I I

Eurocode 2 Table of Reinforcement Anchorage Length and Lap Length

Description:
Design aid - Table of reinforcement anchorage length lbd & lap length l0 and associated detailing rules
According to:
EN 1992-1-1:2004+AC2:2010 Sections 8.4 and 8.7
All Calculations
Input
MPa
Nationally Defined Parameters
According to EN1992-1-1 §3.1.6(2)P and the National Annex.
According to EN1992-1-1 §2.4.2.4 and the National Annex.
According to EN1992-1-1 §2.4.2.4 and the National Annex.
Note: Always verify the validity of the Nationally Defined Parameters. Please inform us of any discrepancy using our Contact Form
Tables
Loading...
error loading table!
Design anchorage length for ribbed bars &Phi;&le;32mm according to EN1992-1-1 &sect;8.4.4 (<i>&gamma;</i><sub>c</sub> = 1.50, <i>f</i><sub>yk</sub> = 500 MPa)
Loading...
error loading table!
Design lap length for ribbed bars &Phi;&le;32mm, when >50% of the bars are lapped in one section, according to EN1992-1-1 &sect;8.7.3 (<i>&gamma;</i><sub>c</sub> = 1.50, <i>f</i><sub>yk</sub> = 500 MPa)
Notes
  1. Other-than-straigh bar shapes include a) standard bend, b) standard hook, and c) standard loop. The detailing rules and the equivalent anchorage length for each of these standard shapes are defined in EN1992-1-1 Figure 8.1.
  2. The condition of adequate cover cd > 3Φ for other-than-straight bars in tension is defined in EN1992-1-1 Figure 8.3. When adequate cover is not present the anchorage and lap lengths for other-than-straight bars in compression should be used instead.
  3. 'Good' bond conditions are applicable when any of the following conditions is fulfilled: a) Vertical bars or almost vertical bars inclined at an angle 45° ≤ α ≤ 90° from the horizontal, b) bars that are located up to 250 mm from the bottom of the formwork for elements with height h ≤ 600 mm, or c) bars that are located at least 300 mm from the free surface during concreting for elements with height h > 600 mm. 'Poor' bond conditions are applicable for all other cases and also for bars in structural elements built with slip-forms, unless it can be shown that 'good' bond conditions exist. See EN1992-1-1 Figure 8.2 for more details.
  4. The anchorage and lap lengths presented in the tables are conservative values for ribbed bars with diameter Φ ≤ 32 mm. The required anchorage and lap length may be further reduced when one or more of the following conditions are present: a) adequate concrete cover, b) adequate confinement by transverse reinforcement, c) welded transverse bars along the anchorage length, and d) compressive pressure transverse to the plane of splitting. The favorable effect of these factors is described in EN1992-1-1 §8.4.4.
  5. The anchorage and lap lengths presented in the tables assume full utilization of the reinforcement bar yield stress, i.e. the stress of the bar is assumed equal to the design yield stress fyd = fyk / γs. For ULS verifications when the provided tensile reinforcement As,prov is more than than the required reinforcement As,req then the required anchorage and lap lengths may be reduced by the ratio As,req / As,prov, however the minimum required anchorage length lb,min the minimum required lap length l0,min should be provided in accordance with EN1992-1-1 §8.4.4(1) and §8.7.3(1).
  6. The lap lengths presented in the tables assume that >50% of the bars are lapped in one section (i.e. α6 = 1.5). If a smaller percentage of bars is lapped in one section then required lap length may be multiplied by the factor α6 / 1.5, where α6 = (ρl / 25)0.5 and ρl is the percentage of the bars lapped in one section. However the minimum required lap length l0,min should be provided in accordance with EN1992-1-1 §8.7.3(1).
  7. According to EN1992-1-1 §8.7.2 laps between bars should normally be staggered and not located in areas of high moments. The required staggering layout is presented in EN1992-1-1 Figure 8.7. Staggering is not required for compression reinforcement and secondary (distribution) reinforcement.
  8. It is possible that laps betweeen bars are not staggered because this is not feasibe or it is very difficult (e.g. column starter bars). This case is not covered explicitly in the current version of EN1992-1-1. The authors of this website recommend to increase the provided lap lengths by a factor of (1.20)3/2 = 1.315 when staggering is not possible. This recommendation is based on the relevant provision of the next issue of EN1992-1-1 that is currently in draft version.
  9. When the reinforcement bars are arranged in more than one horizontal layers then only 50% of the bars may be lapped in tension in one section according to EN1992-1-1 §8.7.2(4). This is not required for compression reinforcement and secondary (distribution) reinforcement.
  10. When individual bars with diameter Φ larger than 32 mm or bundles of bars with equivalent diameter Φn larger than 32 mm are used then the required anchorage and lap lengths are divided by the factor η2 = (132 - Φ) / 100 ≤ 1.0
  11. Transverse reinforcement is generally required in the lap zone to resist tranverse tensile forces. See details below for more information.
Details

Calculation of design anchorage length of longitudinal reinforcement according to EN1992-1-1 §8.4

Ultimate bond stress fbd

The design value of ultimate bond stress for ribbed bars is defined in EN1992-1-1 §8.4.2(2):

fbd = 2.25 ⋅ η1η2fctd

where fctd = αctfctk,0.05 / γc is the design tensile strength of concrete determined according to EN1992-1-1 §3.1.6(2)P.

The coefficient η2 takes into account the effect of large bar diameters Φ > 32 mm as follows:

η2 = min[1.0, (132 - Φ) / 100 ], where Φ in mm

The coefficient η1 is related to the quality of the bond condition and the position of the bar during concreting. The coefficient η1 takes a value of 1.0 when 'good' bond conditions are obtained and a value of 0.7 otherwise i.e. when 'poor' bond conditions exist. The distinction between 'good' and 'poor' bond conditions is provided in EN1992-1-1 Figure 8.2.

'Good' bond conditions are obtained when any of the following conditions is fulfilled:

  • Vertical bars or almost vertical bars inclined at an angle 45° ≤ α ≤ 90° from the horizontal
  • Bars that are located up to 250 mm from the bottom of the formwork for elements with height h ≤ 600 mm
  • Bars that are located at least 300 mm from the free surface during concreting for elements with height h > 600 mm

'Poor' bond conditions are applicable for all other cases and also for bars in structural elements built with slip-forms, unless it can be shown that 'good' bond conditions exist.

Basic anchorage length lb,rqd

The basic required anchorage length lb,rqd for anchoring a straight steel bar with diameter Φ under design stress σsd is defined in EN1992-1-1 Eq. (8.3):

lb,rqd = (Φ / 4) ⋅ (σsd / fbd)

The maximum value of the design steel stress σsd under ULS loads is equal to the design yield strength of the bar fyd = fyk / γs. When the actual design strength of the bar is smaller than fyd then the basic required anchorage length is reduced proportionally.

Minimum anchorage length lb,min

When no other limitation is applicable, the provided anchorage length should be at least equal to the minimum value lb,min as described in EN1992-1-1 §8.4.4(1):

- For anchorages in tension: lb,min ≥ max[0.3⋅lb,rqd, 10⋅Φ, 100 mm]

- For anchorages in compression: lb,min ≥ max[0.6⋅lb,rqd, 10⋅Φ, 100 mm]

Design anchorage length lbd

The design anchorage length lbd is defined in EN1992-1-1 §8.4.4(1) as:

lbd = α1α2α3α4α5lb,rqdlb,min

where the coefficients α1 to α5 are defined in EN1992-1-1 Table 8.2 and account for various factors reducing the design anchorage length as follows:

  • Coefficient α1 accounts for the effect of the shape of the bar (α1 = 1.0 for straight bars, α1 = 0.7 for other-than straight bar shapes such as bend, hook, and loop assuming adequate cover cd > 3⋅Φ, α1 = 1.0 for other-than straight bars without adequate cover), where cd is defined in EN1992-1-1 Figure 8.3.
  • Coefficient α2 accounts for the effect of minimum concrete cover: a) For straight bars in tension α2 = 1 - 0.15⋅(cd - Φ) / Φ) and 0.7 ≤ α2 ≤ 1.0, b) for other-than-straight bars in tension α2 = 1 - 0.15⋅(cd - 3⋅Φ) / Φ) and 0.7 ≤ α2 ≤ 1.0, c) for any bar shape in compression α2 = 1.0
  • Coefficient α3 accounts for the effect of confinement by transverse reinforcement not welded to main reinforcement. For bars in tension it takes values 0.7 ≤ α3 ≤ 1.0 depending on the quantity of transverse reinforcement. For bars in compression α3 = 1.0.
  • Coefficient α4 accounts for the effect of confinement by welded transverse reinforcement. If the requirements of EN1992-1-1 Table 8.2 are fulfilled then it can take the value α4 = 0.7.
  • Coefficient α5 accounts for the effect of confinement by transverse pressure. For bars in tension it takes values 0.7 ≤ α5 ≤ 1.0 depending on the value of transverse pressure. For bars in compression α5 is not applicable.
  • In any case the lower limit of the product (α2α3α5) ≥ 0.7 must be observed.

As a simplified and conservative alternative the equivalent anchorage length lb,eq may be provided that is lb,eq = α1lb,rqd for straight, bend, hook, and loop bar shapes, or lb,eq = α4lb,rqd for bars with welded transverse bars. In the provided tables in this calculation the equivalent anchorage length lb,eq is shown.

Detailing rules for reinforcement anchorage

Standard detailing rules for the anchorage of straight bars and other-than-straight bar shapes (bend, hook, loop) are provided in EN1992-1-1 Figures 8.1 and 8.3. In general for other-than-straight bars with standard details according to EN1992-1-1 Figure 8.1 the equivalent anchorage length lb,eq is measured straight up to the end of the bar shape. For standard details for the anchorage of links and shear reinforcement see EN1992-1-1 Figure 8.5.

Calculation of design lap length of longitudinal reinforcement according to EN1992-1-1 §8.7

Design lap length l0

The design lap length l0 is defined in EN1992-1-1 §8.7.3(1) as:

l0 = α1α2α3α5α6lb,rqdl0,min

where the coefficients α1 to α5 are as defined above in the estimation of the design anchorage length lbd.

The coefficient α6 accounts for the percentage ρl of reinforcement bars lapped within ±0.65l0 from the center of the lap length considered. The coefficient α6 is defined as:

α6 = (ρl / 25)0.5 and 1.0 ≤ α6 ≤ 1.5, where ρl expressed in %.

The maximum value of the coefficient α6 = 1.5 is obtained when the percentage of lapped bars in a section exceeds 50%. In the provided tables in this calculation the design lap length l0 is calculated taking into account the value of coefficient α1 and assuming α6 = 1.5. The provided lap lengths are adequate even when more than 50% of the bars are lapped in a section.

Minimum anchorage length l0,min

When no other limitation is applicable, the provided lap length should be at least equal to the minimum value l0,min as described in EN1992-1-1 §8.7.3(1):

l0,min ≥ max[0.3⋅α6lb,rqd, 15⋅Φ, 200 mm]

Staggering of laps

According to EN1992-1-1 §8.7.2 laps between bars should normally be staggered and not located in areas of high moments (e.g. plastic hinges). The required staggering layout is presented in EN1992-1-1 Figure 8.7. Two adjacent laps are not considered to belong in the same section when the clear distance between the lap ends is ≥ 0.3l0. Staggering is not required for compression reinforcement and secondary (distribution) reinforcement. It is possible that laps betweeen bars are not staggered because this is not feasibe or it is very difficult (e.g. column starter bars). This case is not covered explicitly in the current version of EN1992-1-1. The authors of this website recommend to increase the provided lap lengths by a factor of (1.20)3/2 = 1.315 when staggering is not possible. This recommendation is based on the relevant provision of the next issue of EN1992-1-1 that is currently in draft version.

Detailing rules for reinforcement laps

Standard detailing rules for the arrangement of lapped bars are provided in EN1992-1-1 §8.7.2 and Figure 8.7:

  • The lapped bars may be allowed to touch each other.
  • The clear distance of lapped bars should be in gereral not greater than 4Φ or 50mm. Otherwise the lap length should be increased by a length equal to the clear space where it exceeds 4Φ or 50 mm.
  • The longitudinal distance between two adjacent laps should not be less than 0.3l0.
  • In case of adjacent laps, the clear distance between adjacent lapped bars should not be less than 2Φ or 20 mm.

Transverse reinforcement in the lap zone

The required transverse reinforcement in the lap zone to resist transverse tension forces is described in EN1992-1-1 §8.7.4. When the diameter of the bar is Φ ≥ 20mm the total area of the sum of all legs of transverse reinformement ΣAst, placed perpendicular to the direction of lapped bars, should be at least equal to the area As of one lapped bar:

ΣAst ≥ 1.0 ⋅ As

Additional detailing rules are presented in EN1992-1-1 Figure 8.9:

  • The required transverse reinforcement should be placed at the outer thirds of the lap length l0, i.e. at distance ≤ l0 / 3 from the lap ends.
  • For the case of lapped bars permanently in compression one bar of the transverse reinforcement should be placed outside each end of the lap length and within 4Φ of the end.
  • The spacing between transverse reinforcement bars should not exceed 150 mm.
  • If more than 50% of the reinforcement is lapped at one point and the distance between adjacent laps at a section is ≤ 10Φ transverse reinforcement should be formed by links or U bars anchored into the body of the section.
  • When the diameter of the lapped bars is Φ < 20 mm or the percentage of lapped bars in any section is less than 25%) then any transverse reinforcement or links necessary for other reasons may be assumed sufficient without further justification.