This report present result from dynamic analyses of railway bridges for high-speed trains. A comparison of the dynamic response in 2D vs. 3D has been performed for a limited selection of slab bridges, beam bridges and box girder bridges. Each cross-section has been optimized based on the dynamic requirements for dynamics in 2D, without any consideration of the static design. In many cases, the cross-section probably needs to be increased to fulfil the static load capacity.

Slab bridges with a span length from 10 – 25 m and 1 – 4 spans have been analysed. In several cases, mostly for shorter spans, the natural frequency for bending is lower in 3D compared to 2D. The reason is due to a smaller contributing width, owing to shear-lag. This results in a lower resonance speed and therefore often a larger dynamic response within the same speed range. Apart from that, the dynamic response is found to be similar in 3D compared to 2D. The influence of torsional does not appear to be governing the response for the studied cases.

Using the same method, beam bridges with span length from 20 – 40 m and 1 – 4 spans have been analysed. Similar to the slab bridges, the 3D-model of the beam bridges show lower natural frequency in bending compared to the 2D-model, owing to shear-lag. For double-track bridges, the difference in response between 2D and 3D-models are similar to the findings for the slab bridges. For single-track bridges, some cases of the 3D-model shows significantly lower response without pronounced resonance peaks in the same speed interval as the 2D-model. The reason is likely a combination of the support eccentricity and the mass of the bridge, which for vertical bending results in horizontal inertia. It is shown that this can be simulated with a modified 2D-model in most cases.

Box girder bridges with span length from 40 – 70 m in 1 – 3 spans have also been analysed. Due to the larger torsional stiffness, the torsional mode is often much higher than the first bending mode. Also, the shear-lag effect seems to be smaller and the response from the 3D-model agrees well with the corresponding 2D-model.

In the case dynamic assessment is performed using the simplified methods according to (Svedholm & Andersson, 2016), it is suggested that the following is considered:

• Shear-lag and the eccentricity at the supports should be considered when estimating the first natural frequency for bending, n₀, preferably using a 3D-model.

• If the first torsional mode n_T < 1.2n₀, a full dynamic analysis in 3D should be performed.

• In the case a 3D-model shows several closely spaced bending modes with similar shape, a full dynamic analysis in 3D should be performed.

In this report, so called design charts for dynamic assessment of railway bridges are presented. The aim is to use these diagrams in early stage design of bridges, to determine if they are likely to comply with the requirements for riding comfort and traffic safety stated in SS-EN 1990, section A2.4.4.

The requirements are based on vertical acceleration and vertical displacement of the bridge deck, as well as end rotation at supports. Based on the span length and the fundamental natural frequency, the required mass and stiffness can be obtained directly from the diagrams.

The diagrams are only valid for bridges with ballastless track systems and an allowable speed sth = 320 km/h. The diagrams are developed based on a 2D beam model with constant mass and stiffness and fixed supports. The diagrams are only valid under these assumptions.