# Experimental Investigation of the Fatigue Life of a Bridge Crane Girder Using S-N Method
### Assessment of Fatigue Life and Strength According to STN 270103  
When the crane is classified according to STN 270103 in stress spectrum S2 and operating group J5, according to Table 13 of the standard, the number of cycles \(N\) per technical lifetime is:  
\[N=6\cdot 10^{5}\ \text{to}\ 2\cdot 10^{6}, \tag{7}\]  
When considering notch group K3 (strong notch effect), for welded structure 333, according to Table 25 of the standard mentioned above, the fundamental calculated fatigue strength is \(R_{\text{fat}}(-1)=63.6\ \text{MPa}\). (8)  
According to Figure 8, the following applies:  
\[R_{\text{fat, t}}(0)=\frac{5}{3}R_{\text{fat, t}}(-1)=\frac{5}{3}\cdot 63.6=106 \ \text{MPa}. \tag{9}\]  
The calculated fatigue strength for the ultimate stress ratio \(\chi\cong 0.35\) is according to Table 17 of STN 270103:  
\[R_{\text{fat}}(0.35)=\frac{R_{\text{fat, t}}(0)}{1-\left(1-\frac{R_{\text{fat, t}}(0)}{0.75\cdot\omega_{\text{U}}}\right)\cdot\chi}=\frac{106}{1-\left(1-\frac{106}{0.75\cdot 3.70}\right)\cdot 0.35}=135\ \text{MPa} \tag{10}\]  
where \(\sigma_{\text{U}}=370\ \text{MPa}\) is the ultimate strength of the material. Figure 7: Experimental determination of the dynamic lift coefficient—time courses of calculated normal stresses and visualization of their mean values. According to paragraph 58 of STN 270103:  
\[\left(\frac{\sigma_{\max}}{R_{\text{fat}}(\chi)}\right)^{2}=\left(\frac{116}{13 5}\right)^{2}=0.74\leq 1.1. \tag{11}\]  
This verification realized according to STN 270103 confirms sufficient fatigue strength reserve at the number of cycles \(N=6\cdot 10^{5}\) to \(2\cdot 10^{6}\). Based on the analysis of the time courses of the normal stresses for Modes 1, 2 and 3, as well as by comparing the stress levels obtained at the individual measurement locations, locations B3 and B4 were selected for the experimental-computational verification of the possible fatigue damage accumulation of the bridge crane girders. The maximum ranges of normal stresses were registered at these locations during all investigated operational modes. From the time courses of the normal stresses, the spectra of stress amplitudes were evaluated by the Rainflow Counting method. Figures 9-11 show the stress spectra evaluated at the measurement location B3 for Modes 1, 2, and 3. Figure 8: Dependence between the calculated fatigue strengths \(R_{\text{fat}}\) (\(-1\)) and \(R_{\text{fat}}\) (\(\chi\)). Note: \(\sigma_{\text{U}}\)—ultimate strength, \(\sigma_{\text{Y}}\)—yield strength, \(\sigma_{\max}\)—maximum stress, \(\sigma_{\min}\)—minimum stress, \(\sigma_{\text{fat, t}}\)—fatigue strength by tensile loading, \(\sigma_{\text{fat, c}}\)—fatigue strength by compression. Figure 9: Spectrum of stress amplitudes, Mode 1. Assessment of the fatigue damage accumulation for the measured normal stress time courses (Figures 3-5) and the stress amplitude spectra evaluated from them was performed according to the Palmgren-Miner fatigue damage accumulation hypothesis following Eurocode 3, Part 9 [26]. The input to the hypothesis, in addition to the stress amplitude spectra, are the parameters of the Wohler curve of the welded detail corresponding to the notch group K3 (STN 270103). The fatigue limit for the above welded detail is according to Table 14 of STN 270103 \(\sigma_{\text{c}}=45\) MPa for alternating symmetrical stresses, where the following applies:  
\[\chi=\frac{\sigma_{\text{min}}}{\sigma_{\text{max}}}=-1. \tag{12}\]  
In the described case, it is an alternating stress with \(\chi=0.35\) and mean stress:  
\[\sigma_{\text{m}}=\frac{\sigma_{\text{max}}+\sigma_{\text{gmax}}}{2}=\frac{116 +40}{2}=78\;\text{MPa}. \tag{13}\]  
Figure 11: Spectrum of stress amplitudes, Mode 3. \[R_{\text{fat, t}}(0)=\frac{5}{3}R_{\text{fat, t}}(-1)=\frac{5}{3}\cdot 63.6=106 \ \text{MPa}. \tag{9}\]0 Spectrum of stress amplitudes, Mode 2. According to the Smith diagram, the fatigue limit \(\sigma_{\text{c (m)}}\cong 36\) MPa was determined considering the calculated mean stress \(\sigma_{\text{m}}\).