# A Restoring Force Model for Prefabricated Concrete Shear Walls with Built-In Steel Sections
## 7 Summary and Conclusions  
(1) Four specimens of prefabricated concrete shear walls with built-in steel sections were tested under a constant vertical loading and pseudo-static horizontal cyclic loading. The test results and theoretical failure mechanics of the walls were compared and analyzed.  
(2) Hysteretic and skeleton curves were developed based on the results of the pseudo-static test of prefabricated shear wall specimens. Based on the load and displacement of the walls, the stiffness of the walls at different loading stages was determined based on theoretical calculation and numerical regression. The establishment of a restoring force model provided theoretical support for the nonlinear analysis of such structures under low-cyclic loading.  
(3) According to the skeleton curves obtained from the test, a dimensionless skeleton curve model was obtained by experimental fitting. It can be seen that the vertical load on the top of the wall has a great effect on the shear stiffness of the wall. With a 10% increase of the vertical pressure, a 25% increase of the maximum horizontal resistance can be reached. The connection location, though, has no significant effect on the resistance of the wall.  
(4) Based on the test fitting method, the calculation method of the cracking stiffness for this kind of structure was proposed by means of mechanical calculation and test modifications. Then, the stiffness of yield point, limit point, and failure point were deduced.  
(5) Based on the ultimate equilibrium equation, the calculation method of the ultimate load was proposed. Then, the load of the cracking zone, yield point, and failure point were deduced.  
(6) The restoring force curve model of this kind of structure for nonlinear analysis was obtained. By numerical fitting the unloading stiffness after yielding, the hysteresis loop path was identified. The skeleton curve of the four-fold line considering stiffness degradation was obtained.  
(7) The restoring force model proposed in this paper was verified by the test results, which can be used to reflect the hysteretic performance of prefabricated shear walls with built-in steel sections. It was observed that ductal behavior of shear walls can be achieved by embedding steel sections in the wall. This method can be used as a reference for the elastoplastic seismic response analysis of RC shear wall structures with built-in steel sections.  
Research protocol formation and implementation, T.W.; Assist in research proposal and formulation and analysis, R.J.; Experimental study, S.Y.; Experimental tests, K.Y.; Experimental tests, L.L.; Theoretical analysis, G.Z. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Nature Fund program of Jilin, China (Grant No. 20200201227 JC).  
The data presented in this study are available on request from the corresponding author.  
The authors would like to thank Jilin Nature Fund program for the financial support and thank Changchun Institute of Technology for all the support during this research.  
The authors declare no conflict of interest.