## 5 Conclusions  
In this paper, a new restoring force model for the simulation of the corroded steel frame beam under horizontal cyclic loading was developed, and some conclusions were obtained as follows:  
1. The test results of the corroded steel material verified a widely known fact that corrosion has a significant effect on the mechanical properties of steel. With the increase of the corrosion degree, the mechanical properties of steel have a linear decreasing trend, and the linear regression analysis is carried out to obtain the expressions of various mechanical properties and the weight loss rate.
2. The test results of the corroded steel frame beam under the cyclic loading show that the failure process of the steel frame beam specimen experiences three stages, namely, elasticity, elastoplasticity, and the plastic failure stage. The bottom flange plate is partially buckled first, then the web is convexly curved, and finally the plastic hinge is formed at the bottom of the beam. However, with the increase of the corrosion degree, the horizontal bearing capacity of the specimens is gradually reduced, and the stiffness is significantly degraded. The displacements corresponding to the end flange buckling, the web drum, and the plastic hinge formation are also gradually reduced.
3. Based on the above results, the skeleton curve of the corroded steel beam specimen is simplified to a trilinear model considering the descent segment. The theoretical derivation formulas of the three characteristic points are given in the model. There is good agreement between the calculation value and test value, demonstrating that the established trilinear model in this paper is reasonable.
4. The cyclic degradation index is introduced by considering the effect of the corrosion degree for the hysteresis performance, and the restoring force model of the corroded steel frame beam is established by defining the degradation rule of strength and stiffness. The computed hysteresis curves are in good agreement with the experimental ones, verifying the applicability of the restoring force model. The developed model truly reflects the hysteretic behavior of the corroded steel frame beam, and the research results provide a theoretical basis for the nonlinear seismic response analysis of corroded steel frame structures.
5. Considering the rapid development of structural health monitoring (SHM), we will conduct some investigation on the corrosion monitoring of steel frame beams in the future, including the active sensing method [44; 45; 46], and the electro-mechanical impedance method [47].  
Figure 16: Comparison of calculation hysteresis curves and test hysteresis curves. (**a**) Specim B-1; (**b**) specimen B-2; (**c**) specimen DB700; (**d**) specimen TRS2A.  
**Author Contributions:** [PERSON] and [PERSON] designed and performed the experiments; [PERSON] and [PERSON] analyzed the data; [PERSON] and [PERSON] wrote the paper.  
**Acknowledgments:** The authors appreciate the support of the National Science and Technology Support Program (2013 BAJ08B03), the National Science Foundation of China (51678475), the Natural Science Foundation of Shaanxi Province (2018 JQ5158) and the Scientific Research Program Funded by Shaanxi Provincial Education Department (18 JK0382).  
**Conflicts of Interest:** The authors declare no conflict of interest.