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barcode generator vb.net source code INSTABILITIES IN BEAMS AND COLUMNS 30.11 in Software
INSTABILITIES IN BEAMS AND COLUMNS 30.11 Scanning EAN13 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 encoder for Software Control to generate, create GTIN  13 image in Software applications. INSTABILITIES IN BEAMS AND COLUMNS
Read UPC  13 In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. EAN 13 Printer In Visual C#.NET Using Barcode printer for Visual Studio .NET Control to generate, create EAN13 image in Visual Studio .NET applications. Then we have, from Eqs. (1) through (4), allow = P P 4P 4 + 1+ A [(EA2)/(4 )]( /L)2 P A (5) EAN 13 Generator In VS .NET Using Barcode creator for ASP.NET Control to generate, create European Article Number 13 image in ASP.NET applications. GTIN  13 Printer In .NET Using Barcode generation for .NET Control to generate, create EAN 13 image in Visual Studio .NET applications. Usually P and L are given, and E are the properties of chosen material, and is determined from the clearances, tolerances, and kinematics involved, so that Eq. (5) is reduced to a cubic in A. At the moment, however, we are interested in comparing the allowable nominal column stress P/A with the allowable stress of the material allow for columns of different lengths. Keeping in mind that the radius of gyration r of a circular cross section of geometric radius R is R/2, we will define R =r 2 allow =p P/A E =q allow Then Eq. (5) may be written as p = 1 + 4 + 16 [ 2pq(r/L)2 1] (7) (6) Encode EAN 13 In VB.NET Using Barcode creation for VS .NET Control to generate, create EAN 13 image in .NET applications. Data Matrix Drawer In None Using Barcode encoder for Software Control to generate, create Data Matrix ECC200 image in Software applications. The first term on the right side of Eq. (7) is due to direct compressive stress; the second term is due to the bending moment produced by the load eccentricity; the third term is due to the bending moment arising from the column deflection. When is small, p will be close to unity unless the denominator in the third term on the right side of Eq. (7) becomes small that is, the moment due to the column deflection becomes large. The ratio L/r, whose reciprocal appears in the denominator of the third term, is called the slenderness ratio. Equation (7) may be rewritten as a quadratic in p. Thus, 2q r 2 2 r p (1 + 4 ) 2q L L Printing Code39 In None Using Barcode creation for Software Control to generate, create Code39 image in Software applications. Barcode Creator In None Using Barcode maker for Software Control to generate, create barcode image in Software applications. + 1 p + (1 + 4 ) Code 128A Generator In None Using Barcode generator for Software Control to generate, create Code 128A image in Software applications. Make GS1  12 In None Using Barcode maker for Software Control to generate, create UPC Symbol image in Software applications. 16 =0 Delivery Point Barcode (DPBC) Maker In None Using Barcode printer for Software Control to generate, create Delivery Point Barcode (DPBC) image in Software applications. Paint EAN 13 In None Using Barcode creator for Excel Control to generate, create GTIN  13 image in Office Excel applications. We will take for q the representative value of 1000 and tabulate 1/p for a number of values of L/r and . To compare the value of 1/p obtained from Eq. (8) with the corresponding result from Euler s formula, we will designate the corresponding result obtained by Euler s formula as 1/pcr and recast Eq. (30.9) as 1 r = 2q pcr L UPCA Supplement 2 Creation In None Using Barcode generator for Online Control to generate, create UPCA Supplement 2 image in Online applications. Bar Code Decoder In Visual Studio .NET Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in VS .NET applications. To interpret the results in Table 30.1, note that the quantities in the second and third columns of the table are proportional to the allowable loads calculated from the respective equations. As expected, the Euler formula is completely inapplicable when L/r is 50. Also, as expected, the allowable load decreases as the eccentricity increases. However, the effect of eccentricity on the allowable load decreases as the slenderness ratio L/r increases. Hence when L/r is 250, the Euler buckling load, which is the limiting case for which the eccentricity is zero, is only about 2 percent higher than when the eccentricity is 2 percent. Scanning GTIN  12 In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Printing GTIN  12 In C#.NET Using Barcode drawer for Visual Studio .NET Control to generate, create UPCA image in VS .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. Generating USS128 In .NET Using Barcode encoder for ASP.NET Control to generate, create EAN128 image in ASP.NET applications. Barcode Recognizer In Visual Basic .NET Using Barcode recognizer for .NET Control to read, scan read, scan image in .NET applications. INSTABILITIES IN BEAMS AND COLUMNS 30.12
LOAD CAPABILITY CONSIDERATIONS
TABLE 30.1 Influence of Eccentricity and Slenderness Ratio on Allowable Load
30.6 BEAMCOLUMN ANALYSIS
A member that is subjected to both a transverse load and an axial load is frequently called a beamcolumn. To apply the immediately preceding stresslimiting criterion to a beamcolumn, we first determine the moment distribution, say, Mtr, and the corresponding deflection, say, Ytr, resulting from the transverse load acting alone. Suppose that the transverse load is symmetrical about the column midpoint, and let Ytr, mid and Mtr, mid be the values of Ytr and Mtr at the column midpoint. Then the only modifications necessary in the preceding development are to replace Y by Y + Ytr in Eqs. (30.17) and (30.20), and to replace Ymid by Ymid + Ytr, mid and add Mtr, mid on the right side of Eq. (30.23). If the transverse load is not symmetrical, then it is necessary to determine the maximum moment by using an approach which will now be developed. Note that, at any point, x, the moment about the z axis is M(z) = P(e y Y) + M(z)tr (30.24) where Y includes the deflection due to M(z)tr. M(y) has the same form as Eq. (30.24), but with the roles of y and z interchanged.The maximum stress for any given value of x is given by Eq. (30.23). We seek to apply this equation at that value of x which yields the maximum value of . A method that is reasonably efficient in locating a minimum or maximum to any desired accuracy is the goldensection search. However, this method is limited to finding the minimum (maximum) of a unimodal function, that is, a function which has only one minimum (maximum) in the interval in which the search is conducted. We therefore have to conduct some exploratory calculation to find the stress at, say, a dozen points on the beamcolumn in order to locate the unimodal interval of interest within which to apply the goldensection search. The actual number of exploratory calculations will depend on the individual case. For example, in a simply supported case with a unimodal transverse moment, there is clearly only one maximum. But, in general, we must check enough points to be sure that a potential maximum is not overlooked. The goldensection search procedure is as follows: Suppose that we seek the minimum value of F(x) in Fig. 30.5 within the interval D (note that if we sought a maximum in Fig. 30.5, we would have to conduct two searches). We locate two points x(1) and x(2). The first is 0.382D from the left end of the interval; the second is 0.382D 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.

