PSI - Issue 84

Antonella Ranaldo et al. / Procedia Structural Integrity 84 (2026) 821–828

827

8. Evaluation of the support reaction R and the demand for both the UBM and the LBM The support reaction is evaluated by combining permanent and variable loads. In particular, the permanent loads include the permanent and semi-permanent loads, amplified by the partial factor γ G = 1.3, whereas the live loads account for the traffic action. The last one is modelled using the Load Model 1 geometry, as defined in EN 1991 2:2003, with the load intensity reduced according to Celati et al. (2025), since traffic data were obtained from Weight in-Motion (WIM) systems. The load is applied to the deck as shown in Fig. 3 and the partial factor γ Q = 1.35 is used to amplify the variable action. The transverse distribution of the total load is evaluated using Courbon’s theory, and the half-joint of the most heavily loaded external girder (girder 1 in Fig. 3) is analyzed. Given a permanent load of G = 16.8 kN/m, the resulting support reaction is R = 688.59 kN. The demand for the UBM is evaluated according to Fig. 4b, resulting in a design bending moment of M D = 0.57 ∙ R . Conversely, given the STM geometry, the internal forces are: S1 = R ; S2 = 0.787 ∙ R ; S3 = 0.742 ∙ R ; T1 = 0.362 ∙ R ; T2 = 0.120 ∙ R , T3 = 0.932 ∙ R . 9. Results The obtained results are reported in Table 3 in terms of D/C ratio. The UBM yields to a D/C ratio equal to 0.71, indicating that the safety check is satisfied. This result was expected, since this method reflects the design philosophy adopted at the time of construction. In contrast, the assessment using the STM is not satisfied for the tie T3 , which exhibits a D/C ratio significantly greater than unity. Also this result was expected, as the half-joint was not originally designed using a STM, and it is consistent with findings reported in previous studies. The comparison between the UBM and the STM highlights a marked discrepancy in the predicted safety levels of the half-joint. In particular, the UBM indicates a significant safety margin, whereas the LBM identifies that for the tie T3 the safety check is not satisfied. While the UBM is based on the assumption of a kinematically admissible collapse mechanism, which is more closely aligned with the design concepts historically adopted for half-joint elements, the LBM requires a clear correspondence between the internal forces paths and the actual reinforcement layout. In this case, the reinforcement detailing does not comply with the idealized load-transfer mechanisms assumed by a modern STM formulation. This leads to a force concentration in specific ties, such as in this case the tie T3 . As a consequence, the STM yields a conservative assessment, potentially underestimating the actual load-bearing capacity of the half-joint.

Table 3: Comparison of safety assessment results obtained using the two methods. UBM LBM Demand [kNm] Capacity [kNm] D/C

1 2 3 1 2 3

ST element Demand [kN] Capacity [kN]

D/C 0.92 0.68 0.57 0.90 0.30 2.32

688.59 541.73 510.97 249.43

751.33 794.63 891.83 276.90 276.90 276.90

392.49

556.56

0.71

82.50

641.88

10. Conclusions The paper reviews design and assessment methods for half-joints in existing RC bridges, comparing the UBM and LBM approaches, the latter by means of a STM. The comparison shows notable differences in D/C ratios. In particular, the UBM, historically favored for its simplicity, potentially overestimates the actual load-bearing capacity. In contrast, the LBM approach, aligned with the modern standards, is often difficult to apply on existing RC bridges half-joints due to non-compliance with STM reinforcement layouts. Starting from these results, in the future also FEM models will be implemented, even taking into account degradation effects. These investigations will allow to better understand the influence of reinforcement layouts and the strength reduction due to the deterioration, in order to assess the allowable reduced traffic load and to support maintenance programs of RC bridge having half-joints.