PSI - Issue 84

Giulia Rossini et al. / Procedia Structural Integrity 84 (2026) 1183–1190

1187

3.2. FE model For each case study, a linear elastic numerical analysis of the bridge is performed using a FE model developed in Midas Civil 2025 (v1.1). In these models only the bridge deck is considered, while the piers and abutments are replaced with equivalent constraints. All beam supports are modelled as rollers avoiding vertical displacements, with only one fixed support introduced to ensure a statically determinate scheme. This approach simplifies the modelling process while preserving an accurate representation of the actual support conditions. Given the elapsed time since construction, it was assumed that the long-term effects had already occurred. Each longitudinal and transverse beam, as well as the deck slab, is modelled as a beam element. Self-weight and permanent superimposed loads are considered, while traffic loads are neglected since no vehicles are present during the test’s execution. Only the by bridge’s self-weight was accounted for when the structure was used during testing. A linear structural analysis is carried out with the evaluation of the internal forces, in particular the bending moment M acting along the bridge axis under the characteristic load case combination is evaluated. FE model is used solely to determine the internal actions at the test sections, while the corresponding stresses are subsequently computed analytically (§4). The adoption of a numerical model was essential, since an analytical approach alone would not have adequately accounted for the plan geometry obliquity, the load distribution provided by transverse girders and the contribution of the deck slab. 4. Analytical model The concrete stress in the test location , is calculated using equation 1. The notation “BC” refers to the phases prior to the slab casting (Before Casting), whereas “AC” denotes the phases following the slab casting (After Casting). In the absence of detailed design documents, it is assumed that the strands are tensioned before the slab was cast. , = , , − , ∙ ∙ ( − , ) , + 1 ∙ ( − , ) , + , , + +( ) − , ∙ ∙ ( − , + +( ) ) , + +( ) + ∆ 2+( ) ∙ ( − , + +( ) ) , + +( ) − ∆ ,∞ , + +( ) + ∆ ,∞ ∙ ,∞ ∙ ( − , + +( ) ) , + +( ) − ∆ ,∞ , + +( ) + ∆ ,∞ ∙ ∙ ( − , + +( ) ) , + +( ) (1) Where: • = test location in the vertical direction calculated from the girder intrados; • , and , = total prestressing force of the tendons tensioned BC and AC after short term losses, respectively; • , = transformed section of the girder, only the tendons tensioned BC are considered, For the tendons tensioned AC only the void ducts are considered; • and = eccentricity of the tendons tensioned BC with respect to the girder centroid and of the tendons tensioned AC s with respect to the centroid of the transformed section , + +( ) , respectively; • , = girder centroid measured from the girder intrados (only the tendons tensioned BC are considered, For the tendons tensioned AC only the void ducts are considered); • , = second-order moment of area of the girder about its centroidal axis (only the tendons tensioned BC are considered, For the tendons tensioned AC only the void ducts are considered); • , + +( ) = transformed section of the section composed by girder, slab and grout; • , + +( ) =centroid of the section , + +( ) measured from the girder intrados; • , + +( ) = second-order moment of the section , + +( ) about its centroidal axis; • 1 = bending moment at the test section due to structural loads (g₁); • ∆ 2+( ) = bending moment due to non- structural permanent loads (g₂) and any variable loads applied during testing, such es the by bridge load. The moving load are not considered (see §3.2); • ∆ ,∞ and ∆ ,∞ = Short and Long-term losses in the tendons tensioned BC and AC, respectively; • ,∞ = eccentricity of the tendons tensioned BC relative to the centroid of the composite section , + +( ) considering long-term effects.