629_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

629_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 623 623 SECTION 7.7 Plane Strain Problem 7.7-2 Solve the preceding problem if b 160 mm, h 60 mm, Px 6 410 * 10 6 320 * 10 , and Py . Solution 7.7-2 Plate in biaxial stress For u f 20.56°: âx1 âx1 L d ¢d 6 319.97 * 10 ; 0.0547 mm (b) CHANGE IN ANGLE f Eq. (7-68): a For u b 160 mm ây h 6 320 * 10 gxy h 20.56° arctan b 1b 2 + h2 170.88 mm f Ld âx 60 mm 410 * 10 âx + ây ây âx + 0 2 2 cos 2u + 20.56°: a ây) sin u cos u gxy sin2u 6 240.0 * 10 rad Minus sign means line Od rotates clockwise (angle f decreases.) 6 ¢f 240 * 10 6 ; rad (decrease) (c) CHANGE IN ANGLE c Angle c increases the same amount that f decreases. ¢c (a) INCREASE IN LENGTH OF DIAGONAL âx1 f (âx gxy 2 240 * 10 6 rad (increase) ; sin 2u Problem 7.7-3 A thin square plate in biaxial stress is subjected to stresses sx and sy, as shown in part (a) of the figure . The width of the plate is b 12.0 in. Measurements show that the normal strains in the x and y directions are Px 427 * 10 6 and Py 113 * 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 shear strain g associated with diagonals Od and cf (that is, find the decrease in angle ced). y sy y c sx b e b b f x z d O b (b) (a) PROBS. 7.7-3 and 7.7-4 f x ...
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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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