TABLE OF CONTENTS In this chapter we are concerned with stress, its components, and the relationships between them. Once the stress components are introduced and their symmetry is established we derive the formulas for the stress acting on a plane inclined with respect to the Cartesian coordinate planes. The differential equations of equilibrium of an infinitesimal element are determined in both a Cartesian and a polar coordinate system. Principal stresses and stress invariants are also discussed.
A solid [*] can be subjected to the action of two types of external forces. Concentrated or distributed loads applied to the surface of a solid belong to the first type. These so-called surface tractions result from the contact with other solids or fluids and are transmitted through the surface to the interior of the solid. The second type consists of forces acting directly on all particles of the solid. These forces, called body forces, are proportional to the mass contained in the volume element (e.g., gravity, electromagnetic forces). Let us cut through the solid. The contact forces from the portion of the body removed by the cut act on the cut surface as distributed loads. Both the magnitude of these loads and their directions will vary, in general, from point to point. Now isolate from the surface of the cut (Fig. 2-1) an arbitrary point M, surrounded by a small area ? A, and the corresponding surface load F acting on that area. In general, when
