## 7 Conclusions  
In this study, freeze-thaw cycle and fatigue tests were performed on prestressed hollow slab model components reinforced by pasting steel plates and bonded carbon fiber sheets after fatigue damage. Based on the finite element model for the components reinforced by pasting steel plates, the relevant mechanical properties and fatigue characteristics of the prestressed hollow slab strengthened components with fatigue damage under freeze-thaw cycle erosion were systematically studied. The main conclusions of this study are as follows.  
(1) For a 2 m long hollow slab beam, the midspan deflection in the prestressed hollow slab beam strengthened by pasting steel plates and carbon fiber sheets was less than that in the prestressed hollow slab beam after fatigue damage and prior to strengthening. Under a constant load, the compressive strain generated by the concrete at the top of the midspan of the reinforced test plate was less than that generated in the unreinforced prestressed hollow core slab, and the tensile strain generated at the bottom under a load was also less than that of the unreinforced components.  
(2) The test 2 m long hollow slab beam strengthened using steel plates and carbon fiber sheets could withstand 2 million cycles of fatigue loading at a 0.8 stress level. The test plates exhibited good fatigue resistance characteristics for both methods of reinforcement.  
Figure 21: Fatigue life map of reinforced components under different freeze–thaw cycles: (**a**) 50 freeze–thaw cycles; (**b**) 100 freeze–thaw cycles.  
Figure 22: Fatigue life of reinforced components under different freeze–thaw cycles.  
Under the fatigue load, the original cracks did not expand further and no new cracks appeared in the test plate reinforced by pasting steel plates. The bonded carbon fiber sheet produced new shear cracks during fatigue loading; however, the new cracks expanded slowly during continued loading.  
(3) After the freeze-thaw cycle erosion of the 2 m long hollow slab beams reinforced by pasting carbon fiber sheets during 2 million cycles of fatigue loading, the original cracks were not noticeable, there were a few newly emerged cracks, and the top plate was significantly damaged. Cracks were almost absent during the 2 million cycles of fatigue loading for the bonded steel plate reinforced components, which exhibited good anti-cracking performance. Under fatigue loading, the freezing-thawing cyclic effect increased the deflection and strain of the reinforced components, and the growth rate increased with the number of fatigue loading cycles. In addition, there existed a dynamic displacement of the strengthened components after the erosive effect of the freeze-thaw cycles during fatigue loading. The impact resistance of the strengthened components under the action of the freeze-thaw cycles was weakened.  
(4) By establishing a numerical model for the 2 m long hollow slab beam strengthened by bonded steel plates, the midspan deflection in the strengthened components increased with increasing freeze-thaw cycles, and its rate of increase grew gradually. Furthermore, an increase in the number of freeze-thaw cycles significantly affected the fatigue lives of the components reinforced by bonded steel plate.  
Methodology, Y.Z.; conceptualization, Y.Z. and J.L.; software, Y.Z. and J.L.; writing--original draft preparation, Y.Z. and J.L.; writing--review and editing, Y.Z., C.G. and P.G.; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript.  
This work was supported by National Natural Science Foundation of China (Grant No. 51878623, U2040224), Key Research and Development and Promotion Special Project of Henan Province in 2020 (Key Science and Technology Tack) (Grant No. 202102310241), and Program for Young Backbone Teachers in Colleges and Universities in Henan (Grant 2018 GGJ8005).  
Not applicable.  
Special thanks are extended to the anonymous reviewers for their valuable comments.  
The authors declare that they have no conflict of interest.