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barcode generator vb.net source code RECOMMENDED READING in Software
RECOMMENDED READING UPC  13 Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. GS1  13 Printer In None Using Barcode maker for Software Control to generate, create European Article Number 13 image in Software applications. Proceedings of the Society of Automotive Engineers Fatigue Conference, P109, Warrendale, Pa. April 1982. EAN13 Recognizer In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Making GS1  13 In C# Using Barcode maker for .NET framework Control to generate, create UPC  13 image in .NET framework 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. GS1  13 Generator In .NET Framework Using Barcode creator for ASP.NET Control to generate, create EAN 13 image in ASP.NET applications. EAN13 Generator In Visual Studio .NET Using Barcode maker for VS .NET Control to generate, create EAN13 image in VS .NET applications. Source: STANDARD HANDBOOK OF MACHINE DESIGN
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Intelligent Mail Printer In None Using Barcode printer for Software Control to generate, create USPS OneCode Solution Barcode image in Software applications. Create UPCA In Java Using Barcode generation for BIRT reports Control to generate, create UPC Code image in BIRT applications. 30.1 EULER S FORMULA / 30.2 30.2 EFFECTIVE LENGTH / 30.4 30.3 GENERALIZATION OF THE PROBLEM / 30.6 30.4 MODIFIED BUCKLING FORMULAS / 30.7 30.5 STRESSLIMITING CRITERION / 30.8 30.6 BEAMCOLUMN ANALYSIS / 30.12 30.7 APPROXIMATE METHOD / 30.13 30.8 INSTABILITY OF BEAMS / 30.14 REFERENCES / 30.18 UPC A Creation In Java Using Barcode generation for Java Control to generate, create UPC A image in Java applications. Make UPC Code In Java Using Barcode maker for Java Control to generate, create UPC Symbol image in Java applications. NOTATION
Code 128 Code Set B Encoder In None Using Barcode printer for Microsoft Word Control to generate, create Code 128 Code Set B image in Office Word applications. Make EAN13 In Java Using Barcode generator for Java Control to generate, create EAN13 image in Java applications. A B(n) c(n) c(y), c(z) e E E(t) F(x) G h H I I(y), I(z) J k2 K K(0) Area of cross section Arbitrary constants Coefficients in series Distance from y and z axis, respectively, to outermost compressive fiber Eccentricity of axial load P Modulus of elasticity of material Tangent modulus for buckling outside of elastic range A function of x Shear modulus of material Height of cross section Horizontal (transverse) force on column Moment of inertia of cross section Moment of inertia with respect to y and z axis, respectively Torsion constant; polar moment of inertia P/EI Effectivelength coefficient Spring constant for constraining spring at origin Generate Data Matrix ECC200 In Java Using Barcode generator for Java Control to generate, create Data Matrix image in Java applications. Printing USS Code 128 In ObjectiveC Using Barcode creator for iPad Control to generate, create Code 128 image in iPad applications. 30.1 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. INSTABILITIES IN BEAMS AND COLUMNS 30.2
LOAD CAPABILITY CONSIDERATIONS
K(T, 0), K(T, L) l L Leff M, M M(0), M(L), Mmid M(0)cr Mtr M(y), M(z) n P Pcr r R s t T x y, z Y Ytr Torsional spring constants at x = 0, L, respectively Developed length of cross section Length of column or beam Effective length of column Bending moments Bending moments at x = 0, L, and midpoint, respectively Critical moment for buckling of beam Moment due to transverse load Moment about y and z axis, respectively Integer; running index Axial load on column Critical axial load for buckling of column Radius of gyration Radius of cross section Running coordinate, measured from one end Thickness of cross section Torque about x axis Axial coordinate of column or beam Transverse coordinates and deflections Initial deflection (crookedness) of column Deflection of beamcolumn due to transverse load Factor of safety Stress Angle of twist As the terms beam and column imply, this chapter deals with members whose crosssectional dimensions are small in comparison with their lengths. Particularly, we are concerned with the stability of beams and columns whose axes in the undeformed state are substantially straight. Classically, instability is associated with a state in which the deformation of an idealized, perfectly straight member can become arbitrarily large. However, some of the criteria for stable design which we will develop will take into account the influences of imperfections such as the eccentricity of the axial load and the crookedness of the centroidal axis of the column. The magnitudes of these imperfections are generally not known, but they can be estimated from manufacturing tolerances. For axially loaded columns, the onset of instability is related to the moment of inertia of the column cross section about its minor principal axis. For beams, stability design requires, in addition to the moment of inertia, the consideration of the torsional stiffness. 30.1 EULER S FORMULA
We will begin with the familiar Euler columnbuckling problem. The column is idealized as shown in Fig. 30.1. The top and bottom ends are pinned; that is, the moments 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. INSTABILITIES IN BEAMS AND COLUMNS 30.3
INSTABILITIES IN BEAMS AND COLUMNS
at the ends are zero. The bottom pin is fixed against translation; the top pin is free to move in the vertical direction only; and the force P acts along the x axis, which coincides with the centroidal axis in the undeformed state. It is important to keep in mind that the analysis which follows applies only to columns with cross sections and loads that are symmetrical about the xy plane in Fig. 30.1 and satisfy the usual assumptions of linear beam theory. It is particularly important in this connection to keep in mind that this analysis is valid only when the deformation is such that the square of the slope of the tangent at any point on the deflection curve is negligibly small compared to unity (fortunately, this is generally true in design applications). In such a case, the familiar differential equation for the bending of a beam is applicable. Thus, EI For the column in Fig. 30.1, M = Py We take E and I as constant, and let P = k2 EI Then we get, from Eqs. (30.1), (30.2), and (30.3), d2y + k2 y = 0 dx2 (30.4) (30.3) (30.2) d2y =M dx2 (30.1) FIGURE 30.1 Deflection of a simply supported column. (a) Ideal simply supported column; (b) columndeflection curve; (c) freebody diagram of deflected segment. 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.

