620_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

620_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 614 1:20 PM Page 614 CHAPTER 7 Analysis of Stress and Strain Problem 7.5-12 A circle of diameter d 200 mm is etched on a brass plate (see figure). The plate has dimensions 400 400 20 mm. Forces are applied to the plate, producing uniformly distributed normal stresses x 42 MPa and y 14 MPa. Calculate the following quantities: (a) the change in length ac of diameter ac; (b) the change in length bd of diameter bd; (c) the change t in the thickness of the plate; (d) the change V in the volume of the plate, and (e) the strain energy U stored in the plate. (Assume E 100 GPa and v 0.34.) z y sy d sx a c sx b x sy Solution 7.5-12 Plate in biaxial stress sx 42 MPa sy 14 MPa (c) CHANGE IN THICKNESS Eq. (7-39c): âz Dimensions: 400 * 400 * 20 (mm) Diameter of circle: d 200 mm E 0.34 (Brass) 100 GPa (s + sy) Ex 190.4 * 10 6 ¢ t âz t (decrease) ; 0.00381 mm (a) CHANGE IN LENGTH OF DIAMETER IN x DIRECTION Eq. (7-39a): âx ¢ ac 1 (s Ex sy) 372.4 * 10 âx d 0.0745 mm (increase) (d) CHANGE IN VOLUME 6 Eq. (7-47): ; e V0 (b) CHANGE IN LENGTH OF DIAMETER IN y DIRECTION ¢V Eq. (7-39b): ây ¢ bd 1 (s Ey sx) 2.80 * 10 2 E (sx + sy) (400)(400)(20) 179.2 * 10 6 3.2 * 106 mm3 573 mm3 ; (increase) eV0 6 (e) STRAIN ENERGY ây d 560 * 10 (decrease) 1 6 mm ; Eq. (7-50): u 12 (s + s2 y 2E x 7.801 * 10 U uV0 2 sx sy) 3 MPa 25.0 N # m 25.0 J ; ...
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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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