# Long-Term Behavior of RC Beams Strengthened with Hybrid Composite Beam
## 3 Experimental Results and Discussions
### Evaluation of Time-Dependent Factors  
In this study, time-dependent factors of HCB-strengthened RC beams were investigated to understand the influence of external strengthening of HCB on RC beams. To determine the time-dependent factor from the long-term test, the well-known equation suggested by ACI 318 was adopted. This equation derived the additional long-term deflection resulting from creep and shrinkage of steel-reinforced concrete beams in terms of multiplying the instantaneous deflection by a factor. Therefore, it was assumed that the additional deflection of HCB-strengthened RC beams would be affected by the HCB strengthening, and the ACI equation would provide a somewhat adequate approximation in this study. The modified additional long-term deflection (\(\Delta_{ADD}\)) of HCB-strengthened RC beams in this study may be written as  
\[\Delta_{ADD}=\frac{\xi}{1+50S\rho^{\prime}} \tag{2}\]  
where, \(\xi=\) time-dependent factor for sustained loading level, \(s=\) flexural stiffness ratio between HCB-strengthened and unstrengthened RC beams \(((EI_{beam}+EI_{HCB})/(EI_{beam}))\) and \(\rho^{\prime}=\) compression reinforcement ratio of steel bars in the RC beam section. The time-dependent factors found in this study using Equation (2) may be compared with the values found by [PERSON] (2010) and [PERSON] (2011) with similar FRP systems and ACI equations ([PERSON], 2011). It should be noted that the ACI equation was proposed by steel reinforced concrete beams, while the values of [PERSON]'s study were obtained from RC beams with externally bonded CFRP laminates, and the values of [PERSON]'s study were obtained from CFRP bars reinforced with concrete beams. Table 3 presents the time-dependent factors from the present work with each of the different investigations up to 1 year.  
Figure 9: Percentage variation of longitudinal concrete tensional strains.  
In this investigation, we found that the time-dependent factors of HCB50 were approximately similar to those determined by [PERSON] within 1 year. However, the time-dependent factors of HCB33 differed from those obtained by [PERSON] by as much as 50%. The average time-dependent factors of HCB33 were approximately 50% higher than those of [PERSON], while HCB50 values were approximately 30% lower than those of [PERSON]. Given that the present work and the studies of [PERSON] and [PERSON] were performed using different strengthening materials, types and loading levels, it can be concluded that the time-dependent factor of FRP-strengthened RC beams is strongly dependent upon the type of FRP materials, strengthening method and sustained loading levels. The time-dependent factors of HCB-strengthened RC beams found in this study may also be compared with those values recommended by ACI. The time-dependent factors of HCB33 were on average 26.5% higher than those of ACI, while those of HCB50 were on average 38% lower than those of ACI. In the present work, the ACI equation may not provide a reasonable estimation of the long-term deflection behavior of HCB-strengthened RC beams. For unstrengthened RC beams at the two different loading levels, it was found that the time-dependent factors suggested by ACI ranged from, on average, 60% higher than NHCB50 to 45% lower than NHCB33. Actually, values of time-dependent factors of ACI are derived without a specifically applied sustained loading level. Based on the results of the present work, we suggested that the sustained loading level should not exceed 50% to ensure that the ACI equation can model the time-dependent factor of RC beams. Therefore, further tests with various conditions are needed to verify