Static Flexure of First Order Shear Deformable Thick Beam Resting on Two-Parameter Elastic Foundation – Equilibrium Formulation and Closed Form Solutions

The classical thin beam theory (Euler Bernoulli theory (EBT)) was formulated by Euler and Bernoulli using the Euler-Bernoulli hypothesis that plane cross-sections remain plane and normal to the deformed middle surface, and thus transverse shear deformation is negligibly small [1].EBT is thus inaccurate for moderately thick and thick beams where transverse shear deformation cannot be ignored.The Timoshenko beam theory (TBT) was developed to cater for the inadequacies of the EBT.The TBT considers transverse shear deformations but violates the transverse shear stress-free conditions at the beam surfaces [2].The TBT is a first order shear deformable theory that gives constant transverse shear strain across the beam depth.Higher-order shear deformable beam theories were developed by Levinson, Reddy, by using higher order functions to derive the governing differential equations (GDEs).Their GDEs incorporate higher order derivatives and they provide more accurate results.Higher order shear deformable beam theories have beam used by Ike [3].