## 4 Finite Element Analysis Results and Discussion
### Coefficient of the Bending Moment Transfer by the Eccentric Shear Force  
As shown in Figures 1 and 2, the shear stress on the critical section is composed of the shear stress generated by the vertical load and the additional shear stress generated by the action of the unbalanced bending moment, as defined by ACI318-19 [22] and the Chinese specification GB50010-2010 [19].  
The moment transfer coefficient can be derived by substituting the measured shear stress shown in Section 4.1 into the equivalent concentration reaction force equation of ACI-318, as shown in Equation (2):  
\[\gamma_{v}=\frac{(v_{u}b_{0}d-V)J_{c}}{Mxb_{0}d} \tag{2}\]  
where \(v_{u}\) is the shear stress on the perimeter of the critical section of the eccentric force side, \(b_{0}\) is the critical section's perimeter, \(d\) is the effective slab thickness, \(V\) is the vertical load, \(J_{c}\) is the property of the assumed critical section analogous to the polar moment of inertia, \(M\) is the bending moment generated by the lateral force, and \(x\) is the centroid of the shear perimeter.  
Thus, the moment transfer coefficients obtained by substituting the shear stresses measured under different values of M/V into Equation (2) are listed in Table 3, and the trend is shown in Figure 23. For more comparisons, nine new groups of [PERSON] et al.'s models were simulated at different M/V values. These are models with a stud diameter of 8 mm and 15 mm, and with 2, 4, and 6 studs, respectively. The details are shown in Table 3. The \(\gamma_{v}\) in ACI318-19 and Chinese specification GB50010-2010 is a parameter related only to geometry (Equation (1)). Thus, for these experimental settings, \(\gamma_{v}\) is a constant value of 0.4. The moment transfer coefficients for all of the groups of plates with different numbers and diameters of shear studs and different loading methods do not differ significantly, and can be approximated by one fitted curve to express the trend. It can be seen from Figure 23 that the FEM transfer coefficients are much smaller than the code value (0.4). Therefore, the code calculates this coefficient using only the geometry, which is safe in terms of the performance of the shear reinforcement group, but too conservative for the simulation results.  
Figure 22: Average shear stress versus M/V: (a) [PERSON] et al.’s slabs (b) [PERSON] and [PERSON]’s slabs.  
The fitted equation for the curve of M/V versus \(\gamma_{v}\) for a slab-column connection with shear reinforcement is as follows:  
\[\gamma_{\rm res}=0.3-0.3\times 0.285^{\rm(M/V)} \tag{3}\]  
As can be seen, the moment transfer coefficient is related not only to geometry, but also to other variables, such as concrete strength, reinforcement ratio, etc. These effects should be combined to determine the moment transfer coefficient's value. Therefore, the fitted equation (Equation (3)) cannot be used as a formula for calculating the moment transfer coefficient, because this paper only studies the effect of shear reinforcement and no other variables. To supplement the calculation of this coefficient, more numerical simulations of experiments with different variables are required, and it is possible to use the method of this paper to simulate experiments to refine the formula.