Flexural rigidity is defined as the force couple required to bend a non-rigid structure in one unit of curvature or it can be defined as the resistance offered by a structure while undergoing bending. It is a function of the modulus of elasticity of the material of the beam, and the shape of its cross-section. Based on the elastic deformation theory, the experimental flexural rigidity is obtained as 1:
(?E_C I)?_(exp.)=(7pl^3)/(768?_(exp.) ) (1)
l is each span length, p is the applied load to each span, and E_C is the elasticity modulus of concrete. Fig.14 shows the variation of (?E_C I)?_(exp.) the flexural rigidity for beams (SCS and SCS), which strengthened with NSM CFRP bars, was the highest value before cracking, but their flexural rigidity quickly decreased after cracking. While the strengthening with NSM steel bars gave an approximate flexural rigidity value of the control beam before the cracking loads and this value decreased at a slower rate until the failure, in particular the beam (SSS), which strengthened at the sagging region. The values of the flexural rigidity at the ultimate load for beams (CB, SSH, SCH, SSS, and SCS) were (2.67, 6.66, 8.36, 16.1 and 13.71N.?mm?^2*?10?^12), it is clear that the strengthening at the sagging region had the better advantage than the strengthening at the hogging region, where it led to increase the load on the beam with less deflection. The energy absorption capacity of reinforced concrete (RC) elements is one of the pivotal structural properties that define their seismic resistance. The energy absorption capacity indicates the energy absorbed per unit cross-sectional area of the specimens calculated at any deflection extreme point 2. The energy absorption capacity of the control beam (CB) was higher than the strengthened beams, because the strengthened beams experienced premature failure, so the specimens did not achieve the full flexural strength. As shown in Fig.15.