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632_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 632_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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626 CHAPTER 7 Analysis of Stress and Strain Problem 7.7-7 The strains for an element of material in (see figure) are as follows: , and Determine the principal strains and maximum shear strains, and show these strains on sketches of properly oriented elements. g xy 350 * 10 6 . P y 140 * 10 6 P x 480 * 10 6 , plane strain Solution 7.7-6 Element in plane strain â y 1 101 * 10 6 â x 1 351 * 10 6 g x 1 y 1 490 * 10 6 For u 37.5°: â y 1 â x + â y â x 1 g x 1 y 1 2 â x â y 2 sin 2 u + g xy 2 cos 2 u â x 1 â x + â y 2 + â x â y 2 cos 2 u + g xy 2 sin 2 u g xy 310 * 10 6 â x 420 * 10 6 â y 170 * 10 6 Solution 7.7-7 Element in plane strain P RINCIPAL STRAINS u p 2 67.1° â 2 66 * 10 6 ; u p 1 22.9° â 1 554 * 10 6 ; 554 * 10 6 â x 1 â x + â y 2 + â x â y 2 cos 2 u + g xy 2 sin 2 u For u p 22.9°: u p 22.9° and 67.1° 2 u p

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