Investigation of Euler–Bernoulli Beams in the Elastic Range

This chapter starts with the analytical description of thin beam members. 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. The finite difference method is then used to derive approximate equations for thin beam problems. The subdivision of thin beam members and different considerations of boundary conditions are treated in detail. The presented approach treats thin beams of constant and varying bending stiffnesses.