## 6 Design Method for Tie-Bars in SC Composite Beam under Cyclic Loading  
Based on the existing research on the design of shear connectors in a SC composite structure, a new design method of tie-bars in the SC composite beam under cyclic loading was proposed. For the SC composite beam, \(H\) represents the total thickness, \(H_{c}\) represents the thickness of concrete, \(B\) represents the width, \(s_{L}\) represents the longitudinal space of the tie-bar, and \(s_{T}\) represents the transversal space of tie-bars. It is assumed that the interfacial shear and tension in the oblique section could be offered by tie-bars. The diameter and tensile strength of the tie-bar are assumed to be known, and thus, the tension capacity of the tie-bar could be calculated. The shear capacity of tie-bar under cyclic loading could be determined through the push-out test due to the absence of experimental results. The relationship between the tension capacity and shear capacity of tie-bars could be determined based on the existing research carried out by the authors [14]. The formula is shown in the following:  
\[V/V_{u}+T/T_{u}=1.0 \tag{9}\]  
where \(T\) is the tension of the tie-bar, and \(T_{u}\) is the tensile capacity of the tie-bar. The number, longitudinal space, and transversal space of tie-bar should be designed. The longitudinal space of tie-bars should be less than half of the height of the concrete, and less than 40 times the thickness of the steel plate. The number of tie-bars in the SC composite structure between the maximum bending moment and zero bending moment could be no less than 10. In addition, the tie-bars should satisfy the remand of the lowest reinforcement ratio (\(\rho_{t,\min}\)) [26]. The formula is shown in the following:  
\[\rho_{t,\min}=1.44\times 0.062\frac{\sqrt{0.81f_{c}}}{f_{y,\text{tie}}}\geq 1.4 4\times 0.35\frac{1}{f_{y,\text{tie}}} \tag{10}\]  
Figure 14: Parameter analysis on minimum shear connection ratio. The steps of the design method for tie-bars in the SC composite beam subjected to out-of-plane cyclic loading are shown in the following:  
1. According to the yield tensile capacity of steel plate and space between two steel plates, the theoretical value of the flexural capacity of the SC composite beam could be calculated. Then, the yield tensile capacity of steel plate (\(F_{ys}\)) could be determined. 2. It is assumed that the concrete firstly offers oblique section shear, and the tie-bars offer oblique section tension secondly. Based on the formula in AISC/ANSCI N690s-15, the tension of tie-bars could be calculated. The formula is shown in the following: \[V_{no}=V_{conc}+V_{s}\] \[V_{conc}=0.13(f_{c}^{\prime})^{0.5}H_{c}B\] (11) \[V_{s}=\varphi f_{y,tie}(B/s_{T})(H_{c}/s_{L})\leq 0.67(f_{c}^{\prime})^{0. 5}H_{c}B\] where \(V_{no}\) is the out-of-plane shear, \(V_{conc}\) is the out-of-plane shear contribution from the concrete, \(V_{s}\) is the out-of-plane shear contribution from the shear reinforcement, i.e., tie-bar, \(\varphi=1.0\) for yielding shear reinforcement, and \(\varphi=0.5\) for nonyielding shear reinforcement. 3. According to the simulation results, the minimum shear connection ratio (\(\gamma_{min}\)) of the SC composite beam with different shear span versus depth ratio could be calculated based on linear interpolation. When \(\lambda\) is less than 3.33, the minimum shear connection ratio could be 1.7; and when \(\lambda\) is more than 6.67, the minimum shear connection ratio could be 1.55. The first estimation of the number of tie-bars should be calculated by the formula, \[n_{1}\geq\gamma_{\min}\times F_{y,s}/V_{u}\] (12)
4. The longitudinal space and transversal space of tie-bars could be determined. Meanwhile, the demands about the space of tie-bars should be satisfied. 5. Verify the lowest reinforcement ratio (\(\rho_{t,min}\)). If not satisfied, increase the number of tie-bars or increase the section area of tie-bars. 6. Calculate the tension of tie-bars by the formula \(T=Q_{s}\times s_{T}\times s_{L}/(B\times H)\). \(Q_{s}\) is the out-of-plane shear.