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.