# barcode generator vb.net source code CURVED BEAMS AND RINGS 38.21 in Software Generator GTIN - 13 in Software CURVED BEAMS AND RINGS 38.21

CURVED BEAMS AND RINGS 38.21
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FIGURE 38.9 A portion of the ring has been isolated here to determine the moment and torque at any section D at angle from the fixed end at A.
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These equations are now employed in the same manner as in Sec. 38.5.1 to obtain a11 a12 a21 a22 T1/wr2 b = 1 M1/wr2 b2 (38.50)
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It turns out that the aij terms in the array are identical with the same coefficients in Eq. (38.28); they are given by Eqs. (38.29), (38.30), (38.32), and (38.33), respectively. The coefficients bk are bk = Xk + where X1 = EI Yk GK (38.51) (38.52) (38.53)
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sin2 + sin cos + 2 sin 2 sin2 sin cos + (1 + cos ) 2
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Y1 = 2 sin
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CURVED BEAMS AND RINGS 38.22
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CLASSICAL STRESS AND DEFORMATION ANALYSIS
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X2 = Y2 =
2 2(1 cos ) sin cos + sin2 2 2 2 2(1 cos ) + sin cos sin2 + sin 2 2
(38.54) (38.55)
Solutions to these equations for a variety of span angles are given in Table 38.6. A solution for the deflection at any point can be obtained using a fictitious load Q at any point and proceeding in a manner similar to other developments in this chapter. It is, however, a very lengthy analysis.
REFERENCES
38.1 Raymond J. Roark and Warren C. Young, Formulas for Stress and Strain, 6th ed., McGraw-Hill, New York, 1984. 38.2 Joseph E. Shigley and Charles R. Mischke, Mechanical Engineering Design, 5th ed., McGraw-Hill, New York, 1989. 38.3 J. P. Den Hartog, Advanced Strength of Materials, McGraw-Hill, New York, 1952.