What does this calculator check according to Eurocode 3?

It evaluates cross-section bending resistance (plastic or elastic depending on section class) and shear resistance, both per EN 1993-1-1. It also applies the shear–bending interaction reduction for class 1–2 webs when VEd exceeds 0.5·Vpl,Rd. Global stability checks such as lateral–torsional buckling are not included.

Does it include lateral–torsional buckling (LTB)?

No. The calculator addresses cross-section resistance only. LTB and other stability checks must be performed separately per EN 1993-1-1 clause 6.3.

How are partial safety factors used?

The tool uses γM0 for cross-section resistances (moment and shear). γM1 is shown for completeness but not applied unless explicitly noted by the National Annex for specific checks.

When is the shear–bending interaction reduction applied?

For class 1–2 sections with rectangular webs and when VEd > 0.5·Vpl,Rd, the plastic bending resistance is reduced per EN 1993-1-1 6.2.8. If VEd ≤ 0.5·Vpl,Rd, no reduction is applied.

Is shear buckling of the web considered?

No. The shear resistance assumes no shear buckling or that buckling is prevented (e.g., by stiffeners) such that Av is valid. For slender webs, check EN 1993-1-5.

Eurocode 3 Steel Beam Bending & Shear Resistance Calculator

Q: Which units should I use?

Use SI units consistently: fy in MPa, Wpl,y and Wel,y in mm^3, Av in mm^2, MEd in kNm, and VEd in kN. The calculator outputs M in kNm and V in kN.

Q: Can I use this for class 4 sections?

No. Class 4 sections require effective section properties due to local buckling. This version does not implement effective widths; use specialized software or calculate effective properties per EN 1993-1-1 and EN 1993-1-5.

Professional Eurocode 3 (EN 1993-1-1) steel beam calculator for cross‑section bending and shear resistance with optional shear interaction. Mobile‑first, accessible, and optimized for engineers.

Full original guide (expanded)

Eurocode 3 Steel Beam Bending & Shear Resistance Calculator

This professional tool computes cross-section bending and shear resistance of steel beams according to Eurocode 3 (EN 1993‑1‑1). It is intended for structural engineers and advanced students who need quick, reliable checks for ULS cross-section capacities and shear–bending interaction, with a mobile-first and fully accessible UI.

Calculator

Section class (EN 1993‑1‑1, Table 5.2) *

Class 1 Class 2 Class 3 Class 4 (not supported)

Yield strength fy *

MPa

Partial factor γM0 *

Partial factor γM1

Section properties

Plastic section modulus Wpl,y *

mm³

Elastic section modulus Wel,y *

mm³

Shear area Av (web) *

mm²

Design actions (ULS)

Design bending moment MEd *

kNm

Design shear force VEd *

Results

Plastic bending resistance Mpl,Rd —

Elastic bending resistance Mel,Rd —

Governing Mc,Rd (by section class) —

Shear resistance Vpl,Rd —

Shear interaction factor ρ (if VEd > 0.5·Vpl,Rd) —

Reduced bending resistance due to shear MV,Rd —

Moment utilization μ = MEd / MRd —

Shear utilization ν = VEd / Vpl,Rd —

Status —

Authoritative Data, Methodology, and Guidance

Authoritative Data Source and Methodology

Standard: EN 1993‑1‑1:2005 + A1:2014 — Eurocode 3: Design of steel structures — General rules and rules for buildings. Clauses 6.2.1 (General), 6.2.6 (Shear), and 6.2.8 (Bending and shear interaction).

Publisher: CEN (European Committee for Standardization), 2014. Official publisher pages are accessible via National Standards Bodies or the Eurocodes portal: EU JRC Eurocodes.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

Notes and limitations: The present calculator addresses cross‑section resistances only. It does not include global stability (e.g., lateral–torsional buckling), shear buckling verification for slender webs, or interaction with axial force.

The Formulas Explained

Plastic bending resistance (classes 1–2):

\\[ M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \\]

Elastic bending resistance (class 3):

\\[ M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \\]

Shear resistance (web in shear, no buckling):

\\[ V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \\]

Governing cross‑section bending resistance:

\\[ M_{c,Rd} = \begin{cases} M_{pl,Rd} & \text{for Class 1–2}\\ M_{el,Rd} & \text{for Class 3} \end{cases} \\]

Bending–shear interaction reduction (Class 1–2 webs; typical formulation when \\(V_{Ed} > 0.5\,V_{pl,Rd}\\)):

\\[ \rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \\]

Utilization ratios:

\\[ \mu = \frac{M_{Ed}}{M_{Rd}}, \quad \nu = \frac{V_{Ed}}{V_{pl,Rd}} \\]

Glossary of Variables

fy (MPa): Yield strength of steel (e.g., S355 → 355 MPa).
γM0, γM1: Partial safety factors from EN 1993‑1‑1 and National Annex.
Wpl,y (mm³): Plastic section modulus about the major axis y.
Wel,y (mm³): Elastic section modulus about the major axis y.
Av (mm²): Shear area of the web for shear parallel to the web.
MEd (kNm): Design bending moment about the major axis y.
VEd (kN): Design shear force.
Mpl,Rd (kNm): Plastic cross‑section bending resistance.
Mel,Rd (kNm): Elastic cross‑section bending resistance.
Mc,Rd (kNm): Governing cross‑section bending resistance by class.
Vpl,Rd (kN): Shear resistance without buckling.
ρ (–): Shear–bending interaction factor when VEd > 0.5·Vpl,Rd.
MV,Rd (kNm): Reduced bending resistance due to shear interaction.
μ, ν (–): Moment and shear utilization ratios.

How it Works: A Step-by-Step Example

Given: fy = 355 MPa, γM0 = 1.0, class = 1, Wpl,y = 1.10×10⁶ mm³, Wel,y = 1.00×10⁶ mm³, Av = 900 mm², MEd = 200 kNm, VEd = 60 kN.

Plastic bending resistance: Mpl,Rd = Wpl,y·fy/γM0 = (1.10×10⁶ × 355)/10⁶ = 390.5 kNm.
Elastic bending resistance: Mel,Rd = (1.00×10⁶ × 355)/10⁶ = 355.0 kNm.
Governing Mc,Rd (Class 1): Mc,Rd = Mpl,Rd = 390.5 kNm.
Shear resistance: Vpl,Rd = Av·fy/(√3·γM0) = 900×355/(1.732×1000) ≈ 184.4 kN.
Shear interaction: VEd/Vpl,Rd ≈ 0.326 ≤ 0.5 → no reduction, so MV,Rd = Mc,Rd = 390.5 kNm.
Utilizations: μ = 200/390.5 ≈ 0.51; ν = 60/184.4 ≈ 0.33 → both pass.

Use the “Fill worked example” button to auto-populate these values in the calculator.

Frequently Asked Questions (FAQ)

What checks are covered by this calculator?

Cross-section bending resistance (plastic or elastic by class) and shear resistance without shear buckling. For Class 1–2 webs, if VEd > 0.5·Vpl,Rd, the bending resistance is reduced per EN 1993‑1‑1 6.2.8.

Which units should I use?

fy in MPa, Wpl,y and Wel,y in mm³, Av in mm², MEd in kNm, VEd in kN. The tool outputs M in kNm and V in kN.

Can I use this for Class 4 sections?

No. Class 4 requires effective section properties (EN 1993‑1‑1 and EN 1993‑1‑5). This tool does not compute effective widths.

Does it include lateral–torsional buckling?

No. LTB is a member stability check per EN 1993‑1‑1 6.3 and must be verified separately.

How do I estimate Av?

For rolled I/H sections, Av ≈ tw × hw (clear web height). For precise values, consult section tables or your National Annex recommendations.

Which partial factor applies?

Cross‑section resistances commonly use γM0. Some National Annexes may adapt factors; always follow the NA applicable to your project.

Is shear buckling considered?

No. If the web is slender, check shear buckling per EN 1993‑1‑5, or provide stiffeners to prevent buckling.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Formula (extracted LaTeX)

\[M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \\]

M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \

Formula (extracted LaTeX)

\[M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \\]

M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \

Formula (extracted LaTeX)

\[V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \\]

V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \

Formula (extracted LaTeX)

\[M_{c,Rd} = \begin{cases} M_{pl,Rd} & \text{for Class 1–2}\\ M_{el,Rd} & \text{for Class 3} \end{cases} \\]

M_{c,Rd} = \begin{cases} M_{pl,Rd} &amp; \text{for Class 1–2}\\ M_{el,Rd} &amp; \text{for Class 3} \end{cases} \

Formula (extracted LaTeX)

\[\rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \\]

\rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \

Formula (extracted text)

Plastic bending resistance (classes 1–2): \\[ M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \\] Elastic bending resistance (class 3): \\[ M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \\] Shear resistance (web in shear, no buckling): \\[ V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \\] Governing cross‑section bending resistance: \\[ M_{c,Rd} = \begin{cases} M_{pl,Rd} & \text{for Class 1–2}\\ M_{el,Rd} & \text{for Class 3} \end{cases} \\] Bending–shear interaction reduction (Class 1–2 webs; typical formulation when \\(V_{Ed} > 0.5\,V_{pl,Rd}\\)): \\[ \rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \\] Utilization ratios: \\[ \mu = \frac{M_{Ed}}{M_{Rd}}, \quad \nu = \frac{V_{Ed}}{V_{pl,Rd}} \\]

Variables and units

No variables provided in audit spec.

Sources (authoritative):

EU JRC Eurocodes — eurocodes.jrc.ec.europa.eu · Accessed 2026-01-19
https://eurocodes.jrc.ec.europa.eu/
Engineering — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/engineering

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Eurocode 3 Steel Beam Bending & Shear Resistance Calculator

Calculator

Section class (EN 1993‑1‑1, Table 5.2) *

Class 1 Class 2 Class 3 Class 4 (not supported)

Yield strength fy *

MPa

Partial factor γM0 *

Partial factor γM1

Section properties

Plastic section modulus Wpl,y *

mm³

Elastic section modulus Wel,y *

mm³

Shear area Av (web) *

mm²

Design actions (ULS)

Design bending moment MEd *

kNm

Design shear force VEd *

Results

Plastic bending resistance Mpl,Rd —

Elastic bending resistance Mel,Rd —

Governing Mc,Rd (by section class) —

Shear resistance Vpl,Rd —

Shear interaction factor ρ (if VEd > 0.5·Vpl,Rd) —

Reduced bending resistance due to shear MV,Rd —

Moment utilization μ = MEd / MRd —

Shear utilization ν = VEd / Vpl,Rd —

Status —

Authoritative Data, Methodology, and Guidance

Authoritative Data Source and Methodology

Publisher: CEN (European Committee for Standardization), 2014. Official publisher pages are accessible via National Standards Bodies or the Eurocodes portal: EU JRC Eurocodes.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formulas Explained

Plastic bending resistance (classes 1–2):

\\[ M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \\]

Elastic bending resistance (class 3):

\\[ M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \\]

Shear resistance (web in shear, no buckling):

\\[ V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \\]

Governing cross‑section bending resistance:

\\[ M_{c,Rd} = \begin{cases} M_{pl,Rd} & \text{for Class 1–2}\\ M_{el,Rd} & \text{for Class 3} \end{cases} \\]

Bending–shear interaction reduction (Class 1–2 webs; typical formulation when \\(V_{Ed} > 0.5\,V_{pl,Rd}\\)):

\\[ \rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \\]

Utilization ratios:

\\[ \mu = \frac{M_{Ed}}{M_{Rd}}, \quad \nu = \frac{V_{Ed}}{V_{pl,Rd}} \\]

Glossary of Variables

fy (MPa): Yield strength of steel (e.g., S355 → 355 MPa).
γM0, γM1: Partial safety factors from EN 1993‑1‑1 and National Annex.
Wpl,y (mm³): Plastic section modulus about the major axis y.
Wel,y (mm³): Elastic section modulus about the major axis y.
Av (mm²): Shear area of the web for shear parallel to the web.
MEd (kNm): Design bending moment about the major axis y.
VEd (kN): Design shear force.
Mpl,Rd (kNm): Plastic cross‑section bending resistance.
Mel,Rd (kNm): Elastic cross‑section bending resistance.
Mc,Rd (kNm): Governing cross‑section bending resistance by class.
Vpl,Rd (kN): Shear resistance without buckling.
ρ (–): Shear–bending interaction factor when VEd > 0.5·Vpl,Rd.
MV,Rd (kNm): Reduced bending resistance due to shear interaction.
μ, ν (–): Moment and shear utilization ratios.

How it Works: A Step-by-Step Example

Given: fy = 355 MPa, γM0 = 1.0, class = 1, Wpl,y = 1.10×10⁶ mm³, Wel,y = 1.00×10⁶ mm³, Av = 900 mm², MEd = 200 kNm, VEd = 60 kN.

Plastic bending resistance: Mpl,Rd = Wpl,y·fy/γM0 = (1.10×10⁶ × 355)/10⁶ = 390.5 kNm.
Elastic bending resistance: Mel,Rd = (1.00×10⁶ × 355)/10⁶ = 355.0 kNm.
Governing Mc,Rd (Class 1): Mc,Rd = Mpl,Rd = 390.5 kNm.
Shear resistance: Vpl,Rd = Av·fy/(√3·γM0) = 900×355/(1.732×1000) ≈ 184.4 kN.
Shear interaction: VEd/Vpl,Rd ≈ 0.326 ≤ 0.5 → no reduction, so MV,Rd = Mc,Rd = 390.5 kNm.
Utilizations: μ = 200/390.5 ≈ 0.51; ν = 60/184.4 ≈ 0.33 → both pass.

Use the “Fill worked example” button to auto-populate these values in the calculator.

Frequently Asked Questions (FAQ)

What checks are covered by this calculator?

Which units should I use?

fy in MPa, Wpl,y and Wel,y in mm³, Av in mm², MEd in kNm, VEd in kN. The tool outputs M in kNm and V in kN.

Can I use this for Class 4 sections?

No. Class 4 requires effective section properties (EN 1993‑1‑1 and EN 1993‑1‑5). This tool does not compute effective widths.

Does it include lateral–torsional buckling?

No. LTB is a member stability check per EN 1993‑1‑1 6.3 and must be verified separately.

How do I estimate Av?

For rolled I/H sections, Av ≈ tw × hw (clear web height). For precise values, consult section tables or your National Annex recommendations.

Which partial factor applies?

Cross‑section resistances commonly use γM0. Some National Annexes may adapt factors; always follow the NA applicable to your project.

Is shear buckling considered?

No. If the web is slender, check shear buckling per EN 1993‑1‑5, or provide stiffeners to prevent buckling.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Formula (extracted LaTeX)

\[M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \\]

M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \

Formula (extracted LaTeX)

\[M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \\]

M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \

Formula (extracted LaTeX)

\[V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \\]

V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \

Formula (extracted LaTeX)

\[M_{c,Rd} = \begin{cases} M_{pl,Rd} & \text{for Class 1–2}\\ M_{el,Rd} & \text{for Class 3} \end{cases} \\]

M_{c,Rd} = \begin{cases} M_{pl,Rd} &amp; \text{for Class 1–2}\\ M_{el,Rd} &amp; \text{for Class 3} \end{cases} \

Formula (extracted LaTeX)

\[\rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \\]

\rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \

Formula (extracted text)

Plastic bending resistance (classes 1–2): \\[ M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \\] Elastic bending resistance (class 3): \\[ M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \\] Shear resistance (web in shear, no buckling): \\[ V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \\] Governing cross‑section bending resistance: \\[ M_{c,Rd} = \begin{cases} M_{pl,Rd} & \text{for Class 1–2}\\ M_{el,Rd} & \text{for Class 3} \end{cases} \\] Bending–shear interaction reduction (Class 1–2 webs; typical formulation when \\(V_{Ed} > 0.5\,V_{pl,Rd}\\)): \\[ \rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \\] Utilization ratios: \\[ \mu = \frac{M_{Ed}}{M_{Rd}}, \quad \nu = \frac{V_{Ed}}{V_{pl,Rd}} \\]

Variables and units

No variables provided in audit spec.

Sources (authoritative):

EU JRC Eurocodes — eurocodes.jrc.ec.europa.eu · Accessed 2026-01-19
https://eurocodes.jrc.ec.europa.eu/
Engineering — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/engineering

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Eurocode 3 Steel Beam Bending & Shear Resistance Calculator

Calculator

Section class (EN 1993‑1‑1, Table 5.2) *

Class 1 Class 2 Class 3 Class 4 (not supported)

Yield strength fy *

MPa

Partial factor γM0 *

Partial factor γM1

Section properties

Plastic section modulus Wpl,y *

mm³

Elastic section modulus Wel,y *

mm³

Shear area Av (web) *

mm²

Design actions (ULS)

Design bending moment MEd *

kNm

Design shear force VEd *

Results

Plastic bending resistance Mpl,Rd —

Elastic bending resistance Mel,Rd —

Governing Mc,Rd (by section class) —

Shear resistance Vpl,Rd —

Shear interaction factor ρ (if VEd > 0.5·Vpl,Rd) —

Reduced bending resistance due to shear MV,Rd —

Moment utilization μ = MEd / MRd —

Shear utilization ν = VEd / Vpl,Rd —

Status —

Authoritative Data, Methodology, and Guidance

Authoritative Data Source and Methodology

Publisher: CEN (European Committee for Standardization), 2014. Official publisher pages are accessible via National Standards Bodies or the Eurocodes portal: EU JRC Eurocodes.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formulas Explained

Plastic bending resistance (classes 1–2):

\\[ M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \\]

Elastic bending resistance (class 3):

\\[ M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \\]

Shear resistance (web in shear, no buckling):

\\[ V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \\]

Governing cross‑section bending resistance:

\\[ M_{c,Rd} = \begin{cases} M_{pl,Rd} & \text{for Class 1–2}\\ M_{el,Rd} & \text{for Class 3} \end{cases} \\]

Bending–shear interaction reduction (Class 1–2 webs; typical formulation when \\(V_{Ed} > 0.5\,V_{pl,Rd}\\)):

\\[ \rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \\]

Utilization ratios:

\\[ \mu = \frac{M_{Ed}}{M_{Rd}}, \quad \nu = \frac{V_{Ed}}{V_{pl,Rd}} \\]

Glossary of Variables

fy (MPa): Yield strength of steel (e.g., S355 → 355 MPa).
γM0, γM1: Partial safety factors from EN 1993‑1‑1 and National Annex.
Wpl,y (mm³): Plastic section modulus about the major axis y.
Wel,y (mm³): Elastic section modulus about the major axis y.
Av (mm²): Shear area of the web for shear parallel to the web.
MEd (kNm): Design bending moment about the major axis y.
VEd (kN): Design shear force.
Mpl,Rd (kNm): Plastic cross‑section bending resistance.
Mel,Rd (kNm): Elastic cross‑section bending resistance.
Mc,Rd (kNm): Governing cross‑section bending resistance by class.
Vpl,Rd (kN): Shear resistance without buckling.
ρ (–): Shear–bending interaction factor when VEd > 0.5·Vpl,Rd.
MV,Rd (kNm): Reduced bending resistance due to shear interaction.
μ, ν (–): Moment and shear utilization ratios.

How it Works: A Step-by-Step Example

Given: fy = 355 MPa, γM0 = 1.0, class = 1, Wpl,y = 1.10×10⁶ mm³, Wel,y = 1.00×10⁶ mm³, Av = 900 mm², MEd = 200 kNm, VEd = 60 kN.

Plastic bending resistance: Mpl,Rd = Wpl,y·fy/γM0 = (1.10×10⁶ × 355)/10⁶ = 390.5 kNm.
Elastic bending resistance: Mel,Rd = (1.00×10⁶ × 355)/10⁶ = 355.0 kNm.
Governing Mc,Rd (Class 1): Mc,Rd = Mpl,Rd = 390.5 kNm.
Shear resistance: Vpl,Rd = Av·fy/(√3·γM0) = 900×355/(1.732×1000) ≈ 184.4 kN.
Shear interaction: VEd/Vpl,Rd ≈ 0.326 ≤ 0.5 → no reduction, so MV,Rd = Mc,Rd = 390.5 kNm.
Utilizations: μ = 200/390.5 ≈ 0.51; ν = 60/184.4 ≈ 0.33 → both pass.

Use the “Fill worked example” button to auto-populate these values in the calculator.

Frequently Asked Questions (FAQ)

What checks are covered by this calculator?

Which units should I use?

fy in MPa, Wpl,y and Wel,y in mm³, Av in mm², MEd in kNm, VEd in kN. The tool outputs M in kNm and V in kN.

Can I use this for Class 4 sections?

No. Class 4 requires effective section properties (EN 1993‑1‑1 and EN 1993‑1‑5). This tool does not compute effective widths.

Does it include lateral–torsional buckling?

No. LTB is a member stability check per EN 1993‑1‑1 6.3 and must be verified separately.

How do I estimate Av?

For rolled I/H sections, Av ≈ tw × hw (clear web height). For precise values, consult section tables or your National Annex recommendations.

Which partial factor applies?

Cross‑section resistances commonly use γM0. Some National Annexes may adapt factors; always follow the NA applicable to your project.

Is shear buckling considered?

No. If the web is slender, check shear buckling per EN 1993‑1‑5, or provide stiffeners to prevent buckling.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Formula (extracted LaTeX)

\[M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \\]

M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \

Formula (extracted LaTeX)

\[M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \\]

M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \

Formula (extracted LaTeX)

\[V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \\]

V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \

Formula (extracted LaTeX)

\[M_{c,Rd} = \begin{cases} M_{pl,Rd} & \text{for Class 1–2}\\ M_{el,Rd} & \text{for Class 3} \end{cases} \\]

M_{c,Rd} = \begin{cases} M_{pl,Rd} &amp; \text{for Class 1–2}\\ M_{el,Rd} &amp; \text{for Class 3} \end{cases} \

Formula (extracted LaTeX)

\[\rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \\]

\rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \

Formula (extracted text)

Plastic bending resistance (classes 1–2): \\[ M_{pl,Rd} = \frac{W_{pl,y}\, f_y}{\gamma_{M0}} \\] Elastic bending resistance (class 3): \\[ M_{el,Rd} = \frac{W_{el,y}\, f_y}{\gamma_{M0}} \\] Shear resistance (web in shear, no buckling): \\[ V_{pl,Rd} = \frac{A_v\, f_y}{\sqrt{3}\, \gamma_{M0}} \\] Governing cross‑section bending resistance: \\[ M_{c,Rd} = \begin{cases} M_{pl,Rd} & \text{for Class 1–2}\\ M_{el,Rd} & \text{for Class 3} \end{cases} \\] Bending–shear interaction reduction (Class 1–2 webs; typical formulation when \\(V_{Ed} > 0.5\,V_{pl,Rd}\\)): \\[ \rho = \left(2\frac{V_{Ed}}{V_{pl,Rd}} - 1\right)^2,\quad M_{V,Rd} = (1-\rho)\, M_{c,Rd} \\] Utilization ratios: \\[ \mu = \frac{M_{Ed}}{M_{Rd}}, \quad \nu = \frac{V_{Ed}}{V_{pl,Rd}} \\]

Variables and units

No variables provided in audit spec.

Sources (authoritative):

EU JRC Eurocodes — eurocodes.jrc.ec.europa.eu · Accessed 2026-01-19
https://eurocodes.jrc.ec.europa.eu/
Engineering — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/engineering

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
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Formulas

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Version 0.1.0-draft

Citations

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Changelog

0.1.0-draft — 2026-01-19: Initial draft (review required).