In this thesis, a new non-classical model for Reddy-Levinson beams is developed by using a variational formulation based on Hamilton's principle. A modified couple stress theory and a surface elasticity theory are employed. The equilibrium equations and complete boundary conditions for the beam are derived simultaneously. The new model contains a material length scale parameter to account for the microstructure effect and three surface elastic constants to describe the surface energy effect. The current non-classical Reddy-Levinson beam model reduces to a Bernoulli-Euler beam model incorporating the microstructure and surface energy effects and recovers the classical elasticity-based Reddy-Levinson beam model as special cases. To illustration the new model, the static bending and free vibration problems of a simply supported beam are solved by directly applying the general formulas derived. The solutions are also compared to those based on the classical Reddy-Levinson beam model.
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