## 4 Conclusions  
The article deals with the analysis of a typical construction detail of old steel riveted bridges with member bridge decks, namely, the connection of the stringer to the cross girder where a fatigue crack growing in the stringer web quite often occurs (Figure 1). The main conclusions of the performed numerical and experimental analyses are as follows:  
* The results of the performed analyses confirmed the connection between the appearance of fatigue cracks in this detail and the actual bending stiffness of the stringer-to-cross-girder connection, which used to be neglected at the time of the design of these bridges.
* Although from the point of view of the rigidity of this joint, the mutual connection of the flanges of the stringers connecting to the cross girder is of fundamental importance; even the joint realised only by connecting the webs of the stringers and the cross girder  
Figure 17: Results of fatigue tests and characteristic S-N curve for the stringer-to-cross-girder connection.  
using connecting angles shows a certain bending stiffness. This can be safely neglected when assessing the bending resistance of the stringer in the middle of its span.
* The real stiffness of such a connection causes a more complex stress state in its vicinity than can be provided by simple theoretical models, such as a hinged connection or a rigid connection. In this context, the connection strengthening by end haunches at the lower flange of the stringer proved to be very important.
* In cases where it is necessary to carefully consider the stress in the joint area, it is recommended to model this joint more accurately, for example, by using shell elements when processing the FEM model of the superstructure.
* The fatigue tests of this structural detail were performed on specially prepared laboratory test specimens.
* Based on the linear regression analysis of the obtained test results, the fatigue category of the investigated detail was determined, given by the fatigue strength value \(\Delta\sigma_{\text{C}}=80\) MPa corresponding to the number of load cycles of \(2\times 10^{6}\).
* This detail category can be used to verify the fatigue resistance of old riveted bridges according to European standards.  
Numerical analyses within the theoretical study focused on the stiffness of the investigated connection--[PERSON]; processing of the results of experimental measurements on the real bridge structure--[PERSON]; numerical analysis of the bridge superstructure--[PERSON]; preparation, realization and processing of the results of fatigue tests of the observed detail--[PERSON], [PERSON] and [PERSON]; numerical analyses of the tested fatigue detail--[PERSON]; evaluation of the results of fatigue tests and determination of the fatigue detail category--[PERSON]; supervision and coordination of individual works--[PERSON]; ensuring project administration--[PERSON]; writing--preparation of the original draft--[PERSON] and [PERSON]; writing--review and editing--[PERSON]. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Scientific Grant Agency of the Slovak Republic under project 1/0623/21 \"Analysis of details and failures of railway bridges steel superstructures\".  
Not applicable.  
Data is contained within the doctoral thesis that is available in Central register of final and qualifying theses (in Slovak, [[https://crzp.cvtirs.sk/](https://crzp.cvtirs.sk/)]([https://crzp.cvtirs.sk/](https://crzp.cvtirs.sk/)), (accessed on 5 January 2022)).  
The authors declare no conflict of interest.