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barcode generator vb.net source code STRESS 36.8 in Software
STRESS 36.8 EAN 13 Decoder In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. EAN13 Encoder In None Using Barcode creation for Software Control to generate, create GS1  13 image in Software applications. CLASSICAL STRESS AND DEFORMATION ANALYSIS
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Print Code39 In None Using Barcode generator for Software Control to generate, create Code 3 of 9 image in Software applications. EAN / UCC  13 Encoder In None Using Barcode printer for Software Control to generate, create European Article Number 13 image in Software applications. (36.15) DataMatrix Printer In None Using Barcode encoder for Software Control to generate, create Data Matrix image in Software applications. Print Barcode In None Using Barcode generator for Software Control to generate, create bar code image in Software applications. where T = torque = radius to stress element r = radius of bar J = second moment of area (polar) The total angle of twist of such a bar, in radians, is = Tl GJ (36.16) Generate GTIN  14 In None Using Barcode printer for Software Control to generate, create EAN / UCC  14 image in Software applications. Read Barcode In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java applications. where l = length of the bar. For the shear stress and angle of twist of other cross sections, see Table 36.1. Make Barcode In .NET Using Barcode encoder for ASP.NET Control to generate, create barcode image in ASP.NET applications. GS1128 Creator In Java Using Barcode generator for Java Control to generate, create UCC  12 image in Java applications. 36.3.1 Principal Unit Strains For a bar in uniaxial tension or compression, the principal strains are Data Matrix ECC200 Reader In VS .NET Using Barcode recognizer for VS .NET Control to read, scan read, scan image in .NET applications. GS1128 Maker In .NET Using Barcode generation for Reporting Service Control to generate, create USS128 image in Reporting Service applications. 1 E Barcode Encoder In VS .NET Using Barcode printer for Reporting Service Control to generate, create barcode image in Reporting Service applications. Data Matrix Printer In Visual C#.NET Using Barcode generation for .NET Control to generate, create Data Matrix 2d barcode image in Visual Studio .NET applications. = = (36.17) Notice that the stress state is uniaxial, but the strains are triaxial. For triaxial stress, the principal strains are 1 2 3 E E E 2 1 3 E E E 3 1 2 E E E (36.18) These equations can be solved for the principal stresses; the results are 1 = E 1(1 ) + E( 2 + 3) 1 2 2 E 2(1 ) + E( 1 + 3) 1 2 2 E 3(1 ) + E( 1 + 2) 1 2 2 (36.19) 2 = 3 = The biaxial stressstrain relations can easily be obtained from Eqs. (36.18) and (36.19) by equating one of the principal stresses to zero. 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
TABLE 36.1 Torsional Stress and Angular Deflection of Various Sections
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
TABLE 36.1 Torsional Stress and Angular Deflection of Various Sections (Continued) 36.10 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
TABLE 36.1 Torsional Stress and Angular Deflection of Various Sections (Continued) 36.11 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 36.12
CLASSICAL STRESS AND DEFORMATION ANALYSIS
36.3.2 Plastic Strain It is important to observe that all the preceding relations are valid only when the material obeys Hooke s law. Some materials (see Sec. 32.9), when stressed in the plastic region, exhibit a behavior quite similar to that given by Eq. (36.11). For these materials, the appropriate equation is = K n where = true stress K = strength coefficient = true plastic strain n = strainstrengthening exponent (36.20) The relations for the true stress and true strain are = Fi Ai = ln li l0 (36.21) where Ai and li are, respectively, the instantaneous values of the area and length of a bar subjected to a load Fi. Note that the areas in Eqs. (36.9) are the original or unstressed areas; the subscript zero was omitted, as is customary. The relations between true and engineering (nominal) stresses and strains are = exp = ln( + 1) (36.22) 36.4 FLEXURE
Figure 36.4a shows a member loaded in flexure by a number of forces F and supported by reactions R1 and R2 at the ends. At point C a distance x from R1, we can write MC = Mext + M = 0 (36.23) where Mext = xR1 + c1F1 + c2F2 and is called the external moment at section C. The term M, called the internal or resisting moment, is shown in its positive direction in both parts b and c of Fig. 36.4. Figure 36.5 shows that a positive moment causes the top surface of a beam to be concave.A negative moment causes the top surface to be convex with one or both ends curved downward. A similar relation can be defined for shear at section C: Fy = Fext + V = 0 (36.24) where Fext = R1 F1 F2 and is called the external shear force at C. The term V, called the internal shear force, is shown in its positive direction in both parts b and c of Fig. 36.4. Figure 36.6 illustrates an application of these relations to obtain a set of shear and moment diagrams. 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.

