630_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

630_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 624 1:24 PM Page 624 CHAPTER 7 Analysis of Stress and Strain Solution 7.7-3 Square plate in biaxial stress (b) CHANGE IN ANGLE f Eq. (7-68): a For u f gxy sin2u ây) sin u cos u (âx 45°: a 157 * 10 6 rad Minus sign means line Od rotates clockwise (angle f decreases.) ¢f âx b 12.0 in. ây 113 * 10 f 45° Ld b 12 427 * 10 6 Eq. (7-71b): gxy 0 For u 16.97 in. For u ¢d âx + ây ây âx 2 2 45°: âx1 âx1L d ; rad (decrease) 2 f ây âx gx1y1 2 45°: gx1y1 sin 2u + 314 * 10 gxy 2 6 cos 2u rad (Negative strain means angle ced increases) + f 6 (c) SHEAR STRAIN BETWEEN DIAGONALS 6 g (a) INCREASE IN LENGTH OF DIAGONAL âx1 157 * 10 cos 2u + gxy 2 314 * 10 6 ; rad sin 2u 6 270 * 10 ; 0.00458 in. Problem 7.7-4 Solve the preceding problem if b 225 mm, Px 845 * 10 6 211 * 10 , and Py 6 . Solution 7.7-4 Square plate in biaxial stress (a) INCREASE IN LENGTH OF DIAGONAL âx1 For u ¢d âx + ây ây âx + 2 f 2 45°: âx1 âx1L d cos 2u + 528 * 10 0.168 mm gxy 2 sin 2u 6 ; (b) CHANGE IN ANGLE f b ây Ld b 12 Eq. (7-68): a âx 225 mm 211 * 10 6 845 * 10 f 318.2 mm 45° 6 gxy For u 0 f (âx 45°: a ây) sin u cos u 317 * 10 6 gxy sin2u rad Minus sign means line Od rotates clockwise (angle f decreases.) ¢f 317 * 10 6 rad (decrease) ; ...
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