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 ⋅ η1 ⋅ η2 ⋅ fctd
where fctd = αct ⋅ fctk,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 = α1 ⋅ α2 ⋅ α3 ⋅ α4 ⋅ α5 ⋅ lb,rqd ≥ lb,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 (α2⋅α3⋅α5) ≥ 0.7 must be observed.
As a simplified and conservative alternative the equivalent anchorage length lb,eq may be provided that is lb,eq = α1 ⋅ lb,rqd for straight, bend, hook, and loop bar shapes, or lb,eq = α4 ⋅ lb,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 = α1 ⋅ α2 ⋅ α3 ⋅ α5 ⋅ α6 ⋅ lb,rqd ≥ l0,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⋅α6⋅lb,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.