PSI - Issue 84

Paolo Andrea Miglietta et al. / Procedia Structural Integrity 84 (2026) 1111–1118 P.A. Maglietta et al. / Structural Integrity Procedia 00 (2026) 000–000

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3.1. Definition of time-dependent M- χ and V - γ relationships

For each combination of input parameters and for each year from the construction stage to the end of the service life, both flexural parameters (M cr , M y , M u and χ cr , χ y and χ u ) and shear parameters (V u and γ u ) are computed. For each year considered, the statistical distribution of internal moments, the corresponding curvatures, the ultimate shear and strain are determined. The 16 th (P16), the 50 th (P50) and the 84 th (P84) percentiles are sampled from each distribution, to define time-dependent bending moment-curvature (M- χ) and shear force -shear strain (V- γ) relationships associated with the percentiles considered. Such relationships can be incorporated into the numerical model of the pier, to represent the cross-sectional response in place of the classical fiber-section discretization, thereby reducing computational effort while explicitly accounting for bar-slip effects. It is worth mentioning that for t < t i , only concrete creep effects are addressed. For t i ≤ t < t cr , the corroded steel mechanical properties are considered, while the concrete properties are still assumed as uncracked. For t > t cr , both corroded steel mechanical properties and cracked concrete mechanical properties are considered. 4. Illustrative example The case study archetype pier is part of RC bridge with nine simply supported decks located in L’Aquila (Italy). The upper deck is 10 m wide and consists in a 0.3 m thick RC slab supported by five pre-stressed concrete (PC) I section beams. The pier shaft is 6 m heigh and supports two 25m-long spans. The geometrical details of the pier cross section are provided in Fig. 1 (dimensions are expressed in cm). The resulting total value of self-weight and both structural and non-structural dead loads is equal to 4400 kN. The cylindrical characteristic compressive strength of concrete, f c , is equal to 50 MPa, while the nominal concrete cover depth is 35 mm. Ribbed steel rebars were used for reinforcement, having yielding strength f y =480 MPa, tensile strength f t =570 MPa and ultimate strain ε u =10 %. The rebars nominal diameter, Φ 0 , is equal to 26 mm, whereas 10 mm four-legged stirrups with 100 mm spacing were adopted as transverse reinforcement. The longitudinal rebars’ bond length within foundation elements was assumed equal to 1000 mm. The RH, the number of rainfall days per year, the concrete cover thickness and the concrete compressive strength were selected as random input parameters. Boundary values were defined assuming normal and log-normal distributions for concrete compressive strength and concrete cover depth, respectively, as suggested by Model Code (CEB-FIP, 2010). The statistical distributions of RH and the number of rainfall days per year were defined based on available meteorological data, referring to the site of L’Aquila (Italy). Normal distribution was employed for both parameters. The percentiles sampled from each distribution are summarized in Table 1; while values of the deterministic input parameters are presented in Table 2.

Fig. 1. Geometrical details of the case study pier.