PSI - Issue 62

Simone Celati et al. / Procedia Structural Integrity 62 (2024) 361–368 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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3.1. Capacity model The capacity of a PT structure is mainly owned by the preservation of its cables. The wires that constitute each cable can corrode leading to the degradation of the cable and then the structure’s capacity. Since wires within the same duct are exposed to the same environmental conditions, their is correlated. This correlation is modelled with a correlation coefficient of 0.85 allowing for some variations and acknowledging very limited relevant scientific literature. The yielding strength of a tendon is modelled as a Daniels System (DS) of the 42 wires, with corrosion considered possible for 20. The remaining wires are shielded by the external ones, following a similar approach used for strands in Vereecken et al. (2021). The corrosion-affected 20 wires are modelled with a brittle behaviour, whereas the remaining wires fail ductile. The following equation is employed to estimate the time-dependent yielding resistance of a cable: ( ) = [(42 − 20) ∙ 0 + {(20 − + 1) ( )}] ∙ (8) In Eq (8), the initial area 0 and the yielding stress of a wire are considered. The evolution over time of the resistance of a cable is determined by the variable ( ) that represents the residual area of the wire j at the time . Bending capacity is determined by the resistance model uncertainties ( ), the concrete compressive strength ( ), the width of the concrete slab ( ), which equals to 2.85 meters, the depth of the neutral axis ( ( ) ), and the depth of each cable ( z i ). Eq. (9) models the bending capacity of the concrete girder under monoaxial bending (see Fig. 1). The distributions of variables required for evaluating Eqs. (8-10) are provided in Table 1. ( ) = ( 6 ( ) ∙ 6 + 5 ( ) ∙ 5 +(∑ ( ) ∙ ) 4 =1 −0,32 ∙ ∙ 2 ( )) (9) 3.2. Definition of the demand The bending demand is the result of both traffic loads and permanent loads. Permanent loads, which encompass the weight of asphalt and concrete, are estimated and assumed to follow a Gaussian distribution with a coefficient of variation of 0.05. These loads are then transformed into their bending effects, considering the simply supported configuration. The values and distribution of traffic loads are inferred by assuming that the characteristic values from the EC1 load scheme 1 (Hirt (1993)) are derived from a Gumbel distribution, with a coefficient of variation of 0.05 and a reference period of 1000 years for the three lanes. These values are subsequently converted into annual values. The estimation of bending demand assumes a Courbon redistribution of the loads, assuming a deck width of 12 meters (3 lanes), composed of 4 parallel girders. Finally, the uncertainties in the effect model are defined. The demand evaluation is summarized by the following equation: = ( + ) (11) is the bending due to the permanent loads, is the bending due to the traffic loads after redistribution with annual reference time, and is the effect model uncertainty factor. Their distributions are defined in Table 1. 3.3. Limit state function and summary of probabilistic models The defined bending capacity ( ( ) ) and demand ( ) are compared through the time dependent LSF defined as follows: ( )= ∑ 6 =1 ( ) 0.8 ∙ (10)