Flexural Deformation Calculation Theory and Numerical Method for Steel-Plate–Concrete Composite Reinforcement Considering Interfacial Slip

The steel-plate–concrete composite reinforcement method is derived from the bonded steel plate and increased-section techniques. It is employed to enhance the strength of concrete structures that require a substantial increase in load-bearing capacity. To develop a flexural deformation calculation theory that accounts for slip effects in general reinforced cross-sections with bilateral symmetry, interfacial slip and deflection equations are formulated based on the relationship between interlayer slip and the rotational angle of beams in the plane, as well as the principle of force equilibrium. A numerical method, established based on this theoretical framework, is proposed to facilitate the analytical solution and is verified to be consistent with analytical results. Furthermore, the accuracy of the calculation theory is validated through bending experiments. Finally, the influence of key parameters affecting slip on the flexural stiffness of the reinforced beam is evaluated by determining the stiffness reduction coefficient according to the theory. The results indicate that the flexural stiffness of reinforced beams is governed by three non-dimensional parameters: the boundary condition parameter (μ), composite action parameter (shear connector stiffness (βl)), and relative bending stiffness parameter (G∞/G0). The loading mode does not affect the flexural stiffness of the reinforced beams. As βl approaches 100 and G∞/G0 approaches 1, η approaches 100%. In cases where high stiffness is required, reducing interfacial slip can minimize the loss of flexural stiffness in composite structures. Conservative calculations indicate that satisfying the conditions βl ≥ 8 and G∞/G0 ≤ 1.6 during design can ensure that the reduction in flexural stiffness of the reinforced beam remains above 90%.