Technology & Engineering
Normal Stress
Normal stress refers to the force applied perpendicular to the surface of an object, causing it to deform. In engineering, it is a crucial factor in determining the structural integrity of materials and components. Understanding normal stress helps engineers design and analyze structures to ensure they can withstand the forces they will encounter in real-world applications.
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6 Key excerpts on "Normal Stress"
eBook - PDF- William Bolton(Author)
- 2016(Publication Date)
- Newnes(Publisher)
6 Stress and strain Stress When a material is subject to external forces, such as those applied to stretch it, then internal forces are set up which oppose the external forces. The material can be considered to be rather like a spring. A spring is stretched by external forces, it sets up internal opposing forces which are readily apparent when the spring is released and they force it to contract. A measure of the intensity of the internal forces in a material created as a result of external forces being applied is stress. Stress is defined as the external force acting per unit area: The unit of stress is the pascal (Pa), where 1 Pa = 1 N/m 2 . Multiples of the pascal are generally used, e.g. the megapascal (MPa) which is 10 6 Pa and the gigapascal (GPa) which is 10 9 Pa. Because the area over which the forces act is more generally mm 2 rather than m 2 , it is useful to recognize that 1 GPa = 1 GN/m 2 = 1 kN/mm 2 and 1 MPa = 1 MN/m 2 = 1 N/mm 2 . The stress is said to be a direct stress when the area being stressed is at right angles to the line of action of the external forces. This is the case with materials in tension or in compression. A material in tension has had its length in the direction of the external forces increased; when in compression it is shortened. The convention is to designate tensile stresses as positive and compressive stresses as negative. Shear stresses are not direct stresses, the forces being applied in the same plane as the area being stressed (see later this chapter). The area used in the calculation of the stress is generally the original area that existed before the stress occurred. This stress is sometimes referred to as the engineering stress. The true stress would be the force divided by the actual area existing in the stressed state. Example 1 A bar of material with a cross-sectional area of 50 mm 2 was subjected to tensile forces of 0.1 kN.
- Roy R. Craig, Jr., Eric M. Taleff(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
Throughout the remainder of this book we will be determining the stresses and strains produced in various structural members by the forces and temperature changes acting on them. Figure 2.1 An illustration of internal resultants. x P A B P M(x) M(x) V(x) V(x) F(x) A x (a) A two-force member. (b) Internal resultants: F, V, and M. 26 Chapter 2 Stress and Strain 2.2 | Normal Stress To introduce the concepts of stress and strain, we begin with the relatively sim- ple case of a straight bar undergoing axial loading, as shown in Fig. 2.2. 1 In this section we consider the stress in the bar, and in Section 2.3 we treat the corre- sponding strain. Equal and opposite forces of magnitude P acting on a straight bar cause it to elongate, and also to get narrower, as can be seen by comparing Figs. 2.2a and 2.2b. The bar is said to be in tension. If the external forces had been applied in the opposite sense, that is, pointing toward each other, the bar would have short- ened and would then be said to be in compression. Definition of Normal Stress The thin red arrows in Figs. 2.2c and 2.2d represent the distribution of force on cross sections at A and B, respectively. (A cross section is a plane that is perpen- dicular to the axis of the bar.) Near the ends of the bar, for example, at section A, the resultant normal force, F A , is not uniformly distributed over the cross section; but at section B, farther from the point of application of force P, the force distribution is uniform. In mechanics, the term stress is used to describe the distribution of a force over the area on which it acts and is expressed as force intensity, that is, as force per unit area. Stress Force Area = The units of stress are units of force divided by units of area. In the Interna- tional System of units (SI), stress is specified using the basic units of force (new- ton) and length (meter) as newtons per meter squared (N/m 2 ). This unit, called Figure 2.2 A straight bar undergoing axial loading.
eBook - PDF- William F. Hosford(Author)
- 2009(Publication Date)
- Cambridge University Press(Publisher)
In contrast, if there has been extensive plastic deformation preceding fracture, the material is con-sidered ductile . Fracture usually occurs as soon as a critical stress has been reached; however, repeated applications of a somewhat lower stress may cause fracture. This is called fatigue . The amount of deformation that a material undergoes is described by strain. The forces acting on a body are described by stress. Although the reader should already be familiar with these terms, they will be reviewed in this chapter. 1 2 Mechanical Behavior of Materials Stress Stress , σ , is defined as the intensity of force at a point. σ = ∂ F /∂ A as ∂ A → 0 . (1.1a) If the state of stress is the same everywhere in a body, σ = F / A . (1.1b) A Normal Stress (compressive or tensile) is one in which the force is normal to the area on which it acts. With a shear stress, the force is parallel to the area on which it acts. Two subscripts are required to define a stress. The first subscript denotes the normal to the plane on which the force acts, and the second subscript identifies the direction of the force. ∗ For example, a tensile stress in the x-direction is denoted by σ xx indicating that the force is in the x-direction and it acts on a plane normal to x. For a shear stress, σ xy , a force in the y-direction acts on a plane normal to x. Because stresses involve both forces and areas, they are not vector quantities. Nine components of stress are needed to fully describe a state of stress at a point, as shown in Figure 1.1 . The stress component, σ yy = F y / A y , describes the tensile stress in the y-direction. The stress component, σ zy = F y / A z , is the shear stress caused by a shear force in the y-direction acting on a plane normal to z. Repeated subscripts denote Normal Stresses (e.g., σ xx , σ yy ), whereas mixed sub-scripts denote shear stresses (e.g., σ xy , σ zx ).
- Jonathan Wickert, Kemper Lewis, Jonathan Wickert(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
Image courtesy of the authors. Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 168 Chapter 5 Materials and Stresses these topics lies the discipline known as solid mechanics, and they fit into the hierarchy of mechanical engineering topics shown in Figure 5.2. Tension, compression, and shear stress are quantities that engineers calculate when they relate the dimensions of a mechanical component to the forces acting on it. Those stresses are then compared to the material’s physical properties to determine whether failure is expected to occur. When the strength exceeds the stress, we expect that the structure or machine component will be able to carry the forces without incurring damage. Engineers conduct these types of force, stress, materials, and failure analyses while they design products. ▸ ▸ 5.2 Tension and Compression T he type of stress that is most readily visualized and useful for you to develop intuition about materials and stresses is called tension and compression. Figure 5.3 shows a built-in round rod that is held fixed at its left end and then later placed in tension by the force F that pulls on the right end.
eBook - PDF- Arthur P. Boresi, Richard J. Schmidt(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
CHAPTER 2 THEORIES OF STRESS AND STRAIN I n Chapter 1, we presented general concepts and definitions that are funda- mental 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 fic- titious 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 ΔA of A by the part on the positive side of Q be denoted by ΔF. In accordance with Newton’s third law, the portion of the body on the negative side of Q transmits through area ΔA a force −ΔF. The force ΔF may be resolved into components ΔF N and ΔF S , along unit normal N and unit tangent S, respectively, to the plane Q. The force ΔF N is called the normal force on area ΔA and ΔF S is called the shear force on ΔA. The forces ΔF, ΔF N , and ΔF S depend on the location of area ΔA and the orientation of plane Q. The magnitudes of the – + P 1 P 2 P 3 P 4 p 2 p 1 A Q FIGURE 2.1 A general loaded body cut by plane Q. 25 26 CHAPTER 2 THEORIES OF STRESS AND STRAIN – + P 4 p 2 p 1 A Δ F S Δ A N S Δ F N Δ F Q FIGURE 2.2 Force transmitted through incremental area of cut body. average forces per unit area are ΔF/ΔA, ΔF N /ΔA, and ΔF S /ΔA. These ratios are called the average stress, average Normal Stress, and average shear stress, respectively, acting on area ΔA.
- Wole Soboyejo(Author)
- 2002(Publication Date)
- CRC Press(Publisher)
3 ________________________ Basic Definitions of Stress and Strain 3.1 INTRODUCTION The mechanical properties of materials describe their characteristic responses to applied loads and displacements. However, most texts relate the mechanical properties of materials to stresses and strains. It is, therefore, important for the reader to become familiar with the basic definitions of stress and strain before proceeding on to the remaining chapters of this book. However, the well-prepared reader may choose to skip/skim this chapter, and then move on to Chap. 4 in which the fundamentals of elas-ticity are introduced. The basic definitions of stress and strain are presented in this chapter along with experimental methods for the measurement and application of strain and stress. The chapter starts with the relationships between applied loads/displacements and geometry that give rise to the basic definitions of strain and stress. Simple experimental methods for the measurement of strain and stress are then presented before describing the test machines that are often used for the application of strain and stress in the laboratory. 3.2 BASIC DEFINITIONS OF STRESS The forces applied to the surface of a body may be resolved into compo-nents that are perpendicular or parallel to the surface, Figs 3.1(a)-3.1(c). In 59 (a) 60 (b) Chapter 3 Simple tension,
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