 Home
 Products
 Integration
 Tutorial
 Barcode FAQ
 Purchase
 Company
barcode generator vb.net source code STRESS 36.5 in Software
STRESS 36.5 Scan GS1  13 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Encoding GS1  13 In None Using Barcode creation for Software Control to generate, create EAN13 Supplement 5 image in Software applications. STRESS
Decoding GS1  13 In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. UPC  13 Creation In Visual C# Using Barcode generation for .NET Control to generate, create EAN13 image in Visual Studio .NET applications. FIGURE 36.2 Mohr s circle diagram for plane stress. (From Applied Mechanics of Materials, by Joseph E. Shigley. Copyright 1976 by McGrawHill, Inc. Used with permission of the McGrawHill Book Company.) European Article Number 13 Creation In VS .NET Using Barcode encoder for ASP.NET Control to generate, create EAN13 image in ASP.NET applications. Generate EAN13 In .NET Using Barcode creator for Visual Studio .NET Control to generate, create EAN / UCC  13 image in Visual Studio .NET applications. 36.1.1 Programming To program a Mohr s circle solution, plan on using a rectangulartopolar conversion subroutine. Now notice, in Fig. 36.2, that ( x y)/2 is the base of a right triangle, xy is the ordinate, and the hypotenuse is an extreme of the shear stress. Thus the conversion routine can be used to output both the angle 2 and the extreme value of the shear stress. As shown in Fig. 36.2, the principal stresses are found by adding and subtracting the extreme value of the shear stress to and from the term ( x + y)/2. It is wise to ensure, in your programming, that the angle indicates the angle from the x axis to the direction of the stress component of interest; generally, the angle is considered positive when measured in the ccw direction. European Article Number 13 Generation In Visual Basic .NET Using Barcode maker for .NET framework Control to generate, create EAN13 image in VS .NET applications. Code39 Generator In None Using Barcode generation for Software Control to generate, create Code39 image in Software applications. 36.2 TRIAXIAL STRESS
Barcode Creation In None Using Barcode printer for Software Control to generate, create bar code image in Software applications. USS Code 128 Generator In None Using Barcode maker for Software Control to generate, create Code 128 Code Set B image in Software applications. The general threedimensional stress element in Fig. 36.3a has three normal stresses x, y, and z, all shown as positive, and six shearstress components, also shown as positive. The element is in static equilibrium, and hence Generating European Article Number 13 In None Using Barcode printer for Software Control to generate, create European Article Number 13 image in Software applications. Bar Code Creation In None Using Barcode creation for Software Control to generate, create bar code 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. Draw Interleaved 2 Of 5 In None Using Barcode maker for Software Control to generate, create 2 of 5 Interleaved image in Software applications. Print Code39 In .NET Framework Using Barcode maker for ASP.NET Control to generate, create Code 3/9 image in ASP.NET applications. STRESS 36.6
DataMatrix Creation In VB.NET Using Barcode generator for .NET Control to generate, create ECC200 image in .NET applications. Create UCC.EAN  128 In Java Using Barcode printer for Android Control to generate, create UCC  12 image in Android applications. CLASSICAL STRESS AND DEFORMATION ANALYSIS
Reading Code 39 In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. UCC128 Decoder In VB.NET Using Barcode decoder for .NET Control to read, scan read, scan image in .NET framework applications. FIGURE 36.3 (a) General triaxial stress element; (b) Mohr s circles for triaxial stress.
Code128 Generator In None Using Barcode creator for Microsoft Excel Control to generate, create Code 128 Code Set A image in Excel applications. Bar Code Decoder In Visual Studio .NET Using Barcode scanner for .NET framework Control to read, scan read, scan image in .NET applications. xy = yx
yz = zy
zx = xz
Note that the first subscript is the coordinate normal to the element face, and the second subscript designates the axis parallel to the shearstress component. The negative faces of the element will have shear stresses acting in the opposite direction; these are also considered as positive. As shown in Fig. 36.3b, there are three principal stresses for triaxial stress states. These three are obtained from a solution of the equation 2 2 2 3 ( x + y + z) 2 + ( x y + x z + y z xy yz zx ) 2 2 2 ( x y z + 2 xy yz zx x yz y zx z xy ) = 0 (36.7) In plotting Mohr s circles for triaxial stress, arrange the principal stresses in the order 1 > 2 > 3, as in Fig. 36.3b. It can be shown that the stress coordinates for any arbitrarily located plane will always lie on or inside the largest circle or on or outside the two smaller circles. The figure shows that the maximum shear stress is always max = 1 3 2 (36.8) when the normal stresses are arranged so that 1 > 2 > 3.
36.3 STRESSSTRAIN RELATIONS
The stresses due to loading described as pure tension, pure compression, and pure shear are = F A = F A (36.9) 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 36.7
STRESS
where F is positive for tension and negative for compression and the word pure means that there are no other complicating effects. In each case the stress is assumed to be uniform, which requires that The member is straight and of a homogeneous material. The line of action of the force is through the centroid of the section. There is no discontinuity or change in cross section near the stress element. In the case of compression, there is no possibility of buckling. Unit engineering strain , often called simply unit strain, is the elongation or deformation of a member subjected to pure axial loading per unit of original length. Thus = where = total strain l0 = unstressed or original length l0 (36.10) Shear strain is the change in a right angle of a stress element due to pure shear. Hooke s law states that, within certain limits, the stress in a material is proportional to the strain which produced it. Materials which regain their original shape and dimensions when a load is removed are called elastic materials. Hooke s law is expressed in equation form as =E = G (36.11) where E = the modulus of elasticity and G = the modulus of ridigity, also called the shear modulus of elasticity. Poisson demonstrated that, within the range of Hooke s law, a member subjected to uniaxial loading exhibits both an axial strain and a lateral strain. These are related to each other by the equation = lateral strain axial strain (36.12) where is called Poisson s ratio. The three constants given by Eqs. (36.11) and (36.12) are often called elastic constants. They have the relationship E = 2G(1 + ) By combining Eqs. (36.9), (36.10), and (36.11), it is easy to show that = Fl AE (36.14) (36.13) which gives the total deformation of a member subjected to axial tension or compression. A solid round bar subjected to a pure twisting moment or torsion has a shear stress that is zero at the center and maximum at the surface. The appropriate equations are 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.

