636_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

636_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 630 1:24 PM Page 630 CHAPTER 7 Analysis of Stress and Strain 30 * 106 psi and 0.30 is loaded in biaxial stress by normal stresses sx and sy Poisson’s ratio (see figure). A strain gage is bonded to the plate at an angle f 30°. If the stress sx is 18,000 psi and the strain measured by the gage is P 407 * 10 6, what is the maximum in-plane shear stress (tmax)xy and shear strain (gmax)xy? What is the maximum shear strain (gmax)xz in the xz plane? What is the maximum shear strain (gmax)yz in the yz plane? Problem 7.7-11 A steel plate with modulus of elasticity E y sy sx f x z Probs. 7.7-11 and 7.7-12 Solution 7.7-11 Steel plate in biaxial stress sx E gxy 18,000 psi 30 * 106 psi Strain gage: f sy 0 MAXIMUM IN-PLANE SHEAR STRESS ? â 30° (tmax)xy 6 407 * 10 sy sx 0.30 ; 7800 psi 2 UNITS: All stresses in psi. STRAINS FROM EQS. (1), (2), AND (3) STRAIN IN BIAXIAL STRESS (EQS. 7-39) âx âx 1 (s Ex sy) ây 1 (sy E sx ) âz E (sx 1 6 30 * 10 1 30 * 106 âx1 âx + ây ây âx 2 âz 204 * 10 (2) xy plane: sy) (3) cos 2u + gxy 2 2 ây 6 100 * 10 6 A yz plane: (gmax)xz 2 (4) 0 (gmax) yz 2 gyz A a ây âx 2 0 (gmax) xy gxz sin 2u 1 1 407 * 10 6 a ba b (12,600 + 0.7sy) 2 30 * 106 1 1 + a ba b (23,400 1.3sy) cos 60° 2 30 * 106 sy 2400 psi Solve for sy : (gmax) xy gxy xz plane: 30° (EQ. 7-71a) + 2 5400) (18,000 30 * 106 STRAINS AT ANGLE f (1) 6 MAXIMUM SHEAR STRAINS (EQ. 7-75) (sy 0.3 sy) 0.3sy) (18,000 576 * 10 0 A a 2 âx âz 2 2 b +a ây 2 (gmax) yz gxz 2 780 * 10 âz 2 b +a b 2 6 676 * 10 (gmax) xz a gxy 2 b +a ; b 2 6 ; gyz 2 2 104 * 10 b 6 ; ...
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