ABSTRACT
This chapter deals with the particular case of a cylindrical, homogeneous and isotropic, linearly elastic solid loaded exclusively on its end planes. This solid, known as the Saint Venant solid, represents a relatively simple and highly useful model in the case of beams. All the fundamental loadings are studied, which correspond to the internal reaction characteristics already introduced in Chapter 5: axial force, shearing force, twisting moment and bending moment. For each loading, both the stress condition produced and the corresponding deformation characteristic are obtained: axial dilation, mean shearing strain, unit angle of torsion and curvature. It is shown that, in the case of symmetrical sections, the fundamental reactions are all mutually energetically orthogonal, and that, in this case, the strain energy is a diagonal quadratic form of the reactions themselves.
