## 2 Stiffness of the Stringer-to-Cross-Girder Connection
### Experimental and Numerical Analyses of a Real Railway Bridge  
In order to verify the validity of the results of the presented theoretical study, also in the case of riveted bridge structures, we performed another experimental-numerical analysis on a real steel riveted bridge. The observed bridge is situated near the railway station in Turany at km 303.309 of the Zilina-Kosice track. The investigated superstructure  
Figure 6: Relative bending moment diagrams M\({}_{y}\) of the stringers with different span D and types of connections to the cross girder. forms the first span of a three-simple-span truss bridge with a lower member deck. The theoretical span of the main girders is 43.4 m.  
The bridge superstructure with a width of 5.510 m consists of two main truss girders with a theoretical height of 4.500 m. The length of one field of the truss structure is 4.340 m. The open member bridge deck is created with stringers with a length of 4.340 m and cross girders. The global depth of the riveted plate-girder stringer is 600 mm, and it is created with a web made of P 14 \(\times\) 586 mm and flanges made of angles L 100 \(\times\) 100 \(\times\) 14 mm. The riveted cross girder of 1130 mm high is created with a web made of P 14 \(\times\) 1100 mm, flanges made of angles L 140 \(\times\) 140 \(\times\) 14 mm and a sheet P 15 \(\times\) 320 mm. The bridge was built in 1950 from steel 10,372 (according to previous Czechoslovak standard CSN 1230) corresponding to the current designation of the steel strength class S235. At the time of testing, the bridge was in very good condition. The bridge superstructure was analysed using a beam FEM model by means of SCIA Engineer software [15]. The members of the main truss girders are connected rigidly, while the connections of the cross girders and the horizontal bottom bracing members to the main girders are considered fully hinged. The superstructure was, similarly to the theoretical study, analysed using two types of numerical models, one with hinged stringers and one with rigidly connected stringers. The numerical analysis with a shell FEM model was replaced by an experimental analysis using strain gauges, with the help of which we recorded the stress response of the structure to a real railway traffic load on the chosen stringer in the stringer midspan and near its connection to the cross girder. The measured records of the stress response in the monitored locations were subsequently confronted with the records obtained using numeric simulations of train sets by means of FEM models. During the experimental measurements, the passage of 23 train sets was recorded, namely, 7 freight trains, 8 express trains and 8 passenger trains. The necessary technical data on the train sets (the type of locomotive, the type and number of wagons and the corresponding values of axle forces and their distances) were obtained from the operational information system, which is disposed of by the railway operator of the Slovak Republic. A view of the bridge and scheme of the numerical model of the superstructure are presented in Figures 7 and 8, respectively. The basic geometric parameters of the bridge cross-section are evident in Figure 9. The second stringer from the support was chosen for the analysis. Its connection to the cross girder is made similarly to Type 1 in the theoretical study (Figure 5), i.e., by connecting only the webs using connecting angles but with the use of stiffening haunches. The geometric parameters of the connection as well as the placement of strain gauges installed on the chosen stringer are presented in Figure 10.  
A comparison of the stress responses in the selected locations obtained from the experimental measurements as well as from the numerical simulations using the beam FEM model in Figure 8 is illustrated in the graphs in Figure 11, where the time courses of the stress response to the passing train set consisting of one electric locomotive of the 162 series and eight-passenger wagons are presented.