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barcode generator vb.net source code DEFLECTION in Software
DEFLECTION EAN13 Recognizer In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. UPC  13 Generator In None Using Barcode encoder for Software Control to generate, create UPC  13 image in Software applications. TABLE 37.1 Properties of Beams (Continued) Decode GS1  13 In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Encoding GS1  13 In Visual C# Using Barcode encoder for VS .NET Control to generate, create EAN 13 image in .NET framework applications. 37.9 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. Make EAN13 In .NET Using Barcode creator for ASP.NET Control to generate, create European Article Number 13 image in ASP.NET applications. Paint UPC  13 In Visual Studio .NET Using Barcode encoder for .NET framework Control to generate, create UPC  13 image in VS .NET applications. DEFLECTION
Make GS1  13 In Visual Basic .NET Using Barcode printer for .NET framework Control to generate, create EAN13 Supplement 5 image in Visual Studio .NET applications. Painting Code 39 Extended In None Using Barcode maker for Software Control to generate, create Code39 image in Software applications. TABLE 37.1 Properties of Beams (Continued) Bar Code Printer In None Using Barcode encoder for Software Control to generate, create barcode image in Software applications. Painting Data Matrix In None Using Barcode printer for Software Control to generate, create DataMatrix image in Software applications. 37.10 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. GTIN  12 Maker In None Using Barcode printer for Software Control to generate, create UPCA image in Software applications. EAN / UCC  13 Printer In None Using Barcode creation for Software Control to generate, create EAN128 image in Software applications. DEFLECTION
UCC  14 Generator In None Using Barcode drawer for Software Control to generate, create UPC Case Code image in Software applications. EAN / UCC  13 Creator In None Using Barcode drawer for Online Control to generate, create UCC128 image in Online applications. TABLE 37.1 Properties of Beams (Continued) EAN 13 Decoder In VB.NET Using Barcode reader for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications. Making Code 128 Code Set B In .NET Using Barcode generation for Visual Studio .NET Control to generate, create Code 128 Code Set C image in Visual Studio .NET applications. 37.11 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. Reading Barcode In .NET Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. UCC.EAN  128 Recognizer In Visual Basic .NET Using Barcode scanner for .NET Control to read, scan read, scan image in Visual Studio .NET applications. DEFLECTION
Code39 Creation In None Using Barcode generation for Font Control to generate, create Code 3/9 image in Font applications. ANSI/AIM Code 39 Creation In Java Using Barcode encoder for Java Control to generate, create Code 39 Extended image in Java applications. TABLE 37.1 Properties of Beams (Continued) 37.12 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. DEFLECTION
TABLE 37.1 Properties of Beams (Continued) 37.13 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. DEFLECTION 37.14
CLASSICAL STRESS AND DEFORMATION ANALYSIS
FIGURE 37.2 Frame loaded by three forces.
member has been analyzed and the partial derivatives obtained. The following example demonstrates the technique. Example 1. Find the downward deflection of point D of the frame shown in Fig. 37.3. Solution. A force analysis of the system gives an upward reaction at E of RE = 225 + 3F2. The reaction at A is downward and is RA = 75 2F2. The strain energy for member CE is UCE = 2 RA 2AE
The partial deflection is taken with respect to F2 because the deflection at D in the direction of F2 is desired. Thus UCE 2RA RA = 2AE F2 F2 Also, RA = 2 F2 Thus Eq. (2) becomes UCE (75 2F2 )(30) 37 500 = ( 2) = 0.2E E F2 (3) (2) 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. DEFLECTION 37.15
DEFLECTION
FIGURE 37.3 Frame loaded by two forces. Dimensions in inches: ACE = 0.20 in2 ; IAD = 0.18 in4 ; E = 30 106 psi. Note that we were able to substitute the value of F2 in Eq. (3) because the partial derivative had been taken. The strain energy stored in member ABCD will have to be computed in three parts because of the change in direction of the bending moment diagram at points B and C. For part AB, the moment is MAB = RAx = (75 2F2)x The strain energy is UAB =
2 M AB dx 2EI
Taking the partial derivative with respect to F2 as before gives UAB = F2
2MAB MAB dx 2EI F2
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. DEFLECTION 37.16
CLASSICAL STRESS AND DEFORMATION ANALYSIS
But MAB = 2x F2 Therefore, Eq. (5) may be written UAB 1 = F2 EI =
x(75 2F2 )( 2x) dx
1 0.18E 250x2 dx =
100 000 E where the value of F2 again has been substituted after taking the partial derivative. For section BC, we have MBC = RAx F1(x 6) = 1800 225x 2F2x MBC = 2x F2 UBC = F2 = = 2MBC MBC dx 2EI F2
1 EI
(1800 225x 2F2 x)( 2x) dx
1 0.18E ( 3600x + 850x2 ) dx =
145 926 E Finally, section CD yields MCD = (24 x)F2 UCD = F2 = = = Then yD = = UCE UAB UBC UCD + + + F2 F2 F2 F2 1 (37 500 + 100 000 + 145 926 + 758 519) 30(10)6 (when rounded) 24 8 MCD = (24 x) F2
2MCD MCD dx 2EI F2
1 EI
F2(24 x)2 dx
8 24 1 0.18E (57 600 4800x + 100x2 ) dx
758 519 E = 0.0347 in
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. DEFLECTION 37.17
DEFLECTION
37.4.1 Redundant Members A frame consisting of one or more redundant members is statically indeterminate because the use of statics is not sufficient to determine all the reactions. In this case, Castigliano s theorem can be used first to determine these reactions and second to determine the desired deflection. Let R1, R2 , and R3 be a set of three indeterminate reactions. The deflection at the supports must be zero, and so Castigliano s theorem can be written three times. Thus U =0 R1 U =0 R2 U =0 R3 (37.10) and so the number of equations to be solved is the same as the number of indeterminate reactions. In setting up Eqs. (37.10), do not substitute the numerical value of the particular force corresponding to the desired deflection. This force symbol must appear in the reaction equations because the partial derivatives must be taken with respect to this force when the deflection is found. The method is illustrated by the following example. Example 2. Find the downward deflection at point D of the frame shown in Fig. 37.4. Solution. Choose RB as the statically indeterminate reaction. A static force analysis then gives the remaining reactions as RA = RC = 0.625(F RB) (1) FIGURE 37.4 Frame loaded by a single force. Dimensions in millimeters: AAD = ACD = 2 cm2, ABD = 1.2 cm2, E = 207 GPa, F = 20 kN. 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.

