ABSTRACT
Conceptually, ‘‘stress’’ is an ‘‘area-averaged’’ or ‘‘normalized’’ force. The averaging is obtained by dividing the force by the area over which the force is regarded to be acting. The concept is illustrated by considering a rod stretched (axially) by a force P as in Figure 2.1. If the rod has a cross-section area A, the ‘‘stress’’ s in the rod is simply
s ¼ P=A (2:1)
There are significant simplifications and assumptions made in the development of Equation 2.1: First, recall in Chapter 1, we described a force as a ‘‘push’’ or a ‘‘pull’’ and characterized it mathematically as a ‘‘sliding vector’’ acting through a point. Since points do not have area, there is no ‘‘area of application.’’ Suppose that a body B is subjected to a force system S as in Figure 2.2, where S is applied over a relatively small surface region R of B. Specifically, let the forces of S be applied through points of R. Let F be the resultant of S and let A be the area of R. Then a ‘‘stress vector’’ s may be defined as
s ¼ F=A (2:2)
If R is regarded as ‘‘small,’’ the area A of R will also be small, as will be the magnitude of F. Nevertheless, the ratio in Equation 2.2 will not necessarily be small. If Q is a point within R, then the stress vector at Q (‘‘point stress vector’’) sQ be defined as
sQ ¼ lim A!0
