## 6 Conclusions  
Based on nonlinear FE analysis on lots of specimens and detailed discussion on existing research, influence factors of the single-keyed dry joints in segmental precast bridges under the direct shear loading were investigated. A new shear capacity formula was proposed in this paper, and the main conclusions are as follows:  
1. Considering the plastic damage of concrete, the nonlinear FE model of the single-keyed dry joint was established, the ultimate shear capacity analysis under the direct shear loading was carried out on existed test specimen. Results demonstrated that the simulated results are in good agreement with the existing experimental results. Thus, the feasibility and correctness of the finite element simulation method were verified.
2. Both simulated and experimental results indicated that tensile damage occurred in on the underside of the key root even in the linear stage, which was then developed 45\({}^{\circ}\) upwards or vertically along the key root section. Concrete tensile strength at the key root is critical to the ultimate bearing capacity of the single-keyed dry joint under the direct shear loading.
3. The shear resistance of the concrete key root, related to lateral prestress and concrete tensile strength, is the only contributor to the ultimate shear capacity \(\mathbf{V_{u}}\) of the keyed dry joints. Friction on the joint interface was demonstrated to be only transferring force between the adjacent joints, \(\mathbf{V_{u}}\) does not increase with the increase of friction coefficient. Neither do dimension parameters of the key (such as key depth, key inclination and key aspect ratio) have much effect on \(\mathbf{V_{u}}\). Meanwhile, a reasonable range of key inclination (tan \(\theta\)) would be suggested as 0.7-0.9 to obtain comparatively higher value of \(\mathbf{V_{u}}\).
4. According to the above investigation and supposing the shear stress distributed evenly along key root width, a new formula of the shear capacity of the single-keyed dry joints was proposed based on the maximum principal stress strength criterion. In comparison with the predicted results obtained by other existed formulas, the proposed formula is demonstrated to be in perfect consistency with both tests and the FE simulation results.  
Conceptualization, W.H. and M.P.; methodology, W.H.; software, M.P.; validation, M.P., B.J. and Y.T.; formal analysis, W.H. and L.Z; investigation, M.P.; resources, M.P.; data curation, M.P. and B.J.; writing--original draft preparation, M.P. and W.G.; writing--review and editing, W.H. and Y.T.; visualization, Y.T.; supervision, L.Z.; project administration, W.H.; funding acquisition, W.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Natural Science Foundation of Hunan Province, Grant number 2019 JJ40385.  
Special thanks are extended to the reviewers for their valuable suggestions. The authors would like to thank [PERSON]. [PERSON], University of Tennessee, Knoxville for his help in revising the original manuscript, and the reviewers and the editor for their hard work as well.  
The authors declare no conflict of interest.  
Figure 19: Comparison of the shear capacity predicted by different formulas and FE simulated values.