Design anchorage length for ribbed bars Φ

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Design anchorage length for ribbed bars Φ≤32mm according to EN1992-1-1
§8.4.4 (γc = 1.50, fyk = 420 MPa, γs = 1.15)
Bar Type
Straight in tension/compression
Other-than-straight in compression
Straight in tension/compression
Other-than-straight in compression
Other-than-straight in tension and
adequate cover cd > 3Φ
Other-than-straight in tension and
adequate cover cd > 3Φ
Bond
Conditions
Good
C16/
20
46Φ
C20/
25
40Φ
C25/
30
34Φ
C30/
37
31Φ
C35/
45
28Φ
C40/
50
25Φ
C45/
55
23Φ
Poor
66Φ
57Φ
49Φ
43Φ
39Φ
36Φ
33Φ
Good
32Φ
28Φ
24Φ
22Φ
19Φ
18Φ
17Φ
Poor
46Φ
40Φ
34Φ
31Φ
28Φ
25Φ
23Φ
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 qualitya 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.
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