## 1 Introduction  
The system of reinforced concrete slabs and columns is now widely used worldwide. The benefit of such a system is that the floor is directly supported by columns, there are no beams to block the light, and space is saved. However, the high forces at the slab-column joints lead to high stresses around the columns, making punching shear damage possible [1, 2, 3, 4]. Asymmetry of the span or load causes eccentric punching shear in the practical application of the structure. In addition to vertical shear force, the structure is subject to bending moment action, as illustrated in Figures 1 and 2. Punching resistance is reduced by the transfer of the unbalanced bending moment. [PERSON] (1961) [2] first proposed the transfer coefficient of unbalanced bending moment \(\gamma_{v}\) in his study, believing that \(\gamma_{v}\) fit well with all of his experimental sample results at 0.33. With subsequent research by [PERSON] and [PERSON] (1968) [5], a formula was established in 1970--the ACI-318 [6] design specification--and has been used ever since. The formula shows that its magnitude is only related to the geometry (Equation (1)). \[\gamma_{v}=1-\frac{1}{1+\frac{2}{3}\sqrt{\frac{c_{1}+d}{c_{2}+d}}} \tag{1}\]  
where \(c_{1}\) and \(c_{2}\) are the side lengths of the column, and \(d\) is the effective thickness of the slab. Most of the existing studies on slab-column joints used modeling methods. There are many constitutive models for finite element simulation, such as plastic models, nonlinear elastic models, and damage and plastic models [7; 8; 9]. [PERSON] and [PERSON] (2006) [10] performed a study on the moment-carrying capacity of slab-column connections using many existing experimental data and nonlinear finite element analysis methods; the numerical simulation results were satisfactory, but whether the moment transfer coefficient specified in ACI-318 is related to other factors has not been discussed in the literature. From Equation (1), it can be seen that the ACI-318 code equation specifies that \(\gamma_{v}\) is only related to the geometry of the slab-column connection, so the purpose of this study was to explore the relationship between the moment transfer coefficient and other influencing factors, such as shear reinforcement. Since experiments can be expensive and stochastic in terms of financial and material resources, the slab-column connections were modeled using the commercial finite element software ABAQUS [11]. The post-processing cloud image could depict the crack development process, draw deflection curves, and monitor variables that were not measured during the experiment. To describe the tensile and compressive behavior of the concrete, the concrete damage plasticity model was chosen and built into the ABAQUS library. The model parameters were calibrated by comparing the experimental data with the simulation results [12; 13; 14]. The nonlinear finite element method was used to investigate the effect of shear reinforcement on the moment transfer coefficient as a supplement to existing building design code formulations, which is the main contribution of this paper. Two experiments with different loading methods were simulated. Six interior slab-column connections (S1, S2, S3, S4, S7, and S8) equipped with shear reinforcement as described by [PERSON] et al. (2019) [15] were analyzed. The variables studied were the number and diameter of the shear studs. In order to better investigate the shear studs, a numerical simulation model was used to increase the number of each variable. The loading method was the force directly applied to the slab. The experiments described by [PERSON] and [PERSON] (1999) [16] were conducted by applying loads to columns, with the variables being the number of studs and their arrangement. The experiments only applied concentric forces, so bending moments were included in the numerical simulations for the study.