An improved Reddy beam model accounting for Poisson effect

We propose an enriched version of the classical Reddy beam model, obtained by introducing additional kinematic terms that account for transverse contraction effects. While preserving the structure and simplicity of the original theory, the extended formulation provides a more general representation of the displacement field and of the internal stress state, including transverse normal and shear components that are absent in standard models. An analytical solution for the in-plane problem is derived, and a finite element implementation is developed. Numerical results confirm that the proposed model recovers the classical Reddy solution as a special case, while also revealing localized stress phenomena and deformation modes that are otherwise neglected. These features make the model particularly suited for advanced structural applications where higher-order effects cannot be ignored.