PSI - Issue 84

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

825

decks composed of three simply supported RC girders, each with a span of 11.7 m. The deck has a total width of 9 m, including 7 m for carriageways and two 1 m-wide walkways, one on each side. The half-joint deck constitutes a critical structural component due to its lack of redundancy and is therefore the primary focus of this study for the assessment of the bridge’s structural safety. The central and outer girders have depths of 92 cm and 110 cm, respectively. The central girder is reinforced with10 ϕ 30 longitudinal bars arranged in three layers, whereas the outer beams contain 8 ϕ 30 longitudinal bars arranged in two layers. Shear reinforcement is provided at 20 cm spacing along the entire beam length, except in the half-joint regions, where the spacing is reduced to 10 cm. Fig. 3a,b shows an overview of the bridge and the deck section at the half-joint connection. a b

Fig. 3. (a) Picture of the case-study bridge; (b) deck cross-section at the half-joint connection with the applied traffic loads (dimensions in cm).

The reinforcement of the half-joint connection was originally designed by modeling it simply as a cantilever resisting the reaction force R . Accordingly, the required steel area was computed using the following expression (see Fig. 4a): A s = ( √ 2∙R)/ σ y , which resulted in the adoption of 4 ϕ 30 inclined at 45°. The admissible reinforcement stress σ y = 180 MPa was defined as a fixed percentage, depending on the concrete strength and the cross-sectional geometry, of the steel tensile strength. 5. Definition of the capacity using the UBM To apply the UBM, it is necessary to assume a failure mechanism. In this case, it is assumed a crack inclination of 45° according to the work of Mattock and Chan (1979), developing from the nib end (see Fig. 4a). By imposing the bending equilibrium, the ties resistance is evaluated according to the following Eq. 1 and considering the related lever arms illustrated in Fig. 4b. =2 ∙ ∙ cos( )=2 ∙ 2 4 ∙ cos( ) (1) where f yk is the characteristic yield strength, α i = 45° is the i-th tie inclination angle, and γ S = 1.15 is the steel partial factor. Based on the original design documentation, the Aq 50 steel class was used. Thus, based on Verderame et al. (2011), f yk can be estimated as 318.5 MPa. a b

Fig. 4. (a) Drawing detail of the case study; (b) rigid free body diagram adopted for the UBM analysis (dimensions in mm).