# Retrofit Fatigue Cracked Diaphrag Cutouts Using Improved Geometry in Orthotropic Steel Decks
## 6 Conclusions  
The stress flow method is used to analyze the cause of stress concentration at the diaphragm, the wheel loads on the deck transmit stress to the diaphragms through the U-ribs. In the process of load transmission, the stress flows are obstructed by diaphragm cutouts, resulting in the local high density of stress flows, and hence leading to stress concentrations around the cutouts. According to the analysis of the geometric parameters of diaphragm cutouts, it is found that the geometrical size of the diaphragm cutout should be small, while the radius should be large, the included angle should be negative, and the stress flow should not be obstructed by cutouts. Therefore, an optimized geometry with a radius of 35 mm is recommended to reduce stress concentrations in zone A and zone B and to remove short fatigue cracks at diaphragm cutouts. The maximum principal stresses in zone A and zone B around the cutouts were decreased significantly after the diaphragm cutouts were retrofitted. The local stresses decreased up to 87.6 MPa, and the stress reduction ratio is 59.9%. When the lateral probability distribution is considered, the equivalent constant amplitude stress is reduced by 55.2%. However, the stress at the critical section, which is near the cutout and at the horizontal line in the diaphragm, is increased slightly because this critical section is narrowed due to the increase in the radius of the cutout. Based on the construction detail No. 4 in Table 8.1 in Eurocode 3, the modified nominal stress method, which takes the influence of geometry into consideration, is used to evaluate the fatigue life of diaphragm cutouts. The evaluated fatigue life of diaphragm cutouts, based on FEA and test results, are 1.7 years and 4.9 years respectively, before the cutouts are retrofitted, and increase to 78.1 years and 155.5 years respectively after retrofitting. These results indicate that this retrofitting technology is suitable for fatigue damage rehabilitation in zone A of the diaphragm cutouts. The hot cutting method combined with corner grinding used to retrofit the geometry of diaphragm cutouts causes residual tensile stress, which is ignored in this paper. The residual stress distribution, the influence of the R ratio and a high-precision assessment method for diaphragm cutouts need to be further studied. Conceptualization, Z.-Y.C. and H.-H.X. ; methodology, Z.-Y.C. and C.-X.L. ; software, Z.-Y.C. and J.H. ; validation, Z.-Y.C., C.-X.L. and H.-H.X. ; formal analysis, Z.-Y.C. ; investigation, Z.-Y.C. ; resources, Z.-Y.C. and C.-X.L. ; data curation, Z.-Y.C. ; writing--original draft preparation, Z.-Y.C. ; writing--review and editing, J.H. and H.-H.X. ; visualization, Z.-Y.C. ; supervision, J.H. ; project administration, Z.-Y.C. and C.-X.L. ; funding acquisition, Z.-Y.C. All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China through Grant No. 51708047, 51778069 and 51978081; Horizon 2020- [PERSON] Sklodowska-Curie Individual Fellowship of European Commission (REUSE: 793787); the Natural Science Foundation of Hunan Province through Grant No. 2019 JJ50670; the Excellent youth project of Hunan Provincial Department of Education through Grant No. 19B013, and the Innovative projects in key disciplines through Grant No.18 ZDX11. The authors declare no conflict of interest.