## 5 Comparison Between the Shear Capacity Obtained from Tests and Codes  
The ultimate shear capacity obtained from tests was analyzed with that obtained from various codes in terms of Eurocode 4, AASHTO, JSCE, and GB 50917-2013 [24; 25; 26; 27] to analyze the applicability of these specifications in predicting the shear capacity of group studs. (1) Eurocode 4: The design shear capacity of one stud \(P_{\text{Rd}}\) in Eurocode 4 is calculated as Equations (1) and (2), where \(\gamma_{\text{v}}\) is the partial factor, whose recommended value is 1.25. \(d\) and \(h_{\text{sc}}\) are the shank diameter and nominal height of shear studs, respectively. \(f_{\text{u}}\), \(f_{\text{ck}}\), and \(E_{\text{cm}}\) are the ultimate tensile strength of shear stud, characteristic cylinder compressive strength of concrete, and Young's modulus of concrete, respectively. \[P_{\text{Rd}}=\frac{0.29 ad^{2}\sqrt{f_{\text{ck}}E_{\text{cm}}}}{\gamma_{ \text{v}}}\leq\frac{0.8f_{\text{u}}\pi d^{2}/4}{\gamma_{\text{v}}} \tag{1}\]\[\left\{ \begin{array}{ll}\alpha=0.2\left(\frac{h_{\rm sc}}{d}+1\right)&(3\leq h_{ \rm sc}/d\leq 4)\\ \alpha=1&(h_{\rm sc}/d>4)\end{array} \right. \tag{2}\]  
(2) AASHTO: The design stud shear capacity \(Q_{\rm n}\) is determined as Equation (3), where \(A_{\rm sc}\) is the cross-sectional area of shear studs, \(E_{\rm c}\) denotes the elastic modulus of concrete, and \(f_{\rm c}^{\prime}\) and \(F_{\rm u}\) represent the specified compressive strength of concrete and minimum tensile strength of shear studs, respectively. \[Q_{\rm n}=0.5A_{\rm sc}\sqrt{f_{\rm c}^{\prime}E_{\rm c}}\leq A_{\rm sc}F_{\rm u} \tag{3}\]  
(3) JSCE: The allowable shear capacity \(Q_{\rm n}\) of one stud is determined as Equation (4), where \(d\), \(H\) denote the shank diameter and height of shear studs, respectively. \(\sigma_{\rm ck}\) represents the design strength of concrete. Noticeably, the ultimate shear capacity of one stud is more than six times the \(Q_{\rm n}\). Therefore, the shear capacity of one stud for comparison is set as six times the \(Q_{\rm n}\)  
\[\left\{ \begin{array}{ll}Q_{\rm n}=9.4d^{2}\sqrt{\sigma_{\rm ck}}&({\rm H}/d \geq 5.5)\\ Q_{\rm n}=1.72 dH\sqrt{\sigma_{\rm ck}}&({\rm H}/d<5.5)\end{array} \right. \tag{4}\]  
(4) GB 50917-2013 [27]: The design shear capacity of one stud in GB 50917-2013 is determined as Equation (5), where \(A_{\rm std}\) denotes the cross-sectional area of shear studs, and \(A_{\rm std}\), \(f_{\rm std}\), and \(E_{\rm s}\) denote the cross-sectional area, tensile strength, and elastic modulus of shear studs, respectively. \(f_{\rm cu}\), \(f_{\rm cd}\), and \(E_{\rm c}\) denote the cube compressive strength, design compressive strength, and elastic modulus of concrete, respectively. \(\eta\) represents the reduction factor of group stud effect, and the value of it is 1.0 when the ratio of longitudinal spacing and shank diameter of shear studs \(l_{\rm d}/d\) is larger than 13, while \(l_{\rm d}/d\) is smaller than 13, and the value of \(\eta\) is determined by Equation (6). \[N_{\rm v}^{c}=\min(1.19A_{\rm std}f_{\rm std}(\frac{E_{\rm c}}{E_{\rm s}})^{0.2}(\frac{f_{\rm cu}}{f_{\rm std}})^{0.1},0.43\eta A_{\rm std}\sqrt{f_{\rm cd }E_{\rm c}}) \tag{5}\]  
\[\left\{ \begin{array}{ll}\eta=0.021l_{\rm d}/d+0.73\ ({\rm C30-C40})\\ \eta=0.016l_{\rm d}/d+0.80\ ({\rm C45,\ C50})\\ \eta=0.013l_{\rm d}/d+0.84\ ({\rm C55,\ C60})\end{array} \right. \tag{6}\]  
Table 5 summarizes the shear capacity of a single shear stud obtained from tests and various specifications. For the full-scale specimens Z-40, Z-32, and Z-16, the predictions from the four codes are generally consistent. However, for the scaled-down specimen Z-13, the GB code predicts a lower shear capacity than the other three codes, aligning more closely with the experimental results. This suggests that compared to other codes, the GB code may underestimate the shear capacity of small-diameter shear studs.