Anchorage and lap lengths
Anchorage and lap lengths for reinforcing bars, to EN 1992-1-1 §8.4 and §8.7.
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Tool information
What this calculator computes
The tool determines the anchorage length \(l_{bd}\) (§8.4) and the lap length \(l_0\) (§8.7) for reinforcing bars, to EN 1992-1-1. It covers straight, bent, hooked and looped bars, in tension and in compression.
The calculation chain
Everything starts from the bond stress:
\(f_{bd} = 2.25 \, \eta_1 \eta_2 f_{ctd}\)
\(\eta_1\) reflects the bar's position during casting: 1.0 for good conditions, 0.7 otherwise. The difference is not small — a bar near the top of a deep pour needs an anchorage 43% longer. Rising air and water collect beneath the bar and spoil the bond.
\(\eta_2\) penalises thick bars: 1.0 up to φ32, then \((132 - \phi)/100\).
From this follows the basic length:
\(l_{b,rqd} = \frac{\phi}{4} \cdot \frac{\sigma_{sd}}{f_{bd}}\)
Where the saving is
\(\sigma_{sd}\) is not automatically \(f_{yd}\). It is the actual stress in the bar at the section from which anchorage is measured. If the bar works at 60% of its capacity — the usual situation at a support, where the moment is smaller than at midspan — the length drops proportionally, by 40%.
It is the largest single saving in the whole calculation, and the most frequently missed: \(f_{yd} = 435\) MPa gets used reflexively and tens of centimetres are lost on every bar.
The α coefficients (Table 8.2)
\(l_{bd} = \alpha_1 \alpha_2 \alpha_3 \alpha_4 \alpha_5 \cdot l_{b,rqd} \ge l_{b,min}\)
| Accounts for | Values | |
|---|---|---|
| \(\alpha_1\) | bar shape | 0.7 for bent bars with \(c_d > 3\phi\); otherwise 1.0 |
| \(\alpha_2\) | concrete cover | \(1 - 0.15(c_d - \phi)/\phi\), between 0.7 and 1.0 |
| \(\alpha_3\) | transverse reinforcement | \(1 - K\lambda\), between 0.7 and 1.0 |
| \(\alpha_4\) | welded transverse bar | 0.7 |
| \(\alpha_5\) | transverse pressure | \(1 - 0.04p\), between 0.7 and 1.0 |
\(c_d\) is read from Figure 8.3 and depends on the bar shape: for a straight bar it is the minimum of \(a/2\), \(c_1\) and \(c\); for a bent bar the end cover drops out; for a loop only the cover counts.
The reductions do not accumulate without limit. The note to Table 8.2 caps the product \(\alpha_2 \alpha_3 \alpha_5 \ge 0.7\). With generous cover, dense transverse reinforcement and transverse pressure, the raw product can fall to 0.34 — but the code stops it at 0.7. The page shows both values when this happens.
In compression, Table 8.2 sets \(\alpha_1\), \(\alpha_2\) and \(\alpha_3\) to 1.0 and does not apply \(\alpha_5\) at all. Only \(\alpha_4\) remains. The minimum is stricter too: \(0.6 \, l_{b,rqd}\) instead of \(0.3\).
Laps: the same α, minus one, plus another
\(l_0 = \alpha_1 \alpha_2 \alpha_3 \alpha_5 \alpha_6 \cdot l_{b,rqd} \ge l_{0,min}\)
Note what is missing: \(\alpha_4\) does not appear. A welded transverse bar helps anchorage but not lapping. In its place comes \(\alpha_6\), which penalises the percentage of bars lapped at the same section:
\(\alpha_6 = \sqrt{\rho_1 / 25}, \quad 1.0 \le \alpha_6 \le 1.5\)
| \(\rho_1\) | \(\alpha_6\) |
|---|---|
| ≤ 25% | 1.0 |
| 33% | 1.15 |
| 50% | 1.4 |
| > 50% | 1.5 |
The difference between lapping every bar at one place and staggering below 25% is 50% of the length. Staggering is almost always cheaper than lengthening — especially since above 50% clause 8.7.2 imposes extra conditions.
Detailing minima
\(l_{b,min} = \max\{0.3 \, l_{b,rqd}; \; 10\phi; \; 100 \text{ mm}\} \quad \text{(tension)}\) \(l_{0,min} = \max\{0.3 \, \alpha_6 l_{b,rqd}; \; 15\phi; \; 200 \text{ mm}\}\)
When the demand is low the minimum governs, and reducing \(\sigma_{sd}\) further shortens nothing. The page marks the case with an asterisk, so you know when you have hit the floor.
Input data
- Bar — φ, \(f_{ck}\), \(\sigma_{sd}\), tension or compression, end shape.
- Position — bond conditions, covers \(c\) and \(c_1\), clear spacing \(a\).
- Laps — the percentage of bars lapped at the same section.
- Advanced — \(\Sigma A_{st}\) and \(K\) for \(\alpha_3\), element type, transverse pressure, welded bar.
Assumptions and limitations
Covered: individual straight, bent, hooked and looped bars, in tension and compression; expressions 8.2–8.4 and 8.10.
Not covered: welded mesh (clauses 8.4.4(2) and 8.7.5.2), bundled bars (clause 8.9), headed bars and mechanical anchorages, and the specific rules of clause 8.8 for bars above 32 mm — which include surface reinforcement and lapping restrictions.
Other limitations:
- Above C60/75, clause 8.4.2(2) limits \(f_{ctd}\) to the C60/75 value unless bond above that class is verified by testing. The page does not apply the cap, but flags the case.
- The lap arrangement rules of clause 8.7.2 are not checked: transverse spacing between laps, longitudinal stagger, the conditions for exceeding 50%.
- The transverse reinforcement required in the lap zone (clause 8.7.4), mandatory above φ20, is not computed.
Related calculators
- Concrete cover — \(c_{nom}\), on which \(c_d\) depends
- Reinforced concrete section — where the real bar stress \(\sigma_{sd}\) comes from
- Minimum reinforcement ratios — the detailing minima