Eurocode 2 Reinforcement Anchorage & Lap Length Calculator

Professional Eurocode 2 (EN 1992-1-1) calculator for reinforcement anchorage length and lap splice length. Computes l_b,req, l_bd, and l_0 per EC2 Clause 8.4 and 8.7 with clear step-by-step outputs.

Full original guide (expanded)

CalcDomain

Eurocode 2 Reinforcement Anchorage & Lap Length Calculator

A professional-grade EC2 tool for structural engineers to compute reinforcement anchorage length and lap splice length. It implements EN 1992-1-1 Clause 8 with clear, auditable steps and mobile-first UX.

Calculator

Stress state
mm
Standard ribbed bars per EC2. η2 accounts for diameter effect when φ > 32 mm.
The calculator uses fctk,0.05 per EC2 Table 3.1 and fctd = fctk,0.05/γc with γc=1.5.
–
Design stress entry

For simplicity, α-factors are applied multiplicatively and bounded to ≥ 0.7. Verify exact α-values per EC2 for your detailing.

Results

Concrete fctk,0.05
— MPa
fctd
— MPa
η1 (bond) × η2 (diameter)
—
Design bond fbd
— MPa
σsd (used, capped)
— MPa
Basic required anchorage l_b,req
— mm
α-product (anchorage)
—
l_b,min
— mm
Design anchorage length l_bd
— mm
Lap splice min length l_0,min
— mm
Design lap length l_0
— mm

Data Source and Methodology

Authoritative standard: EN 1992-1-1:2004 + A1:2014 (Eurocode 2: Design of concrete structures – Part 1-1). Key clauses: 3.1 (material properties), 8.4 (bond and anchorage), 8.7 (lap splices). Accessible reference PDF: EN 1992-1-1:2004 (PDF). National Annex provisions may modify recommended values.

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

The Formula Explained

Concrete design tensile strength: $$ f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c} $$

Design bond strength: $$ f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd} $$ with \( \eta_1 = 1.0 \) for good bond (otherwise 0.7) and \( \eta_2 = \begin{cases} 1.0 & \phi \le 32\text{ mm} \\ \max\left(0.7,\frac{132-\phi}{100}\right) & \phi > 32\text{ mm} \end{cases} \)

Basic required anchorage length: $$ l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}} $$ where \( \sigma_{sd} \le \dfrac{f_{yk}}{\gamma_s} \).

Design anchorage length: $$ l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big) $$ with a simplified product of detailing coefficients \( \alpha \ge 0.7 \) and $$ l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big). $$

Design lap length (tension/compression splice): $$ l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big) $$ with $$ l_{0,min} = \begin{cases} \max\!\big(0.3\,l_0,\; 15\phi,\; 200\text{ mm}\big) & \text{tension} \\ \max\!\big(0.3\,l_0,\; 10\phi,\; 100\text{ mm}\big) & \text{compression} \end{cases} $$ Note: Project- and clause-specific α-factors may apply (bar shape, confinement, percentage lapped, etc.).

Glossary of Variables

  • φ: Bar diameter (mm).
  • fck: Concrete cylinder strength (MPa), by class (e.g., C30/37).
  • fctk,0.05: 5% fractile tensile strength of concrete (MPa).
  • fctd: Design tensile strength = fctk,0.05/γc (γc=1.5 recommended).
  • fyk: Characteristic steel yield strength (MPa), e.g., 500 MPa.
  • γs: Partial factor for steel (recommended 1.15).
  • σsd: Design steel stress at anchorage/lap location (MPa), ≤ fyk/γs.
  • η1: Bond condition factor (1.0 good; 0.7 otherwise).
  • η2: Bar diameter factor (1.0 for φ ≤ 32 mm; else (132 − φ)/100, not less than 0.7).
  • fbd: Design bond strength (MPa).
  • l_b,req: Basic required anchorage length (mm).
  • α, α_lap: Simplified products of detailing coefficients (hooks, confinement, devices).
  • l_b,min: Minimum anchorage length (mm) per EC2.
  • l_bd: Design anchorage length (mm).
  • l_0,min: Minimum lap length (mm) per EC2.
  • l_0: Design lap splice length (mm).

How It Works: A Step-by-Step Example

Target: straight 16 mm B500 bar in tension, concrete C30/37, good bond, γs=1.15, γc=1.5.

  1. Material strengths: fctk,0.05 = 2.6 MPa → fctd = 2.6/1.5 = 1.733 MPa.
  2. Bond factors: η1 = 1.0 (good), η2 = 1.0 (φ ≤ 32). Hence fbd = 2.25 × 1.0 × 1.0 × 1.733 = 3.90 MPa.
  3. Steel stress: σsd = fyk/γs = 500/1.15 = 434.8 MPa.
  4. Basic anchorage: l_b,req = (16/4) × (434.8/3.90) = 4 × 111.8 ≈ 447 mm.
  5. α for straight bar = 1.0; l_b,min = max(0.3×447, 10×16, 100) = max(134, 160, 100) = 160 mm.
  6. Design anchorage length: l_bd = max(1.0×447, 160) = 447 mm. Lap in tension: l_0,min = max(0.3×447, 15×16, 200) = max(134, 240, 200) = 240 mm → l_0 = max(447, 240) = 447 mm.

This calculator applies common recommended values. Always check your National Annex and project specifications for any adjustments.

Frequently Asked Questions (FAQ)

Do I need to input the bar stress σsd?

Not necessarily. By default the calculator uses σsd = fyk/γs. If your design causes lower stress at the anchorage, switch to “Enter custom σsd”.

How are minimum lengths enforced?

The tool automatically applies EC2 minima: l_b,min = max(0.3 l_b,req, 10φ, 100 mm). For lap splices it uses 15φ and 200 mm in tension, 10φ and 100 mm in compression.

What bars are assumed?

Ribbed reinforcing bars per EC2. Plain bars or special coatings are not covered; consult the relevant provisions if used.

How is η2 computed for large diameters?

For φ > 32 mm, η2 = (132 − φ)/100, with a floor of 0.7 as a conservative cap.

Can I model hooks and confinement?

Yes, simplified α-factors are provided for hooks/bends and transverse confinement. For exact values, refer to Clause 8.4 and tables in EC2 and your National Annex.

Does this replace engineering judgment?

No. This is an aid to calculation and documentation. The designer is responsible for ensuring compliance with applicable standards and project requirements.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c}\]
f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c}
Formula (extracted LaTeX)
\[f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd}\]
f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd}
Formula (extracted LaTeX)
\[l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}}\]
l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}}
Formula (extracted LaTeX)
\[l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big)\]
l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big)
Formula (extracted LaTeX)
\[l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big).\]
l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big).
Formula (extracted LaTeX)
\[l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big)\]
l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big)
Formula (extracted text)
Concrete design tensile strength: $ f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c} $ Design bond strength: $ f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd} $ with \( \eta_1 = 1.0 \) for good bond (otherwise 0.7) and \( \eta_2 = \begin{cases} 1.0 & \phi \le 32\text{ mm} \\ \max\left(0.7,\frac{132-\phi}{100}\right) & \phi > 32\text{ mm} \end{cases} \) Basic required anchorage length: $ l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}} $ where \( \sigma_{sd} \le \dfrac{f_{yk}}{\gamma_s} \). Design anchorage length: $ l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big) $ with a simplified product of detailing coefficients \( \alpha \ge 0.7 \) and $ l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big). $ Design lap length (tension/compression splice): $ l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big) $ with $ l_{0,min} = \begin{cases} \max\!\big(0.3\,l_0,\; 15\phi,\; 200\text{ mm}\big) & \text{tension} \\ \max\!\big(0.3\,l_0,\; 10\phi,\; 100\text{ mm}\big) & \text{compression} \end{cases} $ Note: Project- and clause-specific α-factors may apply (bar shape, confinement, percentage lapped, etc.).
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
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
CalcDomain

Eurocode 2 Reinforcement Anchorage & Lap Length Calculator

A professional-grade EC2 tool for structural engineers to compute reinforcement anchorage length and lap splice length. It implements EN 1992-1-1 Clause 8 with clear, auditable steps and mobile-first UX.

Calculator

Stress state
mm
Standard ribbed bars per EC2. η2 accounts for diameter effect when φ > 32 mm.
The calculator uses fctk,0.05 per EC2 Table 3.1 and fctd = fctk,0.05/γc with γc=1.5.
–
Design stress entry

For simplicity, α-factors are applied multiplicatively and bounded to ≥ 0.7. Verify exact α-values per EC2 for your detailing.

Results

Concrete fctk,0.05
— MPa
fctd
— MPa
η1 (bond) × η2 (diameter)
—
Design bond fbd
— MPa
σsd (used, capped)
— MPa
Basic required anchorage l_b,req
— mm
α-product (anchorage)
—
l_b,min
— mm
Design anchorage length l_bd
— mm
Lap splice min length l_0,min
— mm
Design lap length l_0
— mm

Data Source and Methodology

Authoritative standard: EN 1992-1-1:2004 + A1:2014 (Eurocode 2: Design of concrete structures – Part 1-1). Key clauses: 3.1 (material properties), 8.4 (bond and anchorage), 8.7 (lap splices). Accessible reference PDF: EN 1992-1-1:2004 (PDF). National Annex provisions may modify recommended values.

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

The Formula Explained

Concrete design tensile strength: $$ f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c} $$

Design bond strength: $$ f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd} $$ with \( \eta_1 = 1.0 \) for good bond (otherwise 0.7) and \( \eta_2 = \begin{cases} 1.0 & \phi \le 32\text{ mm} \\ \max\left(0.7,\frac{132-\phi}{100}\right) & \phi > 32\text{ mm} \end{cases} \)

Basic required anchorage length: $$ l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}} $$ where \( \sigma_{sd} \le \dfrac{f_{yk}}{\gamma_s} \).

Design anchorage length: $$ l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big) $$ with a simplified product of detailing coefficients \( \alpha \ge 0.7 \) and $$ l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big). $$

Design lap length (tension/compression splice): $$ l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big) $$ with $$ l_{0,min} = \begin{cases} \max\!\big(0.3\,l_0,\; 15\phi,\; 200\text{ mm}\big) & \text{tension} \\ \max\!\big(0.3\,l_0,\; 10\phi,\; 100\text{ mm}\big) & \text{compression} \end{cases} $$ Note: Project- and clause-specific α-factors may apply (bar shape, confinement, percentage lapped, etc.).

Glossary of Variables

  • φ: Bar diameter (mm).
  • fck: Concrete cylinder strength (MPa), by class (e.g., C30/37).
  • fctk,0.05: 5% fractile tensile strength of concrete (MPa).
  • fctd: Design tensile strength = fctk,0.05/γc (γc=1.5 recommended).
  • fyk: Characteristic steel yield strength (MPa), e.g., 500 MPa.
  • γs: Partial factor for steel (recommended 1.15).
  • σsd: Design steel stress at anchorage/lap location (MPa), ≤ fyk/γs.
  • η1: Bond condition factor (1.0 good; 0.7 otherwise).
  • η2: Bar diameter factor (1.0 for φ ≤ 32 mm; else (132 − φ)/100, not less than 0.7).
  • fbd: Design bond strength (MPa).
  • l_b,req: Basic required anchorage length (mm).
  • α, α_lap: Simplified products of detailing coefficients (hooks, confinement, devices).
  • l_b,min: Minimum anchorage length (mm) per EC2.
  • l_bd: Design anchorage length (mm).
  • l_0,min: Minimum lap length (mm) per EC2.
  • l_0: Design lap splice length (mm).

How It Works: A Step-by-Step Example

Target: straight 16 mm B500 bar in tension, concrete C30/37, good bond, γs=1.15, γc=1.5.

  1. Material strengths: fctk,0.05 = 2.6 MPa → fctd = 2.6/1.5 = 1.733 MPa.
  2. Bond factors: η1 = 1.0 (good), η2 = 1.0 (φ ≤ 32). Hence fbd = 2.25 × 1.0 × 1.0 × 1.733 = 3.90 MPa.
  3. Steel stress: σsd = fyk/γs = 500/1.15 = 434.8 MPa.
  4. Basic anchorage: l_b,req = (16/4) × (434.8/3.90) = 4 × 111.8 ≈ 447 mm.
  5. α for straight bar = 1.0; l_b,min = max(0.3×447, 10×16, 100) = max(134, 160, 100) = 160 mm.
  6. Design anchorage length: l_bd = max(1.0×447, 160) = 447 mm. Lap in tension: l_0,min = max(0.3×447, 15×16, 200) = max(134, 240, 200) = 240 mm → l_0 = max(447, 240) = 447 mm.

This calculator applies common recommended values. Always check your National Annex and project specifications for any adjustments.

Frequently Asked Questions (FAQ)

Do I need to input the bar stress σsd?

Not necessarily. By default the calculator uses σsd = fyk/γs. If your design causes lower stress at the anchorage, switch to “Enter custom σsd”.

How are minimum lengths enforced?

The tool automatically applies EC2 minima: l_b,min = max(0.3 l_b,req, 10φ, 100 mm). For lap splices it uses 15φ and 200 mm in tension, 10φ and 100 mm in compression.

What bars are assumed?

Ribbed reinforcing bars per EC2. Plain bars or special coatings are not covered; consult the relevant provisions if used.

How is η2 computed for large diameters?

For φ > 32 mm, η2 = (132 − φ)/100, with a floor of 0.7 as a conservative cap.

Can I model hooks and confinement?

Yes, simplified α-factors are provided for hooks/bends and transverse confinement. For exact values, refer to Clause 8.4 and tables in EC2 and your National Annex.

Does this replace engineering judgment?

No. This is an aid to calculation and documentation. The designer is responsible for ensuring compliance with applicable standards and project requirements.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c}\]
f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c}
Formula (extracted LaTeX)
\[f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd}\]
f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd}
Formula (extracted LaTeX)
\[l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}}\]
l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}}
Formula (extracted LaTeX)
\[l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big)\]
l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big)
Formula (extracted LaTeX)
\[l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big).\]
l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big).
Formula (extracted LaTeX)
\[l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big)\]
l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big)
Formula (extracted text)
Concrete design tensile strength: $ f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c} $ Design bond strength: $ f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd} $ with \( \eta_1 = 1.0 \) for good bond (otherwise 0.7) and \( \eta_2 = \begin{cases} 1.0 & \phi \le 32\text{ mm} \\ \max\left(0.7,\frac{132-\phi}{100}\right) & \phi > 32\text{ mm} \end{cases} \) Basic required anchorage length: $ l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}} $ where \( \sigma_{sd} \le \dfrac{f_{yk}}{\gamma_s} \). Design anchorage length: $ l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big) $ with a simplified product of detailing coefficients \( \alpha \ge 0.7 \) and $ l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big). $ Design lap length (tension/compression splice): $ l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big) $ with $ l_{0,min} = \begin{cases} \max\!\big(0.3\,l_0,\; 15\phi,\; 200\text{ mm}\big) & \text{tension} \\ \max\!\big(0.3\,l_0,\; 10\phi,\; 100\text{ mm}\big) & \text{compression} \end{cases} $ Note: Project- and clause-specific α-factors may apply (bar shape, confinement, percentage lapped, etc.).
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
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
CalcDomain

Eurocode 2 Reinforcement Anchorage & Lap Length Calculator

A professional-grade EC2 tool for structural engineers to compute reinforcement anchorage length and lap splice length. It implements EN 1992-1-1 Clause 8 with clear, auditable steps and mobile-first UX.

Calculator

Stress state
mm
Standard ribbed bars per EC2. η2 accounts for diameter effect when φ > 32 mm.
The calculator uses fctk,0.05 per EC2 Table 3.1 and fctd = fctk,0.05/γc with γc=1.5.
–
Design stress entry

For simplicity, α-factors are applied multiplicatively and bounded to ≥ 0.7. Verify exact α-values per EC2 for your detailing.

Results

Concrete fctk,0.05
— MPa
fctd
— MPa
η1 (bond) × η2 (diameter)
—
Design bond fbd
— MPa
σsd (used, capped)
— MPa
Basic required anchorage l_b,req
— mm
α-product (anchorage)
—
l_b,min
— mm
Design anchorage length l_bd
— mm
Lap splice min length l_0,min
— mm
Design lap length l_0
— mm

Data Source and Methodology

Authoritative standard: EN 1992-1-1:2004 + A1:2014 (Eurocode 2: Design of concrete structures – Part 1-1). Key clauses: 3.1 (material properties), 8.4 (bond and anchorage), 8.7 (lap splices). Accessible reference PDF: EN 1992-1-1:2004 (PDF). National Annex provisions may modify recommended values.

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

The Formula Explained

Concrete design tensile strength: $$ f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c} $$

Design bond strength: $$ f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd} $$ with \( \eta_1 = 1.0 \) for good bond (otherwise 0.7) and \( \eta_2 = \begin{cases} 1.0 & \phi \le 32\text{ mm} \\ \max\left(0.7,\frac{132-\phi}{100}\right) & \phi > 32\text{ mm} \end{cases} \)

Basic required anchorage length: $$ l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}} $$ where \( \sigma_{sd} \le \dfrac{f_{yk}}{\gamma_s} \).

Design anchorage length: $$ l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big) $$ with a simplified product of detailing coefficients \( \alpha \ge 0.7 \) and $$ l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big). $$

Design lap length (tension/compression splice): $$ l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big) $$ with $$ l_{0,min} = \begin{cases} \max\!\big(0.3\,l_0,\; 15\phi,\; 200\text{ mm}\big) & \text{tension} \\ \max\!\big(0.3\,l_0,\; 10\phi,\; 100\text{ mm}\big) & \text{compression} \end{cases} $$ Note: Project- and clause-specific α-factors may apply (bar shape, confinement, percentage lapped, etc.).

Glossary of Variables

  • φ: Bar diameter (mm).
  • fck: Concrete cylinder strength (MPa), by class (e.g., C30/37).
  • fctk,0.05: 5% fractile tensile strength of concrete (MPa).
  • fctd: Design tensile strength = fctk,0.05/γc (γc=1.5 recommended).
  • fyk: Characteristic steel yield strength (MPa), e.g., 500 MPa.
  • γs: Partial factor for steel (recommended 1.15).
  • σsd: Design steel stress at anchorage/lap location (MPa), ≤ fyk/γs.
  • η1: Bond condition factor (1.0 good; 0.7 otherwise).
  • η2: Bar diameter factor (1.0 for φ ≤ 32 mm; else (132 − φ)/100, not less than 0.7).
  • fbd: Design bond strength (MPa).
  • l_b,req: Basic required anchorage length (mm).
  • α, α_lap: Simplified products of detailing coefficients (hooks, confinement, devices).
  • l_b,min: Minimum anchorage length (mm) per EC2.
  • l_bd: Design anchorage length (mm).
  • l_0,min: Minimum lap length (mm) per EC2.
  • l_0: Design lap splice length (mm).

How It Works: A Step-by-Step Example

Target: straight 16 mm B500 bar in tension, concrete C30/37, good bond, γs=1.15, γc=1.5.

  1. Material strengths: fctk,0.05 = 2.6 MPa → fctd = 2.6/1.5 = 1.733 MPa.
  2. Bond factors: η1 = 1.0 (good), η2 = 1.0 (φ ≤ 32). Hence fbd = 2.25 × 1.0 × 1.0 × 1.733 = 3.90 MPa.
  3. Steel stress: σsd = fyk/γs = 500/1.15 = 434.8 MPa.
  4. Basic anchorage: l_b,req = (16/4) × (434.8/3.90) = 4 × 111.8 ≈ 447 mm.
  5. α for straight bar = 1.0; l_b,min = max(0.3×447, 10×16, 100) = max(134, 160, 100) = 160 mm.
  6. Design anchorage length: l_bd = max(1.0×447, 160) = 447 mm. Lap in tension: l_0,min = max(0.3×447, 15×16, 200) = max(134, 240, 200) = 240 mm → l_0 = max(447, 240) = 447 mm.

This calculator applies common recommended values. Always check your National Annex and project specifications for any adjustments.

Frequently Asked Questions (FAQ)

Do I need to input the bar stress σsd?

Not necessarily. By default the calculator uses σsd = fyk/γs. If your design causes lower stress at the anchorage, switch to “Enter custom σsd”.

How are minimum lengths enforced?

The tool automatically applies EC2 minima: l_b,min = max(0.3 l_b,req, 10φ, 100 mm). For lap splices it uses 15φ and 200 mm in tension, 10φ and 100 mm in compression.

What bars are assumed?

Ribbed reinforcing bars per EC2. Plain bars or special coatings are not covered; consult the relevant provisions if used.

How is η2 computed for large diameters?

For φ > 32 mm, η2 = (132 − φ)/100, with a floor of 0.7 as a conservative cap.

Can I model hooks and confinement?

Yes, simplified α-factors are provided for hooks/bends and transverse confinement. For exact values, refer to Clause 8.4 and tables in EC2 and your National Annex.

Does this replace engineering judgment?

No. This is an aid to calculation and documentation. The designer is responsible for ensuring compliance with applicable standards and project requirements.

Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c}\]
f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c}
Formula (extracted LaTeX)
\[f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd}\]
f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd}
Formula (extracted LaTeX)
\[l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}}\]
l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}}
Formula (extracted LaTeX)
\[l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big)\]
l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big)
Formula (extracted LaTeX)
\[l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big).\]
l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big).
Formula (extracted LaTeX)
\[l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big)\]
l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big)
Formula (extracted text)
Concrete design tensile strength: $ f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c} $ Design bond strength: $ f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd} $ with \( \eta_1 = 1.0 \) for good bond (otherwise 0.7) and \( \eta_2 = \begin{cases} 1.0 & \phi \le 32\text{ mm} \\ \max\left(0.7,\frac{132-\phi}{100}\right) & \phi > 32\text{ mm} \end{cases} \) Basic required anchorage length: $ l_{b,req} = \dfrac{\phi}{4}\,\dfrac{\sigma_{sd}}{f_{bd}} $ where \( \sigma_{sd} \le \dfrac{f_{yk}}{\gamma_s} \). Design anchorage length: $ l_{bd} = \max\!\Big(\alpha \cdot l_{b,req},\; l_{b,min}\Big) $ with a simplified product of detailing coefficients \( \alpha \ge 0.7 \) and $ l_{b,min} = \max\!\big(0.3\,l_{b,req},\; 10\phi,\; 100\text{ mm}\big). $ Design lap length (tension/compression splice): $ l_0 = \max\!\Big(\alpha_{lap}\cdot l_{b,req},\; l_{0,min}\Big) $ with $ l_{0,min} = \begin{cases} \max\!\big(0.3\,l_0,\; 15\phi,\; 200\text{ mm}\big) & \text{tension} \\ \max\!\big(0.3\,l_0,\; 10\phi,\; 100\text{ mm}\big) & \text{compression} \end{cases} $ Note: Project- and clause-specific α-factors may apply (bar shape, confinement, percentage lapped, etc.).
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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
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Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).