To investigate the shearing effect and size effect of micro-beams, a new Timoshenko beam model based on the modified gradient elasticity (MGE)is developed by using the variational principle. The new model can be simplified to the MGE Bernoulli-Euler beam model when the shearing effect is neglected, also can be simplified to the classical Timoshenko beam model when two internal length scales vanish. To solve this new model, a central finite difference method with virtual nodes is developed. Three numerical examples of the homogeneous beams and a...
