## 4 Results and Discussion
### Comparison of Numerical and Experimental Results
The SL-60S-4 simulation resulted in  
Figure 8: Comparison of load-displacement curves for SL-30S-4. Figure 7: Comparison of load-displacement curves for SL-CTRL. a concrete crushing failure after the tensile reinforcement yielded at the central vertical displacement of 89.51 mm. The SL-60S-4 experimental specimen also exhibited concrete failure in the compression zone after the tensile reinforcement yielded at a central defection of about 80 mm. Figure 10 shows the numerical and experimental results for the load-displacement relationship of SL-90S-4. The initial crack in SL-90S-4, which was strengthened by the three-line Fe-SMA strips, occurred under a numerical load of 16.68 kN, which was about 2.64 kN larger than the experimental result. The numerical yielding load and ultimate load of this specimen were 1.26% and 4.15% higher than the experimental results, respectively. The SL-90S-4 numerical specimen also predicted concrete crushing failure in the compressive zone after the tensile reinforcement yielded. To analyze the reliability of the proposed FE model in this study, [PERSON]'s experimental results were compared with the simulation results from the FE analysis of the proposed FE model. [PERSON] et al. [29] conducted a four-point bending test of RC beams strengthened with NSM using a Fe-SMA strip. The used Fe-SMA was pre-tensioned up to 2% of its original length. The Fe-SMA strip was heated to 160 \({}^{\circ}\)C to activate the shape memory effect, which produced about 250 MPa in recovery stress. The length, width, and thickness of the used Fe-SMA strip were 2600 mm, 20 mm, and 1.7 mm, respectively. Detailed geometry and material properties of the used specimens are referred in [PERSON]'s paper [29]. A comparison of the experimental and the FE analysis results is shown in Figure 11a,b in terms of the initial crack load, the yield load, and the ultimate load. Figure 11a is the load-displacement curve on the RC beam strengthened with non-activated Fe-SMA strip. Figure 11b shows the load-displacement curve with an activated Fe-SMA strip. When the three load stages from the experiments and the FE analyses were compared, as shown in Figure 11a,b, the proposed FE model predicted the experimental results well, with less than 6% error. The FE analysis of the strengthened RC beam with non-activated Fe-SMA strip showed an initial crack load, yield load, and ultimate load of 4.7 kN, 23.3 kN, and 32.02 kN,  
Figure 10: Comparison of load- displacement curves for SL-90S-4. Figure 9: Comparison of load-displacement curves for SL-60S-4. respectively. Errors in the results between the test and simulation for each load stage were 6.0%, 1.7%, and 4.7%, respectively. On the other hand, the RC beam strengthened with the activated Fe-SMA strip exhibited 8.71 kN, 23.37 kN, and 31.52 kN for those three load stages, respectively, showing minor errors of 2.6%, 0.6%, and 3.9% from the experimental results. Figure 12 shows the agreement in the numerical prediction results and experimental results in terms of the initial crack load, yield load, and ultimate load. The ratio of the numerical results to the experimental results averaged 1.04, 1.01, and 1.01, respectively, and the standard deviations were an average of 0.09, 0.03, and 0.07, respectively. In other words, the FE model accurately predicted the flexural behavior of the RC beams strengthened with Fe-SMA strips using the NSM method.