## 3 Design of Different Girder-to-Deck Interface Connections  
### Calculation Theory of Interface Shear Transfer  
In this study, the shear interfaces of the girder-to-deck interface connection are mainly calculated according to AASHTO LRFD bridge design specifications, 9 th Edition (2020) [12].  
According to Article 5.7.4.3 in the AASHTO LRFD, the design of shear interfaces shall satisfy the criteria:  
\[\begin{array}{c}V_{ui}\leq V_{ri}=\phi V_{ni}\\ v_{ui}\leq v_{ri}=\phi v_{ni}\end{array} \tag{1}\]  
where \(V_{ui}\) is the factored interface shear force, \(v_{ui}\) is the factored interface shear stress, \(V_{ni}\) (\(v_{ni}\)) is the nominal interface shear resistance, \(V_{ri}\) (\(v_{ri}\)) is the factored interface shear resistance, \(\phi\) is the resistance factor for shear.  
According to Article C5.7.4.5 in the AASHTO LRFD, the factored interface shear force per unit length (\(V_{ui}\)):  
\[V_{ui}=\frac{V_{u}}{d_{v}} \tag{2}\]  
where \(V_{u}\) is the factored vertical shear force on the beam element, \(d_{v}\) is the distance between the centroid of the bottom flange and the mid-thickness of the slab.  
By dividing the \(V_{ui}\) by the width of the interface (\(b_{vi}\)), the factored interface shear stress (\(v_{ui}\)) is determined utilizing the equation:  
\[v_{ui}=\frac{V_{u}}{b_{vi}d_{v}} \tag{3}\]  
According to the plastic approach adopted by the AASHTO LRFD, the interface shear force between the point of maximum positive moment and the point of zero moment shall be taken as:  
\[V_{ui}=\min(A_{s}F_{y},0.85A_{c}f^{\prime}_{c}) \tag{4}\]  
where \(A_{s}\) is the area of the steel girder, \(F_{y}\) is the yield strength of the steel, \(A_{c}\) is the effective area of the concrete deck, \(f_{c}\)\({}^{\prime}\) is the compressive strength of concrete.  
By dividing the \(V_{ui}\) by the area of the interface, the interface shear stress (\(v_{ui}\)) is determined utilizing the equation:  
\[v_{ui}=\frac{V_{ui}}{L_{s}b_{vi}} \tag{5}\]  
where \(V_{ui}\) is the interface shear force, \(L_{s}\) is the length of the shear span, \(b_{vi}\) the width of the interface.  
The AASHTO LRFD (Article 5.7.4.3) suggests equations to compute the nominal interface shear resistance across any given plane at: a potential or existing crack; an interface between different materials; an interface between two concrete segments cast at different times; or the interface between different elements of the cross section. The nominal interface shear resistance (\(V_{ni}\)) shall be taken as:  
\[\begin{array}{c}V_{ni}=cA_{cv}+\mu(A_{v}f_{y}+P_{c})\\ V_{ni}\leq K_{1}f^{\prime}_{c}A_{cv}\\ V_{ni}\leq K_{2}A_{cv}\end{array} \tag{6}\]  
where \(\mu\) is the friction factor (see Table 1), \(c\) is the cohesion factor (see Table 1), \(A_{cv}\) is the area of concrete section resisting shear transfer, \(A_{v\!f}\) is the area of shear reinforcement crossing the interface, \(f_{y}\) is the reinforcement yield stress, \(P_{c}\) is the permanent net compressive force normal to the shear plane, \(f_{c}\)\({}^{\prime}\) is the compressive strength of concrete, \(K_{1}\) is the fraction of concrete strength available to resist interface shear (see Table 1), \(K_{2}\) is the limiting interface shear strength (see Table 1).  
By dividing the values in Equation (6) by the interface area (\(A_{cv}\)), the nominal interface shear resistance (\(v_{ni}\)) can be calculated from the equation:  
\[\begin{array}{l}v_{ni}=c+\mu(\rho f_{y}+N)\\ v_{ni}\leq K_{1}f_{c}^{\prime}\\ v_{ni}\leq K_{2}\end{array} \tag{7}\]  
where \(N\) is the permanent net compressive stress (=\(P_{c}/A_{cv}\)). \(P\) is the interface shear reinforcement ratio (=\(A_{\
abla f}/A_{cv}\)).  
In addition, according to Article 5.7.4.2 in the AASHTO LRFD, the cross-sectional area of the interface shear reinforcement (\(A_{\
abla f}\)) crossing the interface area (\(A_{cv}\)) shall satisfy:  
\[A_{\
abla f}\geq\frac{0.35A_{cv}}{f_{y}} \tag{8}\]