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barcode generator vb.net source code li = ti = in Software
li = ti = Decode UPC  13 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. EAN13 Supplement 5 Encoder In None Using Barcode printer for Software Control to generate, create EAN13 Supplement 5 image in Software applications. (36.42) Scanning UPC  13 In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. European Article Number 13 Encoder In Visual C#.NET Using Barcode maker for VS .NET Control to generate, create European Article Number 13 image in VS .NET applications. where the subscripts i and o refer to the inner and outer radii, respectively, and the subscripts t and l refer to the tangential (circumferential) and longitudinal directions. Radial stresses of lesser magnitude will also exist, although not at the inner or outer surfaces. If the tubing of Fig. 36.10b is thin, then the inner and outer stresses are equal, although opposite, and are lo = to = ( T)E 2(1 ) (36.43) ( T)E li = ti = 2(1 ) at points not too close to the tube ends. Encoding EAN13 In .NET Using Barcode generation for ASP.NET Control to generate, create EAN 13 image in ASP.NET applications. Paint European Article Number 13 In .NET Using Barcode printer for .NET Control to generate, create GTIN  13 image in .NET framework applications. 36.6 CONTACT STRESSES
GS1  13 Maker In VB.NET Using Barcode printer for VS .NET Control to generate, create GS1  13 image in .NET framework applications. Making Barcode In None Using Barcode generation for Software Control to generate, create barcode image in Software applications. When two elastic bodies having curved surfaces are pressed against each other, the initial point or line of contact changes into area contact, because of the deformation, and a threedimensional state of stress is induced in both bodies. The shape of the contact area was originally deduced by Hertz, who assumed that the curvature of the UPC Code Generator In None Using Barcode generator for Software Control to generate, create GTIN  12 image in Software applications. Data Matrix ECC200 Maker In None Using Barcode printer for Software Control to generate, create Data Matrix image in Software applications. Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright 2004 The McGrawHill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Code 3/9 Creation In None Using Barcode encoder for Software Control to generate, create ANSI/AIM Code 39 image in Software applications. GTIN  13 Generation In None Using Barcode drawer for Software Control to generate, create EAN13 image in Software applications. STRESS 36.20
MSI Plessey Maker In None Using Barcode maker for Software Control to generate, create MSI Plessey image in Software applications. Data Matrix ECC200 Encoder In VS .NET Using Barcode printer for VS .NET Control to generate, create Data Matrix 2d barcode image in VS .NET applications. CLASSICAL STRESS AND DEFORMATION ANALYSIS
Making EAN 13 In .NET Framework Using Barcode creation for Reporting Service Control to generate, create EAN13 image in Reporting Service applications. 2D Barcode Drawer In Java Using Barcode generation for Java Control to generate, create Matrix 2D Barcode image in Java applications. two bodies could be approximated by seconddegree surfaces. For such bodies, the contact area was found to be an ellipse. Reference [36.3] contains a comprehensive bibliography. As indicated in Fig. 36.11, there are four special cases in which the contact area is a circle. For these four cases, the maximum pressure occurs at the center of the contact area and is po = 3F 2 a2 (36.44) UCC  12 Maker In Java Using Barcode encoder for Java Control to generate, create UPCA Supplement 5 image in Java applications. Decoding Bar Code In Java Using Barcode Control SDK for BIRT Control to generate, create, read, scan barcode image in BIRT reports applications. where a = the radius of the contact area and F = the normal force pressing the two bodies together. In Fig. 36.11, the x and y axes are in the plane of the contact area and the z axis is normal to this plane. The maximum stresses occur on this axis, they are principal stresses, and their values for all four cases in Fig. 36.11 are Bar Code Recognizer In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. Encode Universal Product Code Version A In Visual Studio .NET Using Barcode creation for .NET Control to generate, create UPCA Supplement 5 image in .NET framework applications. FIGURE 36.11 Contacting bodies having a circular contact area. (a) Two spheres; (b) sphere and plate; (c) sphere and spherical socket; (d) crossed cylinders of equal diameters. Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright 2004 The McGrawHill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. STRESS 36.21
STRESS
x = y = po po 1 + z2/a2
z 1 1 tan 1 (1 + ) a z/a 2(1 + z2/a2) (36.45) z = (36.46) These equations are plotted in Fig. 36.12 together with the two shear stresses xz and yz. Note that xy = 0 because x = y. FIGURE 36.12 Magnitude of the stress components on the z axis below the surface as a function of the maximum pressure. Note that the two shearstress components are maximum slightly below the surface. The chart is based on a Poisson s ratio of 0.30. The radii a of the contact circles depend on the geometry of the contacting bodies. For two spheres, each having the same diameter d, or for two crossed cylinders, each having the diameter d, and in each case with like materials, the radius is a= 3Fd 1 2 8 E (36.47) where and E are the elastic constants. For two spheres of unlike materials having diameters d1 and d2, the radius is a= 2 1 1 1 2 3F d1d2 2 + E1 E2 8 d1 + d2 1/3 (36.48) Downloaded from Digital Engineering Library @ McGrawHill (www.digitalengineeringlibrary.com) Copyright 2004 The McGrawHill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. STRESS 36.22
CLASSICAL STRESS AND DEFORMATION ANALYSIS
For a sphere of diameter d and a flat plate of unlike materials, the radius is a=
2 2 3Fd 1 1 1 2 + E1 E2 8 1/3 (36.49) For a sphere of diameter d1 and a spherical socket of diameter d2 of unlike materials, the radius is a= 2 2 1 1 1 2 3F d1d2 + E1 E2 8 d2 d1 1/3 (36.50) Contacting cylinders with parallel axes subjected to a normal force have a rectangular contact area. We specify an xy plane coincident with the contact area with the x axis parallel to the cylinder axes. Then, using a righthanded coordinate system, the stresses along the z axis are maximum and are x = 2 po 1+ z2 b2

