Chapter 6 - BEAM ANALYSIS

Abstract

This chapter focuses on beam analysis. The analysis of beams, beam-columns, and plates on elastic foundations is wide-spread in engineering. A common structural system considered in engineering is that of the elastic beam. In mechanics of materials, a number of common assumptions are made to reduce the analysis to a one-dimensional formulation. The most common assumption is that planes in the beam, normal to a fiber along the x -axis, remain normal to that fiber in its deformed state. A variational formulation for the elastic beam is related to minimizing the total energy and work in the system. One important term required for the analysis is the strain energy. That quantity is defined as half the volume integral of the product of the stress and strain. The stresses in a statically indeterminate structure on an elastic foundation are influenced by the deformation of the foundation while the pressure distribution on the foundation is affected by the relative stiffness of the structure and the foundation medium. To allow for this structure-foundation interaction, the finite element method is ideally suited.