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

This study presents a refined beam theory aimed at overcoming the limitations of classical approaches, such as the Euler-Bernoulli and Timoshenko models, which often neglect transverse shear deformation and rotational inertia effects. These limitations become significant when analyzing thick beams or structures made of advanced materials. The proposed theory assumes a linearly elastic, homogeneous, and isotropic material with a uniform rectangular cross-section. While maintaining simplicity and a strong resemblance to the classical Bernoulli-Euler theory, this refined approach provides a more accurate framework for analyzing beam bending. A simplified governing equation is derived, offering a straightforward formulation suitable for practical engineering applications. General analytical solutions are obtained for thick isotropic beams under various boundary conditions, including simply supported, cantilever, and fixed configurations, subjected to both uniformly and unevenly distributed loads. The study derives expressions for transverse displacement, strain components, stress components, and internal forces. The accuracy and applicability of the proposed theory are validated by comparing its results with those of other advanced shear deformation theories, demonstrating its effectiveness for precise structural analysis.