Investigation of Timoshenko Beams in the Elastic Range

This chapter starts with the analytical description of beam members under the additional influence of shear stresses. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law and the equilibrium equation, the set of coupled partial differential equations, which describe the physical problem, are presented. A classical representative of thick beams, i.e., the so-called Timoshenko beam, is considered. The finite difference method is then used to derive approximate equations for thick beam problems. The subdivision of thick beam members and different considerations of boundary conditions are treated in detail.