616_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

616_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 610 1:20 PM Page 610 CHAPTER 7 Analysis of Stress and Strain Problem 7.5-5 Solve the preceding problem for a steel plate with sx sion), ex 420 10 6 (elongation), and ey 300 10 6 10,800 psi (tension), sy (shortening). 5400 psi (compres- Solution 7.5-5 Biaxial stress sx âx 10,800 psi sy 420 * 10 6 5400 psi ây Substitute numerical values: 300 * 10 6 6 E (420 * 10 E( POISSON’S RATIO AND MODULUS OF ELASTICITY 300 * 10 ) 10,800 psi 6 ) ( 5400 psi) 5400 psi (10,800 psi) Solve simultaneously: Eq. (7-39a): âx 1 (s Ex sy) Eq. (7-39b): ây 1 (s Ey 30 * 106 psi sx) 1/3 E ; Problem 7.5-6 A rectangular plate in biaxial stress (see figure) is subjected to normal stresses y 90 MPa (tension) and x 20 MPa (compression). The plate has dimensions 400 * 800 * 20 mm and is made of steel with E 200 GPa and 0.30. (a) Determine the maximum in-plane shear strain gmax in the plate. (b) Determine the change ¢ t in the thickness of the plate. (c) Determine the change ¢ V in the volume of the plate. Solution 7.5-6 Biaxial stress sx E 90 MPa sy 200 GPa 20 MPa 0.30 (b) CHANGE IN THICKNESS Dimensions of Plate: 400 mm * 800 mm * 20 mm Shear Modulus (Eq. 7-38): E 76.923 GPa G 2(1 + ) Eq. (7-26): tmax Eq. (7-35): gmax 90 MPa s2 s2 s1 2 tmax G 20 MPa 55.0 MPa 715 * 10 ¢t âz t E (sx + sy) 2100 * 10 6 105 * 10 ; mm (Decrease in thickness) (c) CHANGE IN VOLUME (a) MAXIMUM IN-PLANE SHEAR STRAIN Principal stresses: s1 Eq. (7-39c): âz 6 From Eq. (7-47): ¢ V V0 ; (400)(800)(20) Also, a ‹ ¢V 1 2 E V0 a 1 2 E b (sx + sy) 6.4 * 106 mm3 b (sx + sy) (6.4 * 106 mm3)(140 * 10 3 896 mm (Increase in volume) ; 6 140 * 10 6 ) 6 ...
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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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