# Flexural Behavior of Self-Prestressed RC Slabs with Fe-Based Shape Memory Alloy Rebar
## 3 Experiment Results and Discussion
### Load-Deflection Relationship
#### 3.4.2 Effect of the Amount of Fe-SMA Rebar  
Figure 11 presents a comparison of the load-displacement relationship of the specimen according to an increase in the amount of Fe-SMA rebar. As shown in Figure 11a, the initial crack loads of SL-2N, SL-3N, SL-4N, and SL-5N, wherein the Fe-SMA rebar was not activated, were 25.59 kN, 27.73 kN, 29.06 kN, and 29.28 kN, respectively. When the amount of Fe-SMA rebar was increased by 100 mm\({}^{2}\), the initial crack load increased slightly (by 4.63% on average). As shown in Figure 11a, when the amount of the Fe-SMA rebar was increased, the flexural stiffness was significantly improved after initial cracking. The ultimate loads of SL-2N, SL-3N, SL-4N, and SL-5N were 58.66 kN, 92.04 kN, 117.01 kN, and 147.91 kN, respectively, and when the amount of the Fe-SMA rebar was increased by 100 mm\({}^{2}\), the ultimate load increased linearly by approximately 30 kN on average. Therefore, the initial cracking load of the member without the activated Fe-SMA rebar was not significantly affected by the amount of Fe-SMA rebar, but the ultimate load was significantly affected. Figure 11b shows a comparison of the load-displacement  
Figure 9: Comparison of load–Fe-SMA rebar strain curves of non-activated specimens according to area of Fe-SMA rebar. relationship of the activated specimens according to the increase in the amount of Fe-SMA rebar. The initial crack loads of the activated specimens SL-2A, SL-3A, SL-4A, and SL-5A were 35.88 kN, 46.92 kN, 52.81 kN, and 59.03 kN, respectively. Unlike the non-activated specimens, when the amount of the Fe-SMA rebar was increased by 100 mm\({}^{2}\), the initial crack load increased by an average of 18.4%. In addition, as the amount of the Fe-SMA rebar was increased, the stiffness of the specimens increased remarkably after the initial crack occurred. In the case of the activated specimens, when the amount of the Fe-SMA rebar was increased by 100 mm\({}^{2}\), the ultimate load increased by about 29 kN, similar to that of the non-activated specimens. The initial cracking moment (\(M_{cr}\)) is the moment that makes the tensile stress of the outermost fiber of the concrete cross-section equal to the flexural tensile strength (\(f_{cr}\)) of the concrete. Figure 11: Comparison of load–deflection curves according to amount of Fe-SMA rebar. (**a**) Non-activated specimens. (**b**) Activated specimens. Figure 10: Comparison of load–deflection curves according to activation of Fe-SMA rebar: (**a**) SL-2N and SL-2A, (**b**) SL-3N and SL-3A, (**c**) SL-4N and SL-4A, and (**d**) SL-5N and SL-5A. The internal stresses of the concrete member with Fe-SMA rebar subjected to external load are composed of the compressive stress (\(f_{c1}\)) generated by the recovery stress of Fe-SMA, the flexural stress (\(f_{c2}\)) generated by the eccentric compressive force, and the flexural stress (\(f_{c3}\)) generated by an external load. These three stresses in the outermost concrete fiber below the neutral axis can be expressed as Equations (1)-(3), respectively. The sum of the bending stresses (\(f_{c}\)) in the outermost concrete fibers below the neutral axis can be expressed as Equation (4). The compressive force (\(P_{rec}\)) generated by the activation of the Fe-SMA rebar of Equation (1) can be calculated through Equation (5), and the recovery stress (\(f_{rec}\)) of the Fe-SMA rebar of 335 MPa was used based on the experimental results:  
\[f_{c1}=\frac{P_{rec}}{A_{c}} \tag{1}\]  
\[f_{c2}=\frac{P_{rec}\times e}{I_{g}}y \tag{2}\]  
\[f_{c3}=-\frac{M_{a}}{I_{g}}y \tag{3}\]  
\[f_{c}=f_{c1}+f_{c2}+f_{c3} \tag{4}\]  
\[P_{rec}=f_{rec}A_{sma} \tag{5}\]  
where \(A_{c}\) is the area of the concrete section, \(e\) is the eccentric distance, and \(A_{sma}\) is the area of the Fe-SMA rebar. In addition, \(y\) represents the distance from the outermost concrete fiber to the neutral axis, \(M_{a}\) is the moment applied to the member by an external load, and \(I_{g}\) is the moment of inertia of the specimen. In ACI 318 [32], \(f_{cr}\) is defined via Equation (6).