628_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

628_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 622 1:24 PM Page 622 CHAPTER 7 Analysis of Stress and Strain Plane Strain y sy When solving the problems for Section 7.7, consider only the in-plane strains (the strains in the xy plane) unless stated otherwise. Use the transformation equations of plane strain except when Mohr’s circle is specified (Problems 7.7-23 through 7.7-28). sx h Problem 7.7-1 A thin rectangular plate in biaxial stress is subjected to b stresses sx and sy, as shown in part (a) of the figure on the next page. The width and height of the plate are b 8.0 in. and h 4.0 in., respectively. Measurements show that the normal strains in the x and y directions are Px 195 * 10 6 and Py 125 * 10 6, respectively. With reference to part (b) of the figure, which shows a two-dimensional view of the plate, determine the following quantities: (a) the increase ¢ d in the length of diagonal Od; (b) the change ¢ f in the angle f between diagonal Od and the x axis; and (c) the change ¢ c in the angle c between diagonal Od and the y axis. x z (a) y d c h f O x b (b) Probs. 7.7-1 and 7.7-2 Solution 7.7-1 Plate in biaxial stress For u ¢d f 26.57°, âx1 âx1L d 6 130.98 * 10 0.00117 in. ; (b) CHANGE IN ANGLE f Eq. (7-68): a For u b ây f Ld h 8.0 in. 125 * 10 1b 2 + h2 h arctan b âx 4.0 in. 6 gxy 195 * 10 6 0 ây âx + 2 6 128 * 10 6 rad (decrease) 2 cos 2u + ¢c gxy 2 sin 2u rad ; Angle c increases the same amount that f decreases. 8.944 in. âx + ây 128.0 * 10 (c) CHANGE IN ANGLE c (a) INCREASE IN LENGTH OF DIAGONAL âx1 26.57°: a gxy sin2u ây) sin u cos u Minus sign means line Od rotates clockwise (angle f decreases). ¢f 26.57° f (âx 128 * 10 6 rad (increase) ; ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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