Anchorage, laps and cover
Anchorage and tension lap length (Eurocode 2 with UK NA)
- where
- design tensile strength of the concrete (MPa)
- long-term coefficient, 1.0 (UK NA)
- characteristic cylinder strength (MPa); above C50/60 0.3fck^(2/3) becomes 2.12 ln(1 + fcm/10) with fcm = fck + 8, capped at C60/75
- partial factor for concrete, 1.5
- design bond stress (MPa)
- bond condition: 1.0 good, 0.7 poor
- bar size factor: 1.0 up to 32 mm, (132 − φ)/100 above
- basic required anchorage length (mm)
- bar diameter (mm)
- design stress in the bar (MPa)
- design anchorage length in tension (mm)
- product α1·α2·α3·α5 for shape, cover, confinement and pressure
- tension lap length (mm)
- lap factor for the share of bars lapped at one section
Explain this equation
Works out how far a bar must run into concrete to develop its strength (anchorage) and how far two bars must overlap at a lap, using Eurocode 2 with the UK National Annex.
fctd is the concrete's design tensile strength, which controls how well it grips the ribs. fbd is the design bond stress: η1 is 1.0 for good bond and 0.7 for top bars in deep pours, and η2 reduces bond for bars over 32 mm. σsd is the stress the bar must carry, 435 MPa when fully stressed. αp and α6 adjust for cover, confinement and how many bars are lapped together.
The force in the bar is its area πφ²/4 times σsd. The grip along a length l is the perimeter πφ times l times fbd. Setting them equal gives lb,rqd = (φ/4)(σsd/fbd). The max() terms apply the code minimums, 10φ and 100 mm for anchorage and 15φ and 200 mm for laps.
Sense check: H16 in C25/30, good bond, fully stressed needs about 40φ (646 mm) anchorage, and about 46φ lap with α6 = 1.15. Poor bond lengthens both by 1/0.7, about 43 per cent.
Watch out: the laps on the drawings govern. This is a check, not a redesign.
Works out the anchorage length and tension lap length of a ribbed B500 bar from the Eurocode 2 bond equations with the UK National Annex values, to check the laps on a drawing or schedule.
Enter your values to see the result.
Good to know
The concrete’s design tensile strength fctd (from the class) sets the bond stress fbd. Good bond (η1 = 1.0) covers bottom bars and bars in members up to about 250 mm deep; top bars in deeper pours are in poor bond (0.7) because water and air collect under them. Bars over 32 mm lose some bond (η2). Fully stressed B500 bars have σsd = 500/1.15 ≈ 435 MPa. α1 to α5 reward cover, confinement and hooks; leaving them at 1.0 is conservative. α6 lengthens laps when many bars are lapped at the same section; 1.5 is the safe value if you do not know. Rounded up, C30/37 in good bond gives about 36φ anchorage and 54φ lap with α6 = 1.5.
Common mistake
Using one lap for every bar: top bars in deep members and laps where all bars stop at one place need much longer laps than bottom bars in a slab.
Limits
Ribbed B500 bars to BS 4449, concrete up to C90/105 (bond capped at C60/75), tension anchorage and laps, αct = 1.0 and γc = 1.5 (UK NA). Compression laps, bundled bars, mesh laps and lightweight concrete are not covered. The laps on the engineer’s drawings and schedule govern.
Sources
- BS EN 1992-1-1:2004 Eurocode 2 (Table 3.1 fctm, fctk,0.05; 3.1.6 fctd; 4.4.1 cover; 8.4 anchorage, Eq. 8.2–8.6; 8.7 laps, Eq. 8.10–8.11)
- UK National Annex to BS EN 1992-1-1:2004+A1:2014 (γc = 1.5, αct = 1.0, Δcdev recommended 10 mm)
- The Concrete Centre, Practical design to Eurocode 2, Lecture 9 Detailing (fbd = 2.25η1η2fctd; H16 C25/30 fbd = 2.693 MPa, lb,rqd = 40.4φ; lap table 46φ good bond, 66φ poor bond)
- IStructE / The Concrete Centre, Standard method of detailing structural concrete (4th edition)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Always work to the engineer’s drawings and bending schedules, BS 8666, BS EN 1992, BS EN 1090-2, BS 5531/the BCSA National Structural Steelwork Specification and manufacturers’ data. Lifting must be planned under LOLER by a competent person.