1.0 OVERVIEW

The ship S.S. Schenectady, shown in Figure 1.1, broke in two because the forces acting on the ship were greater than the ship's strength. ^[1] But what exactly is the strength of a structure? To answer this question, we will introduce a variable called stress, which is a measure of strength. By defining a variable that is a measure of strength, we take the first step toward developing formulas that can be used in strength analysis and the design of structural members.

Figure 1.1: Failure of S.S. Schenectady.

To develop formulas for stress in structural members, we will use a logic that will be fully developed in Section 3.2. Two of the links of that logic are shown in Figure 1.2. What motivates the construction of these two links is something you learned in statics analysis is simpler if, before writing equilibrium equations, any distributed forces that may be on the free-body diagram are replaced by equivalent forces and moments. ^[2] Formulas developed in mechanics of materials relate stresses to internal forces and moments. Free-body diagrams can then be used to relate internal forces and moments to external forces and moments.

Figure 1.2: Two-step process of relating stresses to external forces and moments.

The two learning objectives of this chapter are:

1. Understanding the concept of stress.

2. Understanding the two-step analysis of relating stresses to external forces and moments.