PSI - Issue 84

484 Valentina Giglioni et al. / Procedia Structural Integrity 84 (2026) 481–488 where is the prestress force of the i-th tendon, is the sag of the i-th tendon and is the span of the i-th tendon. In addition, a bending moment evaluated using Eq. (2), is applied at both ends of the beam to ensure that the resulting stress distribution along the beam is equivalent to that produced by the actual prestressing system. , =∑ cos 7 =1 (2) where is the distance from the centre of gravity of the section and each tendon’s anchorage and is the angle of anchorage of each tendon. With the same purpose, an axial load defined in Eq. (3) is finally applied at the external edges: =∑ cos 7 =1 (3) Based on the most common degradation mechanisms observed in real bridges, multiple damage scenarios are simulated into the models and summarized in Table 1.

Table 1. Simulated damage scenarios.

Health-state scenarios

Damage extent - 1 /2 2 /2 1 /2 , 2 /2 1 /2 , 2 /2 2 /2 , 3 /2 2 /2 , 3 /2 3 /2 , 4 /2 3 /2 , 4 /2 3 /2 , 4 /2 3 /2 , 4 /2

Damage intensity

Damage elements

Scenario 0 Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Scenario 7 Scenario 7b Scenario 8 Scenario 8b Scenario 9 Scenario 10 Scenario 11 Scenario 12 Scenario 13 Scenario 14

-

-

20% reduction of Ei 20% reduction of Ei 20% reduction of Ei 20% reduction of Ei 20% reduction of Ei 20% reduction of Ei 20% reduction of Ei 20% reduction of Ei 20% reduction of Ei 20% reduction of Ei

Beams and slab – C1 Beams and slab – C2 Beams and slab – C1, C2

Edge beams and slab – C1, C2

Beams and slab – C2, C3

Edge beams and slab – C2, C3

Beams and slab – C3, C4

Beams – C3, C4

Edge beams and slab – C3, C4

1 2 3 4

Edge beams – C3, C4

30% reduction of prestressing force 30% reduction of prestressing force 30% reduction of prestressing force 30% reduction of prestressing force 30% reduction of prestressing force 30% reduction of prestressing force

Beams – C1 Beams – C2 Beams – C3 Beams – C4

1 , 2 2 , 3

Beams – C1, C2 Beams – C2, C3

In particular, the index “0” indicates undamaged conditions, while scenarios from 1 to 8b involve a 20% reduction of the elastic modulus in selected damage elements located at the midspan of specific spans, extending over approximately half of the span length. Note that the reduction in Young’s modulus is assumed to represent an equivalent effect of material degradation within a specific portion of the structure. Each scenario corresponds to damage in different structural components, such as beams or slabs, and may affect different spans or combinations of spans. Scenarios from 9 to 14 instead represent the lowering of the compression force, modelled by applying a 30% decrease in the equivalent compressive forces to the beams assumed to be damaged. Table 2 includes the results of the calibration process between the SAP (beam) and the ABAQUS (solid) model, in terms of six natural frequencies estimates and Modal Assurance Criterion (MAC) value. Modal analyses are automatically performed to generate a set of pseudo-monitoring data by assigning random values to the elastic moduli, drawn from a Gaussian distribution with an assumed variation of ±1.3%. In total 54