Higher-Order Beam Theories

This chapter presents the analytical description of thick, or so-called shear-flexible, beam members according to the Levinson theory. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, the partial differential equations, which describe the physical problem, are presented. All equations are introduced for single plane bending in the x-y plane as well as the x-z plane. Analytical solutions of the partial differential equations are given for simple cases. In addition, this chapter treats the case of unsymmetrical bending and presents a general systematic for higher-order beam theories.