PSI - Issue 62

Andrea De Flaviis et al. / Procedia Structural Integrity 62 (2024) 871–878 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

874 4

0 0 0

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E

          

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     

     

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   yv yv u w w u z z s  2 , , , yv , , ,

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   

 M Q '' Q    M ΩΩ

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a

IV

a ΩW

t

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  P 0 Ψ' W

2.1. Cross-section analysis

As stated before, the main difference between GBT-D and classical GBT lies in the way cross-section analysis is carried out. In fact, in the classical approach, the cross-section is discretized in a certain number of elements, with “natural nodes” at wall intersections and free ends (divided into dependent and independent nodes) and “intermediate nodes” at all other positions. Then, the deformation modes are determined, assigning unit warp ing (longitudinal) displacements at each independent natural node (keeping null displacement in all other nodes) and unit flexural displacements at each intermediate node (solving a statically indeterminate problem). At the end the GBT matrices (those appearing in Eq. (5)) are calculated and made diagonal, finally obtaining the deformation modes, as better explained in Camotim et al. (2008). However, the same authors developed an improved procedure explained in detail in Bebiano et al. (2015). What is different in GBT-D is that, after the discretization of the section in elements (without distinction between natural and intermediate nodes), it is possible to find the deformation modes simply solving a Planar Eigenvalue Problem (1° PEP for conventional modes and 2° PEP for extensional modes) and a Warping Eigenvalue Problem (for shear modes), thus obtaining a maximum of (3N-M) + M + N = 4N deformation modes, referred to an unconstrained planar frame as that of Fig. 1. Some information about the case study are also given: a single span of the Viaduct San Nicola of the Italian highway A24 is considered, as the static scheme is simply supported and the contribution of the bridge piers is neglected. In Fig. 2, the sketch of the box-girder cross-section is shown, which for this study has been divided into 6 elements. Some of the obtained deformation modes are reported in Fig. 3 (note the 4 rigid modes).

Fig. 2. Geometrical and mechanical properties of Viaduct San Nicola of A24.