Technology & Engineering
Bearing Stress
Bearing stress refers to the pressure exerted on a material when an external force is applied perpendicular to its surface. It is commonly used in engineering to determine the maximum load a material can withstand before it fails. The calculation of bearing stress is important in designing structures and machinery that can support heavy loads.
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7 Key excerpts on "Bearing Stress"
eBook - PDF- William F. Riley, Leroy D. Sturges, Don H. Morris(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
2-7b. 2-4 Bearing Stress Bearing Stresses (compressive normal stresses) occur on the surface of contact between two interacting members. Actually, there are only two types of stress, normal and shear. Bearing Stress is a just a name given to normal stress resulting from contact between two different bodies. For the case of the connection shown in Fig. 2-4, Bearing Stresses occur on d i d o d A = dt t (a) (b) (d o 2 – d i 2 ) A = π _ 4 Figure 2-8 the surfaces of contact between the head of the bolt and the top plate and between the nut and the bottom plate. The force producing the stress is the axial tensile internal force F developed in the shank of the bolt as the nut is tightened. The area of interest for Bearing Stress calculations is the annular area A = π 4 (d 2 o − d 2 i ) of the bolt head or nut (see Fig. 2-8a) that is in contact with the plate. Thus, the average Bearing Stress σ b is expressed as σ b = F A (2-6) Bearing Stresses also develop on surfaces of contact where the shanks of bolts and pins are pressed against the sides of the hole through which they pass. Since the distribution of these forces is quite complicated, an average Bearing Stress σ b is often used for design purposes. This stress is computed by dividing the force F transmitted across the surface of contact by the projected area A = dt shown in Fig. 2-8b, instead of the actual contact area. 2-5 UNITS OF STRESS Stress, being the intensity of internal force, has the dimensions of force per unit area (FL −2 ). Until recently, the commonly used unit for stress in the United States was the pound per square inch (psi). Since metals can sustain stresses of several thousand pounds per square inch, the unit ksi (kip per square inch) is also frequently used (1 ksi = 1000 psi). With the advent of the International System of Units
eBook - PDFApplied Mechanics
Made Simple
- George E. Drabble(Author)
- 2013(Publication Date)
- Made Simple(Publisher)
CHAPTER EIGHT BEHAVIOUR OF MATERIALS: STRESS ANALYSIS Since an engineer is almost always concerned with making something, one of the most important aspects of his profession relates to the nature, pro-perties and diversity of the various materials available to him. The properties that are of the most direct interest are strength, stiffness, workability, resis-tance to corrosion, resistance to abrasion, and appearance. Applied mech-anics is concerned with strength and stiffness only. In a sense, one can say that these two properties are the most important because they determine the ability of the material to perform the job it is called upon to do, although other properties may have a contributory effect. Engineering components usually fail because they break or deform under the load imposed upon them, either because this load is greater than the designer anticipated, or because of some unforseeable overload, or even, perhaps, because the designer failed to allow for load at all in his design. The Tay Bridge disaster of 1879 was due principally to a gross underestimate of the wind force on the bridge. The collapse of a building due to an earthquake or bomb is an example of an unforseeable overload. Failure to allow for load at all is not uncommon in the design and manufacture of many cheap kitchen gadgets and children's toys. An essential requirement of any engineering material is that it should behave satisfactorily under load. This does not mean merely that the com-ponent must not break: it must not deform beyond a certain acceptable limit. It would be quite possible to design and erect a perfectly safe road bridge of strong rubber stretched between the abutments, but it would be a matter of considerable difficulty, and understandably so, to induce any driver to make use of it. The examination of these properties of strength and stiffness is called stress analysis. This has superseded the earlier, and perhaps more familiar name of 'strength of materials'.
eBook - PDFMechanics of Materials
An Integrated Learning System
- Timothy A. Philpot, Jeffery S. Thomas(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Ans. EXAMPLE 1.7 Bearing Stresses also develop on the contact surface between a plate and the body of a bolt or a pin. A bearing failure at a bolted connection in a thin steel com- ponent is shown in Figure 1.6. A tension load was applied upward to the steel component, and a bearing failure occurred below the bolt hole. 11 kips Concrete slab Square steel base plate a a Outside diameter = 6.5 in. Wall thickness = 0.25 in. Figure 1 1.4 Bearing Stress 15 The distribution of Bearing Stresses on a semicircular contact surface is quite complicated, and an average Bearing Stress is often used for design purposes. This average Bearing Stress σ b is computed by dividing the transmitted force by the projected area of contact between a plate and the bolt or pin, instead of the actual contact area. This approach is illustrated in the next example. Jeffery S. Thomas FIGURE 1.6 Bearing Stress failure at a bolted connection. EXAMPLE 1.8 A 2.5 in. wide by 0.125 in. thick steel plate is connected to a support with a 0.75 in. diameter pin (Figure 1). The steel plate carries an axial load of 1.8 kips. Determine the Bearing Stress in the steel plate. Plan the Solution Bearing Stresses will develop on the surface where the steel plate contacts the pin. This surface is the right side of the hole in the illustration. To deter- mine the average Bearing Stress, the projected area of contact between the plate and the pin must be calculated. Solution The 1.8 kip load pulls the steel plate to the left, bringing the right side of the hole into contact with the pin. Bearing Stresses will occur on the right side of the hole (in the steel plate) and on the right half of the pin. Since the actual distribution of Bearing Stress on a semicircular surface is complicated, an average Bearing Stress is typically used for design purpos- es. Instead of the actual contact area, the projected area of contact is used in the calculation.
eBook - PDF- Roger T. Fenner, J.N. Reddy(Authors)
- 2012(Publication Date)
- CRC Press(Publisher)
26 INTRODUCTION Figure 1.21 Stress concentrations in engineering components are important not only because they are responsible for stresses much higher than we would expect from simple calculations, but also because they tend to encourage the formation of cracks, which can lead to catastrophic failure. 1.3.4 Allowable stresses In engineering practice, the calculation of stresses is not an end in itself. The val-ues obtained must be related to the strength properties of the materials concerned, either to help in the assessment of the safety of an existing structure or to assist in the design of a new system. The ultimate tensile strength of a material can be measured as the maximum stress in uniaxial tension that it can withstand. Simi-larly, an ultimate shear strength can also be measured, although this is less widely used. At least for simple states of normal or shear stress, an ultimate load for a component can then be defined as the product of ultimate stress and cross-sectional area. Engineering structures and components must be designed and used in such a way that the actual loads they experience are substantially lower than the ultimate loads they are theoretically capable of sustaining. The maximum permitted actual load is referred to as the allowable load , and the ratio of ultimate to allowable load as the factor of safety Factor of safety = ultimate load allowable load (1.6) In many cases, a linear relationship exists between load and the resulting stress, and the factor of safety may also be defined as 1.3 CONCEPTS OF STRESS AND STRAIN 27 Factor of safety = ultimate stress allowable stress (1.7) For states of stress more complex than normal or shear stress, it is customary to work in terms of stresses rather than loads and it is necessary to use a failure criterion of the type discussed in Chapter 9. The choice of an appropriate factor of safety for a particular situation is a very important engineering task, which requires both experience and judgment.
eBook - PDF- Timothy A. Philpot(Author)
- 2014(Publication Date)
- Wiley(Publisher)
Stress CHAPTER 1 1 The three fundamental areas of engineering mechanics are statics, dynamics, and mechanics of materials. Statics and dynamics are devoted primarily to the study of external forces and motions associated with particles and rigid bodies (i.e., idealized objects in which any change of size or shape due to forces can be neglected). Mechanics of materials is the study of the internal effects caused by external loads acting on real bodies that deform (mean- ing objects that can stretch, bend, or twist). Why are the internal effects in an object impor- tant? Engineers are called upon to design and produce a variety of objects and structures such as automobiles, airplanes, ships, pipelines, bridges, buildings, tunnels, retaining walls, motors, and machines. Regardless of the application, however, a safe and successful design must address the following three mechanical concerns: 1. Strength: Is the object strong enough to withstand the loads that will be applied to it? Will it break or fracture? Will it continue to perform properly under repeated loadings? 2. Stiffness: Will the object deflect or deform so much that it cannot perform its intended function? 3. Stability: Will the object suddenly bend or buckle out of shape at some elevated load so that it can no longer continue to perform its function? 1.1 Introduction 2 STRESS Addressing these concerns requires both an assessment of the intensity of internal forces and deformations acting within the body and an understanding of the mechanical charac- teristics of the material used to make the object. Mechanics of materials is a basic subject in many engineering fields. The course focuses on several types of components: bars subjected to axial loads, shafts in torsion, beams in bending, and columns in compression. Numerous formulas and rules for design found in engineering codes and specifications are based on mechanics of materials funda- mentals associated with these types of components.
eBook - PDFParts Fabrication
Principles and Process
- Richard Crowson(Author)
- 2006(Publication Date)
- CRC Press(Publisher)
It is the desire of this author to present some simple solutions to everyday structural problems to those individuals with little or no knowledge of mechanics. 1.1 DEFINITIONS OF FORCE AND STRESS 1.1.1 Force Force may be defined as that which exerts pressure, motion, or tension. We are con-cerned here with forces at rest or in equilibrium. If a force is at rest, it must be held so by some other force or forces. As shown in Figure 1.1, a steel column in a build-ing structure supports a given load, which due to gravity is downward. The column 1 2 Parts Fabrication: Principles and Process transfers the load to the footing below. The resultant upward pressure on the footing equals the load in magnitude and is called the reaction . The two forces are opposite in direction, have the same line of action, and are equal in magnitude. The system is in equilibrium; that is, there is no motion. The unit of force is usually pounds or kilograms. In practice, the word kip , mean-ing “a thousand pounds,” is frequently used. Thus, 30 kips might also be written 30,000 lb. 1.1.2 Stress Assume that a short column has a load of 100,000 lb applied to its end (see Figure 1.2a). The load, P, is evenly distributed over the cross section X-X. To calculate the area of the cross section in Figure 1.2b Area 3. 3.33 10 in. 2 Or, if it was a circular cross section, as shown in Figure 1.2c, in Area r 2 Where r (radius) 3.568 2 1.784 in., or A 3.14 (1.784) 2 10 in. 2 In the example, the load P is evenly distributed over the cross-sectional area A. We can say that 100,000 lb is distributed over 10 in. 2 , or 100,000 10 10,000 lb acting on each square inch. In this instance, the unit stress in the column is 10,000 lb in. 2 (psi). FIGURE 1.1 Example of forces in equilibrium. The load on the column from the roof is reacted by the footing. LOAD COLUMN REACTION
eBook - PDF- W. C. Bolton(Author)
- 2013(Publication Date)
- Wiley-Blackwell(Publisher)
Chapter 8 Stress and strain analysis 8.1 Complex stress situations The loading and shape of most engineering components are generally such that at any point in the material the stress is more complex than just a tensile or compressive stress in one direction. A section might be subject to direct stresses in two perpendicular directions and a shear stress. For example, in a drive shaft used to transmit power by means of a belt passing over a pulley, the shaft can be subject to bending stresses due to the load exerted by the belt plus pulley and a shear stress from the torque exerted by the belt. In other situations the shaft might be subject to axial stresses and a shear stress from a torque. The stresses encountered in axially loaded bars, beams subject to a bending moment and shafts in torsion are examples of a state of stress known as plane stress. With such a state of stress we have a two-dimensional state of stress rather than three-dimensional. If we consider an element of the material in the form of a cube, then there are only stresses on the faces at right angles to the x -and y -axes, those on the faces at right angles to the z -axis being negligible. 8.2 Simple tension Consider a long uniform bar, cross-sectional area A , subject to an axial tensile force F , as in figure 8.1. For any transverse plane AB through the bar there will be a pure normal stress of σ x acting on it, with σ x = F/A . Now consider an inclined plane BC which is at an angle θ to the y -direction. The force F will have a component of F cos θ at right angles to this plane and Fig. 8.1 Stresses on an inclined plane. 195 196 Mechanical Science F sin θ parallel to the plane BC. The area of the inclined plane is A/ cos θ = A sec θ . Thus the normal stress σ θ acting on the inclined plane is σ θ = F cos θ A/ cos θ = σ x cos 2 θ [1] The stress acting parallel to the plane, i.e.
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