Reinforcement
Tension lap length (Eurocode 2)
- where
- bar size factor
- bar diameter (mm)
- design tensile strength of concrete (MPa)
- characteristic cylinder strength (MPa)
- design bond stress (MPa)
- bond condition (1.0 good, 0.7 poor)
- basic anchorage length (mm)
- design stress in the bar (MPa)
- lap length (mm)
- lap factor for the proportion of bars lapped
- lap as a multiple of bar diameter
Explain this equation
Works out the tension lap length for reinforcing bars by the Eurocode 2 method, so laps can be checked on site against the drawings.
Concrete grips the bar through bond. Its design tensile strength f_ctd is taken from the cylinder strength (0.3 f_ck^(2/3) is the mean tensile strength, 0.7 takes the lower value, and 1.5 is the safety factor). The bond stress f_bd scales that by 2.25 and the bond and bar-size factors. The force in a bar is its area πφ²/4 times its stress, and the bond force along a length is πφ × length × f_bd; setting them equal gives l_b = (φ/4)(σ_sd/f_bd). The lap is l_b times α₆, with minimums of 15φ and 200 mm.
An equilibrium between bar force and bond along the lap.
Sense check: 16 mm bars in C25 concrete, good bond, fully stressed with a third lapped at one place, need about 745 mm, about 46φ.
Watch out: poor bond conditions (top bars in deep pours) need about 40% more. Always follow the designer's lap schedule where one exists.
Works out a tension lap length for ribbed B500 bars from Eurocode 2, as a check on the lap shown on the drawings or a common 40–50 × φ rule of thumb.
Enter your values to see the result.
Good to know
The bond stress depends on the concrete’s tensile strength (from fck), the bar position and the bar size. Good bond is bottom bars and bars in shallow members; poor bond (0.7) is top bars in members deeper than about 250 mm. The lap gets longer when many bars are lapped at the same place (α6). This is the basic method with the cover, confinement and shape factors α1 to α5 taken as 1, which is conservative. The Concrete Centre’s detailing tables for C25/30 give about 46φ (good bond) and 66φ (poor bond).
Common mistake
Using one lap length for every bar: top bars in deep members and laps where all bars are joined at one place need much longer laps than bottom bars.
Limits
Ribbed bars to BS 4449 grade B500, concrete up to C50/60, tension laps, αct = 1 and γc = 1.5 (UK National Annex). The lap length on the engineer’s drawings and BS 8666 schedule takes precedence; ask the designer before changing it.
Sources
- BS EN 1992-1-1:2004 Eurocode 2 (3.1.2 Eq. 3.1/3.2 strength with time; 4.4.1 cover Eq. 4.1/4.2 and 4.4.1.3(4) 40/75 mm against ground; 8.4 and 8.7 anchorage and laps; Annex B Eq. B.10 temperature-adjusted age)
- The Concrete Centre, Practical design to Eurocode 2, Lecture 9 Detailing (fbd = 2.25η1η2fctd; lb,rqd = (φ/4)(σsd/fbd); H16 C25/30 example 40.4φ; lap table 46φ good / 66φ poor bond)
- Reinforcement Products Online, Lapping mesh reinforcement (EC2 lap l0 = α1α2α3α5α6·lb,rqd ≥ max(0.3α6·lb,rqd, 15φ, 200 mm))
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow BS 8500, BS EN 206, BS EN 752, Building Regulations Part H, manufacturers’ data and your engineer’s design. Structural concrete and foundations need a competent designer.