PSI - Issue 84

Sergio Belluco et al. / Procedia Structural Integrity 84 (2026) 607–614 609 where α 1 is a coefficient to account for the type of prestress force release and 2 is a coefficient to consider the prestressing tendon shape, ϕ is the nominal diameter of the prestressing tendon, is the stress in the tendon at the time of prestress force release, f bpd is the design bond strength, and 1 and 1 are two coefficients to account for the prestressing tendon shape and for the effect of the tendon casting position on bond. Finally, the lower bound ( 1 ) and the upper bound ( 2 ) of Eq. (3) can be obtained varying as 1 =0.8 ∙ and 2 =1.2 ∙ . Similarly to the fib Model Code 2020, the formulation in the 2 nd gen. Eurocode 2 (EC2:2023) overcomes the calculation of the bond strength in Eq. (3), providing a formulation to directly compute . The new formulation for the average value of the transmission length that substitutes Eq. (3) is: = 1 . 5 ∙ ∙ 1 ∙ 2 ∙ 1 ∙ ( ) 1 / 2 (4) where ( ) is the characteristic compressive strength of concrete at the time of prestress force release and is the partial safety factor. Then, with respect to Eq. (3), values of α 2 have been modified, as reported in Table 1. Table 1. fib Model Code and Eurocode 2 coefficients. fib Model Code Eurocode 2 Factor Equation Value Description Factor Equation Value Description α p1 (1), (2) 1.00 For gradual prestress release. α 1 (3), (4) 1.00 For gradual prestress release. 1.25 For sudden prestress release. 1.25 For sudden prestress release. α p2 (1), (2) 0.50 For the 5% fractile of ( ,0.05 ). α 2 (3) 0.19 For 3- and 7-wire strands. 0.75 For the 50% fractile of . 0.25 For tendons with circular cross section. 1.00 For the 95% fractile of ( ,0.95 ). (4) 0.26 For 7-wire strands. α p3 (1), (2) 0.50 For 7-wirestrands. 0.40 For indented wires. 0.70 For indented and crimped wires. η p1 (3) 3.20 For 3- and 7-wire strands. η p1 (1) 1.20 For 7-wire strands. 2.70 For indented wires. 1.40 For indented and crimped wires. η 1 (3), (4) 1.00 For good casting position. (2) 0.36 For 7-wire strands. 0.70 For poor casting position. 0.42 For indented and crimped wires. (3), (4) 0.80 For the verification of local stresses at release η p2 (1), (2) 1.00 For good casting position. 1.00 For the basic value of the transmission length 0.70 For poor casting position. 1.20 For ULS verifications of anchorage length, shear, and moment capacity 2.2. Uncertainty assessment of code formulations A database of experimental observations of transmission length has been collected from the literature. This database contains 951 transmission lengths measures at tendon release performed on 587 specimens, since in some specimens, the transmission length was evaluated at both beam ends. A complete description of the database, its derivation and all the references can be found in Faleschini et al. 2023 and Belluco et al. 2023. Then, the collected database was filtered to obtain a homogeneous sample, excluding the specimen with specific characteristics (further details in Belluco et al. 2023). These filtering operations led to a homogeneous sample of 561 observations, where the main variables considered in the MC20 and EC2:2023 models were distributed as shown in Fig. 1. As can be observed, the