PSI - Issue 84

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

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range of basic variables defined in the sample space covers quite well the range of basic variables adopted in common design situations (further details can be found in Belluco et al. 2023).

Fig. 1. Distribution of the main variables in the filtered database of transmission lengths (adapted from Belluco et al. 2023).

Engineering models can be affected by both aleatory and epistemic uncertainties (Kiureghian and Ditlevsen 2009): the first is due to the randomness of known variables considered by the models (such as the physical properties of materials), while the second is due to the lack of knowledge or simplifications made in the models themselves (Holický et al. 2016). According to (Kiureghian and Ditlevsen 2009), denoting by and a vector of known and unknown variables, respectively, by the real response of the structure in the experimental campaigns (that is, in the present study, the measured transmission length) and by the response estimated by a model, the model uncertainty due to Y can be expressed in terms of a multiplicative random variable Θ , such that ( , ) ≈ ∙ ( ) . According to Holický et al. 2016, a sample of Θ (hereafter denoted with the lowercase letter ) can be obtained as = , ( , ) , ( ) ⁄ , where R real , i (X,Y) is the i-th observation of the database, ϑ i is the i-th realization of Θ and , ( ) is the i-th length calculated with the models previously described. For computing R mod , i (X) , all partial safety factors were set equal to 1.00 and the calculated value of was the average. Finally, based on the results of Faleschini et al. 2023, the evaluation of model uncertainties has been performed separately depending on the prestress release procedure. After verifying the independence of Θ against each variable, the Maximum Likelihood Estimation is used for computing the distribution parameters for all cases. Results are shown in Fig. 2, that lists also the expected value [ Θ ] and the coefficient of variation CoV (calculated as the ratio of the standard deviation and [ Θ ] ) for all cases. It can be observed that for gradual release, on average, fib MC20 slightly overestimates the experimental value, while EC2:2023 shows a good fit; in both cases, the associated CoV is around 0.16. For the sudden release case, MC20 gives a better prediction in terms of average value, but in both codes, the associated CoV is quite high (around 0.30, roughly double of the gradual release case).

fib Model Code 2020

Eurocode 2 (2023)

Gradual Sudden Distribution Lognormal Lognormal Lognormal Lognormal [ Θ ] 0.89 1.04 1.04 1.22 CoV 0.16 0.30 0.16 0.30 Sudden Gradual

Fig. 2. Model uncertainty probability distribution for gradual and sudden prestress release for transmission length (adapted from Belluco et al. 2023). Finally, Eq. (1) and Eq (3) are rewritten including a probabilistic coefficient needed for computing a specific quantile of the distribution (and dependent on the prestress release method), resulting in: MC20 = ∙ 3 ∙ 1 ∙ 2 ∙ ( ) 1 / 2 and EC2:2023 = 2 ∙ 1 ∙ ( ) 1 / 2 (5)