## 6 Proposal of the Design Equation  
As analyzed in the previous section, the compressive strength of concrete played a crucial role as well, especially for the monolithic uncracked interface. However, codes that can apply to the monolithic uncracked interface such as the _ACI 318-19_, _PCI_, _AASHTO LRFD_, and _CSA-S6_ do not include the compressive strength of concrete in the equations. The _Eurocode 2_ and _Fib MC 2010_ consider the compressive strength of concrete in the equations but do not apply to the monolithic uncracked interface. Therefore, the equation to determine the interface shear resistance for the monolithic uncracked interface is proposed in this section with consideration of the compressive strength of concrete directly in the equation. In the case of the monolithic uncracked interface, the applied shear is subjected partly by cohesion provided by the concrete and partly by the friction offered by the reinforcement crossing the interface. The dowel action is neglected. Therefore, the general equation is proposed as follows (this is also a general form that often appears in the literature):  
\[v_{u}=c+\mu\rho f_{y} \tag{9}\]  
where \(v_{u}\) is the ultimate interface shear resistance, \(c\) is the cohesion, \(\rho f_{y}\) is the clamping stress, and \(\mu\) is the friction factor. To propose the equation, cohesion \(c\) and friction factor \(\mu\) should be determined based on push-off test results collected from the literature. Figure 11: Effect of compressive strength of concrete \(f_{c}^{\prime}\) on ultimate interface shear stress \(\upsilon_{test}\). First, the experimental results with \(\rho f_{y}^{\prime}=0\) are chosen to determine cohesion \(c\) (these results are highlighted in the gray background in the Appendix A). Now, the shear resistance includes only cohesion \(c\) so the shear resistance \(v_{u}=c\). Cohesion \(c\) is governed by the concrete, in particular the compressive strength of concrete. Therefore, the relationship between cohesion \(c\) and compressive strength of concrete \(f_{c}^{\prime}\) is plotted to determine the correlation coefficients between \(c\) and \(f_{c}^{\prime}\), as shown in Figure 12. From Figure 12, the trend line indicates a good correlation between cohesion \(c\) and compressive strength of concrete \(f_{c}^{\prime}\), with its Pearson correlation coefficient being 0.68. To be safer for design purposes, the equation for calculating cohesion c is suggested as follows (it is also illustrated in Figure 12):  
\[c=0.14\big{(}f_{c}^{\prime}\big{)}^{0.85} \tag{10}\]  
To determine friction factor \(\mu\), the remaining experimental results with non-zero \(\rho f_{y}\) are selected. Friction factors are obtained from these test results by utilizing the following equation:  
\[\mu=\frac{v_{test}-c}{\rho f_{y}} \tag{11}\]  
Friction factors obtained experimentally are plotted as a function of clamping stress \(\rho f_{y}\), as shown in Figure 13. Therefore, the following equation is proposed to express the friction factor as a function of clamping stress. This equation is conservative and can be used for design purposes. \[\mu=2.0\big{(}\rho f_{y}\big{)}^{-0.5} \tag{12}\]  
Substituting Equations (10) and (12) into Equation (9), the equation for predicting interface shear resistance is as follows:  
\[v_{u}=0.14\big{(}f_{c}^{\prime}\big{)}^{0.85}+2.0\sqrt{\rho f_{y}}\leq 0.3f_{c}^{ \prime} \tag{13}\]  
Ultimate interface shear resistance is limited to a value of \(0.3f_{c}^{\prime}\) in the above equation because interface shear resistance does not increase considerably in over-reinforced  
Figure 12: Relationship between cohesion and compressive strength of concrete. Figure 13: Relationship between friction factor and clamping stress. specimens. The compressive strength of concrete governs the failure in such specimens, as indicated in studies [22; 24; 38]. Equation (13) is established from experimental results for normal-weight concrete.