509_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

509_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 06Ch06.qxd 9/24/08 5:32 AM Page 503 503 SECTION 6.2 Composite Beams Problem 6.2-7 The cross section of a sandwich beam consisting of aluminum y alloy faces and a foam core is shown in the figure. The width b of the beam is 8.0 in., the thickness t of the faces is 0.25 in., and the height hc of the core is 5.5 in. (total height h 6.0 in.). The moduli of elasticity are 10.5 106 psi for the aluminum faces and 12,000 psi for the foam core. A bending moment M 40 k-in. acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams, and (b) the approximate theory for sand wich beams. t z C b Probs. 6.2-7 and 6.2-8 Solution 6.2-7 hc h t Sandwich beam I2 bh3 c 12 M 40 k.in. E1I1 + E2I2 110.92 in.4 348.7 * 106 lb-in.2 (a) GENERAL THEORY (EQS. 6-6a AND b) sface s1 M(h/2)E1 E1I1 + E2I2 3610 psi score s2 M(hc / 2)E2 E1I1 + E2I2 4 psi ; ; (1) ALUMINUM FACES: b 8.0 in. t E1 b3 (h 12 h 6.0 in. 10.5 * 106 psi I1 0.25 in. h3) c I1 33.08 in.4 8.0 in. b3 (h 12 h3) c 33.08 in.4 sface hc 5.5 in. E2 Mh 2I1 3630 psi score (2) Foam core: b (b) APPROXIMATE THEORY (EQS. 6-8 AND 6-9) 0 ; ; 12,000 psi Problem 6.2-8 The cross section of a sandwich beam consisting of fiberglass faces and a lightweight plastic core is shown in the figure. The width b of the beam is 50 mm, the thickness t of the faces is 4 mm, and the height hc of the core is 92 mm (total height h 100 mm). The moduli of elasticity are 75 GPa for the fiberglass and 1.2 GPa for the plastic. A bending moment M 275 N # m acts about the z axis. Determine the maximum stresses in the faces and the core using (a) the general theory for composite beams, and (b) the approximate theory for sandwich beams. ...
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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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