PSI - Issue 44

Gianfranco De Matteis et al. / Procedia Structural Integrity 44 (2023) 681–688 Gianfranco De Matteis et al. / Structural Integrity Procedia 00 (2022) 000–000

686

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The simplified 1D model for the local safety assessment of the slab was developed assuming a slab strip having width evaluated starting from the plan diffusion of concentrated loads from the loaded area to the longitudinal main girders, which were assumed to represent supports for the slab, characterised by a null torsional stiffness and an infinite flexural stiffness. For the investigated load configurations, the slab strip widths were 3.82 and 3.6 m for LC1 and LC2, respectively. The above modelling approach is often adopted by practitioners for performing the slab safety assessments through local analyses. The overall 3D model implementing beam elements was developed to more realistically capture the distribution of loads assumed in the 1D model, and to evaluate the relevant effects of the stress resultants on the slab. Beam elements were adopted for both the main longitudinal girders and the cross-beams, as well as for the slab, which was schematised as a beam grid with spacings of about 30×20 cm. Rigid links were used to consider the position of each element centroids, as well as the position of the deck supports. Pictorial views of the model are reported in Fig. 3a. At last, a more refined 3D global model of the deck, implementing solid elements was considered, to evaluate the influence of three-dimensional effects on the stresses (Fig. 3b). Typical dimension of 3D finite elements is equal about to 50 cm × 50 cm × 50 cm, reinforced rebars were also modelled and pinned constraints were considered at the base of the model. The loads were directly applied on the slab according to the same loading combinations used for the beam models. Results of the three linear modelling approaches are presented in terms of bending moments acting on the slab in Table 1, where, for the 1D model, the evaluation of the negative bending moment accounts for the beam width. As expected, results of the 1D model are the most conservative, while those of the 3D models are in very good agreement. From a practical point of view, it may be concluded that 1D models can be adopted by practitioners, in view of their ease of implementation, but 3D models are recommended, and should be suitably adopted in case safety assessments are not satisfied by operating with outcomes of 1D models. On the other side, for the case study at hand, complex 3D models implementing solid elements proved not necessary to improve the understanding of the deck behaviour subjected to vertical loads.

(a)

(b)

Fig. 3. Pictorial views of (a) the 3D beam model with indications of distributed loads, and (b) the 3D solid model.

Table 1. Maximum and minimum bending moments on the slab

Stress resultant

1D model

3D model

3D model

[kNm/m]

Beam elements

Beam elements

Solid elements

Maximum bending moment (sagging region) Minimum bending moment (hogging region)

36.9 -35.1

28.2 -28.7

28.2 -29.1