Stress State

4 Key excerpts on "Stress State"

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  eBook - PDF

  Peterson's Stress Concentration Factors

  • Zhuming Bi, Walter D. Pilkey, Deborah F. Pilkey(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  Every reliability value has an asso- ciated time value. Thus, a time range must be specified when the reliability is evaluated based on a probability density function, R(a ≤ x ≤ b) = ∫ b a f (x) dx (1.6) As shown in Fig. 1.19, the reliability corresponds to a system measure to perform and maintain the expected safe state of materials in normal, hostile, or uncertain application circumstances. 1.7 STRESS ANALYSIS OF MECHANICAL STRUCTURES In engineering design, stress analysis is used to determine the distribution of stresses and iden- tify critical features and locations with the highest possibility of failure. The ultimate goal of stress analysis is to ensure that the design of a structure and artifact can withstand a specified load with a given lifespan, using the minimum amount of material and satisfying other opti- mal criteria. Stress analysis may be performed through classical mathematical techniques, ana- lytic mathematical modeling, computational simulation, experimental testing, or a combination of methods. 1.7.1 Procedure of Stress Analysis The procedure of stress analysis includes the following critical steps: (1) Isolate objects one by one from the system, clarify the functions of every object in terms of external loads, boundary conditions and constraints, (2) Develop the model of objects for the relations of stress distribution and exerted loads, (3) Identify critical features and locations with the maximum stresses, (4) Evaluate the safety of materials by comparing stresses and strengths of materials, and (5) Optimize the design and the dimensions iteratively until all of the design constraints are met and system performances reach their optimums. Before the stress analysis, the first step is to model and represent the geometry of objects appropriately. 1.7.2 Geometric Discontinuities of Solids A machine element corresponds to a solid object, which has its geometry and shape with a fine volume.

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  Mechanical Behavior of Materials

  • 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 ).

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  eBook - ePub

  Practical Engineering Failure Analysis

  • Hani M. Tawancy, Anwar Ul-Hamid, Nureddin M. Abbas(Authors)
  • 2004(Publication Date)
  • CRC Press

    (Publisher)

  τ = 0.

  5.9 Design Stresses

  Most designs for structural applications are based on mechanical property data obtained from tensile tests on smooth bars particularly the yield strength and ultimate tensile strength. However, since the safe lifetime of an engineering structure cannot be predicted from such simple tests, it is a common practice to use a ‘‘factor of safety” to guard against unanticipated fracture during service. A factor of safety is a number N divided into either the yield or ultimate tensile strength obtained from the tensile test to obtain what is known as the allowable stress. Whether the yield strength or ultimate strength is used as the basis for design is dependent upon (i) type of loading and (ii) ductility of the material. It is possible to identify three main types of loading: (i) static, (ii) cyclic, dynamic, or repeated, and (iii) impact or shock. Generally, for brittle materials where the yield strength approaches the ultimate strength, the ultimate strength is used as the basis for design, and therefore the design or allowable stress σd is given by

  For ductile materials, the yield strength is used as the basis for design in the case of a static loading, i.e., However, in the case of cyclic or impact loading, the ultimate strength is used as the basis for design using ductile materials, i.e.,

  σd (cyclic loading or impact loading, ductile material) = σuts /N (5.57)

  Many parts and components are covered by codes and specifications determining the design or allowable stress, e.g., pressure vessels, bolts, and welded components. For parts not covered by codes and specifications, the factors of safety listed in Table 5.1 are usually used to obtain the design stress.

  When parts are subjected to shear stresses during service such as riveted joints and springs, a design shear stress τd is used. However, values of yield strength in shear for different metallic materials are not as commonly reported as yield strength. Usually, the design shear stress is obtained from tensile strength data. It is recalled that a tensile stress σ develops a maximum shear stress τ =

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  Dynamics of Wheel-Soil Systems

  A Soil Stress and Deformation-Based Approach

  • Jaroslaw A. Pytka(Author)
  • 2016(Publication Date)
  • CRC Press

    (Publisher)

  91 4 Stress State under Wheeled Vehicle Loads 4.1 Introduction In many approaches to the problem of off-road mobility, contact pressure is a main input parameter. A concrete surface acts something like a bridge that transfers and distributes wheel loads over a greater surface, while a soft surface deforms intensively because the loads are concentrated on a very small contact surface. Numerous papers have proven the importance and practical meaning of the Stress State under wheels for measuring and predicting off-road traction (D ą browski et al. 2006, Foda 1991, Muro 1993, Hetherington and White 2002, Hetherington and Littleton 1987, Pytka 2007, Shibusawa and Sasao 1996, Shmulevich and Osetinsky 2003, Upadhyaya et al. 1997, Wanjii et al. 1997). In most models, tractive forces— driving force, rolling resistance, and vertical load—are determined based on an analysis of Stress State or stress distribution on a contact surface. These forces are expressed in Bekker’s equations: ∫ = τ α α F d ( ) DR (4.1) ∫ = σ α α F d ( ) RR (4.2) where τ ( α ) is the shear stress component, σ ( α ) is normal stress, and α is a measure of a surface of volume over which the stresses accumulate. Loads applied to a soft contact surface, however, are also distributed into the soil, and the character of this phenomenon depends on the kind of soil and its state as well as factors related to the vehicle such as speed, wheel slip, etc. Just as the load state under a wheel is complex, so is the soil Stress State. The stress tensors change in value and orientation during the pass of a wheel. Knowledge of the dependencies between vehicle ride parameters and stresses may be advantageous for mastering the models of wheel–ground interactions.

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