Generalized Shear Correction Factor for Non-Homogeneous Beam Cross-Sections with an Embedded Steel Core

Accurate prediction of transverse shear deformation is essential for the serviceability assessment, durability-oriented design, and structural health monitoring of hybrid and heterogeneous beam members. This is particularly relevant for lightweight composite components in which a porous cementitious matrix (e.g., perlite-based material) is combined with an embedded steel I-section, yielding strong stiffness contrasts and spatially nonuniform shear transfer. In this study, an energy-consistent analytical–numerical framework is proposed to determine the effective shear correction factor k_s for such non-homogeneous cross-sections within the Timoshenko beam theory. The formulation enforces equivalence between the real heterogeneous shear strain energy, governed by a spatial shear modulus field G(y,z), and its beam-theory representation based on k_s(G_ref A). A pixel/voxel discretization is introduced to evaluate the generalized shear-energy integral and to quantify the deviation of k_s from classical homogeneous benchmarks. The results demonstrate that shear stiffness may be controlled by localized energy concentrations near weak matrix regions and phase interfaces, which can lead to non-negligible errors in deflection predictions when standard shear correction factors are adopted. The proposed framework provides a transparent and computationally efficient tool to support reliability-driven stiffness identification, model updating, and health monitoring strategies for heterogeneous and hybrid beam components.