# Shear Behavior of Superposed Perfobond Connectors Considering Lateral Constraints
## 4 Equation for Calculating Shear Capacity  
### Existing Shear Capacity Equations for the Superposed Perfobond Connectors  
The specimens in this study resembled those of [PERSON] et al. [6], [PERSON] et al. [22], [PERSON] and [PERSON] [23], and [PERSON] et al. [24]. Therefore, Equations (2)-(5) proposed by [PERSON] et al., [PERSON] et al., [PERSON] and [PERSON], and [PERSON] et al. were selected to evaluate the shear capacities of superimposed perfobond connectors, respectively. Here, \(Q_{\mathrm{hole}}\) is the shear capacity of each hole of the perfobond connectors (N); \(A\) is the area of the hole (mm\({}^{2}\)); \(A_{\mathrm{s}}\) is the area of the perforating rebar (mm\({}^{2}\)); \(f_{\mathrm{y}}\) and \(f_{\mathrm{u}}\) are the yield and ultimate strengths of the perforating rebar (MPa); and \(\alpha_{\mathrm{A}}=3.80\) (\(A_{\mathrm{s}}/A\))\({}^{2/3}\). To model different hole shapes, the equations were modified by using \(A=\pi d^{2}/4\) and \(A_{\mathrm{s}}=\pi{d_{\mathrm{s}}}^{2}/4\), respectively.  
\[Q_{\mathrm{hole}}=1.85[(A-A_{\mathrm{s}})f_{\mathrm{cu}}+A_{\mathrm{s}}f_{ \mathrm{u}}]-26,100 \tag{2}\]  
\[Q_{\mathrm{hole}}=11.744(A-A_{\mathrm{s}})f_{\mathrm{t}}+1.156A_{\mathrm{s}}f _{\mathrm{y}} \tag{3}\]  
\[Q_{\mathrm{hole}}=1.76(A-A_{\mathrm{s}})f_{\mathrm{c}}+1.58A_{\mathrm{s}}f_{ \mathrm{y}} \tag{4}\]  
\[Q_{\mathrm{hole}}=1.76\alpha_{\mathrm{A}}(A-A_{\mathrm{s}})f_{\mathrm{c}}+1.58 A_{\mathrm{s}}f_{\mathrm{y}} \tag{5}\]  
Table 5 summarizes the existing experimental results [19, 20, 22, 23, 24, 35] and research findings of this study. All specimens presented in Table 5 neglected the concrete end-bearing effect and the chemical bond between the steel and concrete. The thickness of the perfobond rib exceeded 9 mm, to ensure that the perfobond connectors produced double-sided shear failures. For holes in the steel plate, the number of holes included single, double, and triple-hole categories, with hole sizes ranging from 35 to 75 mm; the hole shapes included circular, long, and high. The diameter of the perforating rebar ranged from 0 to 25 mm, and the yield strength varied as 335-480 MPa. In terms of the concrete, the compressive strength varied as 32.9-72.2 MPa, the side wrap of the slab Cb varied as 30-350 mm, and the top wrap Cu varied as 50-120 mm. For the transverse reinforcement, the diameters varied as 0-10 mm, and the yield strength ranged from 345 to 508.245 MPa. The parameters varied widely and were representative.  
Equations (2)-(5) were applied to compute the shear bearing capacity of the specimens listed in Table 5, with the results compared with the experimental values. As shown in Table 5, Equation (2) significantly overestimated the bearing capacity of the perfobond connectors because the ultimate tensile strength of the perforating rebar was adopted in the analytical model. Equation (3) was too conservative to predict the shear capacity of the perfobond connectors. Equations (4) and (5) slightly overestimated the shear bearing capacity of the connector. In contrast to the test results, the coefficients of standard deviation calculated using Equations (2)-(5) were 0.36, 0.17, 0.23 and 0.24, respectively, indicating a comparatively large discreteness. Therefore, it is necessary to establish a more accurate shear-capacity calculation formula with a clear mechanism.