Static Flexure of First Order Shear Deformable Thick Beam Resting on Two-Parameter Elastic Foundation – Equilibrium Formulation and Closed Form Solutions
DOI:
https://doi.org/10.37933/nipes/7.1.2025.19Abstract
Beams are modeled as thick beams when their depth to span ratios exceed 0.05 and in such cases slender beam theories cannot accurately describe their bending behaviors. This paper derives the differential equations of static equilibrium (DESE) of thick beams on two-parameter elastic soil using first order shear deformable postulations in a first principle manner and via equilibrium formulation method. The equations are a system of two coupled ordinary differential equations (ODEs) with unknown displacements as transverse displacement w(x) and rotation about the neutral axis. The equations are solved in closed form using Navier series method for simply supported boundary conditions. General and specialized solutions are obtained for simply supported beams on two-parameter elastic foundations subjected to uniformly distributed load and sinusoidally distributed loads. The Navier series solution yielded an infinite series from which the maximum deflection at the beam midpoint span can be obtained. Maximum bending moment expressions are also determined for the two cases of transverse loads considered. It is observed that the foundation stiffness parameters reduce the maximum deflection at the center. The present solutions are exact since the boundary conditions and domain equations are simultaneously satisfied. The Navier series solutions are identical to previously obtained exact solutions.