path: /blog/en1993-design-examples/ canonical: https://steelcalculator.app/blog/en1993-design-examples/ metatitle: "EN 1993 Design Examples -- Eurocode 3 Beam, Column & Connection" meta_description: "Full EN 1993 worked examples: HEA 240 beam with lateral-torsional buckling, HEB 200 column buckling check, M20 end-plate connection. Eurocode 3 step-by-step solutions for practicing engineers." robots: "index,follow" lastmod: "2026-05-20" schema_file: "schema/blog_en1993-design-examples.json" FAQPage: "@type": "FAQPage" mainEntity: - "@type": "Question" name: "What are the key differences between EN 1993-1-1 and AISC 360 for beam design?" acceptedAnswer: "@type": "Answer" text: "EN 1993-1-1 uses buckling curves (a0, a, b, c, d) selected by section type and axis, with the reduction factor chi calculated from slenderness lambda-bar. AISC 360 uses a single column curve with the nominal compressive strength P_n = F_cr * Ag, where F_cr depends on whether the section is in elastic or inelastic buckling. EN 1993 applies partial factors (gamma_M0 = 1.00 for cross-section, gamma_M1 = 1.00 for members) while AISC uses resistance factors (phi_c = 0.90). EN 1993 classifies cross-sections as Class 1-4 while AISC uses compact/noncompact/slender." - "@type": "Question" name: "How are load combinations defined in EN 1990 for use with EN 1993?" acceptedAnswer: "@type": "Answer" text: "EN 1990 defines load combinations for ultimate limit state (ULS) as either EQUATION 6.10 (recommended) or EQUATIONS 6.10a and 6.10b (alternative for persistent and transient design situations). The fundamental combination is: SUM(gamma_G * Gk) + gamma_Q * Qk,1 + SUM(gamma_Q * psi_0 * Q_k,i). For buildings, typical values are gamma_G = 1.35 for permanent actions, gamma_Q = 1.50 for variable actions, with psi factors for combination values (psi_0), frequent values (psi_1), and quasi-permanent values (psi_2)." - "@type": "Question" name: "What are the EN 1993-1-1 section classes and why do they matter?" acceptedAnswer: "@type": "Answer" text: "EN 1993-1-1 defines four section classes based on the width-to-thickness ratios of the flange and web. Class 1 can form a plastic hinge with sufficient rotation capacity (plastic design). Class 2 can reach the plastic moment but has limited rotation (plastic resistance used). Class 3 can reach yield at the extreme fiber but local buckling prevents plastic resistance (elastic design). Class 4 is slender and requires effective width reductions for local buckling. The class is determined by the highest (worst) class of all compressed elements. Class determines which resistance formula and which buckling curve applies."

EN 1993 Design Examples -- Eurocode 3 Beam, Column & Connection Worked Solutions

EN 1993 (Eurocode 3) is the European standard for structural steel design, covering everything from material specifications (EN 1993-1-1) to connection design (EN 1993-1-8) and fatigue (EN 1993-1-9). If you are designing steel structures in Europe -- or in any jurisdiction that references Eurocodes -- you need to understand the EN 1993 workflow: section classification, buckling curve selection, partial factor application, and interaction formula checks.

This post provides three worked EN 1993 design examples: a simply supported beam, an axially loaded column, and a bolted end-plate connection. All three use standard European sections and follow the EN 1993-1-1 and EN 1993-1-8 procedures exactly as written in the current standards.

Disclaimer: All numeric examples are illustrative only and must not be treated as design-ready values. Always verify with the governing standard and a qualified Professional Engineer.

The EN 1993 Design Philosophy

Before jumping into the examples, it helps to understand what makes EN 1993 different from other steel codes:

1. Section classification (Class 1-4). Every cross-section is classified before design. Class determines whether you can use plastic, elastic, or effective-width analysis. Unlike AISC (compact/noncompact/slender), EN 1993 uses numerical width-to-thickness ratio limits that depend on the steel grade through the epsilon factor (epsilon = sqrt(235/f_y)).

2. Partial factors, not resistance factors. EN 1993 uses gamma_M factors applied to material strength (gamma_M0 = 1.00 for cross-section resistance, gamma_M1 = 1.00 for member buckling, gamma_M2 = 1.25 for bolts). These are conceptually similar to dividing by phi in AISC/AS 4100 but are applied differently in algebraic expressions.

3. Buckling curves (a0 through d). EN 1993 has five buckling curves selected by section type, axis of buckling, and steel grade. The imperfection factor alpha determines the curve shape, with a0 being the most favourable (lowest alpha) and d being the most conservative (highest alpha). For hot-rolled H-sections buckling about the major axis, curve a or b typically applies; for the minor axis, curve b or c.

4. Interaction formulae (Annex A or Annex B). EN 1993-1-1 offers two methods for combined axial and bending checks. Annex A (Method 1) is more physically based. Annex B (Method 2) is simpler and more conservative. Either may be used at the national annex level.

Worked Example 1: HEA 240 Simply Supported Beam

Design Data

Step 1: Section Classification

For S275 steel, epsilon = sqrt(235/275) = 0.924

Flange (outstand in compression): c_f / t_f = 7.94. Class 1 limit: 9*epsilon = 8.32. 7.94 < 8.32 -- Class 1.

Web (bending only): c_w / t_w = 21.87. Class 1 limit: 72*epsilon = 66.5. 21.87 < 66.5 -- Class 1.

The HEA 240 is Class 1 -- plastic design permitted.

Step 2: ULS Design Moment

Design load: w*Ed = 1.35 * 12.5 + 1.50 _ 15.0 = 39.38 kN/m

Design moment: M*Ed = w_Ed * L^2 / 8 = 39.38 _ 64 / 8 = 315.0 kN-m

Step 3: Cross-Section Resistance

Mpl,Rd = W_pl,y * fy / gamma_M0 = 745 x 10^3 * 275 / 1.00 = 204.9 kN-m

Check: 315.0 / 204.9 = 1.537 > 1.00 -- FAIL.

Upgrade to HEA 320 (W_pl,y = 1,480 x 10^3 mm^3):

M_pl,Rd = 1,480 x 10^3 * 275 / 1.00 = 407.0 kN-m

Check: 315.0 / 407.0 = 0.774 -- OK.

Step 4: Lateral-Torsional Buckling (EN 1993-1-1 6.3.2)

For illustrative purposes, assume the beam is unbraced over 8.0 m:

lambda_LT_bar = sqrt(W_pl,y * f_y / M_cr)

Using the Annex A approach, lambda_LT_bar is approximately 0.48. Buckling curve a (alpha_LT = 0.21):

chi_LT = 0.930

Mb,Rd = chi_LT * Wpl,y * f_y / gamma_M1 = 0.930 * 407.0 = 378.5 kN-m

Check: 315.0 / 378.5 = 0.832 -- OK.

Step 5: Deflection Check

deltaQ = 5 * Qk * L^4 / (384 _ E _ I_y) = 16.6 mm

Limit: L/250 = 32 mm. 16.6 mm < 32 mm -- OK.

Worked Example 2: HEB 200 Axially Loaded Column

Design Data

Step 1: Cross-Section Resistance

Npl,Rd = A * fy / gamma_M0 = 7,810 * 355 / 1.00 = 2,773 kN

Step 2: Flexural Buckling -- Major Axis (y-y)

lambda_bar_y = (L_cr,y / i_y) / (pi * sqrt(E/f_y)) = (4,500/85.4) / 76.4 = 0.690

For HEB 200, curve b (alpha = 0.34):

chi_y = 0.791, N_b,Rd_y = 2,192 kN

Step 3: Flexural Buckling -- Minor Axis (z-z)

lambda_bar_z = (4,500/50.7) / 76.4 = 1.162

For HEB 200, curve c (alpha = 0.49):

chi_z = 0.452, N_b,Rd_z = 1,254 kN

Check: 1,200 / 1,254 = 0.957 -- OK. Governed by weak-axis buckling at 95.7% utilization.

Worked Example 3: Bolted End-Plate Connection

Design Data

Step 1: Bolt Shear Resistance

Fv,Rd = alpha_v * fub * A*s / gamma_M2 = 0.6 * 800 _ 245 / 1.25 = 94.1 kN per bolt

6 bolts: 564.5 kN. Check: 180 / 564.5 = 0.319 -- OK.

Step 2: Bolt Bearing

k1 = 2.5, alpha_b = 0.682

Fb,Rd = k1 * alphab * f*u * d _ t / gamma_M2 = 234.5 kN per bolt

Bolt shear governs (94.1 kN < 234.5 kN).

Step 3: End Plate Bending (T-Stub Model)

l_eff = min(2pim, pim + 2e1) = 236.7 mm

Mpl,Rd = 0.25 * leff * t_p^2 * f_y / gamma_M0 = 6.51 kN-m

F_T,Rd per bolt row = 4 * M_pl,Rd / m = 557.4 kN (far exceeds bolt tension capacity; plate OK).

Code Comparison: EN 1993 vs AISC 360

Key Takeaways

1. Section classification always comes first. The class affects resistance formula, buckling curve, and design method. A Class 4 section requires effective width reductions.

2. The buckling curve matters. Five curves from a0 to d can vary capacity by 10-20%. Always check EN 1993-1-1 Table 6.2 for your section type and axis.

3. The T-stub model for connections is more detailed than AISC prying checks but produces reliable results.

4. UK National Annex deviations modify buckling curves (NA.2.15) and partial factors. Always check the NA alongside the parent Eurocode.

Run This Calculation

Use the Steel Calculator EN 1993 tools to verify the worked examples with your own inputs:

--> Beam capacity calculator -- EN 1993-1-1 mode with section classification, LTB, and deflection.

--> Column capacity calculator -- EN 1993-1-1 mode with buckling curve selection.

--> Bolted connections calculator -- EN 1993-1-8 mode with bolt shear, bearing, and T-stub capacity.

--> Load combinations calculator -- EN 1990 Eq. 6.10 and 6.10a/b for Eurocode-based projects.

Related Blog Posts

• EN 1993-1-8 Steel Connection Design -- Bolt & Weld Checks
• AISC 360 Design Examples -- Beam, Column & Connection Worked Solutions
• AS 4100 Worked Examples -- Beam, Column & Bolt Group Design
• CSA S16 Base Plate Design -- W250x73 Worked Example
• IPE vs HEA vs UB -- Steel Section Comparison Guide
• Base Plate Design Example -- AISC 360, AS 4100, EN 1993 & CSA S16

Related Reference Pages

• EN 1993 Steel Grades -- S235, S275, S355, S460
• EN 1993 Base Plate Design -- Eurocode T-Stub Method
• Steel Fy & Fu Reference -- Yield and Tensile Strength by Grade
• Column K-Factor Table -- Theory and Effective Length Guide
• Moment of Inertia Calculator -- Ix, Sx, Zx for Steel Sections

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice, a design service, or a substitute for an independent review by a qualified structural engineer. Any calculations, outputs, examples, and workflows discussed here are simplified descriptions intended to support understanding and preliminary estimation.

All real-world structural design depends on project-specific factors (loads, combinations, stability, detailing, fabrication, erection, tolerances, site conditions, and the governing standard and project specification). You are responsible for verifying inputs, validating results with an independent method, checking constructability and code compliance, and obtaining professional sign-off where required.

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