An Analytical Framework Based on the Winkler Foundation Model for Structural Analysis of Hinged Prefabricated Frame Beams

This study addresses the reliance on empirical methods in the structural analysis of hinged prefabricated frame beam (HPFM) structures by proposing a theoretically rigorous analytical framework based on the Winkler foundation model. The proposed analytical framework comprises three main steps: (a) The HPFB structure is discretized into individual beam segments supported on a Winkler foundation, based on the locations of anchorage points and hinge connections; (b) A system of linear equations is formulated using static equilibrium and deformation compatibility conditions at both anchorage points and hinge joints. Solving this system yields the distribution of concentrated loads—applied perpendicular to the slope surface at anchorage points—among horizontal and longitudinal beam segments of the cross beams, and simultaneously determines the shear forces transferred through hinge joints to adjacent beam ends; and (c) The deflection and internal forces for each Winkler-supported beam segment are evaluated using the computed loads and beam-end shear forces obtained in the previous step. To evaluate the validity and practical applicability of the proposed framework, a simplified HPFB structure was analyzed in terms of load distribution, beam-end shear forces, deflections, and internal forces. The results were compared with those from a traditional frame beam (TFB) structure under identical conditions to assess differences in mechanical behavior between the two structures. Deformation analysis at both the anchorage points and hinge joints indicates that the proposed analytical framework inherently satisfies deformation compatibility conditions at the anchorage points and hinge joints. Consequently, the results demonstrate improved accuracy compared to those derived from empirical methods. Comparative analysis reveals that, relative to the TFB structure, the HPFB structure exhibits larger deflections near the beam ends and smaller deflections in regions farther away from the beam ends, along with a reduced maximum negative bending moment, an increased maximum positive bending moment, and lower maximum shear forces. These results suggest that the HPFB structure offers improved mechanical performance. A sensitivity analysis was further performed to quantify the influence of the subgrade reaction coefficient on the mechanical behavior of the HPFB structure. As the subgrade reaction coefficient increases multiplicatively, the concentrated loads allocated to the shorter horizontal beam segments and their corresponding beam-end shear forces exhibit a progressive increase. Conversely, the loads assigned to the longer longitudinal beam segments and the associated beam-end shear forces demonstrate a consistent decrease.Variations in beam loading induced by a multiplicative increase in the subgrade reaction coefficient significantly influence beam deflection, yet exert only a minimal effect on both the bending moment and shear force. Consequently, the proposed analytical framework establishes a robust theoretical foundation for the rational design of HPFB structures, diminishing the dependency on empirical approaches and enhancing the reliability of structural performance predictions.