Eurocode 2 Anchorage Length & Lap Length Calculator (EN 1992‑1‑1)
Compute basic required anchorage length, design anchorage length and lap splice length for reinforcing bars according to Eurocode 2 (EN 1992‑1‑1 §8.4–8.7). Includes modification factors for bar shape, cover, confinement and welded transverse bars.
Input parameters
Cylinder strength (e.g. C30/37 → fck = 30 MPa).
Often taken as 0.87·fyk for fully yielded bars.
Hooks/bends increase anchorage efficiency (α2 factor).
Minimum of concrete cover and bar spacing to edge, per EN 1992‑1‑1 §8.4.4.
Results
Basic required anchorage length lb,rqd
– mm
Before modification factors (α) and minimum limits.
Design anchorage length lb
– mm
Including bond condition, bar shape, cover and confinement factors.
Minimum anchorage length lb,min: – mm
Design note
This tool follows the main EN 1992‑1‑1 formulas with typical National Annex assumptions. Always check against your National Annex, project specifications and detailing rules (bar spacing, cover, transverse reinforcement, bar grouping, etc.).
Eurocode 2 anchorage length – formulas used
Anchorage length is the straight or curved length of reinforcing bar required to develop the design stress in the bar through bond with the surrounding concrete. Eurocode 2 defines:
1. Basic required anchorage length \( l_{b,rqd} \)
EN 1992‑1‑1, Eq. (8.3):
\[ l_{b,rqd} = \frac{\phi}{4} \cdot \frac{\sigma_{sd}}{f_{bd}} \]
where:
- \(\phi\) = bar diameter (mm)
- \(\sigma_{sd}\) = design stress in the bar at the section considered (MPa)
- \(f_{bd}\) = design value of bond strength (MPa)
The design bond strength is:
\[ f_{bd} = 2.25 \cdot \eta_1 \cdot \eta_2 \cdot f_{ctd} \]
with:
- \(f_{ctd} = \dfrac{f_{ctk,0.05}}{\gamma_c}\) (design tensile strength of concrete)
- \(\eta_1\) = coefficient for bond condition (1.0 for good, 0.7 for poor)
- \(\eta_2\) = coefficient for bar diameter (1.0 for \(\phi \le 32\) mm)
The calculator estimates \(f_{ctk,0.05}\) from \(f_{ck}\) using the standard Eurocode 2 expressions for normal‑weight concrete.
2. Design anchorage length \( l_b \)
The design anchorage length is obtained by applying modification factors to \(l_{b,rqd}\) and checking against minimum values:
\[ l_b = \alpha_1 \alpha_2 \alpha_3 \alpha_4 \alpha_5 \, l_{b,rqd} \quad \text{but} \quad l_b \ge l_{b,min} \]
Typical factors (simplified, may vary with National Annex):
- \(\alpha_1\): bar shape (straight vs hooked/bent)
- \(\alpha_2\): concrete cover and confinement (links, welded bars)
- \(\alpha_3\): transverse pressure (often 1.0 in building design)
- \(\alpha_4\): welded transverse reinforcement (if present)
- \(\alpha_5\): effect of excess reinforcement (ratio of required/provided steel)
This tool groups these into practical options:
- Anchorage type → affects \(\alpha_1\)
- Cover & confinement → affects \(\alpha_2\) and \(\alpha_4\)
- Bond condition → affects \(f_{bd}\) via \(\eta_1\)
Minimum anchorage length is checked as:
\[ l_{b,min} = \max \left( 0.3 \, l_{b,rqd}, \; 10\phi, \; 100 \text{ mm} \right) \]
3. Lap splice length \( l_0 \)
For tension lap splices, Eurocode 2 requires a lap length based on the anchorage length and additional factors for bar arrangement and percentage of lapped bars. A simplified expression used here is:
\[ l_0 = \alpha_6 \, l_{b,rqd} \quad \text{but} \quad l_0 \ge l_{0,min} \]
with typical minimum:
\[ l_{0,min} = \max \left( 0.3 \, l_{b,rqd}, \; 15\phi, \; 200 \text{ mm} \right) \]
The calculator assumes moderate bar congestion and standard detailing (no bundled bars) and applies a conservative \(\alpha_6\) consistent with common practice.
Worked example
Consider a tension bar in a C30/37 slab:
- Concrete: C30/37 → \(f_{ck} = 30\) MPa
- Steel: B500B → \(f_{yk} = 500\) MPa
- Bar: φ16, tension, good bond, straight bar
- Design stress: \(\sigma_{sd} = 0.87 f_{yk} = 435\) MPa
Using the calculator with these inputs you will obtain:
- Basic required anchorage length \(l_{b,rqd}\) ≈ 460–480 mm
- Design anchorage length \(l_b\) ≈ 500–550 mm (after factors and minimum check)
- Minimum lap length \(l_0\) (if requested) typically ≥ 15φ = 240 mm and ≥ 200 mm
Practical tips for Eurocode 2 anchorage design
- Always verify that bar spacing and cover satisfy the detailing rules in §8.2–8.3.
- Top bars in deep members often have poor bond and require longer anchorage.
- Hooks and bends are very effective in reducing required straight length, especially near edges.
- Good confinement (closed stirrups, welded transverse bars) improves bond and may reduce length.
- For heavily congested zones (beam‑column joints, pile caps), consider using smaller bars with longer laps instead of very large diameters.
Limitations and disclaimer
This calculator is intended as a design aid for qualified structural engineers. It implements the core Eurocode 2 equations with typical assumptions, but:
- It does not replace the National Annex or project specifications.
- It does not check all detailing rules (bar spacing, cover, bar grouping, seismic provisions, etc.).
- It assumes normal‑weight concrete and ribbed reinforcing bars.
Always cross‑check results with hand calculations and the relevant code clauses before issuing drawings or construction documents.