Shear and torsion in a prestressed through railway bridge

Abstract

With the arrival of the Eurocode, the calculations regarding shear resistance, have become increasingly conservative compared to former concrete standards. For example in Voorschriften Beton 1974 (VB 74), a former concrete standard, a shear resistance combination of concrete, stirrups and prestress was allowed. Whereas the Eurocode assumes the shear resistance of the concrete is zero if it’s standalone contribution is insufficient. Meaning that once stirrups are required, the total applied shear stress is controlled by the stirrups.
Prorail is the party in the Netherlands which is responsible for the construction and maintenance of the railway infrastructure. The change in regulations results in concerns for parties like Prorail and in particular to the shear resistance of concrete railway bridges constructed according to the VB 74.

A through railway bridge consists of a relatively thin floor and two prestressed girders. Whenever a train drives over the floor, a great deal of the loading is spread in transverse direction, causing large shear forces and torsion in the two prestressed girders. Because this combination can be critical for the shear resistance, two prestressed through railway bridges, constructed according to the VB 74, are investigated in this master thesis.
It is verified with hand calculations whether or not these existing structures can guarantee structural safety by considering three shear resistance checks; the risk of shear tension failure, capacity of the stirrups and resistance against fatigue. Ultimately it is concluded, that the largest unity check is 1,01 and that both bridges can guarantee structural safety regarding shear resistance.

The reassessment of an through bridge, is an typical assignment for engineering firm such as Witteveen+Bos. But because hand calculations are too time consuming, the design loads are determined with SCIA Engineer (FEA program).
However in the earlier days FEA programs were not available and torsion in the girders was derived from a set of differential equations (analytical solution). Because structural engineers from today completely rely on programs like SCIA, a comparison is drawn up between SCIA and the analytical solution for torsion in the girder.

The plate, beam model 1A and 1B are the three types of models available in SCIA to model a through bridge. The plate model consists of a 2D-floor and 2D-girder, where the beam models form a combination of a 2D-floor and 1D-girder. But the plate and beam model 1B have in common that rigid connections are applied every ¼ meter between the girder and floor.
The analytical solution is derived with the assumption that the bridge is divided into strips with a length of 1,0 meter, which is implemented in the plate and beam models by reducing the E-modulus of the floor to roughly a third (cracked floor). For the governing load combination, this leads to values for torsion, which remain 10-15%, 40% and 10% behind the analytical solution for respectively the plate and beam model 1A and 1B. The large deviation of beam model 1A is remarkable and can be explained from the fact that no rigid connections between the girder and floor are applied, resulting in a loss of bending and torsional stiffness of the girder.

To conclude, the analytical solution is based on a number of assumptions, like no load distribution of the floor in longitudinal direction. In reality loads will be as well distributed in longitudinal as transverse direction and the analytical solution therefore needs to be considered as an safe upper limit.