Deflection Analysis of Steel Truss Web–Concrete Composite Beams Based on Zigzag Beam Theory

To address the inherent inaccuracies of the classical beam theory (which overestimates the flexural stiffness) and the “quasi-plane section method” (which neglects the shear deformation) in the deflection analysis of steel truss web–concrete composite beams, this study homogenizes discrete steel truss web members into a continuous steel web with equivalent thickness based on the strain energy equivalence principle. This homogenization is conducted under the assumption of fixed-end constraints for web members, thus establishing a sandwich laminated beam model. Incorporating the assumptions of zigzag axial displacement and layer-wise quadratic parabolic transverse shear stress, this study adopts the governing equations for static bending of composite beams derived via Hamilton’s mixed energy variational principle—this theory eliminates the need for an artificial shear correction factor, as the transverse shear stress naturally satisfies the zero boundary conditions at the upper and lower surfaces and the continuity condition at the interlayers. Analytical solutions for bending deflection under uniformly distributed loads are derived and validated against three-dimensional (3D) finite element (FE) models. The analysis results of a 45-meter-span beam demonstrate that the relative error in the maximum deflection of both simply supported beams and cantilever beams calculated by the proposed method is approximately 5%, which is significantly superior to the classical beam theory; the deflection induced by the zigzag effect at the mid-span of simply supported beams accounts for 15% of the total deflection, making it an indispensable key component in structural design. This method enables accurate deflection prediction and provides reliable technical guidance for the preliminary design of steel truss web–concrete composite beam bridges.