Bending theories for beams and plates with single generalized displacement

Classical bending theories for beams and plates can not be used for short, stubby beams and thick plates since transverse shearing effect is excluded, and ordinary theories with multiple generalized displacements can not be u sed for long, slender beams and thin plates since the innate relation betwe en rotation angle and deflection is ignored. These two types of theories ar e not consistent due to the contradiction of dependence and independence of the rotation angle. Based on several basic assumptions, a new type of theo ries which not only include the transverse shearing effect is presented, bu t also the relation between potation angle and deflection is obtained. Anal ytical solutions of several simple beams are given. It has been testified b y numerical examples that the new theories can be used for either long, sle nder beams and thin plates or short, stubby beams and thick plates.