PSI - Issue 64

Pavel Ryjáček et al. / Procedia Structural Integrity 64 (2024) 228 – 237 Pavel Ryjacek/ Structural Integrity Procedia 00 (2019) 000 – 000

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3. The advanced nonlinear model of the footbridge segment The advanced 3D FEM model of the typical segment was performed in the ATENA software, see Fig. 3b. The model was used to analyse the effect of the failure of the Alpha and Beta cables on the stiffness of the joint between bridge segments. The gap opening values for different variations of cable corrosion loss were determined and then implemented in the global model of the bridge. The overall result of the predicted maximum corrosion of 80% loss of the Alpha cables and 100% loss of the Beta cables was that there is a joint opening of 1.83 mm (as observed during inspections on the bridge). 4. The 3D detailed numerical model and its validation The footbridge was modelled as a global 3D shell model with beam elements. Due to the nonlinear behaviour, the model and its deformation were analysed using 3rd order theory in Scia Engineer software, see Fig. 3a.

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b Fig. 3 (a) Visualization of the model of the footbridge, (b) advanced model in Athena – typical segment

The individual segments were modelled by a group of plate elements, modelled as a sandwich system and placed in the correct height position using the eccentricity of the element. The element is longitudinally connected to internal member elements which have a cross-sectional area identical to the main support cables and the prestressing cables. The bridge is further fitted by the railing elements. Prestressing is introduced in both the main load bearing (Alpha) cables and the prestressing (Beta) cables using the 'initial stress' function. 5. Analysis of the results based on the change of eigenmodes and frequencies and advanced dynamic methods Based on the developed model, a sensitivity analysis of the superstructure to different influences based on the damage scenarios was carried out with the eigenmodes and frequencies change. The next tool was the change of mode surface curvature CAMOSUC(j),x (Change of mode surface curvature). The modal flexibility matrix [  ] can also be used to analyse the observed modal characteristics. From the mode shapes normalized to the structure's mass matrix, their contribution to the structure's flexibility can be directly determined. The change in the corresponding diagonal members of the matrix [  ], i.e., the change in the deflections of the structure induced by a fictitious unit force applied at point r , can be used to assess the change in the dynamic behaviour between the undamaged XX and the damaged YY state of the structure. The second derivative of the change in the modal flexibility matrix  r was used as an additional criterion to determine the location and level of damage to the structure. For the purpose of detecting possible damage, two grids were selected on the model. In each section, two points were selected at a distance of 1.9 m from the axis of the bridge. In the longitudinal direction, 86 points were selected for the first grid with a distance of 3 m (corresponding to the length of the segment) and 24 points were selected for the second grid based on the initial dynamic test performed after the completion of the footbridge.