S420/S460. A higher beta_w reduces the weld design resistance.
Can I use the calculator for Eurocode seismic design? The calculators provide static resistance checks per EN 1993. For seismic design to EN 1998, additional requirements apply: overstrength factors, ductility class-dependent detailing, capacity design principles, and prequalified connection types. These are not covered by the calculator.
What is the component method? The component method (EN 1993-1-8 Cl. 6) is a systematic procedure for analyzing the stiffness and resistance of beam-to-column joints by decomposing them into basic components (T-stub in tension, column web in compression, etc.). It has no direct equivalent in AISC or AS 4100. Our calculators use direct resistance checks rather than the full component method.
Related Pages
- Design Codes Overview
- AISC 360 Design Guide
- AS 4100 Design Guide
- CSA S16 Design Guide
- Tools Directory
- Reference Tables
- EN 1993-1-8 Steel Connections Guide
- IPE vs HEA vs UB Section Comparison
- How to verify calculator results
- Disclaimer (educational use only)
Copyright and Standards Notice
This page is a high-level educational guide to help engineers navigate EN 1993 provisions and use our calculators effectively. It does not reproduce copyrighted code text, proprietary tables, or design examples from the published standard. For authoritative requirements, purchase the official EN 1993 from your national standards body (BSI, DIN, AFNOR, UNI, etc.) or from CEN.
Disclaimer
This page is provided for general technical information and educational use only. It does not constitute professional engineering advice or a substitute for review by a qualified structural engineer. All structural design depends on project-specific loads, combinations, stability requirements, detailing, fabrication tolerances, and the governing code edition and National Annex. You are responsible for verifying inputs, validating results independently, and obtaining professional sign-off. The site operator provides this content "as is" without warranties of any kind.