631_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

631_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 1:24 PM Page 625 SECTION 7.7 Plane Strain (c) SHEAR STRAIN BETWEEN DIAGONALS Eq. (7- 71b): ây âx g x1y1 2 2 For u sin 2u + gxy 2 cos 2u f 45°: gx1y1 634 * 10 6 625 rad (Negative strain means angle ced increases) g 634 * 10 6 rad y Problem 7.7-5 An element of material subjected to plane strain (see figure) has strains as follows: Px 220 * 10 6, Py 480 * 10 6 and , gxy 180 * 10 6. Calculate the strains for an element oriented at an angle u 50° and show these strains on a sketch of a properly oriented element. ey gx y 1 O ex 1 x Probs. 7.7-5 through 7.7-10 Solution 7.7-5 Element in plane strain âx 220 * 10 6 gxy 180 * 10 6 âx + ây âx âx1 gx1 y1 For u ây + 2 2 ây âx 2 ây1 ây 2 âx + ây 480 * 10 cos 2u + sin 2u + g xy 2 gxy 2 6 sin 2u cos 2u âx1 50°: âx1 461 * 10 6 ây1 239 * 10 6 gx1y1 225 * 10 6 Problem 7.7-6 Solve the preceding problem for the following data: Px and u 37.5°. 420 * 10 6 , Py 170 * 10 6 , gxy 310 * 10 6, ...
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