# Shear Behavior of Superposed Perfobond Connectors Considering Lateral Constraints
## 4 Equation for Calculating Shear Capacity
### Proposed Shear Capacity Equation
#### 4.2.2 Lateral Constraint Composition  
1. Concrete wrapping  
Concrete wrapping can provide lateral constraints to connectors. This includes concrete wraps on the sides and tops of the perfobond rib for the superposed perfobond connectors. [PERSON] et al. [33] obtained the concrete strain distribution and deformation law by setting strain and displacement measuring points on the surface of the side concrete wrap. That is, the strain distribution of the concrete section passing through the perfobond rib resembled a linear distribution, and its stress and deformation were similar to the cross-section of an eccentric tensile member (see Figure 18a). The binding failure realized by concrete wrapping was due to the crack generated along the edge of the perfobond rib through its concrete section, and it extended to the outer edge of the specimen (see Figure 18b,c). Therefore, the weak point of the section was located near the edge of the perfobond rib, and the lateral constraints provided by the concrete wrapping on the perfobond connector depended on the corresponding load when the concrete was cracked. Based on the above analysis of the concrete wrapping action mechanism, a method for calculating the constraint force realized by the concrete wrapping around the perfobond rib can be obtained. For the superposed perfobond connector, the plate on one side was taken for calculation and analysis, and the lateral constraints provided by the concrete wrapping \(T_{\rm c}\) could be calculated according to  
\[T_{\rm c}=T_{\rm cb}+T_{\rm cu} \tag{11}\]  
\[T_{\rm cb}=\frac{f_{\rm t}}{\frac{e_{\rm b}y_{\rm b}}{I_{\rm cb}}+\frac{1}{A_ {\rm cb}}} \tag{12}\]  
\[T_{\rm cu}=\frac{f_{\rm t}}{\frac{e_{\rm b}y_{\rm u}}{I_{\rm cu}}+\frac{1}{A_ {\rm cu}}} \tag{13}\]  
where \(T_{\rm cb}\) and \(T_{\rm cu}\) are the lateral constraints provided by the concrete wraps on the side and top of the perfobond rib, respectively (N); \(e_{\rm b}\) and \(e_{\rm u}\) are the distances from the neutral axis of the side and top concrete wraps to the ends of the perfobond rib (where \(e_{\rm b}=C_{\rm b}/2\) and \(e_{\rm u}=C_{\rm u}/2\)), respectively; \(y_{\rm b}\) and \(y_{\rm u}\) are the distances from the neutral axis of the side and top concrete wraps to the hole center (where \(y_{\rm b}=C_{\rm b}/2+h/2\) and \(y_{\rm u}=C_{\rm u}/2+B/2\)), respectively; \(I_{\rm cb}\) and \(I_{\rm cu}\) are the (independent) moments of inertia of the concrete wrapping on the side and top (for the plain concrete slab, \(I_{\rm cb}=B{C_{\rm b}}^{3}/12\) and \(I_{\rm cu}=B{C_{\rm u}}^{3}/12\)), respectively; and \(A_{\rm cb}\) and \(A_{\rm cu}\) are the areas of concrete wrapping on the side and top (for the plain concrete slab, \(A_{\rm cb}=BC_{\rm b}\) and \(A_{\rm cu}=hC_{\rm u}\)), respectively. Figure 18: Constraining force calculation of concrete wrap for superposed perfobond connectors: (a) Side concrete wrap [35]; (b) Cracking of side concrete wrap; (c) Cracking of upper concrete wrap. The axial tensile strength of concrete in [36] is \(f_{\rm t}\) = 0.395\(f_{\rm cu}\)\({}^{0.55}\). Meanwhile, by substituting Equations (12) and (13) into Equation (11), the concrete wrapping force \(T_{\rm c}\) can be calculated as  
\[T_{\rm c}=0.395\Bigg{(}\frac{1}{\frac{\tau_{\rm th}y_{\rm th}}{T_{\rm ob}}+\frac{ 1}{A_{\rm cb}}}+\frac{1}{\frac{\tau_{\rm th}y_{\rm th}}{T_{\rm cu}}+\frac{1}{A_{ \rm cu}}}\Bigg{)}f_{\rm cu}^{0.55} \tag{14}\]  
(2)  
By analyzing the strain data on the perforating rebar, the axial force of the through-steel bar was found to increase under load increases. When the connectors reached peak load, the perforating rebar essentially did not yield and remained in the elastic state. Figure 10 shows that the constraining force of the perforating rebar exerts an upper limit on the shear-capacity enhancement.