## 2 Background and Design Provisions of Interface Shear
#### PCI Design Handbook, seventh edition  
The _PCI Design Handbook_[17] (Article 5.3.6) suggests two equations to calculate the interface shear resistance across an interface with reinforcement perpendicular to the interface:  
\[v_{n}=\mu_{e}\rho f_{y} \tag{3a}\] \[v_{n}=\mu\rho f_{y}\] (3b) \[\mu_{e}=\frac{\phi 1000\lambda\mu}{v_{u}}(\mathrm{psi})=\frac{\phi 6.895\lambda\mu}{v_{u}}( \mathrm{MPa})\]  
\[v_{n}\leq v_{n,max}\]  
where \(\mu_{e}\) is the effective coefficient of friction (limited by the values given in Table 2), \(\phi\) is the strength reduction factor, \(v_{u}\) is the factored shear stress demand, \(\lambda\) is the concrete weight reduction factor (see Table 2), \(\mu\) is the friction factor (see Table 2), \(\rho\) is the interface \begin{table}
\begin{tabular}{l l l} \hline \hline \multicolumn{1}{c}{**Contact Surface Condition**} & \multicolumn{1}{c}{\(\mu\)} & \multicolumn{1}{c}{\(v_{n,max}\) **(MPa)**} \\ \hline Concrete placed monolithically & \(1.4\lambda\) & \\ Concrete placed against hardened concrete that is & & For normal-weight concrete \\ clean and intentionally roughened to a full & \(1.0\lambda\) & (monolithic or roughened), \\ amplitude of approximately 6 mm & & least of \(\left\{\begin{array}{l}0.2f_{c}^{\prime}\\ 3.31+0.08f_{c}^{\prime}\\ 11.03\end{array}\right\}\) \\ \hline Concrete placed against hardened concrete that is & & & \\ clean and not intentionally roughened & & For all other cases, lesser of \\ \hline Concrete anchored to as-rolled structural steel by & & \\ headed studs or by reinforcing bars where all steel in & & \\ contact with concrete is clean and free of paint & & \\ \hline \hline \multicolumn{1}{c}{\(\lambda\) = modification factor for concrete weight (\(\lambda\) = 1.0 for normal-weight concrete, \(\lambda\) = 0.85 for sand lightweight concrete, \(\lambda\) = 0.75 for all lightweight concrete). \(f_{c}^{\prime}\) = compressive strength of concrete.} \\ \end{tabular}
\end{table} 
Table 1: Friction coefficients and upper limits. shear reinforcement ratio = \(A_{\textit{eff}}/A_{\textit{cv}}\), \(A_{\textit{eff}}\) is the area of the shear reinforcement crossing the interface, \(A_{\textit{cv}}\) is the area of the concrete section resisting shear transfer,\(f_{y}\) is the reinforcement yield stress (limited in design to 413.7 MPa), \(v_{n,max}\) is the maximum nominal interface shear resistance (see Table 2), and \(v_{n}\) is the nominal interface shear resistance. Substituting \(v_{n}/\phi\) by the nominal shear resistance \(v_{n}\) and combining Equation (3a) and the equation for the calculation of \(\mu_{e}\) gives Equation (4):  
\[v_{n}=\sqrt{6.895\mu\lambda\rho f_{y}} \tag{4}\]  
From the above equation, the shear resistance \(v_{n}\) is proportional to the \(\sqrt{\rho f_{y}}\) instead of \(\rho f_{y}\). This increases the shear resistances at low values of clamping stress and thus has some similarities with the cohesion term addition. Monolithic interfaces and intentionally roughened cold joints are recommended using Equation (3a), while steel-to-concrete interfaces and non-roughened cold joints should utilize Equation (3b). The _PCI_ uses the strength reduction factor \(\phi\) = 0.75. _Aashtto LrfD (2020)_[18]  
The _AASHTO LRFD Bridge Design Specifications_[18] (Article 5.7.4) suggests equations to compute the nominal shear resistance across any given plane. The _AASHTO LRFD_ uses the modified shear friction model including the cohesion mechanism (adhesion and aggregate interlock). The strength reduction factor in the _AASHTO LRFD_ is 0.9. The nominal interface shear resistance shall be taken as:  
\[ \begin{array}{l}v_{n}=c+\mu(\rho f_{y}+N)\\ v_{n}\leq K_{1}f_{c}^{\prime}\\ v_{n}\leq K_{2}\end{array}