ABSTRACT
In Chapter 9 we were concerned with the analysis of stresses and strains at a point in a solid body. For this purpose, we considered elements of material sufficiently small for stresses and strains to be regarded as constant and equal to the values at the point concerned. In most situations of practical interest, both stresses and strains vary from point to point. To be able to determine these variations, we must now consider the relationships between stresses and strains at adjacent points. In the case of stresses, the approach is similar to that used in Section 5.2.2 to derive relationships between distributed lateral force, shear force, and bending moment in a beam [Equations (5.10) and (5.11)]. In other words, we establish differential equations of equilibrium describing the variations. Similarly, for strain variations we derive differential equations of compatibility.
