ABSTRACT
Let us review the position we have reached. In Chapter 1 (Section 1.5), we established the three physical principles governing the mechanics of deformable solids, namely, equilibrium of forces, compatibility of strains (geometry of deformation), and material stress-strain characteristics. While the complete solution of any problem, including the determination of all the forces, stresses, displacements, and strains, requires the use of all three of these, in some cases we can find just the forces and stresses in a system without introducing either the compatibility of strains or the material properties. Such systems we have classified as statically determinate, and in Chapter 2 we analyzed some common practical problems of this type. If we wish to find displacements and strains in a system, be it statically determinate or statically indeterminate, then we must consider strain compatibility and stress-strain relationships. In Chapter 3 we established these relationships for linearly elastic materials and used them to find the deformations of statically determinate systems.
