Analytical solutions of Reddy, Timoshenko and Bernoulli beam models: A comparative analysis

The purpose of this paper is to compare the generalized stress/strain and corresponding local quantities obtained from three classical beam models commonly used in the literature: the Euler–Bernoulli, Timoshenko (or first-order shear deformation), and Reddy (or third-order shear deformation) beam models. In particular, we present an analytical solution for the equations governing the Reddy beam model, which is typically solved numerically. By expressing the solutions of all three models in terms of constants with the same physical meaning, we are able to make a direct comparison between them and identify the additional contributions of the higher-order models. We also compare the results with approximate solutions and find that while they provide satisfactory solutions for generalized displacement, they can lead to a significant underestimation of the stress field, with percentage errors that are greater than tolerable for practical purposes. This study provides new insights into the behavior of different beam models and their limitations in engineering applications.