## 6 Further Research on Hybrid Connection  
### Analytical Research on Hybrid Connection  
[PERSON] et al., 1999 [39] performed a nonlinear push-over static and time-history analysis of two six-story frames with hybrid connections. Fiber and spring analytical models were developed. They reported that hybrid frames were adequate for severe seismic loads in terms of strength, ductility, and self-centering capabilities. Hybrid frames had large displacements compared to monolithic frames due to the small amount of energy dissipation, whereas the residual displacement could be smaller. [PERSON] et al., 1998 [40] developed a hysteretic model based on hysteretic behavior from phase IV-B experiments. They modelled the stiffness, strength degradation, and pinching to characterize force-deformation loops. Their empirical approach is not reliable because of the complex nonlinear behavior of hybrid frames. The combined behavior of unbonded PT  
Figure 21: Shear transfer by the diagonal compression strut. Figure 22: Spiral reinforcement at the compression zones. and mild steel does not follow the strain compatibility. Hence, it is difficult to predict the moment curvature of the hybrid frame connection. [PERSON] et al., 2000 [41] developed a method for section analysis of hybrid connections based on member strain compatibility and local strain incompatibility between steel and concrete. His proposed method correctly predicted the experimental results of phase IV-B. [PERSON] et al., 2009 [42] performed nonlinear finite element analysis for hybrid connections to predict behavior under cyclic loads. The model predicted the experimental behavior with good accuracy. Laboratory experiments are best for studying connection behavior, but they are tedious and expensive. If carefully modelled, numerical analysis can be a good alternative to laboratory experiments. They allow the investigation of connections with different loadings and design parameters. This is particularly the case with the availability of high-performance computers. [PERSON] et al., 2006 [35; 36] developed a non-dimensional design procedure for the design of hybrid frames. Laboratory results from phase IV indicated that the failure mode of precast hybrid connections was due to bar fracture and bond failure. [PERSON] et al. developed bar fracture criteria which consider low-cycle fatigue under combined axial and bending strains. The proposed formulation is simple compared to the iterative step-by-step procedure. [PERSON] et al., 2020 [43] developed an automatic optimum design procedure for the hybrid system using a genetic algorithm in MATLAB. The proposed formulation is simple compared to the iterative step-by-step procedure. [PERSON] et al., 2006 [44] experimented hybrid connections with different percentages of mild steel, and found that a 30% mild steel contribution to overall flexural capacity was sufficient for negligible residual displacement. With an increase in the mild steel percentage, the energy dissipation increased. However, with excess mild steel, residual displacement may not be negligible due to PT force not being sufficient to yield the mild bars in compression and bring the system back to the initial position. [PERSON] et al., 2010 [45] proposed a new method for hybrid frame section analysis and a hysteretic model based on residual deformation because of the strain incompatibility between concrete, mild steel, and PT steel. The proposed model shows good comparison with test results. [PERSON] et al., 2002 [46] studied the beam growth phenomenon in RCC frames. Due to flexural cracking at the beam column joint, the horizontal distance between the column and centerlines increases. This is termed as beam growth (Figure 23). He reported an increase in column shear demands of up to 86% due to beam growth. The phenomenon also exists in hybrid frames, as PRESS program experiments reported an up to 13 mm gap opening at the column-beam interface. Figure 23: Frame sway including beam growth [46].