# Experimental Investigation of the Fatigue Life of a Bridge Crane Girder Using S-N Method
### Calculation of Maximum Stresses Taking into Account the Validity of STN 270103  
According to STN 270103 standard \"Design of steel structures of cranes\", the calculation for fatigue resistance is described in Part VIII [23]. According to STN 270103 standard and Appendix II, the analyzed crane can be classified under number 1.1.5/4. For this classification, the lifting class is H3, the type of operation is D2, the stress spectrum is S2, and the working group is J5. The coefficients resulting from STN 270103 for the equipment mentioned above are [23]:  
* load factor from self-weight \(\gamma_{g}=1.1\);
* load factor from the rated load for D2 \(\gamma_{t0}=1.3\);
* dynamic lift coefficient for H3 \(\delta_{h}=1.37\). The other coefficients are not shown because they are not necessary for the assessment or are reflected in the measured strain courses and the corresponding stress courses calculated from the operational measurements (Figures 3-5). Table 4 shows that the maximum normal stress of 71 MPa considers the weight of the load (20,930 kg), the crab weight and the dynamic effects of the operation. However, the mentioned maximum stress does not take into account the stresses from the self-weights of the permanent loads, i.e., from the self-weight of the bridge crane girders and the permanent loads stored on them. These loads were determined based on the operator's data as a distributed load of constant intensity:  
\[q=4.94\ \text{kNm}^{-1}. \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stress** & **Measured Location** & **Normal/Shear Stress at Load 20,930 kg (MPa)** & **Absolute Difference (MPa)** \\ \hline \multirow{8}{*}{Normal} & A1 & \(-\)54.3 & \(0.1\) \\  & A1 & \(-\)54.2 & \(0.1\) \\ \cline{1-1}  & B3 & \(-\)70.8 & \(4.6\) \\ \cline{1-1}  & B4 & \(-\)66.2 & \(7.3\) \\ \cline{1-1}  & B7 & \(-\)46.4 & \(7.3\) \\ \cline{1-1}  & A8 & \(-\)53.7 & \(7.3\) \\ \hline \multirow{2}{*}{Shear} & B5 & - & \\ \cline{1-1}  & A6 & \(16.0\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum stress values measured when handling steel coil 6 in Mode 3. For the bridge span of 28,500 mm, the maximum bending moment \(M_{\text{max}}\) from the self-weight is:  
\[M_{\text{max}}=\frac{q\cdot\ell^{2}}{8}=\frac{4.94\cdot 28.5^{2}}{8}=501.6\text{ kNm}. \tag{2}\]  
Figure 6 gives a view of the cross-sections of the girders at mid-span. Figure 6a shows the cross-section at mid-span without the reinforcing rib. Figure 6b shows the cross-section at a 300 mm distance from the girder center, with the reinforcing rib welded approximately at 1/4 of the cross-section height. For the cross-section depicted in Figure 6a, the values of the cross-sectional characteristics are:  
Due to the difference in thickness of the top (12 mm) and bottom (10 mm) flanges, the cross-sectional characteristics for the compressed (\(-\)) and tensioned (\(+\)) branches are different in the ratio  
\[c=\frac{W_{z}^{-}}{W_{z}^{+}}=1.068\cong 1.07. \tag{3}\]  
The maximum normal stress (in the lower fibers) from the self-weight with \(\gamma_{g}=1.1\) is equal to:  
\[\sigma_{\text{gmax}}=\frac{\gamma_{g}\cdot M_{\text{max}}}{W_{z}^{+}}=\frac{1. 1\cdot 501.6\cdot 10^{6}}{13.83\cdot 10^{6}}\cong 40\text{ MPa}. \tag{4}\]  
The resulting maximum normal stress (in the lower fibers) for the weight of load 20,930 kg is:  
\[\sigma_{\text{max}}=\sigma_{\text{gmax}}+c\cdot 71=40+1.07\cdot 71\cong 116 \text{ MPa}. \tag{5}\]  
Considering the coefficient \(\gamma_{\ell 0}=1.3\),, the maximum stress cannot exceed the value of:  
\[\sigma_{\text{MAX}}=\sigma_{\text{gmax}}+\gamma_{\ell 0}\cdot c\cdot 71=40+1. 3\cdot 1.07\cdot 71\cong 139\text{ MPa}. \tag{6}\]  
The mentioned values of stresses are valid for girder's material 11 373 (yield strength \(\sigma_{\text{Ymin}}=210\text{ MPa}\)[25]) with a safety factor from 1.51 to 1.80 depending on the calculation value.