621_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

621_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 07Ch07.qxd 9/27/08 1:22 PM Page 615 615 SECTION 7.6 Triaxial Stress Triaxial Stress When solving the problems for Section 7.6, assume that the material is linearly elastic with modulus of elasticity E and Poisson’s ratio n. y a c Problem 7.6-1 An element of aluminum in the form of a rectangular parallelepiped (see figure) of dimensions a 6.0 in., b 4.0 in, and c 3.0 in. is subjected to triaxial stresses sx 12,000 psi, sy 4,000 psi, and sz 1,000 psi acting on the x, y, and z faces, respectively. Determine the following quantities: (a) the maximum shear stress tmax in the material; (b) the changes ¢ a, ¢ b, and ¢ c in the dimensions of the element; (c) the change ¢ V in the volume; and (d) the strain energy U 0.33.) stored in the element. (Assume E 10,400 ksi and b O x z Probs. 7.6-1 and 7.6-2 Solution 7.6-1 Triaxial stress sx 12,000 psi sy sz 1,000 psi a 6.0 in. b E 4,000 psi 10,400 ksi 3.0 in. bây 0.0029 in. ( decrease) ¢c câz 0.0011 in. ( decrease) 0.0079 in. ( increase) 0.33 ( aluminum) (a) MAXIMUM SHEAR STRESS s1 12,000 psi s2 s3 4,000 psi tmax aâx ¢b 4.0 in. c ¢a s3 s1 1,000 psi 1 e ; 8,000 psi 2 (c) CHANGE IN VOLUME Eq. (7-56): 2 E V (sx + sy + sz) M ; 228.8 * 10 abc ¢V e (abc) 0.0165 in.3 ( increase) ; (b) CHANGES IN DIMENSIONS Eq. (7-53 a): âx sx E (d) STRAIN ENERGY E (sy + sz) Eq. (7-57a): u 1312.5 * 10 Eq. (7- 53 b): ây E E (sz + sx) 733.7 * 10 Eq. (7-53 c): âz sz E 6 1 (s â + sy ây + sz âz) 2 xx 9.517 psi sy E 6 (sx + sy) 350.0 * 10 6 6 U u (abc) 685 in.-lb ; ...
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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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