PSI - Issue 84

Galileo Tamasi et al. / Procedia Structural Integrity 84 (2026) 709–716

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6. Computational methodology: integrated loading scenarios and bending moment envelopes The structural assessment of the bridge follows a multi-stage computational workflow, integrating permanent and accidental load effects to define the critical design envelope. The primary system consists of a symmetrical three-span reinforced concrete continuous beam with spans of 12.00 m, 15.00 m, and 12.00 m, totaling a length of 39.00 m. The cross-section features four longitudinal girders with a spacing of 2.11 m, with the central girder serving as the reference for the longitudinal analysis. The initial phase of the study focuses on the dead loads, which are determined based on the geometric properties and material unit weights established in the 1960 design documentation. For the internal longitudinal girder, the permanent load is calculated at 1.938 t/m. The longitudinal response is evaluated using the three-moment equation (Clapeyron's theorem), which, for the permanent load configuration, yields negative moments at the intermediate supports B and C of approximately -220.723 kgm and a maximum positive moment in the central span of 115.033 kgm. In accordance with the historical regulatory framework of Ministerial Circular n. 6018, accidental loads are modeled using a standard truck train (12 t per vehicle) and a distributed pedestrian load on the sidewalks. To optimize the analysis for programmable calculators such as the HP 97, the discrete concentrated loads of the truck train are converted into an equivalent uniformly distributed load. This equivalent load is derived by positioning the truck train on the 12-meter side spans to identify the configuration that maximizes the internal forces. The final stress state is determined through the principle of superposition, combining the fixed dead load effects with various live load hypotheses. Three distinct loading configurations are analyzed: live loads applied exclusively to the side spans, live loads applied exclusively to the central span, and live loads applied simultaneously across the entire bridge length. This systematic approach results in the construction of the bending moment envelope, historically referred to as the fuso dei diagrammi , which illustrates the absolute maximum and minimum moments along the entire longitudinal development of the bridge. The replication of this historical analytical process is performed using the HP 97 simulator (Limpid Fox) and original software routines. The global longitudinal analysis utilizes the CE1-15A program (Six-Span Continuous Beams), which solves for the support moments across the various load hypotheses by iterating through the three-moment equations. This integrated methodology ensures that the final envelope values represent the definitive input for the subsequent verification of the reinforced concrete sections, allowing for the calculation of the required reinforcement area (As) in cm² for both rectangular and T-shaped sections using the CE1 The final stage of the structural design involves the detailed verification of the main girder sections, utilizing the peak internal forces extracted from the previously calculated bending moment envelope. The 1960 design documentation adopts a stress-permissible approach, ensuring that the working stresses in both concrete and steel remain within the safety limits established for the specified materials: concrete Type 680 and Aq 50 high-strength steel. The verification process focuses on the critical sections of the continuous beam: the negative moment regions at the intermediate supports (B and C) and the positive moment regions at the mid-spans. For the negative moment at the supports, where the girder behaves as a rectangular section of 0.33 m by 1.50 m, the design requires a significant concentration of longitudinal reinforcement to resist the peak moment. According to the original calculations, the maximum negative moment leads to the specification of multiple groups of 22 mm diameter bars (Ø 22), arranged to match the resistance requirements of the envelope diagram. To validate these results through historical digital tools, the CE1-17A program (Reinforced Concrete Beams) of the HP Civil Engineering Pac is employed. By inputting the geometric parameters - width (b = 33 cm for support sections or b = 211 cm for T-shaped mid-span sections) and effective depth (d) - along with the material strengths (f y and f c ), the simulator computes the required area of reinforcement (A s ) in cm². For the T-sections in the spans, the program automatically verifies the position of the neutral axis to ensure it remains within the 0.20 m thick slab, confirming the efficiency of the flange in compression. The strong convergence between the 1960 manual calculations and the HP 97 output validates the bridge's structural adequacy. This comparison highlights the evolution from traditional manual methods to the early computational routines of modern engineering. 17A program, based on the peak values extracted from the simulated stress envelope. 7. Verification of reinforced concrete sections: historical and simulated analysis