I In Chapter 1, we presented general concepts and definitions that are fundamental to many of the topics discussed in this book. In this chapter, we develop theories of stress and strain that are essential for the analysis of a structural or mechanical system subjected to loads. The relations developed are used throughout the remainder of the book. 2.1 DEFINITION OF STRESS AT A POINT Consider a general body subjected to forces acting on its surface (Figure 2.1). Pass a fictitious plane Q through the body, cutting the body along surface A (Figure 2.2). Designate one side of plane Q as positive and the other side as negative. The portion of the body on the positive side of Q exerts a force on the portion of the body on the negative side. This force is transmitted through the plane Q by direct contact of the parts of the body on the two sides of Q. Let the force that is transmitted through an incremental area AA of A by the part on the positive side of Q be denoted by AF. In accordance with Newton's third law, the portion of the body on the negative side of Q transmits through area AA a force-AF. The force A F may be resolved into components AFN and AFs, along unit normal N and unit tangent S, respectively, to the plane Q. The force AF, is called the normal force FIGURE 2.1 A general loaded body cut by plane 0.
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