PSI - Issue 62

Francesco Mariani et al. / Procedia Structural Integrity 62 (2024) 955–962 Mariani et al / Structural Integrity Procedia 00 (2019) 000 – 000

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Comprehensive viscoelastic analyses are conducted on each of the 12 models considering both instantaneous and delayed losses on prestressed steel tendons and incorporating rheological properties of concrete. The results obtained for the long-term deflections, illustrated in Figure 4, are then compared with the measured displacements to estimate the relative error corresponding to each numerical point of measurement. Specifically, analytically and experimentally determined vertical displacements at 26 locations along the deck are compared, providing relative errors ɛ Δ ,p . These results are then aggregated, using equation (1), to compute the mean error in deflection for each Young’s modulus considered in the model . The in-situ relief reveals that the spans with vertically prestressed internal joints exhibit a maximum downward shift of about 300 mm. Similar outcomes are observed in models T2 and T3, with elastic moduli of 24500 MPa and 25000 MPa, respectively. Meanwhile, the spans without joints show positive deflections, and in this case, models with elastic moduli of concrete closer to the design value better replicate the deformed shape. Specifically, the T10 model, characterized by the design Young’s modulus of 32836 MPa, accurately reproduces the upward displacements but significantly underestimates the downward shifts at the internal joints by more than 70 %. The error analysis indicates that model T0, despite producing a significant overestimation of mid-span displacements, yields the minimum overall error.

Fig. 4. Deformed shapes obtained from the different FE models.

6.2 Frequency comparison Conducting modal analyses on the models involves considering the different Young’s modulus values of concrete. The primary objective is to identify the frequencies of the five distinct vertical modes presented in Section 3.2. The obtained values from various Finite Element (FE) models for each mode of vibration are then compared with the experimentally determined values of the corresponding modes to calculate the relative error ɛ f,n obtaining the errors displayed in Table 3. These relative errors from different models are combined using equation (2) to derive the mean error for each of the 12 models. Notably, models T2, T3 and T4 demonstrate the best fit between numerical and experimental features, exhibiting a maximum mean error of 1.15% . Model T4, with a Young’s modulus of E=25400MPa, stands out for its exceptional accuracy, displaying a relative error of 0.02%.

Table 3. Percentage errors obtained from the frequencies comparison. Model ID Relative error ɛ f,n= f n,FEM /f n,exp [%]

Mean error [%]

Mode 1

Mode 2

Mode 3

Mode 4

Mode 5

T0 T1 T2

-6.57 -4.42 -1.62

-7.34 -5.19 -2.37

-5.88 -3.73 -0.91

-5.34 -3.02 0.05

-4.75 -2.42 0.64

5.98 3.75 1.12