PSI - Issue 5

Pavel Ryjáček et al. / Procedia Structural Integrity 5 (2017) 1051 – 1056 Ryjacek/ Structural Integrity Procedia 00 (2017) 000 – 000

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structural damping of railway bridges was used to precise the damping values. The procedure is based on the summation of various damping impacts that are used on the bridge, as shown in the Table 1. In the method M1, the additional damping from ballast was not assumed, in the method M2 the ballast damping was assumed for the steel deck.

Table 1. Damping values Structural element

Bridge deck (in the method M2)

Main structure and arch (in the method M2, in the M1 also for bridge deck)

Hangers

Material damping – steel  m

0,0008 0,0032 0,0024

0,0008

0,0008

Nonmaterial structural damping – ballast  s Nonmaterial structural damping – steel welded structure Interaction damping – sliding bearings  i

0

0 0

0,0024

0,0024 0,0088

0,0024 0,0054

0

Total damping  tot

0,0008

The load was applied according to the EN 1991-2, Annex F that describes the real trains running on the conventional railway network, named A to F. Because the allowed speed on the track was lower than 160 km/h, HSLM models were no applied. The speed range was up to 120% of maximum allowed speed, which means 192 km/h. The load was applied as moving vertical forces in the time history dynamic analysis. The direct integration and modal analysis were used, but because of the time requirements, the parametric study was based on the modal analysis.

2.2. Parametric study results

The parametric study was focused on the displacement and acceleration of the arch and the main girder in the vertical and horizontal direction, as shown on the Figure 3. For that, the 6 models with the same stiffness properties, but different skew angle were created. The dynamic analysis for the real trains and various speeds was done. Based on that, the envelope of the displacement and acceleration was analyzed.

a

b

Fig. 3. (a) The numerical model and position of the analyzed acceleration; (b) Deflection during the passing of the train

The results are shown on the Fig. 4. It is obvious, that acceleration of the arch is increasing together with decreasing skew angle and becomes more faster from 60°. A significant increase is also between 45° and 40°. The horizontal vibrations of the arch are not only negative for the arch itself, but they have significant impact of the horizontal vibrations of the hangers, as they move horizontally with the top part of the hanger. This impact is significant and can not be neglected.