PSI - Issue 84

Sergio Belluco et al. / Procedia Structural Integrity 84 (2026) 607–614

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Table 3. Model uncertainty expected value, and coefficient of variation for anchorage length. fib Model Code 2020 2 nd gen Eurocode 2 (2023) Gradual Sudden Gradual Sudden Distribution Lognormal Lognormal Lognormal Lognormal [ Θ ] 0.86 1.23 1.00 1.43 CoV 0.18 0.16 0.18 0.16

Similarly to the transmission length, the two formulations for the anchorage length have been rearranged including a probabilistic factor for bond (Table 4) calibrated to ensure a target reliability (the complete derivation of the coefficients is described in Belluco and Faleschni 2025). The proposed equation for anchorage length is: MC20 = 1 ∙ 2 ∙ ∙ 1 / 2 ( 3 ∙ ( ) 1⁄3 + ) and EC2:2023 = ∙ 2 1 ∙ ∙ 1 / 2 ( ( ) 1⁄3 +2 ) (8) Difference between current code models (denoted with markers) and proposed formulations (represented with straight lines) is shown in two case studies, illustrated in Fig. 6 that show that that MC20 lengths are always over conservative and thus they can be shortened. For 2 nd gen EC2 and gradual prestress release, predicted lengths are very close to the ones obtained with the calibrated model, while for sudden release, obtained lengths are shorter than the proposed ones, and thus they need to be increased. Table 4. Probabilistic coefficient for bond strength for design formulation of anchorage length. Probability of under-exceedance = Φ ( − ∙ ) Partial safety factor = ∙ Proposed Gradual Sudden Gradual Sudden = Φ ( − 0.8 ∙ 3.3) 1.40 (CC1) 1.43 1.05 1.43 1.05 fib Model Code 2020 = Φ ( − 0.8 ∙ 3.8) 1.50 (CC2) 1.43 1.05 1.43 1.05 = Φ ( − 0.8 ∙ 4.3) 1.60 (CC3) 1.42 1.05 1.43 1.05 2 nd gen. Eurocode 2 (2023) = Φ ( − 0.8 ∙ 3.8) 1.50 (CC2) 1.37 1.01 1.37 1.01

Fig. 6. Difference between current and proposed models for anchorage length (adapted from Belluco and Faleschini 2025).

Finally, the proposed formulations are validated by assessing the level of reliability of some practical case studies. The FORM method has been implemented according to the Hasofer-Lind-Rackwitz-Fiessler (HLRF) algorithm, investigating the classical limit state function: = − , where M R is the flexural capacity of a concrete cross section at a distance from the beam end (considering the bond and anchorage capacity in the evaluation of the tendon strength) while M E is the flexural demand. The complete derivation of the reliability assessment can be found in Belluco and Faleschini 2025; here, for the sake of brevity, only the final results are reported (Fig. 7).