Refined Theories for Beam Bending: A Simplified Approach to Structural Analysis

Abstract

This study develops a refined beam theory that improves upon classical models by accurately capturing transverse shear deformation without requiring shear correction factors. The proposed approach maintains the simplicity of the Bernoulli-Euler theory while achieving higher precision in predicting transverse deflections, axial stresses, and shear stresses. A linearly elastic, homogeneous, and isotropic material with a uniform rectangular cross-section is assumed. The accuracy of the proposed theory is validated through comparisons with advanced shear deformation theories, showing that it provides reliable results with reduced computational complexity. Furthermore, the theory's applicability is demonstrated through case studies, showcasing its effectiveness in practical structural design and analysis Numerical comparisons indicate minimal percentage differences, with a maximum deviation of -0.37% for simply supported beams and -0.82% for fully clamped beams in transverse deflection predictions. The results align well with advanced shear deformation theories and two-dimensional elasticity solutions, confirming the model’s reliability. This theory enhances structural analysis, particularly for thick and shear-deformable beams, with potential extensions to anisotropic materials, dynamic loading, and complex boundary conditions in future research.