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barcode generator vb.net source code MODIFIED BUCKLING FORMULAS in Software
30.4 MODIFIED BUCKLING FORMULAS Reading EAN13 Supplement 5 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. EAN13 Maker In None Using Barcode maker for Software Control to generate, create UPC  13 image in Software applications. The criticalload formulas developed above provide satisfactory values of the allowable load for very slender columns for which buckling, as manifested by unaccept Decode EAN 13 In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. GS1  13 Generation In C#.NET Using Barcode maker for Visual Studio .NET Control to generate, create EAN13 image in Visual Studio .NET 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. EAN 13 Drawer In Visual Studio .NET Using Barcode generator for ASP.NET Control to generate, create EAN13 image in ASP.NET applications. EAN13 Supplement 5 Creator In VS .NET Using Barcode printer for VS .NET Control to generate, create EAN13 Supplement 5 image in Visual Studio .NET applications. INSTABILITIES IN BEAMS AND COLUMNS 30.8
Print EAN13 Supplement 5 In Visual Basic .NET Using Barcode generation for VS .NET Control to generate, create EAN13 Supplement 5 image in VS .NET applications. Painting Code39 In None Using Barcode generator for Software Control to generate, create Code39 image in Software applications. LOAD CAPABILITY CONSIDERATIONS
EAN / UCC  13 Maker In None Using Barcode generation for Software Control to generate, create EAN / UCC  13 image in Software applications. Creating Bar Code In None Using Barcode drawer for Software Control to generate, create bar code image in Software applications. ably large deformation, will occur within the elastic range of the material. For more massive columns, the deformation enters the plastic region (where strain increases more rapidly with stress) prior to the onset of buckling. To take into account this change in the stressstrain relationship, we modify the Euler formula. We define the tangent modulus E(t) as the slope of the tangent to the stressstrain curve at a given strain. Then the modified formulas for the critical load are obtained by substituting E(t) for E in Eq. (30.9) and Eq. (30.13) plus Eq. (30.14) or Eq. (30.16) plus Eq. (30.14). This will produce a more accurate prediction of the buckling load. However, this may not be the most desirable design approach. In general, a design which will produce plastic deformation under the operating load is undesirable. Hence, for a column which will undergo plastic deformation prior to buckling, the preferred designlimiting criterion is the onset of plastic deformation, not the buckling. Painting Bar Code In None Using Barcode creator for Software Control to generate, create bar code image in Software applications. Painting UCC  12 In None Using Barcode drawer for Software Control to generate, create GTIN  128 image in Software applications. 30.5 STRESSLIMITING CRITERION
Printing Royal Mail Barcode In None Using Barcode creation for Software Control to generate, create British Royal Mail 4State Customer Code image in Software applications. Creating GS1128 In Java Using Barcode creator for Java Control to generate, create UCC.EAN  128 image in Java applications. We will now develop a design criterion which will enable us to use the yield strength as the upper bound for acceptable design regardless of whether the stress at the onset of yielding precedes or follows buckling. Here we follow Ref. [30.1]. This approach has the advantage of providing a single bounding criterion that holds irrespective of the mode of failure. We begin by noting that, in general, real columns will have some imperfection, such as crookedness of the centroidal axis or eccentricity of the axial load. Figure 30.4 shows the difference between the behavior of an ideal, perfectly straight column subjected to an axial load, in which case we obtain a distinct critical point, and the behavior of a column with some imperfection. It is clear from Fig. 30.4 that the loaddeflection curve for an imperfect column has no distinct critical point. Instead, it has two distinct regions. For small axial loads, the deflection increases slowly with load. When the load is approaching the critical value obtained for a perfect column, a small increment in load produces a large change in deflection. These two regions are joined by a knee. Thus the advent of buckling in a real column corresponds to the entry of the column into the second, abovetheknee, loaddeflection region. A massive column will reach the stress at the yield point prior to buckling, so that the yield strength will be the limiting criterion for the maximum allowable load. A slender column will enter the abovethe DataMatrix Creator In .NET Using Barcode encoder for Visual Studio .NET Control to generate, create Data Matrix 2d barcode image in .NET applications. Draw Barcode In .NET Using Barcode creation for Visual Studio .NET Control to generate, create bar code image in .NET framework applications. FIGURE 30.4 Typical loaddeflection curves for ideal and real columns.
Drawing Barcode In Java Using Barcode drawer for Android Control to generate, create barcode image in Android applications. Scanning UPC Code In Java Using Barcode scanner for Java Control to read, scan read, scan image in Java 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. Bar Code Recognizer In Java Using Barcode decoder for Java Control to read, scan read, scan image in Java applications. Matrix 2D Barcode Drawer In Java Using Barcode printer for Java Control to generate, create 2D Barcode image in Java applications. INSTABILITIES IN BEAMS AND COLUMNS 30.9
INSTABILITIES IN BEAMS AND COLUMNS
knee region prior to reaching the stress at the yield point, but once in the abovetheknee region, it requires only a small increment in load to produce a sufficiently large increase in deflection to reach the yield point. Thus the corresponding yield load may be used as an adequate approximation of the buckling load for a slender column as well. Hence the yield strength provides an adequate design bound for both massive and slender columns. It is also important to note that, in general, columns found in applications are sufficiently massive that the linear theory developed here is valid within the range of deflection that is of interest. Application of Eq. (30.1) to a simply supported imperfect column with constant properties over its length yields a modification of Eq. (30.4). Thus, d2y + k2y = k2 (e Y) dx2 (30.17) where e = eccentricity of the axial load P (taken as positive in the positive y direction) and Y = initial deflection (crookedness) of the unloaded column. The x axis is taken through the end points of the centroidal axis, so that Eq. (30.5) still holds and Y is zero at the end points. Note that the functions in the right side of Eq. (30.8) form a basis for a trigonometric (Fourier) series, so that any function of interest may be expressed in terms of such a series. Thus we can write Y= where c(n) = 2 L

