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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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624 CHAPTER 7 Analysis of Stress and Strain Solution 7.7-3 Square plate in biaxial stress (a) I NCREASE IN LENGTH OF DIAGONAL ¢ d â x 1 L d 0.00458 in. ; For u f 45°: â x 1 270 * 10 6 â x 1 â x + â y 2 + â x â y 2 cos 2 u + g xy 2 sin 2 u L d b 1 2 16.97 in. f 45° g xy 0 â y 113 * 10 6 b 12.0 in. â x 427 * 10 6 (b) C HANGE IN ANGLE Minus sign means line rotates clockwise (angle decreases.) (c) S HEAR STRAIN BETWEEN DIAGONALS (Negative strain means angle increases) g 314 * 10 6 rad ; ced For u f 45°: g x 1 y 1 314 * 10 6 rad Eq. (7-71b): g x 1 y 1 2 â x â y 2 sin 2 u + g xy 2 cos 2 u ¢ f 157 * 10 6 rad (decrease) ; f Od For u f 45°: a 157 * 10 6 rad Eq. (7-68): a ( â x â y ) sin u cos u g xy sin 2 u f Problem 7.7-4 Solve the preceding problem if , and P y 211 * 10 6 . b 225 mm, P x 845 * 10 6 Solution 7.7-4 Square plate in biaxial stress
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