## 3 Design Code Provisions and Previous Test Results  
The horizontal shear stress acting on the interface may be computed as the shear flow due to the moment difference along the horizontal shear length (\(l_{vh}\)) as defined in Figure 2. It can also be calculated as Equation (1) from the actual change in compression force or tension force as shown in Figure 3.  
\[v_{u}=\frac{F_{h}}{A_{cr}}=\frac{F_{h}}{b_{v}l_{vh}}\approx\frac{M_{max}/(0.9d )}{b_{v}l_{vh}}, \tag{1}\]  
Figure 1: Interface location and principal stresses of the composite PC beams. where \(F_{h}=\min.\{C\ or\ T\}\), as shown in Figure 3, \(A_{cr}=\) interface area, \(l_{vh}=\) length between maximum moment and inflection point, and \(b_{v}=\) interface width. The equation for calculating the horizontal shear strength is divided into two categories, \"horizontal shear transfer in composite members\" (hereafter Case 1) and \"shear friction\" (hereafter Case 2), which is specified in ACI 318 [27] and PCI [28] provisions. * Case 1: horizontal shear transfer in composite members (ACI 16.4 and PCI 5.3.5)  
If a minimum amount of shear reinforcement is provided and contact surfaces are intentionally roughened to a full amplitude of approximately 6 mm, the horizontal shear strength can be computed as follows:  
\[v_{n}=\big{(}1.8+0.6\rho_{v}f_{y}\big{)}\lambda\ (\text{MPa}), \tag{2}\]  
Figure 3: Horizontal shear force (\(F_{h}\)) for the interface of a continuous composite beam. Figure 2: Horizontal shear transfer length (\(l_{vh}\)). where \(\rho_{v}\) is the shear reinforcement ratio (\(=\frac{A_{v}}{B_{v}\text{ s}}\)), and \(\lambda\) is the factor to account the unit weight for the concrete. * Case 2: shear friction (ACI 22.9 and PCI 5.3.4)  
ACI further states that the shear friction design can be used for horizontal shear stresses greater than 3.5 MPa. \[v_{n}=\mu\rho_{v}f_{y}\ (\text{MPa}), \tag{3}\]  
where the friction factor (\(\mu\)) is used for the shear friction design of ACI, and the effective friction factor \(\mu_{e}=\frac{6.9\ \lambda^{2}\ \mu}{v_{n}}=\frac{6\phi.9\ \lambda^{2}\ b_{v}\ l_{ bulk}\ \mu}{F_{v}}\leq\mu_{e}(max)\) is used for the shear friction design of PCI instead of the friction factor (\(\mu\)). In previous studies [24; 25; 26], tests of composite concrete beams were performed to investigate the horizontal shear performance through three phases as shown in Table 1. All specimens were designed to have a vertical shear strength greater than the flexural strength, so that the yield strength was governed by the flexural yield prior to shear failure. Therefore, when the composite PC beam reaches the flexural yielding, the tensile force caused by the tensile reinforcement acts as a horizontal shear force that induces sliding shear in the horizontal interface. Therefore, the magnitude of the horizontal shear stress on the interface is determined by the amount of change in the tensile force formed in the horizontal shear transfer length. The horizontal interface of the specimens is sprayed with a retarder at the time the surface hardening is in progress on the PC beam in which concrete is placed, and a high-pressure spray is used to remove fine aggregates and laitance from the surface for the roughened condition. Meanwhile, medium roughness of interface was achieved with a rake of approximately 4 mm amplitude. The beam flexure tests were conducted for 17 composite beam specimens, whose variables were interface locations, surface roughness, and clamping stress levels. In the phase 1 study, three PC composite beam-column connections were tested to evaluate the shear friction strength of the interface and the flexural behavior of the composite section. In the phase 2 study, the clamping stress level, the surface roughness, and the covering of shear connector were selected as variables for six composite beam specimens with T-type interface. In the phase 3 study, the structural performance was evaluated for eight composite beam specimens with respect to the interface location of T-type or C-type, and clamping stress levels.