Chap1_VABLE - M Vable Mechanics of Materials Stress 1 1...

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1 1 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd Mechanics of Materials: Stress M. Vable January, 2010 CHAPTER ONE STRESS Learning objectives 1. Understanding the concept of stress. 2. Understanding the two-step analysis of relating stresses to external forces and moments. _______________________________________________ On January 16th, 1943 a World War II tanker S.S. Schenectady, while tied to the pier on Swan Island in Oregon, fractured just aft of the bridge and broke in two, as shown in Figure 1.1. The fracture started as a small crack in a weld and propagated rapidly overcoming the strength of the material. But what exactly is the strength? How do we analyze it? To answer these questions, we introduce the concept of stress . Defining this variable is the first step toward developing formulas that can be used in strength analysis and the design of structural members. Figure 1.2 shows two links of the logic that will be fully developed in Section 3.2. What motivates the construction of these two links is an idea introduced in Statics—analysis is simpler if any distributed forces in the free-body diagram are replaced by equivalent forces and moments before writing equilibrium equations (see Appendix A.6). Formulas developed in mechanics of materials relate stresses to internal forces and moments. Free-body diagrams are used to relate internal forces and moments to external forces and moments. Figure 1.1 Failure of S.S. Schenectady. Figure 1.2 Two-step process of relating stresses to external forces and moments. Static equivalency Equilibrium
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1 2 Printed from: http://www.me.mtu.edu/~mavable/MoM2nd Mechanics of Materials: Stress M. Vable January, 2010 1.1 STRESS ON A SURFACE The stress on a surface is an internally distributed force system that can be resolved into two components: normal (perpendicu- lar) to the imaginary cut surface, called normal stress, and tangent (parallel) to the imaginary cut surface, called shear stress. 1.1.1 Normal Stress In Figure 1.3, the cable of the chandelier and the columns supporting the building must be strong enough to support the weight of the chandelier and the weight of the building, respectively. If we make an imaginary cut and draw the free-body diagrams, we see that forces normal to the imaginary cut are needed to balance the weight. The internal normal force N divided by the area of the cross section A exposed by the imaginary cut gives us the average intensity of an internal normal force distribution, which we call the average normal stress: (1.1) where σ is the Greek letter sigma used to designate normal stress and the subscript av emphasizes that the normal stress is an average value. We may view σ av as a uniformly distributed normal force, as shown in Figure 1.3, which can be replaced by a statically equivalent internal normal force. We will develop this viewpoint further in Section 1.1.4. Notice that N is in boldface italics, as are all internal forces (and moments) in this book.
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