PSI - Issue 84

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

608

1. Introduction In pretensioned concrete (PC) elements, shear and bending capacity are strictly correlated with the development of stresses in the bonded strands. However, quantifying bond in PC members is experimentally complicated, and therefore transmission length and anchorage length are often considered in design practice as an indirect measure of the bond strength. These two terms represent the lengths needed to anchor the tendon force at release and at failure of the PC member, respectively. Design codes use the results of such studies providing semi-empirical models to predict the anchorage length, being this value necessary for a correct design of a PC element where anchorage failures should be avoided. In general terms, the accuracy of a resistance model depends on the considered variables (e.g., the physical properties of materials, the geometry of the element, etc.), but also, on the uncertainties of the model itself (Holický et al. 2016, Pourreza et al. 2021). To the best knowledge of the authors, there are no recent studies that address in detail the reliability of the design formulations for anchorage length of prestressing strands. Thus, in this contribution, the reliability of the transmission and anchorage length formulations proposed in the fib MC20 and in the 2 nd gen. EC2 is investigated, to quantify the model uncertainties and propose new probabilistic coefficients that comply with the safety format prescribed by the two codes. More details about the herein presented work can be found in Faleschini et al. 2023, Belluco et al. 2023, Belluco and Faleschini 2025. 2. Trasmission length 2.1. Current formulations According to fib Model Code 2010, the transmission length can be computed as: = 1 ∙ 2 ∙ 3 ∙ ∙ with = ∙ and = 1 ∙ 2 ∙ ( ) (1) where α p1 is a coefficient to account for the type of prestress force release; α p2 is a coefficient associated with the characteristic lower ( , 0 . 05 for the 5% fractile) and upper ( , 0 . 95 for the 95% fractile) value of the transmission length, and α p3 is a coefficient to account for the prestressing tendon shape. Then f pi is the stress in the tendon at the time of prestress force release and f ptd is the design tensile strength of the tendon. The quantity l bp represents the basic anchorage length, that is the length needed to anchor the full strength in an untensioned tendon, and can be computed from the nominal diameter ϕ , the area of the prestressing tendon A sp and the design bond strength f bpd . This latter quantity depends on two coefficients η p1 and η p2 considering respectively the prestressing tendon shape and the effect of the tendon casting position on bond. Finally f ctd (t) is the design concrete tensile strength, evaluated at the time of prestress force release (obtained dividing its characteristic tensile strength f ctk , min by the partial safety factor . The values of these coefficients are reported in Table 1. The new formulation in the recently published fib Model Code 2020 (MC20) does not substantially modify the approach of fib Model Code 2010, and most of the coefficients remain the same. However, the calculation of the bond strength has been avoided, and the model that defines the basic anchorage length has been modified as reported below: = ∙ 1 ∙ 2 ∙ ( ) 1 / 2 (2) where ( ) is the characteristic compressive strength of concrete at the time of prestress force release and is the partial safety factor for concrete. Then, with respect to Eq. (1), the values of 1 have been modified, as reported in Table 1. Eq. (2) for the basic anchorage length can be directly adopted in the Eq. (1) to compute the transmission length (all the coefficients of Eq. (1) have remained the same). Similarly to fib Model Code 2010, in the 1 st generation Eurocode 2 (2004) the transmission length was computed as: = 1 ∙ 2 ∙ ∙ with = 1 ∙ 1 ∙ ( ) (3)