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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Each tendon element comprises 24 wires with a diameter of 8 mm and is represented in the model with tendon elements having an area of 1200 mm 2 . The tendons are grouped and introduced into the model across distinct construction stages, allowing for the consideration of different loading times. The tension at the jacks for all tendons is set to 1100 MPa, except for those located in spans without internal joints, which are tensioned at 800 MPa. Additionally, construction stages are reconstructed within the FE model to account for concrete ageing during the application of different loads, changes in boundary conditions, and modifications in load configuration. All these features enable a comprehensive time-dependent analysis to assess the impact of creep, shrinkage, and prestress losses in accordance with the CEB-FIP Model Code 1990 (Comite Euro-International Du Beton 1993).

Table 2. Concrete Young’s modulus of the 12 FE models. Model ID T0 T1 T2

T3 T11 Young’s modulus [MPa] 21891 23000 24500 25000 25400 27000 27353 28500 30000 31500 32836 33500 T4 T5 T6 T7 T8 T9 T10

5. Error estimation methodology The resulted obtained from analyzing each of the 12 FE models are compared with those experimentally determined, both in terms of long-term deflections and modal features. The vertical displacements obtained with the long-term viscoelastic analysis for each measurement position along the bridge length are compared with the in-situ measured displacements at corresponding locations. The mean deflection error ɛ Δ ,mean is determined by the following equation: Δ, =∑ | Δ, | = =1 ∑ |( , / , )| =1 (1) where ɛ Δ ,p = ν p,FEM / ν p,exp is the ratio between the p-th numerically and experimentally determined vertical displacements, and P is the total number of selected points of measurement. Then, by performing modal analysis of the aforementioned models, resonant frequencies are determined for each value of concrete Young’s modulus. The mean natural frequencies error is computed through the equation: , =∑ | , | = = 1 ∑ |( , / , )| = 1 (2) where ɛ f,n =f n,FEM /f n,exp is the ratio between the n-th numerical and experimental natural frequency and N is the number of considered modes. The function, J(E), representing the overall error, encompassing deflections and frequency data based on the elastic modulus of concrete, is defined as follows: ( ) = α , + Δ, (3) where α and β are two weighting coefficients representing the reciprocal importance of the experimental campaign results depending on the number of tests conducted and the employed instrumentation. The optimal Young’s modulus that reduces the error between the analytical and detected behavior of the viaduct can be obtained by minimizing the function J. 6. Results 6.1 Long-term vertical displacement comparison