# Retrofit Fatigue Cracked Diaphrag Cutouts Using Improved Geometry in Orthotropic Steel Decks
## 5 Results and Discussion
### Principal Stresses around diaphragm Cutouts  
Principal stresses were acquired by three-direction rosette gauges arranged at the side of the diaphragm, 20 and 80 mm away from the edge of the diaphragm cutout. The measurements from the rosette gauges on both sides of the diaphragm were averaged. Figure 19a-c shows the test data along the horizontal line, 45\({}^{\circ}\) directional line and parallel U-rib web line, respectively. The abbreviations A-1 and A-3 represent the first and the third principal stresses of gauge A.  
Figure 19: The relationship between the longitudinal loading position and the stresses on the diaphragm: (**a**) the stresses at the horizontal line, (**b**) the stresses at the 45\({}^{\circ}\) direction line, (**c**) the stresses at the straight line parallel to the U-rib web.  
Figure 19a shows that at measuring points A and B, the third principal stresses after retrofit are generally larger than those before retrofit, and the maximum stress at the measuring point B increases by 6.4%. It shows that increasing the diaphragm cutout weakens the sectional area of the diaphragm, leading to the increase in stress in the diaphragm, but this increment in stress is small, and could not result in new fatigue cracks. The third principal stresses at the measuring points before and after the retrofit are large, and the first principal stresses are small, indicating that this is an area of primarily compressive stress, and the direction of the principal stress is vertically downward. The stress at point A near the diaphragm cutout is greater than that at point B, and the third principal stress difference at the location of peak stress is about 15 MPa, indicating that the stress concentration effect of the incision does occur but is not significant. After the retrofit of the diaphragm cutout, the stress concentration effect of the incision is reduced.  
According to the data presented in Figure 19b, the third principal stress (C-3) of measuring point C before the retrofit is larger than that after the retrofit. The effect of stress concentration on the diaphragm cutout before reinforcement on the measuring point C is greater than the effect of the change in the cross-sectional area of the diaphragm, thus causing an increase in the average stress. Increasing the radius of the diaphragm cutout can effectively reduce the stress concentration effect in the area around the diaphragm cutout. The third principal stress at the measuring point C after retrofit is larger than that at the measuring point D, and the maximum difference between the stress curves is about 10 MPa. The stress gradient between measurement point C and measurement point D after retrofit is 166.6 MPa/m. Before the retrofit, the stress gradient between point C and point D was 283.3 MPa/m. The results show that the stress gradient on the diaphragm can be effectively reduced with diaphragm cutout optimization.  
The data in Figure 19c demonstrates that before and after the diaphragm cutouts were retrofitted, the change in stress of the diaphragm near the U-rib is small, which does not affect the fatigue performance of the weld joint between the diaphragm and U-rib. Therefore, the stress concentration effect of the diaphragm cutout has little effect at this position. The first and third principal stresses at the measurement points of the diaphragm in the direction parallel U-ribs are almost equal, but in opposite direction.