A refined beam theory based on the refined plate theory

Summary Based on the refined plate theory, a refined theory of rectangular beams is derived by using the Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. The solutions based on the new theory are the same as the exact solutions of elasticity theory. In three examples it is shown that the new theory provides as good or better results than Levinson’s beam theory when compared to those obtained from the linear theory of elasticity.