Moment stiffer than the sagging moment region. Although

Moment redistribution
The moment redistribution ratio (?) given in Table 6 was calculated for the sagging and the hogging bending moment at midspan and at the central support at any stage of the loading. The ratio was calculated by:
?=(M_(e )- M_ex)/M_e *100 (2)
Where M_(e ), is the value of the moment at central support and mid-span is based on the elastic analysis and M_ex is the experimental value of bending moment at any stage of loading.
From Table 7, Fig.17 and Fig.18, it can be seen that the redistribution of the internal force from the sagging to the hogging region gradually decreased at the beginning of the test until the cracking load for the control beam, CB, where the moment redistribution ration was almost equal to zero. After the cracking load and before reaching the steel yielding (P_y=278 kN), the moment redistribution ratio increased with a slow rate where the maximum moment redistribution ratio was -9.9% and 14.76% at the sagging and the hogging regions respectively. The moment redistribution reduced after the steel yielding and this could be attributed to the reduced flexural stiffness due to the extensive cracking observed in the higher load span. Regarding the effect of the strengthening region, both beams SSH and SCH redistributed moments in a similar manner up to failure. The difference in the strengthening at the hogging region was that the internal forces redistributed from the sagging to the hogging moment region up to failure because the NSM bars was able to control the crack widths which in turn, made the middle support region stiffer than the sagging moment region. Although the moment redistribution ratio decreased due to the convergence of the flexural rigidity between the mid-span region and the central support region, this ratio increased again after the yielding of the sagging steel and up to failure as a result of the increase in the cracks width at the sagging region. The moment redistribution ratio for the beam (SSH) at the steel yielding was 11.5% and -15.56% at the sagging and the hogging region respectively, and then the rapid increase until failure, especially for the negative moment. The moment redistribution ratio at the failure was 16.15% and -23.43%. For the strengthened beam (SCH), the moment redistribution ratio significantly reduced and this value was roughly equal to zero at steel yielding. Where the percentage reduced to 0.5% and -0.8% at the sagging and the central support region respectively, because the axial stiffness of the upper main reinforcement with the NSM bars was slightly higher than the axial stiffness of the bottom main reinforcement. Close to failure, beam SCH achieved 10.12% and -16.7% moment redistribution at the mid-span and the hogging region, respectively. Beams SSS and SCS demonstrated load redistribution from the middle support to the mid-span section such as the control beam. This is due to the stiffness at the mid-span section was 2.66 and 2.17 times the hogging section of beam SSS and SCS, respectively. As it was indicated in the other beams, the deviation in the load-moment redistribution ratio curve was at the sagging steel yielding. The beam SSS achieved -21.28% and 35.93% moment redistribution at the sagging and the hogging region before the steel yielding, while these percentage reduced at the failure to -16.4% and 27.33%. The maximum value for the moment redistribution ratio was achieved by the beam SCS, the percentages of moment redistribution were -25.2% and 42% at the sagging and the middle support, respectively.


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